03_Power System Analysis Functions

DIgSILENT PowerFactory

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Power System Analysis Functions 22: Load Flow Analysis 23: Short-Circuit Analysis 24: Harmonics Analysis 25: Stability and EMT Simulations 26: Modal Analysis / Eigenvalue Calculation 27: Model Parameter Identification 28: Contingency Analysis 29: Reliability Assessment 30: Optimal Power Flow 31: Optimization Tools for Distribution Networks 32: Protection 33: Network Reduction 34: State Estimation

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Chapter 22 Load Flow Analysis Load flow calculations are used to analyze power systems under steady-state and non-faulted (short-circuit-free) conditions. The load flow calculates the active and reactive power flows for all branches, and the voltage magnitude and phase for all nodes. The main areas for the application of load flow calculations are: 

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Calculation of branch loadings, system losses and voltage profiles for system planning and operation (normal and abnormal conditions). Contingency analysis, network security assessment (abnormal conditions). Optimization tasks, i.e. minimizing system losses, minimizing generation costs, open tie optimization in distributed networks, etc. (normal or abnormal conditions). Verification of system conditions during reliability calculations. Automatic determination of optimal system resupplying strategies. Optimization of load-shedding (abnormal conditions). Calculation of steady-state initial conditions for stability simulations or short-circuit calculations using the complete superposition method (usually normal conditions).

A distinction should be made regarding the simulation of ''normal'' and ''abnormal'' system conditions. This distinction affects the modelling of the system. Under normal operating conditions the generator dispatches as well as the loads are known, and it is therefore sufficient for the load flow calculation to represent these generator dispatches and to provide the active and reactive power of all lo ads. The results of the load flow calculation should represent a system condition in which none of the branch or generator limits are exceeded. The representation of abnormal conditions requires a higher degree of accuracy from the models. Here it can no longer be assumed that the entire system is operating within limits. The models must be able to correctly simulate conditions which deviate from the normal operating point. Hence the reactive power limits of generators or the voltage dependency of loads must be modelled. Additionally, in many applications, the active power balance cannot be established with a single slack bus (or machine). Instead, a more realistic representation of the active and reactive power control mechanisms have to be considered to determine the correct sharing of the active and reactive power generation. Besides the considerations regarding abnormal conditions presented above, the assumption of balanced systems may be inappropriate for certain distribution networks. State of the art computational tools for power systems analysis must be able to represent unbalanced networks for load flow calculations. The calculation methods and the options provided by PowerFactory 's 's load flow analysis f unction allow the accurate representation of any combination of meshed 1-, 2-, and 3-phase AC and/or DC systems. The load flow tool accurately represents unbalanced loads, generation, grids with variable neutral potentials, HVDC systems, DC loads, adjustable speed drives, SVSs, and FACTS devices, etc., for all AC and DC voltage levels. With a more realistic representation of the active and reactive power balance mechanisms, the traditional requirement requirement of a slack generator is left optional to the user. For very fast and reliable analysis of complex transmission networks, where only the flow of active power through the branches is considered, PowerFactory PowerFactory offers offers an additional load flow method, namely DC load flow, which determines the active power flows and the voltage angles within the network. The following sections introduce the calculation methods and the options provided with PowerFactory 's 's load flow tool. This information is a guide to the configuration of the PowerFactory lo PowerFactory load ad fl flow ow an anal alys ysis is co comm mman and d(

).

22.1: Technical Background 22.2: Executing Load Flow Calculations 22.3: Load Flow Calculation Options 22.4: Troubleshooting Load Flow Calculations 22.5: Load Flow Sensitivities


22.1 Technical Background 22.1.1: Network Representation and Calculation Methods 22.1.2: Active and Reactive Power Control 22.1.3: Load Flow Analysis of Low Voltage Systems This section presents the general aspects of the implementation of PowerFactory 's 's load flow calculation tool. An understanding of the concepts introduced here should be sufficient background to manage the options presented in the load flow analysis command dialogue. Further technical details about the models implemented in PowerFactory for PowerFactory for load flow calculations are provided in t he Technical References of the corresponding network components.



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22.1.1 Network Representation and Calculation Methods

A load flow calculation determines the voltage magnitude ( V) and the voltage angle ( ϑ) of the nodes, and the active ( P) and reactive ( Q) power flow on branches. Usually, the network nodes are represented by specifying two of these four quantities. Depending on the quantities specified, nodes can be classified as: 

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PV nodes: constant active power and voltage magnitude are specified. This type of node is used to represent generators whose active power and voltage magnitude are controlled, and synchronous condensers. In order to consider equipment limits under abnormal conditions (as mentioned in the previous section), reactive power lim its for the corresponding network components are also used as input information. PQ nodes: active and reactive power are specified. This type of node is used to represent loads and generators with fixed dispatch. L oads can also be set to change (from their original Po and Qo values at nominal voltage) as a function of the voltage of the node to which the load itself is connected. Slack bus: voltage magnitude and angle are fixed. In traditional load flow calculations th e slack node (associated with a syn chronous generator or an external network) carries out the balancing of power in the system. Device nodes: special nodes used to represent devices such as HVDC converters, SVSs, etc., w ith specific control conditions (for example the control of active power flow at a certain MW threshold in a HVDC converter, or the control of the voltage of a busbar by an SVS).

Note: In traditional load flow calculations, asynchronous machines are represented by PQ nodes, assuming that the machine operates at a certain power factor, independent of the busbar voltage. Besides this traditional representation, PowerFactory offers a more accurate "slip iteration" (AS) representation based on the model equivalent circuit diagrams. For further information please refer to the corresponding Technical corresponding Technical Reference .

In contrast to other power system calculation programs, PowerFactory does not directly define the node characteristic of each busbar. Instead, more realistic control conditions for the network elements connected to these nodes are defined (see the Load Flow tab of each element's dialogue). For example, synchronous machines are modelled by defining one of the fol lowing control characteristics: 

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Controlled power factor ( cos(ϑ)), constant active and reactive power ( PQ); Constant voltage, constant active power ( PV ) on the connected bus; Secondary (frequency) controller ('slack', SL).

It is also important to note that in PowerFactory PowerFactory the the active and reactive power balance of the analyzed networks is not only possible through a slack generator (or external network). The load flow calculation tool allows the definition of more realistic mechanisms to control both active and reactive power. For further information please refer to Section 22.1.2 22.1.2.. AC Load Flow

In PowerFactory PowerFactory the the nodal equations used to represent the analyzed networks are implemented using two different formulations:  

Newton-Raphson (Current Equations) Newton-Raphson (Power Equations, classical)

In both formulations, the resulting non-linear equation systems must be solved by an iterative method. PowerFactory PowerFactory uses uses the Newton-Raphson method as its non-linear equation solver. The selection of the method used to formulate the nodal equations is user-defined, and should be selected based on the type of network to be calculated. For large transmission systems, especially when heavily loaded, the standard Newton-Raphson algorithm using the "Power Equations" formulation usually converges best. Distribution systems, especially unbalanced distribution systems, usually converge better using the "Current Equations" formulation. In addition to the Newton-Raphson iterations, which solve the network nodal equations, PowerFactory applies an outer loop when the control characteristic of automatic transformer tap changers and/or switchable shunts is considered. Once the Newton-Raphson iterations converge to a solution within the defined tolerance (without considering the setpoint values of load flow quantities defined in the control characteristic of the tap changers/switchable shunts (see Figure 22.1 22.1)), )), the outer loop is applied in order to reach these target values. The actions taken by the outer iterative loop are: 

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Increasing/decreasing discrete taps; Increasing/decreasing switchable shunts; and Limiting/releasing synchronous machines to/from max/min reactive power limits.

Once the above-listed actions are taken, a new Newton-Raphson load flow iteration takes place in order to determine the new network operating point.

Fig. 22.1: Setting of the Control Mode for an Automatic Tap Changer

In the classical load flow calculation approach, the unbalances between phases are neglected. For the analysis of transmission networks this assumption is generally admissible. In distribution networks this assumption may be i nappropriate depending on the characteristics of the network. PowerFactory PowerFactory allows allows for the calculation of both balanced (AC Load Flow, balanced positive sequence) and unbalanced ( AC Load Flow Unbalanced, 3-phase (ABC)) load flows according to the descriptions above. DC Load Flow

In addition to the ''AC'' load flow calculations presented in this section, PowerFactory PowerFactory offers offers a so-called ''DC'' load flow calculation method (applied to AC systems), for fast analyses of complex transmission networks where only the flow of active power through branches is considered. In this case the non-linear system resulting from the nodal equations is simplified due to the dominant relation that exists between voltage angle and active power flow in high voltage networks. A set of linear equations is thereby obtained, where the voltage angles of the buses are directly related to the active power flow through the reactances of the individual components. The DC load flow does not require an iterative process and the calculation speed is therefore considerably increased. Only active power flow without losses is considered.



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22.1.2 Active and Reactive Power Control 's load flow calculation tool provides other Besides the traditional approach of using a slack generator to establish the power balance within the system, PowerFactory 's active power balancing mechanisms which more closely represent the reality of transmission networks (see selection in the Active Power Control tab of the load flow command). These mechanisms mechanisms are implemented in the steady-state according to the control processes that follow the loss o f large power stations: 

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According to Secondary Control: If an unbalance occurs between the scheduled active power values of each generation u nit and the loads plus losses, primary control will adapt (increase/decrease) the active power production of each unit, leading to an over- or under-frequency situation. The secondary frequency control will then bring the frequency back to its nominal value, r e-establishing cost-efficient generation delivered by each unit. Secondary control is represented in PowerFactory 's 's load flow calculations by network components called 'Power Frequency Controllers' ( ElmSecctrl ). ). If the Active Power Control option According to Secondary Control is selected, the generators considered by the Power Frequency Controllers establish the active power balance according to their assigned participation factors (for further information, please refer to the corresponding Technical Reference). Reference ). According to Primary Control: Shortly following a disturbance, the governors of the units participating in primary control will increase/decrease their turbine power and drive the frequency close to its nominal va lue. The change in the generator power is proportional to the frequency deviation and is divided among participating units according to the gain ( Kpf ) of their primary controllers. If the Active Power Control option According to Primary Control is selected in PowerFactory 's 's load flow command, the power balance is established by all generators hav ing a primary controller gain (parameter Prim. Frequency Bias from the Load Flow tab of the synchronous generator), according to the corresponding frequency droop. According to Inertias: Immediately following a disturbance, the missing/excess power is delivered from the kinetic energy stored in the rotating mass of the turbines. This leads to a deceleration/acceleration and thus to a decrease/increase in the system frequency. The contribution of each individual generator towards the total additional po wer required is proportional to its inertia. If the Active Power Control option According to Inertias is selected in PowerFactory 's 's load flow command, the power balance is established by all generators. Individual contributions to the balance are proportional to the inertia/acceleration time constant of each generator (defined on the RMS-Simulation tab of the synchronous generator type's dialogue).

The reactive power reserves of synchronous generators in transmission networks are used to control the voltages at specific nodes in the system and/or to control the reactive power exchange with neighboring network zones. In PowerFactory 's 's load flow calculation, the voltage regulator of the generators has a voltage setpoint which can be set manually (defining a PV characteristic as introduced in Section 22.1.1 22.1.1), ), or from an Automatic Station Controller (ElmStactrl ( ElmStactrl ). ). This Automatic Station Controller combines several sources of reactive power to control the voltage at a given bus. In this case the relative contribution of each reactive power source (i.e. generators, SVSs) is defined in the Station Controller dialogue. For further details about the use and definition of Automatic Station Controllers please refer to Appendix C.26 Station Controller (ElmStactrl) .


22.1.3 Load Flow Analysis of Low Voltage Systems

In a low voltage system every load may consist of a fixed component with a deterministic amount of power demand plus a variable component comprising many different, small loads, such as lights, refrigerators, televisions, etc., whose power varies stochastically between zero and a maximum value. Under such conditions, PowerFactory PowerFactory uses uses a probabilistic load flow calculation, which is able to calculate both maximum and average currents as well as the average losses and maximum voltage drops. The probabilistic load flow calculation used by PowerFactory PowerFactory can can be applied to any system topology, including meshed low-voltage systems. PowerFactory 's 's probabilistic load flow calculation uses low voltage loads comprised of several customers with fixed and variable (stochastic) demand components. The maximum value of the variable component (which is dependent upon the number of customers, n) is described by the following f ormula:

Where Smax is the maximum variable load per connection (customer) and the function g(n) describes the maximum coincidence of loads, dependent upon the number of connections, n. If a Gaussian distribution is assumed, the coincidence function is:

The average value of the variable component is:

Note: Low voltage loads can be represented in PowerFactory by Low Voltage Load (ElmLodlv) elements which can be directly connected to terminals or by Partial Low Voltage Loads (ElmLodlvp) which are defined along transmission lines/cables (see the Definition of Line Loads section on the Load Flow tab of transmission line/cable elements - ElmLne).


22.2 Executing Load Flow Calculations A load flow calculation may be initiated by:

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Pressing the icon on the main toolbar; Selecting the Calculation −> Calculation −> Load Flow ... option from the main menu.

An example of the load flow command dialogue dialogue is shown in Figure 22.2 22.2..


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Fig. 22.2: Load Flow Command (ComLdf ) Dialogue

The following pages explain the load flow command options. Following this, some hints are given regarding what to do if your load flow cannot be solved.


22.3 Load Flow Calculation Options This section describes PowerFactory 's load flow calculation command ( ComLdf ). Further technical background regarding the options presented here is given in Section 22.1. 22.3.1: Basic Options 22.3.2: Active Power Control 22.3.3: Advanced Options 22.3.4: Iteration Control 22.3.5: Outputs 22.3.6: Low Voltage Analysis 22.3.7: Advanced Simulation Options


22.3.1 Basic Options Calculation Method AC Load Flow, balanced, positive sequence Performs load flow calculatio ns for a single-phase, positive sequence network representation, valid for balanced symmetrical networks. A bala nced representation of unbalanced objects is used (for further details please refer to Section 22.1.1). AC Load Flow, unbalanced, 3 Phase (ABC) Performs load flow calculatio ns for a multi-phase network representation. It can be used for analyzing unbalances of 3-phase systems , e.g. introduced by unbalanced loads or non-transposed lines, or for analyzing all kinds o f unbalanced system technologies, such as single-phase- or two-phase systems (with or without neutral return). For further details please refer to Section 22.1.1. DC Load Flow (linear) Performs a DC load flow based on a set of linear equations, where the voltage angles of the buses are strongly related to the active power flow through the reactances of the individual components (for further details please refer to Section 22.1.1). Reactive Power Control

This option is available only for AC load flow calculations. Automatic Tap Adjust of Transformers Adjusts the taps of all transformers which have the option Automatic Tap Changing enabled on the Load Flow tab of their element dialogues. The tap adjustment is carried out according to the control settings defined in the transformer element's dialogue (for further information plea se refer to the corresponding Technical Referencein C.1 and C.2). Automatic Shunt Adjustment Adjusts the steps of all switchable shunts that have the option Switchable enabled on the Load Flow tab of the shunt's element dialogue (for further information please refer to corresponding Technical Referencein C.23). Consider Reactive Power Limits Considers the reactive power limits defined by generators and SVSs. If the load flow cannot be solved w ithout exceeding the specified limits, a convergence error is generated. If this option is not enabled, PowerFactory will print a warning message if any of the specified limits are exceeded. Consider Reactive Power Limits Scaling Factor This option is only available if Consider Reactive Power Limits is enabled. If selected, the reactive power limits of generators are scaled by the relaxation factors: Scaling factor (min) and Scaling factor (max) which are set on the Load Flow tab of the generator element's dialogue. Note that the reactive power limits of generators are also defined on the Load Flow tab of the generator element's dialogue by one of the following: maximum/minimum values, Capability Curves for Generators, or according to the generator's assigned type. Load Options Consider Voltage Dependency of Loads The voltage dependency of loads with defined voltage dependency factors ( Load Flow tab of the general- and complex load types, technical reference in C.12) will be considered. Feeder Load Scaling

Scales loads with the option Adjusted by Feeder Load Scaling enabled on the Load Flow tab of their element dialogue by the Scaling Factor specified in the Load Scaling section of the feeder element (for information about feeder elements please refer to Section 7.3.3 Network Data ). In this case, the Scaling Factor specified on the Load Flow tab of load element dialogue is disregarded. Consider Coincidence of Low-Voltage Loads Calculates a 'low voltage load flow' as described in Sections 22.1.3 and 22.3.6, where load coincidence factors are considered (for Load Low Voltage (ElmLodlv) and


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Load Partial (ElmLodlvp) objects), so as to produce maximum branch currents and maximum voltage drops. Since co incidence factors are used, the result of low voltage ana lysis will not obey Kirchhoff's current law. After the load flow has been successfully executed, maximum currents ( Imax ), maximum voltage drops (dumax ) and minimum voltages (umin , Umin ) are displayed in every branch element and at every busbar. The usual currents and voltages represent here average values of voltages and currents. Losses are calculated based on average values, and maximum circuit loading is calculated using maximum currents. Scaling Factor for Night Storage Heaters This is the factor by which the night storage heater power (as found in Low Voltage Load elements) is multiplied for all low voltage loads.


22.3.2 Active Power Control Active Power Control

As explained in Section 22.1.2, PowerFactory 's load flow calculation offers several options for maintaining power balance within the system under analysis. These options are: as Dispatched:

If this option is selected and no busbar is assigned to the Reference Busbar (Reference Bus and Balancing section of the Active Power Control tab), the total power balance is established by one reference generator/external grid ("slack"-generator). The slack generator can be directly defined by the user on the Load Flow tab of the target element. The program automatically sets a slack if one has not been already defined by the user. according to Secondary Control: Power balance is established by all generators which are considered by a "Secondary Controller" as explained in Section 22.1.2. Active power contribution is according to the secondary controller participation factors. according to Primary Control: Power balance is established by all generators having a Kpf -setting defined (on the Load Flow tab of a synchronous machine element dialogue), as explained in Section 22.1.2. Active power contribution is according to the droop of every generator. according to Inertias: Power balance is established by all generators, and the contribution of each is according to the inertia (acceleration time constant) as explained in Section 22.3.2. Consider Active Power Limits: Active power limits for generators (as defined on the element's Load Flow tab) participating in active power balance, wil l be applied. If this option is disabled, the active power output limits may be violated, in which case a warning is issued. This option is not available when the Active Power Control option is set to either as Dispatched or according to Inertias. Reference Bus and Balancing

If as Dispatched is selected in the Active Power Control section of the tab, further options regarding the location of the reference busbar and the power balancing method are available: Reference Busbar:

A different busbar to the one connecting the slack machine (or network) can be selected as a reference for the voltage angle. In this case the user must specify the value of the voltage angle at this selected reference bus, which will be remotely controlled by the assigned slack machine (or network). Angle:

User-defined voltage angle for the selected reference busbar. The value will be remotely controlled by the slack machine (external network). Only available if a Reference Busbar has been selected. P-balancing:

If a Reference Busbar is specified, the load ( ElmLod ), generator or static generator ( ElmGenstat) connected to the reference busbar wil l be selected for balancing active power. Otherwise the "Reference Machine" will be used.


22.3.3 Advanced Options Load Flow Method

As explained in Section 22.1.1, the nodal equations used to represent the analyzed networks are implemented using two different formulations: 

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Newton-Raphson (Current Equations) Newton-Raphson (Power Equations, classical)

In both formulations, the resulting non-linear equation systems must be solved using an iterative method. PowerFactory uses the Newton-Raphson method as its non-linear equation solver. The selection of the method used to formulate the nodal equations is user-defined, and should be selected based on the type of network to be calculated. For large transmission systems, especially when heavily loaded, the classical Newton-Raphson algorithm using the Power Equations formulation usually converges best. Distribution systems, especially unbalanced distribution systems, usually converge better using the Current Equations formulation. Load Flow Initialisation No Topology Rebuild Will speed up large sets of consecutive load flow calculations. Enabling this option means that the topology of the system will not be rebuilt when calculating the next load flow. If no topological changes will be made to the sy stem between these consecutive load flow calculations, then this option may be enabled. No Initialisation (no flat-start) Initializes a load flow from a previously convergent solution (no flat-start). Consideration of transformer winding ratio Sets the manner in which voltage initialisation takes place at nodes. Reducing the relaxation factor results in an increased number of iterations, but yields greater numerical robustness. Tap Adjustment Method

The direct method will include the tap controller models in the lo ad flow calculation (i.e. in the internal loop involving the Newton-Raphson iterations). The new tap positions will then be calculated directly as a variable and are therefore known following a single load flow calculation. The stepped method will calculate a load flow with fixed tap positions, after which the required tap changes are calculated from the observed voltage deviations and the tap controller time constants. The load flow calculation is then repeated with the new tap positions, until no further changes are required. These tap adjustments take place in the outer loop of the calcul ation. Min. Controller Relaxation Factor The tap controller time constants are used in the automa tic tap changer calculations to determine the relative speed of the various tap controllers during the load flow iterations. The relaxation factor can be used to slow down the overall controller speeds (in case of convergence problems, set a factor of less than 1.0), or to speed them up (for a faster load flow, set a factor of greater than 1.0). Station Controller

Available on the second page ( ) of the Advanced Options tab. The options presented in this field determine the reactive power flow from generators participating in station controllers (ElmStactrl ). Please refer to Appendix C.26 Station Controller (ElmStactrl) for information on station controllers and their control modes. Modeling Method of Towers with in/output signals The equations of the lines are modelled in the tower. It should be noted that selecting this option will result in slower performance.

ignore couplings Inter-circuit couplings are ignored.

equations in lines The constant impedance and admittance matrices are calculated by the tower and used to develop the equations of


the

lines.

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The equations involving coupling are modeled in the lines; performance than using option with in/output signals.

consequently,

using

this

option

results

in

faster

Use this load flow for initialization of OPF

The results of this load flow calculation are used to initialize the OPF calculation.


22.3.4 Iteration Control

The options on this tab relate to the non-linear equation solver and are therefore only available for PowerFactory 's AC load flow calculation methods. Max. Number of Iterations for

The load flow calculation comprises an inner loop involving the Newton-Raphson method (see Section 22.1.1), and an outer loop to determine changes to tap settings and to consider generator reactive power limits. Default values for the maximum number of iterations for these two loops are 25 iterations for the inner loop, and 20 iterations for the outer loop. Newton-Raphson Iteration - itrlx The inner loop of the load flow involves the Newton-Raphson iterations. This pa rameter defines the maximum number of iterations (typically 25). Outer Loop - ictrlx

The outer loop of the load flow calculation will determine changes to the tap changer (depending on the tap adjustment method selected), and considers reactive power limits of generators, etc. These are adjusted in the outer loop and then a new iteration of the inner loop is started again (see Section 22.1.1). The maximum number of outer loop iterations (typically 20) is set by this parameter. Number of Steps - nsteps Problematic load flows with slow convergence may be improved by starting a load flow calculation for a low load level, and then increasing the load level in a number of steps. This is achieved by s etting the Number of Stairs to a value greater than one. For example, nsteps =3 begins a load flow at a load/generation level of 1/3 and the increases the power to 100% over two further steps. Max. Acceptable Load Flow Error for

A higher precision or a faster calculation can be obtained by changing the maximum allowable error (i.e. tolerance). The values of the calculated absolute error for nodes, or the calculated relative errors in the model equations, e.g. voltage error of voltage controlled generators, are specified here. Nodes - errlf Maximum Iteration Error of Nodal Equations (typical value: 1 kVA). Model Equations - erreq Maximum Error of Model Equations (typical value: 0.1%). Convergence Options Relaxation Factor

A Newton-Raphson relaxation factor smaller than 1.0 will slow down the convergence speed of the load flow calculation, but may result in an increased likelihood of convergence for systems which are otherwise difficult to solve. Automatic Model Adaptation for Convergency The PowerFactory load flow calculation will always first try to find a solution using non-linear mathematical power system models. If a solution cannot be found, and this option is enabled, an adaptive algorithm will change these models slightly to make them more linear, until a solution is found. Any model adaptations are reported in the output window.


22.3.5 Outputs Show Verification Report Produces a table in the output window with a list of overloaded power system elements and v oltage violations, according to the val ues specified in the Check Devices section of the Outputs tab. Show Convergence Progress Report Will print detailed reports throughout the load flow calcula tion, which may be used to sol ve convergence problems. Show 'Outer Loop' messages Will print reports concerning the outer loop iterations, which may be used to solve convergence problems. Calculate Power at Risk Calculates the SPAR (System Power At Risk) parameter, which is shown in the 'Total System Summ ary Report'. The SPAR equals the minimum amount o f power that will be shed in order to make the highest branch loading equal to the Max. Loading of Edge Element (Check Devices section). The SPAR calculation uses a linear optimization technique to calculate the least power that m ay be shed in order to alleviate al l overloading. This minimum power that will be shed is call ed the "Power At Risk". Output

Displays the report format definition that will be used. The arrow button ( Show Verification Report is selected.

) can be pressed to edit or inspect the report settings. This option is only available if

Check Devices Max. Loading of Edge Element Reference value of the maximum loading used by the 'Verification Report' and by the 'SPAR' function (only available if Show Verification Report and/or Calculate Power at Risk are selected). Lower Limit of Allowed Voltage Reference value for the minimum allowed voltage used by the 'Verification Report' (only available if Show Verification Report is selected). Higher Limit of Allowed Voltage Reference value for the maximum allowed voltage used by the 'Verification Report' (only available if Show Verification Report is selected).


22.3.6 Low Voltage Analysis

As explained in Sections 22.1.3 and 22.3.1, low voltage loads (ElmLodlv and ElmLodvp ) are modelled in PowerFactory with fixed and variable (stochastic) components. The parameters which define these fixed and variable components are set in both the lo ad flow command dialogue (i.e. globally), and in the load ty pes' dialogues (i.e. locally) according to the settings defined below. Definition of Fixed Load per Customer

The fixed load is the non-stochastic component of the load, which is not subject to coincidence factors. The active and reactive power defined in this field, multiplied by the number of customers (defined in the load element itself), are added to the fixed load component defined for each low voltage load ( ElmLodlv and ElmLodvp ). For further information about LV loads please refer to the corresponding technical references: Load Low Voltage (ElmLodlv) and Load Partial (ElmLodlvp). Definition of Variable Load per Customer

The variable component of low voltage loads can be globally defined using the parameters in this section or by specifically defining LV lo ad types for the target loads. The Max. Power per Customer is the independent maximum kVA per customer. This value, multiplied by the Coincidence Factor (ginf) (see Section 22.1.3), gives the "Average Power" per customer, which is used in load flow calculations. The 'total' maximum variable power per load is calculated using the Max. Power per Customer, the Coincidence Factor (ginf ), and the number of customers (defined in the load element itself) as described in Section 22.1.3. For further information about LV loads please refer to the corresponding technical references: Load Low Voltage (ElmLodlv) and Load Partial (ElmLodlvp).


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Note The factors defined in the section 'Definition of Variable Load per Customer' are used as global data for the load flow calculation. If specific LV load types are defined, the locally-defined data in the type is used by the corresponding loads. For all other LV loads with no type assigned, the global data from the load flow command is used. Voltage Drop Analysis

For the consideration of the stochastic nature of lo ads, PowerFactory offers two calculation methods:  

Stochastic Evaluation Maximum Current Estimation

The Stochastic Evaluation method is the more theoretical approach, and can also be applied to meshed network topologies. The Maximum Current Estimation method applies stochastic rules only for the estimation of maximum branch flows. Based on the maximum current flow in each branch element, maximum voltage drops are calculated and added along the feeder. Obviously, this method has its limitations in case of meshed LV networks.


22.3.7 Advanced Simulation Options

This page, as shown in Figure 22.3, is not only important for load flow but also for other calculation functions such as transient simulation. Utilizing the options on this page can result in improved performance; i.e. the speed of a transient simulation may improved when protection devices are neglected in the calculation.

Fig. 22.3: Advanced Simulation Options in the ComLdf command dialogue Consider Protection Devices Calculates the tripping times for all mo deled relays and fuses. This will also show the load currents in the overcurrent plots and/or the meas ured impedance in the RX diagrams. Disabling this option will speed up the calculations. Ignore Composite Elements Disables all controller models. The panes Models Considered and Models Ignored are used to disable specific groups of controller models. Model names can be moved between these panes by either double-clicking on them or by selecting them and using the a rrow buttons. Enabling this option may result in faster convergence, or an increased likelihood of convergence for systems w hich are otherwise difficult to solve.


22.4 Troubleshooting Load Flow Calculations In general, if a solution can be found (in other words, the network is mathematically solvable), PowerFactory will find a solution. In some cases the user may have made an error which will not allow a solution to be found; i.e. a large load causing a voltage drop so large that a voltage collapse results. In a real-world power system the same problem would be found. When creating a network for the first time it is best to enter the data for only a small part or 'path' of the network and solve the network by calculating a load flow. PowerFactory has a data verification process in which certain checks are performed, such as whether a line is connected between nodes of the same voltage; and the correct voltage orientation of transformers, etc. Error messages regarding these issues are printed to the output window, listing the element and its associated error. These messages are interactive and the user may: 

Right-click −> Mark in Graphic to show the element on the single line graphic; or



double-click on the description of the element (i.e. ' South Grid\MV-K6.ElmLne' in the example below) to view the element dialogue.

In the following example the messages in the output window state that the line element called 'MV-K6', which is found in t he 'South Grid' folder, is missing type data. DIgSI/wrng DIgSI/err DIgSI/err DIgSI/err DIgSI/err DIgSI/info

-

Protection Devices are not considered. 'South Grid\MV-K6.ElmLne': missing type ! last command leads to error(s), see output window ! Error in load-flow data! Load-flow calculation not executed

Once these errors have been corrected and the load flow still cannot be solved, use the Show Verification Report and Show Convergence Progress Report options found in the Outputs tab of the load flow dialogue (for further information on these options, see Section Outputs). These will print messages to the output window and provide clues as to where any problems may li e. The graphic can also be colored to show low and high voltages and overloading. This will also provide a good indication of possible problems. Look at the undervoltage nodes and overloaded elements and investigate why they are overloaded; look at load setpoints, line lengths and line type data (the impedances may be too high, for example). Note There are 3 different types of messages that are printed to the output window: warning, error and information messages. Only error messages must be corrected for a load flow to solve. Take note of the warning messages and evaluate them in terms of your system, however these do not need to be corrected for the load flow to solve. "Unsupplied Areas" mean that a node or branch element has no supply (i.e. a breaker is open).

If there is still no convergence then set the option Out of Service for most of the elements (see each elements Basic Data tab). Following this, bring these elements back into service, one at a time, from t he source element 'downwards', performing a load flow calculation each time. When experiencing large unbalances, such as when there are a number of single or dual phase elements, or when using power electronics elements, select the Raphson (Current Iteration) option on the Advanced tab of the load flow dialogue.

Newton-


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22.5 Load Flow Sensitivities PowerFactory 's Load Flow Sensitivities (C omVstab ) command is shown in Figure 22.4. This command performs a voltage sensitivity analysis based on the linearization of the system around the operational point resulting from a load flow calculation (as explained in Section 22.5.3). The ComVstab command is accessible by the foll owing means:





selecting the 'Additional Tools' icon (

) for the toolbar (in PowerFactory 's main icon bar) and then clicking on the ComVstab icon (

); or

right-clicking on a busbar/terminal or transformer and selecting Calculate --> Load Flow Sensitivities... . In this case the command will be automatically set to calculate the sensitivity to power injections/tap changes on the selected busbar/transformer. The selected terminal/transformer will be automati cally set in the Busbar (or Transformer ) reference.

Fig. 22.4: Load Flow Sensitivities Command (ComVstab ) Dialogue

22.5.1: Load Flow Sensitivities Options 22.5.2: Load Flow Sensitivities Execution and Results 22.5.3: Technical Background


22.5.1 Load Flow Sensitivities Options

The options available for the Load Flow Sensitivities command (Figure 22.4) are: Initialization Load Flow:

Displays which load flow command will be used to initialize the sensitivity analysis. If no load flow calculation has been executed before opening the Load Flow Sensitivities (ComVstab ) command, or if the calculation has been reset, the Load Flow displays the most recently executed load flow command in the active study case. Sensitivities Diagonal Elements Only:

The effect of the injections of ∆P and ∆Q at each busbar are evaluated for the busbar itself (effect on voltage magnitude voltage angle

,

,

, and on

for each busbar) and the corresponding adjacent branches. In this mode, the calculated sensitivities

, and , , in the branches (index n) always refer to derivations and of the adjacent buses (index i). This means that the sensitivities a re calculated for all busbars and for all branches, according to variations in power ( ∆P and ∆Q) at the directly connected busbars. Sensitivity to a Single Busbar: The effect of the injections of ∆P and ∆Q at the selected busbar are calculated for the whole network (i.e. for all buses and branches). The target busbar can be

selected using the Busbar button ( ) located at the bottom of the dialogue. Alternatively, the target bus can be selected in the single line graphic by rightclicking on it and selecting Calculate --> Load Flow Sensitivities from the context-sensitive menu. The sensitivities of all busbars and branches are calculated according to variations in power (∆P and ∆Q) at the selected busbar. Sensitivity to a Single Transformer Tap Position: This option evaluates the effect of changing the tap position of a selected transformer in the network. The sensitivities dP/dtap [MW/tap step ], dQ/dtap [Mvar/tap step ] for branches, and dphi/dtap [deg/tap step ], dv/dtap [ p.u./tap step ] for buses are calculated. The target transformer can be selected using the Transformer button ( ) located at the bottom of the dialogue. Alternatively, the target transformer can be selected in the single line graphic by right-clicking on it and selecting Calculate -> Load Flow Sensitivities from the context-sensitive menu. Modal Analysis:

This option performs an eigenvalue calculation on the sensitivity matrix as explained in Section 22.5.3. The number of eigenvalues to be calculated is defined in the Number of Eigenvalues field at the bottom of the dialogue. The eigenvalues are a lways calculated in order of their la rgest magnitude, so selecting n eigenvalues will display the n eigenvalues in descending order according to magnitude (note that the larger the number of desired eigenvalues, the longer the calculation wil l take). In the Display Results for Mode field, the user can specify the number of a specific eigenvalue, for which the stability behavior (i.e. the eigenvectors and participation factors) is to be analyzed. The algorithm then additionally calculates the ,


,

(branch sensitivities) and the

(bus sensitivities) which correspond to the mode specified (see Section 22.5.3 for further technical background).


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22.5.2 Load Flow Sensitivities Execution and Results

When the ComVstab command has been configured and the Execute button has been pressed, the program calculates several sensitivity factors such as ,

,

,

etc., according to the selected options, for buses and branch elements.

Upon completion of the sensitivity factor calculation, the following message appears in the output window: DIgSI/info - Load Flow Sensitivities calculated!

The calculated results can be displayed via the 'Flexible Data Page' (see Section 11.5) by selecting the sensitivities from the load flow variables (Variable Set: 'Current, Voltages and Powers'). The names of the variables correspond to the calculated derivations, i. e. the result of the expression dvdP ; and likewise the result of the expression

is stored in the variable named

is stored in the variable dphidQ .

When the Modal Analysis option is selected, the calculated eigenvalues are displayed (in descending order according to magnitude) in the output window. The eigenvectors and participation factors can be displayed using the 'Flexible Data Page'.


22.5.3 Technical Background PowerFactory 's Load Flow Sensitivities function (ComVstab ) performs a static voltage stability calculation as described below.

Linearizing the load flow equations around the actual operating point leads to the following equation system:

(22.1) The equation system in (22.1) shows that changes in the voltage magnitude and angle due to small changes in the active and reactive power can be directly calculated from the load flow Jacobian matrix. For example if ∆P is set to 0, the sensitivities of the type dv/dQ are calculated from (22.1) according to:

(22.2) where:

(22.3) As can be seen from (22.2), the variation of voltage magnitude at each busbar can be described by a linear combination of small reactive power variations according to:

(22.4) In this case the diagonal elements Si1 of S represent the voltage variation at bus i due to a variation of reactive power at the same point. The non-diagonal elements Sij describe the voltage variation at busbar i due to the variation in reactive power at a different point on the network. Positive dv/dQ sensitivity indicates stable operation. High sensitivity means that even small changes in reactive power cause large changes in the voltage magnitude; therefore the more stable the system, the lower the sensitivity (high vo ltage sensitivities are indicative of weak areas of the network). Note: Recall that in HV networks branches are predominantly reactive. Voltage magnitudes depend primarily on reactive power flows and voltage angles depend on active power bus injections.

The sensitivity analysis can be extended in order to determine the active and reactive power variations on branches (in the PowerFactory network model all components carrying a flow, i.e. lines, transformers, generators are regarded as branches) due to variations in active and reactive power busbar injections. In this case the sensitivities are calculated using the branch-node Jacobian matrix. By applying a modal transformation to ( 22.2) the dV/dQ sensitivity can be expressed as an uncoupled system of the form:

(22.5) where:

(22.6) In (22.5), is a diagonal matrix whose elements correspond to the eigenvalues of the sensitivity matrix, SvQ, from (22.2). Therefore, the voltage variation at each mode depends only on the reactive power variation at the same mode:

(22.7) The eigenvalues λi, which are real, provide the necessary information about the voltage stability of the system. If λi is positive, the modal voltage increase and the modal reactive power variations are in the same direction and the system is therefore stable. The magnitude of the eigenvalue indicates how far/close one voltage mode is to instability. -1

In (22.5), T= [υ1...υn] corresponds to the matrix of right eigenvectors of SvQ, while T

corresponds to the left eigenvectors matrix:

(22.8) The participation factor of bus k to mode i is defined by the product of the kth component of the left and right eigenvector of mode i:

(22.9) The sum of the participation factors of all nodes corresponds to the scalar product of the left and right eigenvector, and is therefore equal to one. In this sense, the participation factor gives an indication of the extent of the influence the variation of active power on a node has on a voltage mode.

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Chapter 23 Short-Circuit Analysis The short-circuit calculation in PowerFactory is able to simulate single faults as well as multiple faults of almost unlimited complexity. As short-circuit calculations can be used for a variety of purposes, PowerFactory supports different representations and calculation methods for the analysis of short-circuit currents. One application of short-circuit calculations is to check the ratings of network equipment during the planning stage. In this case, the planner is interested in knowing the expected maximum currents (for the correct sizing of components) and the minimum currents (to design the protection scheme). Short-circuit calculations performed at the planning stage commonly use calculation methods that require less detailed network modelling (i.e. methods which do not require load information) and which will apply extreme-case estimations. Examples of these methods include the IEC 60909/VDE 0 102 method and the ANSI method. A different field of application is the precise evaluation of the fault current in a specific situation, i.e. to find out whether the malfunction of a protection device was a relay failure or was t he consequence of improper settings (i.e. operational error). These are the typical applications of exact methods such as the superposition method (also known as the `complete' method), which is based on a specific network operating point. This chapter presents the handling of the short-circuit calculation methods as i mplemented in PowerFactory . Further background on this topic can be found in Section 23.1 Technical Background . 23.1: Technical Background 23.2: Executing Short-Circuit Calculations 23.3: Short-Circuit Calculation Options


23.1 Technical Background Apart from load-flow analysis, short-circuit analysis is the most frequently used calculation function when dealing with electrical networks. I t is used in system planning as well as system operations (see Figure 23.1, in special cases Methods 2.1 and 2.2 are also used for network planning). Calculation quantities which have been newlyintroduced in PowerFactory Version 14 are shown in Figure 23.1, and a graphical representation of the short-circuit current time function is given in Figure 23.2.

Fig. 23.1: Areas of Application of Short-Circuit Calculations

Fig. 23.2: Short-Circuit Current Time Function

Example applications of short-circuit analysis in system planning include: 

 

 

Ensuring that the defined short-circuit capacity of equipment is not exceeded with system expansion and system strengthening. Co-ordination of protective equipment (fuses, over-current and distance relays). Dimensioning of earth grounding systems. Verification of sufficient fault level capacities at load points (e.g. uneven loads such as arc furnaces, thyristor-driven variable speed drives or dispersed generation). Verification of admissible thermal limits of cables and transmission lines.


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Example applications of short-circuit analysis in system operations include: 

   

Ensuring that short-circuit limits are not exceeded with system reconfiguration. Determining protective relay settings as well as fuse sizing. Calculation of fault location for protective relays, which store fault disturbance recordings. Analysis of system faults, e.g. misoperation of protection equipment. Analysis of possible mutual interference of parallel lines during system faults.

The fundamental difference between the assumptions used by the calculation methods is that for system planning studies the system operating conditions are not yet known, and therefore estimations are necessary. To this end, the method which uses an equivalent voltage source at the fault location has become generally accepted in Western Europe according to IEC 909 (VDE 0102). A revised version of this was published as IEC 60909 in July 2001. This method works independently of the load flow (operating point) of a system. It is based on the nominal and/or calculated dimensions of the operating point of a system and uses correction factors for voltages and impedances, to give conservative results. For the calculation of minimum and maximum short-circuit currents, different correction factors are applied. However, it should be mentioned that both IEC 60909 and VDE 0102 do not deal wit h single phase elements (expect single phase elements in the neutral conductor). For short-circuit calculations in a system operation environment, the exact network operating conditions are well-known. If the accuracy of the calculation according to IEC 60909 is not sufficient - or to verify the results of this method - the superposition method can be used. The superposition method calculates the expected short-circuit currents in the network based on the existing network o perating condition. If the system models are correct, the results from this method are always more exact than the results of the IEC 6090 9 method. The system analyst is, however, responsible that she/he has chosen the most unfavorable conditions with respect to the sizing of plant. In some cases, this might result in extensive studies required. 23.1.1: The Complete Method 23.1.2: The IEC 60909/VDE 0102 Method


23.1.1 The Complete Method

The complete method (sometimes also known as the superposition method) is, in terms of system modeling, an accurate calculation method. The fault currents of the shortcircuit are determined by overlaying a healthy load-flow condition before short-circuit inception with a condition where all voltage supplies are set to zero and t he negative operating voltage is connected at the fault location. The procedure is shown in Figure 23.3. The initial point is the operating condition of the system before short-circuit inception (see Figure 23.3a). This condition represents the excitation conditions of the generators, the tap positions of regulated transformers and the breaker/switching status reflecting t he operational variation. From these pre-fault conditions the pre-fault voltage of the faulted busbar can be calculated. For the pure fault condition the system condition is calculated for the situation where, the negative pre-fault busbar voltage for the faulted bus is connected at the fault location and all other sources/generators are set to zero (see Figure 23.3b). Since network impedances are assumed to be linear, the system condition after fault inception can be determined by overlaying (complex adding) both the pre-fault and pure fault conditions (see Figure 23.3c).

Fig. 23.3: Illustration of the Complete Method

The Complete Method for calculating short-circuits has been improved in PowerFactory Version 14 as described below. Additionally, the quantities described below are shown in Figure 23.1. 



 



i A more precise Peak Current, p is calculated based on the accurate subtransient short-circuit current (which is calculated using the complete method) and the R/X ratio (which is , based on the IEC 60909 standard); The Breaking Current, Ib, (RMS value) is calculated based on the subtransient short-circuit current and the transient short-circuit current (both of which are calculated by the complete method); The Peak Breaking Current, ib, is calculated from the RMS breaking current, Ib, and the decaying d.c. component; The Thermal Current, Ith is calculated based on the IEC standard, using the m and n factors (see Figure 23.1). The n-factor calculation uses the transient current instead of the , steady-state current; Additionally, loads can have a contribution to the short-circuit current, which can be defined in the load element ( Fault Contribution section of Complete Short-Circuit tab).



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23.1.2 The IEC 60909/VDE 0102 Method

The IEC 60909/VDE 0102 method uses an equivalent voltage source at the faulted bus and is a simplification of the superposition method. It is illustrated in Figure 23.4. The goal of this method is to accomplish a close-to-reality short-circuit calculation without the need for the preceding load-flow calculation and the associated definition of actual operating conditions. Figure 23.4 illustrates how the equivalent voltage source method can be derived from the superposition method. The main simplifications in comparison to the superposition method are as follows:  

 

Nominal conditions are assumed for the whole network, i.e. U = U . i n,i Load currents are neglected, i.e. I = 0. Op A simplified simulation network is used, i.e. loads are not considered in the positive and negative sequence network. To ensure that the results are conservatively estimated, a correction factor, c, is applied to the voltage at the faulted busbar. This factor differs for the calculation of the maximum and the minimum short-circuit currents of a network.

The short-circuit calculation based on these simplifications may be insufficient for some practical applications. Therefore, additional impedance correction factors are applied to the physical impedances of the network elements. This method is described in detail in the following section. Please note in addition that both IEC 60909 and VDE 0102 do not deal with single phase elements (expect single phase elements in the neutral conductor).

Fig. 23.4: Illustration of the IEC 60909/VDE 0102 Method The IEC Impedance Correction Factors

The IEC method uses only the rated parameters of network elements. This is advantageous in that only little information is necessary to perform a short-circuit calculation. However, considering that, for example, the short-circuit contribution of a synchronous generator depends heavily on the excitation voltage and on the unit transformer tap changer position, the worst-case value of this impedance is considered by applying a correction factor (< 1). This idea is illustrated in Figure 23.5. The correction factor c should be determined so that I" k = I"k,IEC. The IEC standard defines an equation for the correction factor for each element type.

Fig. 23.5: Principle of Impedance Correction (IEC/VDE Method)

As the IEC standard includes a worst-case estimation for minimum and maximum short-circuit currents, some PowerFactory elements require additional data. These elements are: Lines

In their type, the maximum admissible conductor temperature (for minimum short-circuit currents) must be stated. Line capacitances are not considered in the positive/negative sequence systems, but must be used in the zero-sequence system. Transformers

Require a flag indicating whether they are unit or network transfo rmers. Network transformers may be assi gned additional information about operational l imits which are used for a more precise calculation o f the impedance correction factor. Unit transformers are treated differently depending on whether they have an on-load or a no-load tap changer. Synchronous Machines Subtransient impedances are used. Additionally, information regarding the voltage range must be given. Asynchronous Machines The ratio of starting current to rated current is used to determine the short-circuit impedance.

Please refer to the IEC 60909 standard to find detailed information regarding specific equipment models and correction factors for each element.


23.2 Executing Short-Circuit Calculations There are different methods of initiating the short-circuit calculation command ( ComShc ) in PowerFactory , which may result in a different configuration of the command. These methods are described in Sections Toolbar/Main Menu Execution and Context-Sensitive Menu Execution. 23.2.1: Toolbar/Main Menu Execution 23.2.2: Context-Sensitive Menu Execution 23.2.3: Faults on Busbars/Terminals 23.2.4: Faults on Lines and Branches


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23.2.5: Multiple Faults Calculation


23.2.1 Toolbar/Main Menu Execution

The short-circuit command may be executed from the toolbar or main menu in PowerFactory as follows:

 

By pressing the icon on the main toolbar; or By selecting the Calculation -> Short-Circuit ... option from the main menu.

In both of these cases, the short-circuit command will be configured in an identical manner. If no short-circuit command already exists in the active study case, the command will by default execute a short-circuit calculation on all busbars/terminals in the network. If a short-circuit calculation does already exist in the active study case, the above mentioned means of executing the calculation will cause the calculation to execute using its most recent configuration.


23.2.2 Context-Sensitive Menu Execution

The short-circuit command may be executed from the context-sensitive menu in PowerFactory by selecting an element(s) in the single-line diagram, right-clicking and selecting one of the following options: 

: performs a short-circuit calculation for each element selected by the user. It should be noted that the short-circuit calculation for each element is carried out completely independently of the short-circuit calculation for each other element. For this calculation, only the following combinations of elements may be selected: Single or multiple terminals/busbars; or A single line; or A single branch. Calculate... Short-Circuit



 

If several terminals/busbars are selected for analysis, the results of each individual short-circuit calculation will be displayed together on the single-line graphic. 

: performs a short-circuit calculation according to the complete method, for the `simultaneous' short-circuit of all elements selected by the user. Any combination of busbars, terminals, lines and branches can be selected for this calculation. Additionally, switch/circuit breaker open/close operations can also be included in the calculation. When this calculation i s selected, the option Multiple Faults in the ( ComShc ) dialogue will be automatically ticked. Calculate... Multiple Faults


23.2.3 Faults on Busbars/Terminals

The short-circuit command should first be called using one of the methods described in Sections Toolbar/Main Menu Execution and Context-Sensitive Menu Execution. The simplest way to calculate several busbar/terminal short-circuits individually and to then combine t he results into one diagram is to select the option All Busbars (or alternatively, Busbars and Junction/Internal Nodes ) in the Fault Location section of the Short-Circuit Calculation (ComShc) dialogue, as displayed in Figure 23.6. Note that to access this option, Multiple Faults in the dialogue must be unticked.

Fig. 23.6: Short-Circuit Calculation Command ( ComShc ) Dialogue: Faults at All Busbars

If the user would instead like to select from the single-line diagram a single busbar/terminal, or multi-select several busbars/terminals for calculation, the dialogue will be configured as follows: 



When only a single busbar/terminal is selected, a nd Calculate −> Short-Circuit is chosen from the context-sensitive menu, the Fault Location reference (bottom of dialogue) is set to the selected element. When two or more busbars/terminals are selected and Calculate −> Short-Circuit is chosen from the context-sensitive menu, the Fault Location reference (bottom of dialogue) is set to a so-called "Selection Set'' ( SetSelect) object, which contains a list of references to the selected busbars/terminals.

In either case, various options for the calculation can be modified. Please refer to Section 23.3 Short-Circuit Calculation Options for a detailed description of the options available. It should be noted that selecting or deselecting the option Multiple Faults may change the selection of fault locations and may therefore lead to a calculation for locations other than the busbars/terminals selected in the single line graphic. After pressing the Execute button, the calculation is executed and, if successful, the results are displayed in the single line graphic. In addition, a result r eport is available and may be printed out. Once a selection of fault locations is made and the short-circuit calculation is performed, it is simple to execute further calculations based on the same selection of elements. This can be done by the f ollowing alternative means of executing the short-circuit calculation command:

 

By pressing the icon on the main toolbar; or By selecting the Calculation -> Short-Circuit ... option from the main menu.

The short-circuit setup dialogue then shows the previously selected busbars/terminals in the Fault Location section under User Selection .


23.2.4 Faults on Lines and Branches

It is not only possible to calculate short-circuits on busbars and terminals, but also on lines and branches. It should be noted, however, that only a single line or a single branch can be selected at a time, for each short-circuit calculation. It is not possible to select multiple lines and/or branches for calculation. To calculate a short-circuit on one of these types of elements, proceed as follows:  



In the single-line diagram, select a si ngle line or a single branch where the fault should be mo deled. Right-click on the element and select Calculation -> Short-Circuit ... . The short-circuit command ( ComShc ) dialogue opens and the user can then define the location of the fault relative to the element's length (see Figure 23.7), including which terminal the fault distance s hould be calculated from. It should be noted that the Short-Circuit at Branch/Line section of this tab is only available when a li ne or branch has been selected for calculation. Clicking the button

located in the Short-Circuit at Branch/Line section of the tab will enable the user to select whether the fault location is defined as a percentage


Page 14 of 168

or as an absolute value.

Fig. 23.7: Configuration of Line/Branch Faults in ComShc Dialogue

When a fault on a line/branch is calculated, a box containing the calculation results is displayed next to the selected element.


23.2.5 Multiple Faults Calculation

Multiple faults involve the simultaneous occurrence of more than one fault condition i n a network. To calculate simultaneous multiple faults, proceed as follows:  

 

Select two or more elements (i.e. busbars/terminals, lines, ...) and right-click. Select the option Calculate -> Multiple Faults . The Short-Circuits dialogue pops up, displaying the short-circuit event list. A 3-phase fault is assumed at all locations in the event list. Click OK. The Short-Circuit command dialogue then pops up. In this dialogue, the Multiple Faults option is ticked in combination with the complete short-circuit method . Next, the event list has to be adapted to reflect the intended fault conditions. This is described in detail below. Finally, press Execute to start the calculation.

The short-circuit event list is a special case of the general event list, which contains the event definitions for dynamic simulations. To edit the list of events (short-circuits at selected locations), please proceed as follows: 

Open the short-circuit events object using one of the following methods: 

In the Fault Location section of the short-circuit ( ComShc ) dialogue, press the button Contents (see Figure 23.8); or

next to Short-Circuits . To access the events stored within this object, press



Press the



In a Data Manager window open the IntEvshc object from the current study case, also denoted by the

icon on the main toolbar; or icon.

Fig. 23.8: Accessing the Short-Circuit Events List 



A window opens up which shows the list of events (i.e. short-circuits at the selected locations). When double-clicking on one entry in this list (i.e. its entire row), a window with a description of the event is opened. The short-circuit event settings can now be modified. The list of fault locations consists of a "Short-Circuit Event List'' ( IntEvtshc ) object, which holds one or more short-circuit events (EvtShc ). Each of these events has a reference to a fault location (a busbar/terminal, line, etc) and displays a short description of the fa ult type. An example is shown in Figure 23.9.

Fig. 23.9: A Short-Circuit Event (EvtShc )

Note To re-use the event list (IntEvtshc) later, this object can be copied to a user-defined folder in the Data Manager. This will prevent it from being modified during future calculations. When repeating the calculation with the same configuration, the reference in Calculate -> Multiple Faults can be set to this object.

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23.3 Short-Circuit Calculation Options The following sections describe the options available in PowerFactory 's short-circuit calculation command. Some of these options are dependent upon the selected calculation method, therefore separate sections dedicated to each method are presented. 23.3.1: Basic Options (All Methods) 23.3.2: Verification 23.3.3: Basic Options (IEC 60909/VDE 0102 Method) 23.3.4: Advanced Options (IEC 60909/VDE 0102 Method) 23.3.5: Basic Options (ANSI C37 Method) 23.3.6: Advanced Options (ANSI C37 Method) 23.3.7: Basic Options (Complete Method) 23.3.8: Advanced Options (Complete Method) 23.3.9: Basic Options / Advanced Options (IEC 61363)


23.3.1 Basic Options (All Methods)

The options presented in this section are common to all implemented calculation methods and are used to define the general settings of the short-circuit calculation. The specific options for each method are presented below in separate sections.

Fig. 23.10: IEC Calculation - Basic Options

An example of the short-circuit command dialogue is shown in Figure 23.10 (IEC calculation in this case). The sections of the dialogue which are common to all calculation methods are: Method

PowerFactory provides the following calculation methods for short-circuit calculation: 

according to VDE 0102/0103 (the German VDE standard);



according to IEC 60909 (the International IEC standard);



according to ANSI (the American ANSI/IEEE C37 standard);



complete (superposition method which considers the pre-fault load-flow results (see Section 23.1.1));



according to IEC 61363 .

The specific options for each of t hese methods are available on the Advanced Options tab of the short-circuit command ( ComShc ) dialogue. Fault Type

The following fault types are available:  

 

 

  

 

3-Phase Short-Circuit 2-Phase Short-Circuit Single Phase to Ground 2-Phase to Ground 1-Phase to Neutral 1-Phase Neutral to Ground 2-Phase to Neutral 2-Phase Neutral to Ground 3-Phase to Neutral 3-Phase Neutral to Ground 3-Phase Short-Circuit (unbal.)

The fault types with a neutral conductor should o nly be used for lines which are modeled using neutral conductors. Fault Impedance

The fault impedance corresponds to the reactance and the resistance of the fault itself (i.e. the impedance of the arc or of the shortening path). This can be defined by means of an enhanced model, where line to line ( Xf(L-L), Rf(L-L) ) and line to earth (Xf(L-E), Rf(L-E) ) impedances are regarded (note: requires option Enhanced Fault . Impedance to be enabled). If the option Enhanced Fault Impedance is not enabled, fault impedances are defined by their equivalent values, Xf and Rf Figures 23.11 to 23.13 illustrate the differences between the enhanced and the simplified representation of fault impedances for the following fault types: (i) 3-phase shortcircuits; (ii) 2-phase faults to ground; and (iii) 2-phase faults.


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Fig. 23.11: Fault Impedance Definition: 3-Phase Short-Circuit

Fig. 23.12: Fault Impedance Definition: 2-Phase to Ground Fault

Fig. 23.13: Fault Impedance Definition: 2-Phase Fault Output

A textual report is automatically written to PowerFactory 's output window when the On option in the Output section of the dialogue is enabled. The command which generates this report is displayed in blue text next to the Command button . The user can click on this button to select which type of report will be printed out. Immediately below the Command button, blue text informs the user of the currently-selected report type. Fault Location

The fault location selection options are: At User Selection:

In this case a reference to a single terminal/busbar/line/branch or to a selection of busbars/terminals ( SetSelect ), as explained in Sections 23.2.3 and 23.2.4 Faults on Lines and Branches must be given. At Busbars and Junctions/Internal Nodes: For every terminal (ElmTerm ) in the network, a short-circuit calculation is carried out, independently (i.e. one after the other). At All Busbars: For every terminal (ElmTerm ) in the network whose Usage is set to Busbar (see Section 7.3.2), a short-circuit calculation is carried out, independently (i.e. one after the other).

If the option Multiple Faults has been ticked when the Complete Method is being used, a reference to a set of fault objects ( IntEvtshc ), as explained in Section 23.2.5, must be set. This is done in the Fault Location section of the dialogue; using the Short Circuits reference. Note: Multiple faults will only be calculated for the 'Complete Method', when the option 'Multiple Faults' is enabled. When this option is enabled, a short- circuit calculation is carried out for each individual fault location, simultaneously. When this option is disabled, cases where more than one fault location have been selected (i.e. several busbars/terminals), a sequence of short-circuit calculations is performed (i.e. each short-circuit calculation is carried out independently of each other short-circuit calculation).


23.3.2 Verification

When enabled, the Verification option will write a lo ading report to the output window. This report shows the various maximum and calculated currents for rated devices. Rated devices include, for instance:  

Lines which have a rated short-time current in their line type which is greater than zero; and Breakers or coupling switches which have a type with a valid rated current.


23.3.3 Basic Options (IEC 60909/VDE 0102 Method)

The Basic Options tab of the Short-Circuit Calculation dialogue is shown in the previous section i n Figure 23.10.


Page 17 of 168

In general, please note that the calculation according to IEC 60909 and VDE 0102 does not take into account line capacitances, parallel admittances (except those of the zero-sequence system) and non-rotating loads (e. g. ElmLod). Single phase elements are considered only if they are located in the neutral conductor. Published

This option offers a sub-selection for the selected Method , where the version of the standard to be used can be selected according to the year in which it was issued. The most recent standard is 2001, however 1990 is still available for the v erification of documented results. Calculate

The drop-down list offers the choice between the minimal or maximal short-circuit current. Max. Voltage tolerance for LV systems

In accordance with the IEC/VDE standard, this voltage tolerance is used to define the respective voltage correction factor, c. The voltage tolerance is not used when a userdefined correction factor is defined. Short-Circuit Duration

The value for the Breaker Time is used to calculate the breaking current of a circuit breaker. The value for the Fault Clearing Time (Ith) is required for the equivalent thermal current. Note: The fields 'Method', 'Fault Type', 'Fault Impedance', 'Output' and 'Fault Location' are described in Section 23.3.1 Basic Options (All Methods) .


23.3.4 Advanced Options (IEC 60909/VDE 0102 Method)

Fig. 23.14: IEC calculation - Advanced Options

Generally, the Advanced Options tab (shown in Figure 23.14) is used for settings to tune the various short-circuit calculation methods. Familiarization with the IEC/VDE standard before modifying these options is strongly recommended. Grid Identification

The calculation of the factor kappa is different in the cases of meshed or radial feeding of the short-circuit. Normally PowerFactory will automatically find the appropriate setting. The option Always meshed will force a meshed grid approach. c-Voltage Factor

The standard defines the c-voltage factor to be used for the di fferent voltage levels. In special cases the user may want to define the correction factor. In this case, activate the box User-Defined , then a specific c-factor can be entered. Asynchronous Motors

Whether the calculation considers the influence of asynchronous motors on short-circuit currents depends on this setting, which may be Always Considered , Automatic Neglection, or Confirmation of Neglection. Conductor Temperature

When activating the User-Defined option, the initial (pre-fault) conductor temperature can be set manually. This will influence the calculated maximum temperature of the conductors, as caused by the short-circuit currents. Decaying Aperiodic Component

Allows for the calculation of the DC current component, for which the decay time must be given. According to the IEC/IEC standard, methods B, C and C' can be selected. The following nomenclature is used: T Breaker Time (see Short-Circuit command) b f Nominal frequency n I " Initial short-circuit current k Method B: Uses the complex calculated equivalent impedance of the network with a security factor of 1.15:

Method C: Uses the R/X ratio calculated with the equivalent frequency method. The equivalent frequency is dependent on the breaking time (see Table 23.1). This method is


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recommended for maximum accuracy. f

n

*T

b

f /f

c

n

<1

< 2.5

<5

< 12.5

0.27

0.15

0.092

0.055

Table 23.1: Breaking Times

The ratio Rc/Xc is the equivalent impedance calculated at the frequency given by:

Method C': Uses the R/X ratio as for the peak sho rt-circuit current, thus selecting the ratio f /f = 0.4. This option speeds up the calculation, as no additional equivalent impedance needs c n to be calculated. Peak Short-Circuit Current (Meshed network)

In accordance with the IEC/VDE standard, the following methods for calculating kappa can be selected: Method B': Uses the ratio R/X at the short-circuit location. Method C(1):

Uses the ratio R/X calculated at a virtual frequency of 40% of nominal frequency (20 Hz for fn = 50 Hz, or 24 Hz for fn=60 Hz), ba sed on the short-circuit impedance in the positive sequence system. Method (012):

Like C(1), but uses the correct short-circuit impedance based on the positive-, negative- a nd zero-sequence system. Calculate Ik

The steady-state short-circuit currents can be calculated using different means to consider asynchronous machines: Without Motors DIgSILENT Method

Will disconnect all asynchronous motors before calculating the current I . k Considers all asynchronous motors according to their breaker current. The breaker opens after the maximum possible time.

Ignore Motor Contributions Considers asynchronous motor impedances during the calculation, but will reduce the calculated results for motor contributions. Consider Protection Devices

This option will calculate measured currents for all protection devices and will evaluate tripping times. To increase the speed of the calculation, this option can be disabled when protection devices do not need to be analyzed. Calculate max. Branch Currents = Busbar Currents

This option is used to check the rating of the circuit breakers against the system breaker currents. Normally the breaker currents are calculated as max{Ibus-Ibranch, Ibranch}. If this option is activated, the busbar short-circuit current is used as the breaker current, which is actually an over-estimation of the currents. Automatic Power Station Unit detection

The IEC/VDE standard forces a different impedance correction factor to be applied to separate generators and transformers than that applied to a unit/block (power station) consisting of a generator including its step-up transformer. PowerFactory tries to detect power stations. When this option is disabled, block transformers must be marked accordingly by setting the Unit Transformer option available in the VDE/IEC Short-Circuit tab of the transformer element dialogue.


23.3.5 Basic Options (ANSI C37 Method)


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Fig. 23.15: ANSI calculation - Basic Options Prefault Voltage

Value of the pre-fault pre-fault voltage (required by the ANSI standard). Consider Transformer Taps

The ANSI standard optionally allows the current tap positions of the transformers to be considered. This can be selected here. NACD Mode

The NACD factor is the ratio of remote current contribution to the total fault current: NACD = I remote /Ifault. This NACD factor is used to calculate the breaker currents, including the DC component of the current. The remote current contribution required to evaluate the NACD factor is the sum of all remote generator contributions (induction generators, synchronous machines, and external grids). The calculation of the NACD factor can be very time consuming, as the contribution of each generator is calculated individually. Therefore, different approximation methods can be selected, which represent the most common interpretations of the ANSI standard: Interpolated The NACD factor is calculated, and the correction factor for the a symmetrical fault current is interpolated between the "dc decay only" and "AC/DC decay" curves with the following equation: MF = AC/DC factor + (DC factor - AC/DC factor)*NACD If (NACD = 1) then only the DC factor is used; if (NACD = 0) then only the AC/DC factor is used. Predominant The the NACD factor is calculated. If the resulting factor i s greater than or equal to 0.5, then the "dc decay only'' curve is used, which means that the remote generation is higher than the local generation. All Remote All contributions are set to `remote'; the NACD factor factor is not calculated, but assumed equal to 1 and only the "dc decay only'' curve is used. All Local All contributions are set to `local'; the NACD factor is not calculated, but assumed equal to 0 and only the "AC/DC decay" curve is used. Current/Voltages for

The calculation mode for the currents and voltages to be evaluated: LV/Momentary

Evaluates the subtransient short-circuit currents. LV/Interrupting

Evaluates the breaker currents. 30 Cycle Evaluates the 30-cycle (steady-state) current.

Note: The fields 'Method', 'Fault Type', 'Fault Impedance', 'Output' and 'Fault Location' are described in Section 23.3.1 Section 23.3.1 Basic Options (All Methods) . Methods) .


23.3.6 Advanced Options (ANSI C37 Method)


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Fig. 23.16: ANSI Calculation - Advanced Options Calculate

This option is used to select the various currents (according to the ANSI standard) which are to be calculated. The options are as follows: 

  

Momentary Current Interrupting Current 30 Cycle Current Low-Voltage Current

Bypass Series Capacitance

Series capacitances may be optionally bypassed for the ANSI short-circuit calculation. Alternatively, they may be not bypassed, always bypassed/neglected or this option may be set depending on the type of short-circuit being calculated. The options are as follows: 

 



No Bypassing All Currents LV & Interrupting & 30 Cycle Current 30 Cycle Currents

X/R Calculation

The user may select between a complex number R/X ratio calculation, or a calculation which considers R and X separately. Consider Protection Devices

This option will calculate measured currents for the selected protection devices and will evaluate tripping times. To increase the speed of the calculation, this option can be disabled when protection devices do not need to be analyzed. Calculate max. Branch Currents = Busbar Currents

This option is used to check the rating of the circuit breakers against the system breaker currents. Normally the breaker currents are calculated as max{Ibus-Ibranch, Ibranch}. If this option is activated, the busbar short-circuit current is used as the breaker current, which is actually an over-estimation of the currents.


23.3.7 Basic Options (Complete Method)


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Fig. 23.17: Complete Method - Basic Options

As opposed to the calculation calculation methods according according to IEC/VDE and ANSI, ANSI, which represent represent short-circuit currents by approximations, approximations, the complete complete method evaluates evaluates currents without using approximations. This accurate evaluation of the currents takes into account the system conditions immediately prior to the onset o f the fault. Load Flow

The pre-fault system condition used by the complete method can be determined either by the evaluation of a lo ad flow, or by means of a simplified method, which initializes the internal voltages of all components that contribute to the short-circuit current with their nominal values, multiplied by a scalar factor, c. The load flow command used to initialize the short-circuit calculation (when Load Flow I nitializatio 23.3.8)) nitialization n on the Advanced Options tab is selected, see Section 23.3.8 is displayed next to the button labelled Load Flow ( ). The load flow comm command and can be acce accessed ssed and modi modified fied by pres pressing sing this butto button n displayed here is initially taken from the currently active study case.

. The The load load flow comm command and

Short-Circuit Duration

The value for the Break Time (Global) is used to calculate the breaking current of circuit breakers. Depending on the user selection, the value used for the break time within the calculation is: global

The Break Time (Global) defined in the short-circuit command. min. of local

The shortest Break Time of all circuit breakers (defined in the Complete Short-Circuit tab of ElmCoup of ElmCoup objects) objects) connected to the busbars being studied. local

For each connected circuit-breaker, its own Break Time (defined in the Complete Short-Circuit tab of ElmCoup of ElmCoup objects) objects) is used for the calculation of the breaking current, however for busbar results, the fastest of these Break Time s is used.

Note: The fields 'Method', 'Fault Type', 'Fault Impedance', 'Output' and 'Fault Location' are described in Section 23.3.1 Section 23.3.1 Basic Options (All Methods) . Methods) .


23.3.8 Advanced Options (Complete Method)


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Fig. 23.18: Complete Method - Advanced Options Initialisation

The user may select to initialize the complete method by one o f the following options:  

the load flow calculation referred to in the Load Flow field of the Basic Options tab; or the nominal voltages with a user-defined correction factor ( c-Factor ). It should be noted that this option is only available in the dialogue when Load Flow Initialisation is unticked.

Peak, DC Currents, R/X ratio (ip,ib,idc)

This option allows the definition o f the method used to determine the factor kappa (κ ) and the R/X_b ratio, required for the calculation of the peak and the DC component of the short-circuit current. The methods available correspond to those given in the IEC/VDE standard. B

Uses the ratio R/X at the short-circuit location. In this case both ratios ( R/X_p for the calculation of κ , and R/X_b) are equal. C(1)

For κ , the ratio R/X_p calculated at a virtual frequency of 40% (based on the short-circuit impedance in the positive sequence system) is used. The R/X_b ratio is calculated according to the equivalent frequency method, considering the breaking time and the positive sequence impedance (as for Method C from the IEC standard, however it should be noted that the IEC correction factors are not considered). C(012)

Like C(1) described directly above, but uses the correct short-circuit impedance based on the positive-, negative- and zero-sequence system. Consider Protection Devices

This option will calculate measured currents for all protection devices and will evaluate tripping times. This option can be disabled to increase the calculation speed when protection devices do not need to be analyzed. Calculate max. Branch Currents = Busbar Currents

This option is used to check the rating of the circuit breakers against the system breaker currents. Normally the breaker currents are calculated as max{I -I , bus branch I }. If this branch option is activated, the busbar short-circuit current is used as the breaker current, which is an over-estimation of the currents. Overhead Line Modelling: Phase Matrices For the unbalanced short-circuit calculation, PowerFactory always uses the phase component matrix. The following options define which phase matrix is used: Untransposed: the short-circuit calculation uses the untransposed phase matrix. Symmetrically Transposed: the short-circuit calculation uses the symmetrically transposed phase matrix for untransposed lines.


23.3.9 Basic Options / Advanced Options (IEC 61363)

For detailed information about the IEC 61363 method and its options, please open the Technical Reference paper.


Chapter 24 Harmonics Analysis One of several aspects of power quality is the harmonic content of voltages and currents. Harmonics can be analyzed in either the frequency domain, or in the ti me-domain with post-processing using Fourier Analysis. The PowerFactory harmonics functions allow the analysis of harmonics in the f requency domain. Two different functions are provided by PowerFactory :






Page 23 of 168

Harmonic Load Flow Frequency Sweep

PowerFactory 's harmonic load flow calculates actual harmonic indices related to voltage or current distortion, and harmonic losses caused by harmonic sources (usually

non-linear loads such as current converters). Harmonic sources can be defined by a harmonic current or a harmonic voltage spectrum. In the harmonic load flow calculation, PowerFactory carries out a steady-state network analysis at each frequency at which harmonic sources are defined. A special application of the harmonic load flow is the analysis of ripple-control signals. For this application, a harmonic load flow can be calculated at one specific frequency 's frequency sweep performs a continuous frequency domain analysis. A typical application of the frequency only. In contrast to the harmonic load flo w, PowerFactory sweep function is the calculation of network impedances. The result of this calculation facilitates the identification of series and parallel resonances in the network. These resonance points can identify the frequencies at which harmonic currents cause low or high harmonic voltages. Network impedances are of particular importance for applications such as filter design. PowerFactory provides a toolbar for accessing the different harmonic analysis commands. This toolbar can be displayed (if not already active) by selecting the Harmonics

icon (

) on the main toolbar. The harmonics toolbar provides two icons to open pre-configured command dialogues for the two different calculations:



: Calculate Harmonic Load Flow



: Calculate Impedance Frequency Characteristics (Frequency Sweep)

The command dialogues can be also accessed through the main menu by selecting:  

Calculation −> Harmonics −> Voltage/Current Distribution...; or Calculation −> Harmonics −> Impedance Frequency Characteristic... .

Additionally, following the calculation of a harmonic load flow, a third icon on this toolbar is activated. The icon is used to open the Filter Analysis (ComSh) command dialogue. The Filter Analysis command analyzes results from the most recent harmonic load flow calculation and outputs results to PowerFactory 's output window. All functions and their usage are described in this chapter. 24.1: Harmonic Load Flow 24.2: Frequency Sweep 24.3: Filter Analysis 24.4: Modelling Harmonic Sources 24.5: Definition of Result Variables


24.1 Harmonic Load Flow To calculate a harmonic load flow, click on the

icon to open the dialogue for the ComHldf command as shown in Figure 24.1.

Fig. 24.1: Harmonic Load Flow Command (ComHldf )

For a detailed description of the harmonic calculations, refer to the Section 24.4 Modelling Harmonic Sources , in which the analysis and the harmonic indices are described. The following sections describe the options available in the harmonic load flow command. 24.1.1: Basic Options 24.1.2: Advanced Options


24.1.1 Basic Options

Network Representation Calculate Network Representation Balanced

In the case of a symm etrical network and balanced harmonic sources, characteristic h armonics either appear in the negative sequence component (5th, 11th, 19th, etc.), or in the positive sequence component. Hence, at all frequencies a s ingle-phase equivalent (positive or negative sequence) can be used for the analysis. Unbalanced, 3 Phase (ABC) For analyzing non-characteristic harmonics ( 3rd-order, even-order, inter-harmonics), or harmonics in non-symmetrical networks, the Unbalanced option for modelling the network in the phase-domain should be selected. Calculate Single Frequency


Page 24 of 168

Selecting this option will perform a single harmonic load flow calculation at the given Output Frequency (parameter name: fshow ) or at the given harmonic order. A common application for this mode is the analysis of ripple control systems. The results of the analysis are shown in the single line diagram, in the same way as for a normal load flow at the fundamental frequency. All Frequencies Selecting this option will perform harmonic load flow calculations for all frequencies for which harmonic sources are defined. These frequencies are gathered automatically prior to the cal culation. The results are stored in a result file, which can be used to create harmonic bar graphs (see als o Section 20.1.2 Plots ). Nominal Frequency, Output Frequency, Harmonic Order Nominal Frequency

PowerFactory can only calculate harmonics of AC-systems with identical fundamental frequencies. The relevant nominal frequency must be entered here (usually 50Hz or 60Hz). Output Frequency

This is the frequency for which results are displayed. In the case of a Single Frequency calculation, this is the frequency for which a harmonic load flow is calculated. When option All Frequencies is selected, only the display of results in the single line diagram is influenced by this input parameter, not the calculation itself. In this case, the results displayed in the single line diagram are for the defined Output Frequency . Harmonic Order

This is used to check or to alter the Output Frequency . It is the same as the Output Frequency but input as the Harmonic Order (f/f n). The harmonic order multiplied by the Nominal Frequency always equals the Output Frequency . Both floating-point and integer values are valid. Result Variables and Load Flow Result Variables

This option is used to select the target result object for storing the results of the harmonic frequency sweep. See Section 24.5 Definition of Result Variables for more information regarding specifying and defining result variables. Load Flow

This displays the load flow command used by the calculation. Click on the arrow button (

) to inspect and/or adjust the load flow command settings.


24.1.2 Advanced Options Based on Fundamental Frequency Values (IEEE) All values are based on fundamental frequency values, as defined by IEEE standards. Based on Total RMS-Values (DIN) All values are based on "true RMS''-values, as defined by DIN standards.


24.2 Frequency Sweep . This function is To calculate frequency dependent impedances, the impedance characteristic can be computed for a given frequency range using ComFsweep available by clicking on the

icon.

The harmonic frequency sweep command is shown in Figure 24.2.

Fig. 24.2: Harmonic Frequency Sweep Command (ComFsweep )

Harmonic analysis by frequency sweep is normally used for analyzing self- and mutual- network impedances. However, it should be noted that not o nly self- and mutual-impedances can be analyzed and shown. The voltage source models available in PowerFactory allow the definition of any spectral density function. Hence, impulse or step responses of any variable can be calculated in the frequency domain. One common application is the analysis of series resonance problems. The following sections describe the options available for the harmonic frequency sweep calculation. 24.2.1: Basic Options 24.2.2: Advanced Options



Network Representation Impedance Calculation Nominal Frequency, Output Frequency, Frequency Sweep Result Variables and Load Flow Network Representation


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Balanced, positive sequence This option uses a single-phase, positive sequence network representation, valid for balanced symmetrical networks. A balanced representation of unbalanced objects is used. Unbalanced, 3 Phase (ABC) This option uses a full multiple-phase, unbalanced network representation. Impedance Calculation

The frequency sweep will be performed for the frequency range defined by the Start Frequency and the Stop Frequency , using the given Step Size. An option is available which allows an adaptive step size. Enabling this option will normally speed up the calculation, and enhance the level of detail in the results by automatically using a smaller step size when required. The settings for step size adaptation can be changed on the Advanced Options tab. Nominal Frequency, Output Frequency, Frequency Sweep Nominal Frequency

This is the fundamental frequency of the system, a nd the base frequency for the harmonic orders (usually 50Hz o r 60Hz) Output Frequency

This is the frequency for which the results in the single li ne diagram are shown. This v alue has no effect on the actual calcula tion. Harmonic Order

This is used to check or to alter the output frequency. It is the harmonic order equivalent of the Output Frequency . The Harmonic Order multiplied by the Nominal Frequency always equals the Output Frequency . Both floating-point and integer values are valid. Result Variables and Load Flow Result Variables

Used to select the result object which will store the results of the harmonic frequency sweep. See Section 24.5 Definition of Result Variables for more information about specifying result variables. Load Flow

This displays the load flow command used by the calculation. Click on the arrow button (

) to inspect and/or adjust the load flow command settings.

The results of PowerFactory 's frequency sweep analysis are the characteristics of the impedances over the frequency range.


24.2.2 Advanced Options

Selecting the option Automatic Step Size Adaptation on the Basic Data tab of the ComFsweep command is one way to increase the speed of the calculation. This option enables the use of the step size adaptation algorithm for the frequency sweep. With this algorithm, the frequency step between two calculations of all v ariables is not held constant, but is adapted according to the shape of the sweep. When no resonances in the impedance occur, the time step can be increased without compromising accuracy. If the impedance starts to change considerably with the next step, the step size will be reduced again. The frequency step is set such that t he prediction error will conform to t he two prediction error input parameters, as described below: errmax Maximum Prediction Error (typical value: 0.01) errinc Minimum Prediction Error (typical value: 0.005) ninc Step Size Increase Delay (typically 10 frequency steps) Calculate R, X at output frequency for all nodes

Normally, PowerFactory calculates the equivalent impedance only at selected nodes. When this option is selected, following the harmonic calculation, the equivalent impedance is calculated for all no des.


24.3 Filter Analysis The Filter Analysis command is a special form of the Output of Results command ( ComSh). It is used to analyze the results from the previous harmonic load flow and to output results to the PowerFactory output window. It outputs a summary of the harmonics for the terminals/busbars and branch elements at a specified frequency, which is specified in the Output Frequency field of the ComHldf command. It also reports the parameters and different variables for the i nstalled filters. The filter analysis report generator can be activated using the icon or by using the Output Calculation Analysis icon from the main menu (see also Section 20.2.5: Output of Results). This will open the same dialogue as that used for the reporting of harmonic results, as displayed in Fi gure 24.3. In the dialogue, the Output Frequency specified in the harmonic load flow command is displayed in red text (see top of dialogue in Fi gure 24.3). There are four different reports to choose from: Busbars and Branches This displays the results of the harmo nic load flow for all node and branch elements in the network. The distortion for vari ous electrical variables is printed and summarized. Busbars/Terminals

For the electrical nodes, the rated voltage, the voltage at the cal culation frequency, as well as R MS values and distortion at the nodes are di splayed. Filter Layout The filter layout of all active filters in the network is calcula ted for the given frequency. The rated values and impedances of the filter as well as the type and vector group are printed to the output window. Additionally, the currents through the different components and the losses are shown. Filter Results

The filter results show the main lay out of all filters in the network fo r the calculation frequency. For a set of frequencies, the voltages and currents through the filter are tabulated.


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Fig. 24.3: Filter Analysis Report Command ( ComSh) Dialogue

The default format used for the report in the output window is defined in the Used Format section of the dialogue and can be set or changed by clicking on the Filter Layout button (

).


24.4 Modelling Harmonic Sources Every switched device produces harmonics and must therefore be modelled as a harmonic source. In PowerFactory , harmonic sources can be both current or voltage sources. The following models can generate harmonics: 

 

 

General loads, if they are modelled as a current source (which can be defined in the load type); Thyristor rectifiers; PWM-converters, which are generally modelled as a harmonic voltage source; Voltage sources, which may also be used for ripple control applications; Current sources, with a user-defined spectrum of harmonic injections.

The spectrum of harmonic infeeds must be defined using the Harmonic Sources type object ( TypHmcCur ). The spectrum may be entered according to one of two options: balanced or unbalanced (shown in Figures 24.4 and 24.5, respectively). This object is a PowerFactory 'type' object, which means that it may be used by many elements who have the same basic type. Multiple current source loads may, for example, use the same TypHmcCur object. Note that PowerFactory has no corresponding element for this type.

Fig. 24.4: Balanced Harmonic Source Type (TypHmccur )

Fig. 24.5: Unbalanced Harmonic Source Type ( TypHmccur )

The spectrum object is independent of the whether the harmonic source is either a voltage source or a current source. The decision as to whether harmonic sources are fed into the system as harmonic voltages or as harmonic currents is made exclusively by the element to which the spectrum type is associated. 24.4.1: Harmonic Distortion Results 24.4.2: Magnitudes and Phase values 24.4.3: Frequency Dependent Parameters 24.4.4: Waveform Plot


24.4.1 Harmonic Distortion Results

The harmonic distortion of a current or of a voltage can be quantified in terms of the Harmonic Distortion (HD), as described by (24.1). To describe the overall distortion, the Total Harmonic Distortion index THD (see (24.2)) has been introduced. An alternative, less common index is the Total Arithmetic Distortion TAD (see (24.3)). All distortion indices are described by their equations (below) for the current, but may be similarly described for voltage distortion.


Page 27 of 168

Eqn 24.1:

Eqn 24.2:

(Total Harmonic Distortion)

Eqn 24.3:

(Total Arithmetic Distortion)

where I(f ) Component of the current at frequency f i i I Reference value for the current ref

Eqn 24.4:

(Total RMS value)

Eqn 24.5:

(Arithmetic Sum value)

The reference value I depends on the standard used. The two possible options are the calculation according to DIN (24.6) and according to IEEE (24.7), as presented ref below:

Eqn 24.6: Eqn 24.7:

(DIN Standard) (IEEE Standard).

Another value which may be of importance is the Total Power (see (24.8)), which describes the power absorbed over all frequency components:

Eqn 24.8:

(Total Power)


24.4.2 Magnitudes and Phase values

The quantities of the spectrum type are rated to current/voltage at the fundamental frequency in the balanced case. Hence, in the case of a harmonic current source, the actual harmonic current at frequency f is calculated by: h

where

The values at the fundamental frequency, I and ϕ , are taken from a preceding load flow calculation. A normal load flow calculation is therefore required prior to a harmonic 1 1 load flow calculation. In case of balanced systems in which only characteristic harmonics of orders 5, 7, 11, 13, 17, etc. occur, the option Balanced should be selected in the Balanced/Unbalanced Sources section (as shown in Figure Balanced Harmonic Source Type (TypHmccur)). In this context, Balanced refers to characteristic harmonics. In the balanced case, the harmonic frequencies are determined by the program (note that i n the unbalanced case, the harmonic frequencies can be freelydefined). For harmonic sources which produce non-characteristic, unbalanced or inter-harmonics, the option Unbalanced should be set in the Balanced/Unbalanced Sources section. In the Unbalanced ' case, the harmonic frequency, magnitude and phase angle of each phase can be chosen individually for each harmonic frequency. This mode therefore caters for every possible kind of harmonic source. The problem commonly arises as to how one can represent the harmonic content in a system which differs to the native modal system (positive, negative or zero sequence system). The following example illustrates how to represent the 3rd harmonic in a positive or negative sequence system (as opposed to the native zero sequence system). In the symmetrical case, the phase shift between the three phases is: A: 0° B: -120° C: +120° (-240°)

For harmonics of order n: A: 0° B: -n*120° C: +n*120°

Taking the 3rd harmonic as an example: A: 0° B: -360°(= 0°)


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C: +360° (=0°)

Consequently, the 3rd harmonic in the ideally balanced case only in the zero sequence component, as their native modal system. For representing 3rd harmonics (and multiples thereof) in the positive sequence system, the following phase correction needs to be entered: A: 0° B: +(n-1)*120° C: -(n-1)*120°

Again taking the 3rd harmonic as an example: A: 0° B: -360° + 240° = -120° C: +360° - 240° = 120°


24.4.3 Frequency Dependent Parameters

Due to the skin effect and v ariations in the internal inductance, resistances and inductances are usually frequency dependent. This can be modeled in PowerFactory by associating a "frequency characteristic'' to these quantities. Two types of characteristic may be used: either a polynomial characteristic ( ChaPol) as illustrated in Figure 24.6, or a user-defined frequency table ( TriFreq and ChaVec ). These kinds of characteristics are then assigned via the Harmonics tab of the correspoding element's dialogue, as illustrated by the example in Figure 24.7 for a line element.

Fig. 24.6: The Frequency Polynomial Characteristic ( ChaPol )

For the polynomial characteristic object shown in Figure 24.6, the following formula is used:

The parameters a and b are specified in the ChaPol dialogue. Variable y is usually expressed in % of the corresponding input parameters. For example, the resulting line resistance is obtained by:

An example of the use of the polynomial characteristic for a line type is shown in Figure 24.7.

Fig. 24.7: Frequency Dependencies in a Line Type

It also is possible to define f requency dependent characteristics using vectorial characteristics ( ChaVec ). An example for a grid impedance defined with a ChaVec is shown in Figure 24.8.

Fig. 24.8: Frequency Dependent Grid Impedance as Vectorial Characteristic

The following objects can have frequency dependent parameters defined using a frequency characteristic: TypLne Line Type TypAsm Asynchronous Machine Type TypSym Synchronous Machine Type ElmShnt Shunt/Filter ElmVac AC Voltage Source ElmNec NEC/NER

Lines which are represented by a tower type TypTow are automatically assigned a harmonic characteristic. The same applies to cables using the detailed cable representation type TypCab .

DIgSILENT GmbH


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www.digsilent.de Tel: +49 (0)7072 9168-50 Fax: +49 (0)7072 9168-88 [email protected]

24.4.4 Waveform Plot

The waveform plot is used to display the waveform of a voltage or a current following a harmonic load flow calculation. The harmonics are typically emitted by a harmonic voltage or current source, as described in Section 24.4. In this plot, a waveform is generated using the magnitude and phase angle of the harmonic frequencies. With this diagram, a variable such as the voltage or current, which is defined in a harmonic source (i.e. a power electronic device or a load), can be easily shown as a time dependent variable. This way the real shape of the voltage can be seen and analyzed. For a more detailed description, see Section 20.1.6 The Waveform Plot .


24.5 Definition of Result Variables Before a Frequency Sweep calculation can be performed, all variables of interest must be defined for recording. These variables can be defined by right-clicking on a network component (or multi-selecting several components and right-clicking), either in the single-line diagram or in the data manager, and selecting the option Define − >Variable Set (Harmonics Load-Flow); or Define −>Variable Set (Frequency Sweep). This will add a new (but still empty) variable set for the selected object to the result object (referred to by parameter Result Variables on the Basic Options tab of the Harmonic Load Flow command dialogue). All results of harmonic analyses, with the exception of the single frequency harmonic load flow, are stored in a normal result object ( ElmRes). This result object stores graphs of result variables vs. frequency. For more information about the result o bject, see Section 20.2.1 Result Objects . New result variables may also be added by clicking on the Edit Result Variable icon (

) on the main toolbar. There are two instances of this button; one for each

harmonic analysis function, i.e. one associated with the Harmonic Load Flow . and one associated with the Frequency Sweep . Select the button associated with the relevant calculation. This will open the variable set manager, which displays the list of all defined variable sets for that calculation. Each variable set contains the variables of interest for a single object. A wi ndow is opened automatically whenever a new variable set is defined, as shown in Figure 24.9, displaying the list of variable sets. A new variable set can also be defined by clicking on the New icon (

).

Fig. 24.9: Example of a List of Variable Sets

It should be noted that the column labelled Object must be set before any variables can be defined. This can be done by either double-clicking the appropriate cell, or by right-clicking the cell and selecting Select Element.... A single variable set from the variable sets list can be accessed (and the desired variables defined) by either double-clicking on the icon in the corresponding row, or right-clicking on the icon and selecting the Edit menu option. The Variable Set object ( IntMon) dialogue opens, as shown in Figure 24.10. Select the Harmonics tab of the IntMon dialogue and then a list of all results that are available for the selected object (relevant to harmonics analysis) will be available for selection.

Fig. 24.10: Harmonics Result Variables for a Terminal

Result variables may be added or removed from the set of selected variables by pressing the or buttons. Additionally, different variables are available for selection depending on the selection made from the Variable Set drop-down list. This is available in the Filter for section on the Harmonics tab of the IntMon dialogue. It should be noted that as the results of the discrete harmonic analysis are discrete, the plots generated from the result file should have the Bars option enabled. To do this, open the subplot dialogue by double-clicking on a subplot, going to the Advanced tab, and selecting Bars in the Presentation section.



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Chapter 25 Stability and EMT Simulations The transient simulation functions available in DIgSILENT PowerFactory are able to analyze the dynamic behavior of small systems and large power systems in the time domain. These functions therefore make it possible to model complex systems such as industrial networks and large transmission grids in detail, taking into account electrical and mechanical parameters. Transients, stability problems and control problems are important considerations during the planning, design and operation of modern power systems. Studies involving electro-magnetic transients and different aspects of stability may be conducted using time-domain simulations for varying time periods, or dynamic or small-signal stability analysis tools using (for example) eigenvalue analysis. A large range of AC and DC systems can be analyzed (i.e. transmission systems with detailed models of power plants, complex HVDC systems, motor start-up), as well as a combination of both. Applications such as wind power integration or power electronics constitute new challenges in the analysis of power systems, and as a result new models and techniques are provided in PowerFactory to meet these requirements. For modelling a variety of machines and controller units, as well as the electrical and mechanical components of power plants, etc., PowerFactory 's global library provides a large number of predefined models. This library includes models of generators, motors, controllers, motor driven machines, dynamic loads and passive network elements. As an example, this library contains the IEEE standard models of power plant controllers. Furthermore, the user can model specific controllers and develop block diagrams of power plants with a large degree of freedom. A Stability simulation in PowerFactory is started by:







Selecting the Stability toolbar by clicking on the Stability

icon from the Select toolbar;

Calculating the initial conditions for the simulation by either pressing the from the main menu; When the initial values have been calculated successfully, the

icon on the main toolbar, or by selecting Calculation −> Stability −> Initial Conditions...

icon on the main toolbar will be activated and can be pressed to start the simulation.

25.1: Introduction 25.2: Calculation Methods 25.3: Setting Up a Simulation 25.4: Result Objects 25.5: Events 25.6: Running a Simulation 25.7: Models for Stability Analysis 25.8: User Defined (DSL) Models 25.9: The DIgSILENT Simulation Language (DSL) 25.10: Matlab Integration


25.1 Introduction The study of power system stability involv es the analysis of the behavior of power systems under conditions before and after sudden changes in load or generation, during faults and outages. The robustness of a system is defined by the ability of the system to maintain stable operation under normal and perturbed conditions. It is therefore necessary to design and operate a power system so that transient events (i.e. probable contingencies), can be withstood without the loss of load or loss of synchronism in the power system. Transients in electrical power systems can be classified according to three possible timeframes:   

short-term, or electromagnetic transients; mid-term, or electromechanical transients; long-term transients.

The multilevel modelling of power system elements and the use of advanced algorithms means that the functions in PowerFactory can analyse the complete range of transient phenomena in electrical power systems. Consequently, there are three different simulation functions available: 1. 2. 3.

A basic function which uses a symmetrical steady-state (RMS) network model for mid-term and long-term transients under balanced network conditions; A three-phase function which uses a steady-state (RMS) network model for mid-term and long-term transients under balanced and unbalanced network conditions, i.e. for analyzing dynamic behaviour after unsymmetrical faults; An electromagnetic transient (EMT) simulation function using a dynamic network model for electromagnetic and electromechanical transients under balanced and unbalanced network conditions. This function is particularly suited to the analysis of short-term transients.

In addition to the time-domain calculations, two other analysis functions are available: 



Parameter Identification Modal Analysis or Eigenvalue Analysis

Time-domain simulations in PowerFactory are initialized by a valid load fl ow, and PowerFactory functions determine the initial conditions for all power system elements including all controller units and mechanical components. These initial conditions represent the steady-state operating point at the beginning of the simulation, fulfilling the requirements that the derivatives of all state variables of loads, machines, controllers, etc., are zero. Before the start of the simulation process, it is also determined what type of network representation must be used for further analysis, what step sizes to use, which events to handle and where to store the results. The simulation uses an iterative procedure to solve AC and DC load flows, and the dynamic model state variable integrals simultaneously. Highly accurate non-linear system models result in exact solutions, including during high-amplitude transients. Various numerical integration routines are used for the electromechanical systems (including voltage regulators and power system stabilisers) and also for the hydro-mechanical or thermo-mechanical models. The process of performing a transient simulation typically involves the follo wing steps: 1. 2. 3. 4. 5. 6. 7.

Calculation of initial values, including a load flow calculation; Definition of result variables and/or simulation events; Optional definition of result graphs and/or other virtual instruments; Execution of simulation; Creating additional result graphs or virtual instruments, or editing existing ones; Changing settings, repeating calculations; Printing results.


25.2 Calculation Methods 25.2.1: Balanced RMS Simulation


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25.2.2: Three-Phase RMS Simulation 25.2.3: Three-Phase EMT Simulation


25.2.1 Balanced RMS Simulation

The balanced RMS simulation function considers dynamics in electromechanical, control and thermal devices. It uses a symmetrical, steady-state representation of the passive electrical network. Using this representation, only the fundamental components of voltages and currents are taken into account. Depending on the models of generators, motors, controllers, power plants and motor driven machines used, the following studies may be carried out:    

transient stability (e.g. determination of critical fa ult clearing times); mid-term stability (e.g. optimization of spinning reserve and load shedding); oscillatory stability (e.g. optimization of control device to improve system damping); motor start-up (e.g. determination of start-up times and voltage drops);

Various events can be included in the simulation, including the following examples:  

 

 

 



start-up and/or loss of generators or motors; stepwise variation of loads; load-shedding; line and transformer switching/tripping; symmetrical short-circuit events; insertion of network elements; power plant shut down; variations of controller setpoint; change of any system parameter.

Because of the symmetrical network representation, the basic simulation function allows the insertion of symmetrical faults only.


25.2.2 Three-Phase RMS Simulation

If asymmetrical faults or unbalanced networks have to be analysed, the three phase RMS simulation function must be used. This simulation function uses a steady-state, three-phase representation of the passive electrical network and can therefore compute unbalanced network conditions, either due to unbalanced network elements or due to asymmetrical faults. Dynamics in electromechanical, control and thermal devices are represented in the same way as in the basic RMS simulation function. Asymmetrical electromechanical devices can be modelled, and single-phase and two-phase networks can also be analysed using this analysis function. In addition to the balanced RMS simulation events, unbalanced fault events can be simulated, such as:  

 

single-phase and two-phase (to ground) short-circuits; phase to phase short-circuits; inter-circuit faults between different lines; single- and double-phase line interruptions.

All of these events can be modelled to occur simultaneously or separately, hence any combination of symmetrical and asymmetrical faults can be modelled.


25.2.3 Three-Phase EMT Simulation

Voltages and currents are represented in the EMT simulation by their instantaneous values, so that the dynamic behavior of passive network elements is also taken into account. This is necessary for the following applications: 

 

  



DC and harmonic components of currents and voltages; Exact behavior of inverter-driven machines; Exact behavior of HVDC transmission systems; Non-linear behavior of passive network elements such as transformer saturation; Overvoltage phenomena in switching devices; Lightning strikes and travelling waves; Analysis of the exact behavior of protection devices during faults.

The high level of detail used to represent the modelled network means that all phases and all defined events (symmetrical and asymmetrical) can be simulated. The EMT function can also be used for the simulation of longer-term transients. However, due to the passive network elements being represented dynamically, the integration step size has to be significantly smaller than in the case of a steady-state representation and as a result, the calculation time increases.


25.3 Setting Up a Simulation Based on the results of a load flow calculation, all internal variables and the internal operating status of connected machines, controllers and other transient models have to be determined. As a result of this calculation, the synchronous generator excitation voltages and load angles are calculated. Additionally, all state variables of controllers and power plant models, and any other device which is active and wil l affect the time-domain simulation, are also calculated. The calculation of initial conditions is started by either:

 

Selecting the icon from the icon toolbar, and then pressing the icon; Selecting Calculation −> Stability −> Initial Conditions... from the main menu.

In the Initial Conditions command ( ComInc ) dialogue all simulation settings can be defined, such as the simulation type ( i.e. RMS or EMT, balanced or unbalanced) and simulation step size settings.


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These settings include: Basic Options

The simulation type is selected here (RMS, EMT; balanced, unbal anced), and the load flow command, the result object and the event list are defined. Step Sizes Maximum and minimum step size are specified for use by the step size algorithms. Step Size Adaptation Enables the variable step size algorithm. Advanced Options Includes various error margins, iteration limits, damping factors, etc. Noise Generation Defines parameters of the noise generation for stochastic applications.

Fig. 25.1: The Initial Conditions Command (ComInc ) Dialogue

25.3.1: Basic Options 25.3.2: Step Sizes 25.3.3: Step Size Adaptation 25.3.4: Advanced Options 25.3.5: Noise Generation 25.3.6: Advanced Simulation Options - Load Flow



The basic options are used to select the simulation type and the network representation. References to the result object, the event list and the load flow command are available for inspecting or editing these objects, by clicking on the respective

icon.

Verify Initial Conditions

If the initial conditions can be fulfilled, the power system will be in a steady-state condition. When the Verify Initial Conditions options is enabled, then the condition dx/dt=0 is checked for all state variables. If one or more of the state variable derivatives does not equal zero, the power system may start 'moving' from the very beginning of the simulation, even without the application of an external event. In this case the user sho uld analyse the relevant controller or model and its defined initial conditions carefully. All warnings or error messages issued in the output window should be checked carefully. Typical problems are devices which are overloaded or operate above or below signal limitation from the beginning of the simulation. The error message displayed in the output window might look as follows: DIgSI/err DIgSI/err DIgSI/err DIgSI/err

-

Some models could not be initialized. Please check the following models: 'Simple Grid\AVR Common Model.ElmDsl': Initial conditions not valid !

Automatic Step Size Adaptation

This option enables the step size adaptation algorithm, and can be used to speed-up the simulation considerably. PowerFactory adjusts the step size to the actual course of each state variable at any moment in time. Based on the local discretisation error, PowerFactory calculates an optimal step size that keeps the numerical errors within the specified limits. A step size controller adjusts the integration step size. As a result, when fast transients have decayed, PowerFactory automatically increases the step size and speeds up the simulation process considerably. In the case of events (external or internal), the step size is always set back to the Minimum Step Size. This way, the behavior of the system during a transient event is represented with the best accuracy. If this option is activated, two integration step sizes are available on the Step Size tab of the dialogue: Electromagnetic Transients/Electromechanical Transients Minimum step size for EMT and RMS simulations, respectively. Maximum Step Size

Maximum step size for the simulation.

Further parameters to adapt this algorithm can be found on the Step Size Adaptation tab.


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25.3.2 Step Sizes Integration Step Sizes

When using a fixed step size for the simulation (deactivate Automatic Step Size Adaptation on the Basic Options tab), the integration step size for EMT or RMS has to be set. It is often unnecessary to plot every single calculated time step, and this reduction in plotted data can also result in a reduced simulation time. For this purpose, the step size for the output graphs can be set, so that not every point in t ime throughout the simulation time will be drawn on t he virtual instruments plot. By selecting a larger Output step size, the simulation process will speed up without influencing the calculation process. It should be noted, however, that fast changes may not be seen in the reported results. The parameters which are available for the step size are: dtemt Electromagnetic Transients (typical value: 0.0001 sec) dtgrd Electromechanical Transients (sym, asm, vco, pss) (typical 0.01 sec) dtout Output (typical equal to dtemt for EMT; and dtgrd for RMS simulation) Start Time

The start time of the simulation. T his is typically negative, a llowing the first event to be analysed to ta ke place at t=0s. Note When setting up time-domain simulations, it is very important to use the correct time steps for simulations in order to observe the right phenomena in the results. For the RMS simulation the minimum time step should always be smaller then the time constants in the system. In controllers one must consider both the open-loop and the closed-loop time constants. For electromagnetic transients, e.g. when analyzing travelling waves, the smallest travelling time would be the upper limit for the minimum time step.

In addition to the Newton-Raphson based algorithm for the solution of "weak'' non-linearities (i.e. saturation effects in synchronous and asynchronous machines), the EMT simulation function allows interrupts for the simulation of "strong'' non-linearities (i.e. switches, two-slope transformer saturation or thyristors). These interrupts can also occur between time steps. In case of such an interrupt, all ti me dependent variables are interpolated to the instant of interrupt and the simulation restarts at that point. This prevents numerical oscillations and allows much a lower integration step size to cater for power electronics devices. The dynamic model equations of the voltage-controllers (vco) and the power system stabilisers (pss) are solved simultaneously with the electrical generator and passive network equations (stepsize dtgrd ).


25.3.3 Step Size Adaptation

If option Automatic Step Size Adaptation is enabled on the Basic Options tab, further step size options are available on the Step Size Adaptation tab. These options are: errmax Maximum Prediction Error (typical value: 0.01) errinc Minimum Prediction Error (typical value: 0.01) ninc Delay for Step Size Increase (typical value: 10 time steps) finc Speed Factor for increasing the time step (default value: 1.5) fdec Speed Factor for decreasing the time step (default value: 2) ddtemt_max Maximum increase of step size (typical values: 0.05 for RMS; 0.001 sec for EMT)

Note The simulation time can be very sensitive to some of the parameters. For example when you increase the maximum time step the duration of calculating transients may not always increase. If this time step is increased over an "optimal'' time step the simulation time may increase as well. It is strongly recommended to critically observe the simulation time and the results for different simulation parameters.



The advanced options may be used to tune the performance of the simulation algorithm. Less experienced users are recommended to use the default values. Event Control

Resolution Factor

The value entered here (parameter name: kres) determines the time interval used to synchronize events. Every time an internal or external event occurs (usually between two integration time steps), PowerFactory interpolates all state variables up to the moment in time at which the event has occurred and restarts the simulation from there. In the case of large disturbances it is possible t hat a very large number of events occur almost simultaneously. As this would slow down the simulation considerably, PowerFactory executes all events that occur within a time interval of duration kres*dtmin at the same time. All system variables are then interpolated up to the point in time when the event takes place, and the simulation is started from there. A higher resolution factor decreases the minimum time interval between events. The default value of 0.001 is usually sufficient. If an event occurs, there are two different options available: Interpolation at user defined events 

Calculation of v(t) and v(t+h) as usual. PowerFactory uses special numerical methods to allow this without numerical oscillations.

Re-Initialize After Event 

Calculation of v(t) and v(t+h), hence two values at the same time, one before the occurrence of the event, and one after. The second method is applied if the option After Event is enabled.

Further parameters can be changed to control the simulation algorithm. Integration Control Iteration Control Local/Global Reference System Calculate Maximum Rotor Angle Deviation A-stable integration algorithm for all models Integration Control errseq Maximum Error of State Equations (typical value: 0.1%) itrpx Maximum Number of Successive State Iterations (typical value: 10) alpha_rms Damping Factor (RMS) (typical value: 1)

Re-initialize


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alpha_emt Damping Factor (EMT) (typical value: 0.99) Iteration Control errsm Maximum Iteration Error of Nodal Equations (typical value: 10*errlf ) The iteration error errsm depends on the nominal power of the machines a nd the voltage levels. As an adequate starting value, errsm should be set to: errsm = 10*errlf, where errlf is the Max. Allowable Load-Flow Error for each Bus . Checking is best done by plotting some voltages at generator busbars. If voltage steps are observed, the value of errsm should be reduced. erreq Maximum Error of Model Equations (typical value: 1%) itrlx Maximum Number of Iterations (typical value: 25) itrpx specifies the max. number of iterations at each integration step which are allowed to reach the max. tolerable bus-error errsm . During the transient simulation process, the typical number of iterations required is between 1 and 5. Under certain conditions - i.e. after switching operations - up to 25 iterations may be observed. itrjx Iteration Limit to Recompute Jacobian Matrix (typical value: 5) Signal Buffer Reference System Local/Global Reference System

The PowerFactory stability analysis uses the angle of a reference machine and refers all other angles to this reference angle. This is a numerically very efficient approach. After running initial conditions, the reference machine is displayed in the output window. It is usually the "Slack''-machine of the load-flow calculation. In case of several isolated islands, PowerFactory offers the option of using one reference machine for the whole system ( Global Reference System), or to use an individual reference machine for each island. The first case should be used if the islands are re-synchronised again later in the simulation. In all other cases the option (Local Reference System) should be used because it leads to a higher numerical stability and to faster simulation times. Calculate Maximum Rotor Angle Deviation

PowerFactory can also calculate the maximum deviation between the rotor angles between the synchronous machines in the system. This variable is then called dfrotx and can be chosen and displayed from the variables of all synchronous generators in the system. This variable can be used as an indicator for the synchronous operation of a large transmission system. A-stable integration algorithm for all mode ls

If you enable this option, PowerFactory uses an A-stable numerical integration algorithms for all models to solve the simulation. In this case dynamic model equations and network equations are solved simultaneously. This algorithm is (slightly) slower in case of small step sizes but converges much better in case of large step sizes. Typical applications are longer term simulations, in which the simulation step size is increased considerably after fast transients have decayed. Another typical application are systems with power electronics. Even if power electronics devices are usually equipped with very fast controls, the A-stable algorithm still allows reasonable step sizes, at which the relaxation method would fail. When using a conventional, explicit numerical integration algorithm, such as Runge-Kutta (not an A-stable algorithm), the integration step size must be adjusted to the eigenvalues of a system. Such a method (Relaxation Method) means a mutual solution of dynamic model equations and network equations until convergence is reached: This algorithm is fast for small step sizes bu t fails to converge when the step size is increased. Best choice for classical transient stability applications. But if excessively large step sizes are used, the numerical solution becomes unstable, even if fast modes have fully decayed and are no longer apparent in the system. With the PowerFactory A-stable algorithm, the step size can be adjusted to the actual course of all state variables without considering numerical stability. When fast transients have decayed, the step size can be adjusted to the speed of slower transients, etc. If some very fast modes are not o f interest, a large step size can be selected from the beginning, and the algorithm will automatically smooth fast variations. A typical application of this type of algorithm is the simulation of long-term phenomena - where it is necessary to increase the simulation step size to the range of minutes, even if f ast modes are present in the system. However, if power electronics are involved, characteristic time constants can be extremely short (i.e. 1ms), even if a stability model w ith steady-state equations for the electrical network is used. Hence, using a classical integration algorithm would require the use of step sizes significantly smaller than the smallest time constant of the system, otherwise it would be numerically instable. Note A requirement for using the A-stable integration algorithm is that just "true" input and output signal variables are used for exchanging information between different models.

It should be mentioned, that it is also possible to choose the usage of an A-stable algorithm for some element models only (not for all models), so that it is possible to run just a part of the models with the A-stable algorithm (for example the power electronic converters or fast controllers). This option is available in the dialogues of the elements. With the A-stable algorithm, these systems can be analysed with reasonable step sizes. Hence, the A-stable algorithm cannot be described as using simplified models but as a different type of nu merical integration algorithm.


25.3.5 Noise Generation

The Noise Generator element ( ElmNoise) can be used in a transient simulation to produce a noise signal based on random numbers. On the Noise Generation page of the ComInc dialogue, the random number generation method can be selected. The random number generator can be selected to be automatic (by selecting option auto ), which is the default value and the most commonly u sed. Alternatively, the option renew may be selected, in which case the random seed of the noise generator can be selected manually from "A" to "K". Thus the noise signal will look the same in every simulation, i.e. the results o f a former simulation can be reproduced exactly.


25.3.6 Advanced Simulation Options - Load Flow

There are further options which can influence the simulation process and its results. In the load flow command dialogue ( ComLdf , see also Section 22.3.1) on the Advanced Simulation Options tab, the influence of protection devices or various controller models can be neglected. Hence the chosen models or protection devices will be ignored during the simulation as well as in load flow and other calculations. This is illustrated in Figure 25.2.


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Fig. 25.2: Advanced Simulation Options in the ComLdf Command Dialogue

The options available for the consideration of protection devices are: none

No protection devices are considered in the calculations all

All protection devices are considered main

Only the protection devices are in operation, which are defined a s 'main' devices backup

Only the 'backup' protection devices are considered. According to the controller models, there is the possibility to ignore all controllers and mechanical elements with the option Ignore Composite Elements . If there are only some specific model types one would like to neglect in the simulation, they can be moved from the left window Considered Models to the right window, Ignored Models .


25.4 Result Objects During an EMT or RMS simulation, a large number of signal variables are changing over time. To reduce the available data and to narrow down the n umber of variables to those necessary for the analysis of each particular case, a selection of these signals for later use has to be defined. Therefore, one or more result objects containing the result variables can be configured. The simulation function needs the reference to a result o bject to store the results. The command dialogues for calculation functions, that produce signals, have result object references, as depicted in Figure 25.3 for the Initial Conditions (ComInc ) dialogue. See also Figure 25.1 for the complete dialogue.

Fig. 25.3: Result Object Reference

Such a result object reference refers to the currently used result object. The downward arrow button ( the referenced result object.

) is used to select or reset the reference, or to edit the contents of

The right-arrow button ( ) is used to edit the result object itself. When editing the output variables press this Edit button and then Contents to get access to the list of variables stored inside the result object. This will pop up the corresponding ElmRes edit dialogue. An easier way to edit or inspect the result object is to press the icon on the main toolbar, or to select the Data −> Stability −> Result Variables option from the main menu. This will enable the user to edit the contents of the currently selected Result object in the Initial Conditions (ComInc ) command dialogue. Result objects (ElmRes) are treated in detail in Chapter 20 Reporting Results in PowerFactory . To add variables of different elements to the result object for RMS and EMT simulations, right-click on the desired element in the single-line graphic and select Define...--> Variable Set (Sim)... as shown in Figure 25.4.


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Fig. 25.4: Defining a Variable Set for a Line Element

This element will then be monitored during the simulation. A browser window is automatically opened, and by double-clicking on the variable set icon ( row, the variables of interest to be recorded can then be selected. See also Section 20.2.1 Result Objects .

) of the relevant

Note Most of the variables for RMS and EMT simulations are identical. Nevertheless there may exist variables that are valid for EMT but not for RMS calculations. It is advisable to only use variables for the calculation which is currently being performed.

25.4.1: Saving Results from Previous Simulations


25.4.1 Saving Results from Previous Simulations

The variables to be monitored are stored (by default) in the result object All calculations. The results of the variables in t he current simulation are stored in this file also. If the results of two different simulations are to be displayed, e.g. in one virtual instrument, there is the possibility to save the result object of a previous simulation simply by copying the result object All calculations and renaming it to something else. This can be done easily in the data manager. The result object can be found in the currently active study case. Copy the result object and paste it into the same study case. Following this, a second result object will be created with the name All calculations(1). If desired, the object can be renamed to something more appropriate. In the following simulation, the default result object All calculations will be overwritten with the new results, but the copied results will not be modified and can be displayed together with the new simulation results in one plot. For further information see Section 20.1.2 Plots .


25.5 Events Besides the reference to a result object, the simulation function needs a reference to an event object to determine the simulation events. The default event object in PowerFactory is Simulation Events and, like the result object, is also stored inside the study case. External events are used in steady-state calculations (e.g. short-circuit calculations) as well as for transient calculations (Simulations). PowerFactory offers several kinds of events for t ime-domain simulations: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Switch events (EvtSwitch) Parameter events (EvtParam ) Short-circuit events (EvtShc ) Intercircuit fault events (EvtShcll) Synchronous machine events ( EvtSym ) Load events (EvtLod ) Outage of element ( EvtOutage) Message events (EvtMessage) Set integration step size event ( EvtStep ) Tap event (EvtTap )

The different events are stored in the event object. The contents of the currently selected event object (labelled Events) can be found in the ComInc dialogue. This object can be edited using the right-arrow (

) button followed by the Contents button to access the event list stored inside the event object.

Alternatively, the event object can be easily accessed from the main toolbar by pressing the Edit Simulation Events icon. A list of the currently defined events will be displayed including the set simulation time, when the event will occur, and the r elated object. Figure 25.5 shows an example set of events.


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Fig. 25.5: The Event Object Including a Set of Events

When creating a new event, use the icon in the toolbar, as can be seen in the Simulation Events object dialogue in Figure 25.5. The event type can be chosen from the list in the element selection dialogue which pops up, as shown in Figure 25.6. The events can also be modified during a simulation by stopping the calculation, editing the events and continuing the simulation.

Fig. 25.6: Defining a New Simulation Event

An alternative means of defining events is as follows: upon calculation of the initial conditions ( ), or when the simulation is already running, double-click on the desired cubicles to create switch events. Additionally, the user can right-click on an element and then select an element-related event such as Define... −> Switch Event, Define... −> Load Event or Define... −> Short-Circuit Event. During a simulation all previous events (i.e. events which have already occurred), are displayed in a grey font style and can no longer be edited or changed. When the simulation is finished or is stopped manually, the events which are still to come in the simulation can be altered and new events can be created. Note At the end of a simulation the event list shows all events, which are now grey in color. They can no longer be modified for this simulation, because the simulation could be restarted from this point on. To change the events for a new simulation one must first initialise the calculation again (

25.5.1: Switch Events 25.5.2: Parameter Events 25.5.3: Short-Circuit Events 25.5.4: Intercircuit Fault Events 25.5.5: Events of Synchronous Machines 25.5.6: Events of Loads 25.5.7: Outage of Element 25.5.8: Save Results 25.5.9: Set Integration Step Size 25.5.10: Tap Event


25.5.1 Switch Events

), so the simulation time is reset to the beginning.


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Switch events are used only in transient simulations. To create a new switch event, press the containing all defined simulation events. Click on the

icon on the main menu (if this icon is available), which will open a browser

icon in this browser, which will show a IntNewobj dialogue which can be used to create a new switching event.

Fig. 25.7: Creation of a New Switch Event (IntNewobj)

After pressing OK, the reference to the switch (labelled Breaker or Element) must be manually set. Any switch in the power system may be selected, thus enabling the switching of lines, generators, motors, loads, etc. The user is free to select the switches/breakers of all phases or of only one or two phases. It should be noted that more than one swi tching event must be created if, for instance, a line has to be opened at both ends. These switch events should then have the same execution time.


25.5.2 Parameter Events

With this type of event, an input parameter of any element or DSL model can be set or changed. First, a time specifying when the event will occur is inserted. Then an element has to be to specified/selected using the down-arrow button value of a valid element parameter.

. Then choose Select... from the context-sensitive menu. Afterwards insert the name and the new


25.5.3 Short-Circuit Events

This event applies a short-circuit on a busbar, terminal or o n a specified point on a lin e. The fault type (three-phase, two-phase or single-phase fault) can be specified as well as the fault resistance and reactance and the phases which are affected. The duration of the fault cannot be defined. Instead, to clear the fault, another short-circuit event has to be defined, which will clear the fault at the same location. An example is shown in Figure 25.5.


25.5.4 Intercircuit Fault Events

This type of event is similar to the short-circuit event described in Section 25.5.3 Short-Circuit Events . Two diff erent elements and their respective phases are chosen, between which the fault occurs. As for the short-circuit event ( EvtShc ), four different elements can be cho sen: 

 

Busbar (StaBar ) Terminal (ElmTerm ) Overhead line or cable ( ElmLne)


25.5.5 Events of Synchronous Machines

There is a special event for synchronous machines, which is used to easily change the mechanical torque of the machine. The user specifies the point in time in the simulation for the event to occur, and an active synchronous machine ElmSym . The user can then define the additional mechanical torque supplied to the generator. The torque can be positive or negative and is entered in per unit values.


25.5.6 Events of Loads

The user specifies the point in time i n the simulation for the event to occur, and a load element ( ElmLod , ElmLodlv or ElmLodlvp ). The value of the load can then be altered using the load event. There are different ways to change the power of the selected load: Step

Changes the current value of the power (positive or negative) by the given value (in % of the nominal power of the load) at the time of the event. Ramp

Changes the current value of the power by the given value (in % of the nominal power of the load), over the time specified by the Ramp Duration (in seconds). The load ramping starts at the time of the event.


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25.5.7 Outage of Element

This event can only be used during an RMS simulation, when an element is to be put out of service at a specific point in time. The option Take element out of service should be selected within the dialogue. It should be noted that it is not possible to bring the outaged elements back into service during the transient simulation. This is only possible in steady-state calculation functions, e.g. short-circuit calculation or reliability assessment. In time-domain simulation the following error message will occur in the output window: DIgSI/err (t=000:000 ms) - Outage Event in Simulation not available. Use Switch-Event instead!


25.5.8 Save Results

This event is only used in the PowerFactory Monitor of the program. It cannot be used during time-domain simulations.


25.5.9 Set Integration Step Size


25.5.10 Tap Event

The user specifies the point in time i n the simulation for the tap event to occur, and a shunt or transformer element ( ElmShnt, ElmTr2, etc). The Tap Action can then be specified.


25.6 Running a Simulation Upon successful calculation of the initial conditions (i.e. execution of ComInc simulation.

), the

icon on the main toolbar will be activated and can be pressed to start the

The simulation is performed for the time interval between the start time defined in the initial conditions command ComInc , and the stop time (parameter name: tstop ), which can be specified in the simulation ( ComSim ) dialogue. After a simulation has finished, it may be continued by pressing the time. In this case, the stop time may also be entered relative to the current simulation time. A running simulation may be interrupted by pressing either the

icon or the

while the simulation is paused. The simulation is then continued by pressing the

icon again, and entering a new stop

icon on the main toolbar. Additional events can be created and results may be viewed icon again. Pausing and continuing the simulation may be done as often as required.


25.7 Models for Stability Analysis Stability analysis calculations are typically based on predefined system models. In the majority of cases the standard IEEE definitions for controllers, prime movers and other associated devices and functions are used. For planning purposes, this approach might be acceptable. The predefined sets of parameters will allow a favorable and reasonable behavior of the analyzed system. This approach is often also applied to operation analysis, and the system should show a response similar to a real system. For systems and configurations for which no IEEE models exist, such as wind generators, HVDC-systems, etc., powerful tools for user defined modelling are required. For this purpose, highly specialised, exact models can be created in PowerFactory . In cases when manufacturers are able to supply exact controller models including real parameters, the system model can be improved by not using the IEEE standard models, but instead building a new block diagram of the individual controller/mechanical system to represent the device. This facilitates highly accurate system modelling. Utilities and consultants often conduct system operation performance and optimization studies, and therefore have a clear need for accurate methods and tools for creating accurate transient models for stability analysis. This includes complex operation analysis and special component planning problems. This demand led to the development of highly flexible and accurate DIgSILENT PowerFactory time-domain modelling features, which are introduced in this chapter. 25.7.1: System Modelling Approach 25.7.2: The Composite Model 25.7.3: The Composite Frame 25.7.4: The Common Model 25.7.5: The Composite Block Definition 25.7.6: Drawing Composite Block Diagrams and Composite Frames


25.7.1 System Modelling Approach


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System modelling for stability analysis purposes is one of the most critical issues in the fi eld of power system analysis. Depending on the accuracy of the implemented model, large-signal validity, available system parameters and applied faults or tests, nearly any result could be produced and arguments could be found for its justification. This is one aspect of the complexity of a transient stability study. The other aspect results from the often large set of time-domain models that are required, each of which may be a combination of other models. All these time-domain models are ultimately wired together into one large, single transient model from which the basic set of system differential equations can be obtained. Given this complexity of a transient analysis problem, the PowerFactory modelling philosophy is targeted towards a strictly hierarchical system modelling approach, which combines both graphical and script-based modelling methods. The basis for the modelling approach is formed by t he basic hierarchical levels of time-domain modelling: 





The DSL block definitions , based on the " DIgSILENT Simulation Language" (DSL ), form the basic building blocks to represent transfer functions and differential equations for the more complex transient models. The built-in models and common models . The built-in models or elements are the transient PowerFactory models for standard power system equipment, i.e. for generators, motors, static VAr compensators, etc. The comm on models are based on the DSL block definitions and are the front-end of the user-defined transient models. The composite models are based on composite frames and are used to combine and interconnect several elements (built-in models) and/or common m odels. The composite frames enable the reuse of the basic structure of the composite model.

The relation between these models and the way that they are used is best described by the following example. Suppose the frequency deviation due to the sudden loss of a fully-loaded 600 MW unit in a particular network is to be analyzed. Depending on the network and the required detail in the calculated results, such analysis may ask for a detailed modelling of the voltage controllers, prime movers and primary controllers, or any other important equipment for all large generators in the system.

Fig. 25.8: Example of a Composite Generator or Power Plant Model

Figure 25.8 shows a typical configuration of a synchronous generator with power system stabilizer, voltage controller, primary controller, and prime mover model. The primary controller and prime mover can be summarized as the primary controller unit model. To create this ki nd of model, the following actions are r equired: 1. 2. 3. 4.

Transient models for each required controller type or unit type have to be defined ( Model/Block Definition ). For each generator, the transient models of the individual controller must be customized by setting the parameters to the correct values ( Common Model ). A diagram has to be made defining the connections between the inputs and outputs of the various models ( Composite Frame ). For each generator, the diagram and the customized transient models are to be grouped together to define an unique 'composite' generator model ( Composite Model ).

It may seem unnecessary to include steps 2 and 3: it would be possible to create customized transient models for each generator directly, with 'burned-in' parameter settings, and to link these models to a generator without having to define a diagram first. This, however, would mean that one w ould have to create a new voltage controller, e.g. for each generator in the system. Often the design of many of these vo ltage controllers will be similar. To omit the need of creating copies of these controllers for each generator and to avoid redundant copies of controllers or also of whole generator models. Here the same relationship as that between individual controller (Common Model) and controller definition (Model Definition) is used; this time between the generic power plant diagram (Composite Frame) and the in dividual power plant (Composite Model). DIgSILENT PowerFactory uses two key objects in creating composite models, which can be compared to the element definition of the different elements: 



The Common Model (ElmDsl ) combines general time-domain models or model equations (a block definition) with a set of parameter values and creates an integrated time-domain model. The Composite Model (ElmComp ) connects a set of time-domain models inside a diagram (a composi te frame) and creates a 'composite model'.

The following diagrams explain the relation between the Composite Model (which is using a Frame as type) and the Common Model (based on a block diagram as type) in detail. 









The Composite Model (ElmComp ), see Figure 25.9, references the definition of a composite frame. This composite frame is basically a schematic diagram containing various empty slots, in which controller or elements can be assigned. These slots are then interconnected according to the diagram, see Section Composite Block Definitions (part of Section 25.8.3: Defining DSL Models). The slots in the composite fram e are pre-configured for specific transient models. The schematic diagram in Figure 25.10 shows a Composite Frame (BlkDef ) which has one slot fo r a synchronous machine, one for a primary controller unit (pcu slot), and one for a voltage controller (vco slot). T he composite model, which uses this composi te frame, shows a list o f the available slots and th e name of the slot. Now the specific s ynchronous generator, voltage controller or primary controller unit model can be inserted into these slots. The synchronous machine that is used in the Composi te Model is called a Built-In Model , see Figure 25.11. This means that such elements are pre-configured elements which do not need a specific model definition. Any ki nd of element which is able to provide input or output variables, e.g. converters, busbars, etc, can be inserted into the sl ots. The voltage controller, and primary controller unit, however, are user-defined Common Models , see Figure 25.12. The 'front-end' of all user-defined transient models is always a common model (ElmDsl), which combines a model definition wi th specific parameter settings. There are predefined definitions as well, so that the user can create her/his own model definitions. The common model has a reference to the Model Definition (BlkDef ), which looks similar to the composite frame (shown in Figure 25.13). Here different blocks are defined and connected together according to the diagram. The input and output variables have to fi t with the slot definition of the slot that the model is defined for.

Not all slots of the composite model must necessarily be used. There can also be empty slots. In such cases, the input of this slot is unused and the output is assumed to be constant over the entire simulation. The usage of composite models with a composite frame, and the common model with its block definitions are described in the next sections. The design and creation of user defined common models using the " DIgSILENT Simulation Language" ( DSL ) can be found in Section 25.8 User Defined (DSL) Models .


Fig. 25.9: Example of a Composite Model Using the Frame "Frame_Generator"

Fig. 25.10: Composite Frame "Frame_Generator"

Fig. 25.11: Generator "G1" (Built-In Model)

Fig. 25.12: Example of a Common Model Using the Definition "vco_simple"

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Fig. 25.13: Example of a Model Definition "vco_simple"


25.7.2 The Composite Model

A composite model element (ElmComp ) can created using the "New Object" ( ) icon, located in the toolbar of the data manager and selecting Composite Model from the available options. The next step is to select the composite frame. The composite frame can be stored either in the global library or in the local library, and is conceptually similar to a type definition for an electrical element. The composite model then shows the list of slots in the composite frame as shown in Figure 25.14. Existing controllers or models can be assigned to a slot manually by right-clicking the slot and selecting Select Element/Type , as depicted in Figure 25.14. A data manger window will pop up and the user can then browse the grid for the element to insert into the selected slot.

Fig. 25.14: Editing the Composite Model (ElmComp ) Dialogue

When inserting controller models into a slot, it is often the case that the controller element has not yet been created. To create a new controller element select New Element/Type from the slot's context-sensitive menu. PowerFactory will automatically jump to the project Library and show a list of available user defined models (ElmDsl). Selecting a model definition from the project library or the global library will open the element dialogue of the newly-created common model, so that its parameters can be defined, similar to (for example) a transformer element. If no suitable model is found, a block definition has to be selected prior to setting the model parameters (see Section 25.7.3 The Composite Frame and Figure 25.13). If an element is assigned to a slot, it is possible to edit the assigned element by simply right-clicking and selecting Edit Element/Type . The right-mouse button menu entry Reset Element/Type will reset the slot, so that it is empty again. Note Depending on the settings of the individual slot, the menu entry Reset Element/Type will not only clear the marked slot but also delete the built-in or common model, if it is stored inside the composite model in the data manager. These settings are explained in detail in Section 25.7.3 The Composite Frame .

A faster method for defining standard composite models is to right-click on an object in the single line diagram and select Define... from the context menu of the element. When a standard composite model is available for the selected object, a list of the available controllers is shown. Selecting a controller will add it to the composite model, which is automatically created when no composite model yet exists for the selected object. Standard composite models are available for:   

The synchronous motor and generator; The asynchronous motor and generator; The static VAr system.

Slot Update Step Response Slot Update

The Slot Update button in the composite model ( ElmComp ) dialogue will re-read the slot definitions from the composite frame and will cancel all invalid slot assignments. A slot assignment is invalid when a model has been assigned to a slot which is not suited to receive this kind of model, i.e. a voltage controller cannot be assigned to a slot defined for a primary controller model. All built-in models and common models which have been created for a specific composite model are stored in that composite model itself. The contents of a composite model are shown in the data manager where the composite model is treated as a normal database folder. Basic power system equipment, such as synchronous machines or static VAr compensators, are normally not stored in the composite folder, but in the grid itself. The slot update will try t o re-assign each model found in its contents to the corresponding slot.The options defined for each slot are important, and are described in the


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paragraph Classificationin Section 25.7.3 The Composite Frame . Step Response

The Step Response button in the composite model ( ElmComp ) dialogue will activate the Step Response command ( ComStepres). The dialogue can be seen in Figure 25.15. Next to the references to the composite model, the template and the target directory, the two step response tests, which will be created, can be specified. The study case to be activated can also be selected. When Execute is pressed, PowerFactory will create a new folder in t he current project named Step Response Test. Figure 25.16 shows this folder in the data manager.

Fig. 25.15: Step Response Command (ComStepres) Dialogue

Fig. 25.16: Step Response Folder in the Data Manager

Inside the Step Response Test folder, a second folder is created, named according to the composite model which is to be tested. Here the simple test grid can be found including only the generator, the complete composite model and a load. Additionally there will be two new study cases in which a step response for the AVR and the PCU, respectively, of the composite model can be tested. The user can switch between these two study cases and her/his previously-used study cases by activating and deactivating them. Note There is now no longer any connection between the original elements and the new elements of the composite model. Therefore, you can change any controller settings without changing your network.

After testing the controller, the folder Step Response Test can be deleted completely without loss of information in the original network.


25.7.3 The Composite Frame

A composite frame is a block diagram which defines two or more slots, their input and output signals, and the connections between them. A composite frame is defined graphically by drawing it. Drawing a composite model frame is similar to drawing a normal block diagram. The main difference is that instead of common blocks, only slots may be used. To create a new composite frame select the Insert New Graphic icon on the main toolbar (in the graphics window) and then select Block/Frame Diagram and press Execute as shown in Figure 25.17. This new block definition will then be automatically created in the local library.

Fig. 25.17: Creating a New Composite Frame

An empty diagram of the frame will appear in the graphics window. A slot is then created by selecting the icon in the graphics toolbox and positioning the slot on the drawing surface by clicking once at the desired location. This is similar to placing elements in the single-line diagram. An empty slot will be drawn on the page. To define the slot's input and output signals and different parameters, edit the slot by double-clicking it. The slot edit dialogue will pop up as shown in Figure 25.18.


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Fig. 25.18: Slot Dialogue (BlkSlot)

Name and Sequence

The name of the slot will appear later in the composite model dialogue, and it is therefore recommended to name this element according to which slot it w ill be assigned (e.g. 'vco slot'). The Sequence parameter defines the order of the slots appearing in the composite model dialogue. Classification

The classification options only effect the external behavior of the slot. Linear The slot representation in the frame diagram will be as a linear or non-l inear model. Automatic, model will be created When this option is activated, the function 'Slot Update' (see Section 25.7.2: The Composite Model) will automatically create a DSL model and ask for a block definition from the library. Local, Model must be stored inside This option is activated by default. This means that when a Slot Update is executed in the composite model, PowerFactory will only search for elements which are stored inside the ElmComp . A reference to models which are stored outside, i.e. the synchronous generator in a plant model, will be removed from the slot.

Not all input or output signals of built-in elements or common models have to be used and defined in the slot. A slot may only have an input or an output signal. For example, the voltage or frequency of an AC voltage source ElmVac may be controlled by an external function. Therefore, the slot for the source will only have two input signals u0 and f0. More information about drawing composite frame diagrams can be found in Section 25.7.6 Drawing Composite Block Diagrams and Composite Frames . Input and Output Signals

The input and/or output signal(s) have to be defined for each slot. The available signal names for the Built-In transient models can be found in the corresponding Technical References of the elements. The given input and output signal names in this slot dialogue have to match the input/output signals of the given transient model exactly, or the signals will not be connected properly and an error message will result. Only after one or more input and output signals have been defined for a slot, is it possible to connect the slot with signal lines to other slots. It is therefore recommended to first position and edit all slo ts and to draw the signal connections thereafter. Limiting Signals

There is also the possibility to enter 'limiting signals'. These signals are handled by PowerFactory exactly like normal input signals. The difference is only in the graphical representation in the block diagram. These signals will be shown as inputs on the top or bottom of the slot. Class/Name Filter

There is also the possibility to specify a filter for the class name and/or for the model name to be inserted. This makes sense when (for example) only synchronous machines should be assigned to the slot. In t his case, the class name ElmSym* would be entered. PowerFactory then will only allow the element class "synchronous machine'' to be inserted into the slot. A filter for a specific (part of an) element name can also be defined. Assigning a Block Definition to a Slot

A block definition (BlkDef ) can be assigned directly to a slot. This option will simplify the handling of the slot and prevent errors due to mis-matched signal names of slot and assigned block. To assign the external form of a block definition to the selected slot, edit the slot by double-clicking it and choose the "select" button for the "Block Definition" in the dialogue. Now the block definition can be selected, e.g. the type of controller o r built-in element, which should be assigned to this slot later. As an example, if the newly-defined slot ought to represent a synchronous machine in the frame diagram, a predefined block definition can be chosen to insert the input and output signals to this slot available for the element ElmSym . A controller should, for example, only be assigned to a slot, when only this type of controller is to be inserted into this slot, and no other model can be. Some predefined block definitions can be found in the global library in the path Library\ Models\Built-in . When the block definition is selected (in our example the ElmSym.BlkDef ), the input and output as well as limiting signals will disappear from the slot dialogue. The filter for the class name will automatically be entered. When clicking on the Ok button, the slot will then show the right inputs and outputs of the block definition. Note When a block definition is assigned directly to a slot, only the input/output signals are set automatically. The internal equations/definitions of the block definition are not implemented in the slot and the slot itself remains empty. There is always the need to create a common model, which is the model inserted into the slot of the composite model. When the slot refers to an outside block definition, beware that this reference is also inside your project. If the reference to the definition is invalid or changed, the slot may be chan ged as well. Therefore, assign a block very carefully.


25.7.4 The Common Model

The common model element ( ElmDsl, ) is the front-end object for all user-defined block definitions. This means that user-defined transient models, but also the block diagrams that are ready-shipped with the PowerFactory program, cannot be used other than through a common model. The common model combines a model or block definition with a specific set of parameter values. The common model shown in Figure 25.19 uses the block definition "vco_Simple". Typically the model definition is implemented as a block definition, such as that shown in Figure 25.20. A model definition contains block references which may in turn either point to a primitive block definition (see Figure 25.21) or to a another composite block definition (see Figure 25.22 . The structure of the block definition is thus recursive and the user should check that this recursive structure does not contain circular references to composite


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block definitions. A primitive block definition contains one or more DSL expressions and forms a basic block for more complex transient models. A description of how to use and create DSL models can be found in Section 25.8 User Defined (DSL) Models . It is also possible to implement the model definition not as a block definition, but directly as a primitive block definition (Figure 25.21), coded using DSL. Each block definition generally has one or more parameters which can be changed to define the model's behavior. Two kinds of parameters are supported:  

Scalar parameters, i.e. amplification factors, offsets, setpoints, etc. Two and three dimensional array parameters, which are used in the DSL lapprox()/lapprox2() and sapprox()/sapprox2() functions.

Fig. 25.19: Common Model for the VCO

Fig. 25.20: Block Definition of the VCO, Using a Sub-Definition

Fig. 25.21: Implementation of the Limiter Block, Using a DSL Routine

Fig. 25.22: Implementation of the Controller, Defining a Sub-Block

To create a common model, use the "New Object" ( ) icon in the toolbar of the data manager and select Common Model . The block/model definition has to be selected first. Similar to the composite frame, this definition is either stored in the global library or in the local library. The common model then displays the list of available parameters and arrays from the block diagram, as shown in Figure 25.23. All parameters are listed on the first page of


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the common model, and their values can be specified there.

Fig. 25.23: Common Model with Parameter List

If the selected block definition uses one or more arrays in its definition, then these arrays are displayed on the second page (for simple characteristics) and third page (for two-dimensional characteristics) of the ElmDsl object. In Figure 25.24 an example is shown for a 1 3x4 array definition.

Fig. 25.24: Common Model with Array List

The characteristics are defined as follows: Characteristic In the row labelled 'Size', insert the number of rows in the first cell; the number of columns is set a utomatically. If the number of row s is changed, jump to the previous

page

and back again

to update the characteristic.

Two-Dimensional Characteristic In the row labelled 'Size', insert the number of rows in the first cell and the number of columns in the second cell. If one of these numbers is changed, jump to the

previous page

and back again

to update the characteristic.


25.7.5 The Composite Block Definition

A composite block diagram of the model definition is a graphical representation of a mathematical transfer function, which produces one or more output signals as a function of one or more input signals. A block diagram may also have limits (minimal and maximal values) as input signals. A block diagram may thus be described as: (y_0, y_1, ...) = function(u_0, u_ 1, ...) where y_0, y_1, ... represent output signals 0, 1, ... and u_0, u_1, ... represent for input signals 0, 1, .... These signals are all functions of time. Block diagrams consist basically of the following elements: Summation Points

which produce the single output y=(u_0+u_1+...) Multipliers which produce the single output y=(u_0*u_1*...) Divisors which produce the single output y=(u_0/u_1/...) Switches which produce the single output y=u_0 or y=u_1 Signal Lines which produce one or more outputs from one input: y_0=y_1=...=u Block References

which are used to include other block definitions.

Block references can be looked upon as macros that insert a lo w-level block definition inside a composite block diagram definition. A block r eference may either point to another composite block definition or to a primitive block definition. The PowerFactory program is shipped with a large set of primitive block diagrams for most common controller elements like PID-controllers, Dead Bands, Valve Characteristics, etc., and can be found in the PowerFactory tree under Database | Library | Models |Global_Macros . These predefined DSL primitives may be copied and altered for specific needs. A block reference is created by using the

icon in the graphics toolbox. This creates an empty square which can then refer to any existing block definition in the library.

Note The composite frame and the model definition are very similar and their usage is almost identical. When creating one or the other PowerFactory recognizes the class when you place the first slot or block. If you place a block ( ) first, the icon for the slot will become inactive, so the user cannot inadvertently mix up slots and blocks in one diagram. See also Section 25.7.6 Drawing Composite Block Diagrams and Composite Frames .


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If the block type is selected, PowerFactory inserts all available parameters of the referred block. The user may change the name of any parameter, however ensure that the order of the parameters is not changed. The order is important so that the right parameter is assigned to the parameters inside the block definition. Signal lines are directed branches, connecting input and output signals. A single output line may be branched off and connected to more than o ne input terminal. After the block reference has been edited, it will show the input, output and limiting signal connection points of the referenced block definition as one or more colored dots on the left and right side, respectively, on the upper and lower side of the box. Signal lines may then be connected to these points. It is allowed to r efer to the block definition more than once in the same block diagram. This way, it is possible to use a particular PID-controller, for instance, twice or more in the same model definition. An example of a simple block diagram, comprising a multiplier, a summation point and a standard PI block, is shown in Figure 25.25.

Fig. 25.25: Example of a Simple Block Diagram

When rebuilding a diagram (by pressing the 25.25, this results in the following output:

icon), the DSL representation of the block diagram is written to the output window. For the example block diagram in Figure

model o1 = 'MyBlock'(i1,i2;x1;Kp,Ti;yi) s1 = '\System\Library\Models\DSL\PI.BlkDef'(xe;x1;Kp,Ti;yi) xe = i1*i2 o1 = s1+i2+i1

This simple example shows the whole meaning of the block diagram graphics: it is a convenient way to define specific controllers, based on standard components. However, it would also be possible to define exactly the same block diagram by entering the above DSL script manually and thereby create a primitive block definition.


25.7.6 Drawing Composite Block Diagrams and Composite Frames

Although the composite block diagram and the composite frame diagram should be distinguished from one other, they are drawn in the same way. The basic distinction between a block diagram and a frame diagram is that the latter contains only slots and signals, whilst the block diagram must not contain any slots. A new block or frame diagram can be created in various ways: 

Selecting the main menu entry File −> New or Strg-N and then selecting the option Block/Frame Diagram from the "New" command dialogue (ComNew);



By clicking on the Insert New Graphic



By right-clicking on, or inside a (library) folder in the active project in the data manager and selecting New... −> Block/Frame - Diagram from the context-sensitive menu;



By using the New Object

icon on the toolbar of an open graphic, and selecting the option Block/Frame Diagram ;

icon in the database manager and selecting Block Definition (BlkDef) .

Note The two later options only create a block definition object (BlkDef), but no graphic. This method is therefore not suitable for creating a composite block or frame diagram, but only for creating primitive block definitions by entering the DSL code.

In the first two methods, a graphic will be created and will appear in the open graphics board. A new graphics board will be created when no graphics board is open. The new block/frame diagram graphic will show a single rectangular block, which depicts the block or f rame. The name of the new diagram will appear on top of the frame. Inside this rectangle the following objects can be placed from the graphic toolbox for the block diagram: Node objects: 

 

 



block references summation points multipliers divisors switches different kinds of graphical objects

Branch objects: 

signals lines

Inside a frame diagram only the following elements are allowed: Node objects: 



slots different kinds of graphical objects

Branch objects: 

signals lines

These objects can be selected from the Drawing Toolbox. The toolbox also has buttons for pure graphical add-on objects (lines, polygons, rectangles, texts, etc.) as shown in Figure 25.26. It should be noted that the availability of this toolbox is according to whether or not the graphic is `frozen' ( is available, and likewise, when the graphic is frozen for editing, the toolbox is hidden.

). When the graphic is not frozen, the toolbox

Fig. 25.26: Block/Frame Diagram Objects

Note When creating a frame or a block definition, PowerFactory recognizes the type of definition when you place the first slot or block. Because a composite frame diagram may only contain slots and signal lines, creating a slot will disable all other node objects in the drawing toolbox. If you


place a block (

) first, the icon for the slot

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will become inactive, so you can't mix up slot and block eleme nts in one diagram.

Adding a Block Reference Adding Calculation Blocks Connecting Signals Resize Additional Equations Adding a Block Reference

Drawing the block objects and connecting them with signals is done in a similar way as is done with elements in the single line graphic. A block reference is first displayed as an empty square which has to be edited in o rder to assign a (low level) block diagram to it. Because of lack of information about the number of inputs and outputs of the new block reference before a (lower level) block definition is assigned to it, it is not possible to connect signals to the empty block. It is t herefore recommended to first draw all block references and to assign block definitions to them. The block references then show all available input and output signal connections. A block reference is edited by right-clicking on it and selecting Edit from the context-sensitive menu, or simply by double-clicking on it. The dialogue as displayed in Figure 25.27 will pop up.

Fig. 25.27: Edit Dialogue of the Block Reference

Use the Select button ( Models .

in Figure 25.27) to select a model definition. Predefined standard block diagrams for your usage are located in the folder Database\ Library\

It is also possible to create a block in the graphical Block Definition by dragging Macros from the global library or project library into the drawing area of the Block Definition, using the Drag & Drop f unctionality. Adding Calculation Blocks Summation Point

Every dot can be used as an input to the summation point. The sign of signals at summation points can be changed by editing the summation point object. The "edit" dialogue will pop up, where any connected input connection can be inverted. It should be noted that not all dots have to be used and only one dot can be defined as an output. Multiplier

Every grey dot of this block can be used as an input or output of the multiplier. An output of three input signals will thus be: out=(in_0*in_ 1*in_2). It should be noted that not all dots have to be used and only one dot can be defined as an output. Divisor

Every grey dot of this block can be used as an input or output for the divisor. T he first input will be the numerator and thus will be divided by the second (and if existing, the third) input. The order of the signals will be clockwise beginning from the left. An output of three input signals w ill then be: out=(in_0/in_1/in_2). Mind that not all dots have to be used and only one dot can be defined as an o utput. Switch

Two input signals can be applied to this block, which will be connected to the output according to the position of the switch. Additionally a control signal has to be connected to the top, which will define the operation of the switch. If the control signal is 0.5 or less, the switch will stay in the displayed state, whereas a signal greater than 0.5 will cause the switch to change to the upper signal and the other way round. In the edit dialogue the zero position of the switch may be altered. Connecting Signals

After drawing and defining the block references, slots or other node elements, they can be connected with signal lines. After selecting the button from the graphical toolbox, a signal line is drawn by first clicking on a 'from' node (output of a block/slot), optionally clicking on the drawing surface to make a non-direct connection, and finally clicking on a 'to' node (input to a block/slot). The input and output terminals of common blocks and other node elements are depicted with colored dots (see Figure 25.28).

Fig. 25.28: Block Signal Connections Green: Input Red: Output Blue: Min. Limitation Pink: Max. Limitation Gray: Every signal can be connected

The signal lines can also be edited in the corresponding dialogue, which provides the possibility to change the name of the signal. Multi-Signal Connections Block Diagram Input and Output Definitions Multi-Signal Connections

Signals normally connect a single output parameter with a single input parameter. Especially in the case of three phase signals, as is often the case for voltage or current signals, multi-signal connections may be used. A multi-signal is defined by writing two or more signal names together, separated by semicolons, e.g "I_A;I_B;I_C''. In Figures 25.29 and 25.30, the multi-signal output and input of two block definitions are shown. Both blocks will sho w a single input or ou tput connection point. They can be connected to each other by a single signal l ine, as illustrated in Figure 25.31.


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Fig. 25.29: Output Definition of Block 1

Fig. 25.30: Input Definition of Block 2

Fig. 25.31: Multi-Signal Connection

Note The number of variables and their order in the output signal must be equal to the number of signals in the input signal. Block Diagram Input and Output Definitions

The composite block diagram normally has input, output and limiting signals of its own. Input signal points are defined by starting a n ew signal line on the left, top or bottom side of the frame enclosing block diagram. This will create a new input signal for the composite block definition. New output signals are defined by ending a signal line by clicking on the right side of the enclosing rectangle frame. Signals, which are thus connected to the rectangular frame, have the following meanings: 

 



connected to the left side: Input connected to the right side: Output connected to the bottom side: Minimum Limitation connected to the top side: Maximum Limitation

Note The names of the input and output signals must be the same as the names of the input and output signals defined in the slot or block to which it is intended to assign the definition. Resize

If a marked symbol has small black squares at its corners, it can be resized by left clicking one of the squares, as can be seen in Figure 25.32 25.32.. The cursor will change to a double diagonal arrow, and moving it (while holding down the left mouse button) resizes the object. Release the mouse when the new size is correct.

Fig. 25.32: Resizing an Object

It is also possible to make the object(s) have a new size by clicking on one side of the marking box. The marked object(s) will only resize in one direction in that case. This is not possible for all objects. Some objects may only be resized with a fixed X/Y- ratio; some other objects cannot be resized at all. Additional Equations

After the internal structure structure of the block diagram has been defined defined graphically, the block block diagram itself can can be edited. This can be done without having having to close the graphical graphical representation of the block diagram. By left or double-clicking the enclosing rectangular frame, the block diagram edit dialogue will pop up. This dialogue will show all i nput, output and internal signals, as have been defined graphically. On the second page page of the dialogue, which which can be accessed accessed by pressing the button, information information and equations equations for the initialisation of the block can/has to be entered. entered. Additionally, the name name and the unit of the parameters parameters to be defined defined in the common common model can be specified specified (see also Section Section 25.8: User Defined (DSL) Models). Models ). Additional DSL equations can can be defined on the second second page of the block block diagram edit dialogue. dialogue.


25.8 User Defined (DSL) Models System modeling for stability analysis purposes is one of the most critical issues in the field of power system analysis. Depending on the accuracy of the implemented models, large signal validity, available system parameters and applied faults or tests, nearly any result could be produced and arguments could be found for its justification. A simple example illustrates this. In a 10 GW power system the expected steady-state frequency deviation when losing a fully loaded 2000 MW unit depends highly on the frequency dependency, dependency, K_f, of l oads. Assuming a total system droop of 7% and a K_f value of 0, the steady-state frequency deviation will be approximately 700 mHz. Now with a more realistic coefficient of K_f = 5 %/Hz, the steady-state frequency deviation is expected to be 596 mHz only. On the other hand, the frequency dependency might be slightly higher or lower, but the non-linear characteristics of hydro turbine efficiencies and steam valve non-linearities could be more relevant at a certain unit loading point. Consequently, as long as only one or two different l oading scenarios are considered, average values with reasonable simple models may give acceptable results by tuning only some key parameters like the frequency dependency dependency of loads or droop settings. Thus system model structures and parameter settings are to be best evaluated against the following main criteria: System size Large and small systems have different "key parameters''. Referring to the above example, for a smaller power system the frequency dependency of loads is irrelevant, while in large systems such as UCTE or UPS/IPS, frequency dependency may cover the spinning reserve requirements totally. Unit size Steady-state and transient behavior of large units is more decisive for the overall system response than s maller units which might have a very negligible effect on the total system. System structure

Independent of system and unit size, the system structure may be mo re relevant than any other factor. This can be easily demonstrated when weak systems with a longitudinal geographical extension or appropriate substructures are analyzed. System fault Most relevant to system modeling considerations are the applied faults and related problems which are to be a nalyzed. The analysis of s ystem damping and PSS tuning will not necessarily require the boiler dynamics to be considered. On the other hand, load shedding optimization and frequency restoration would not give appropriate results if mid- and long-term characteristics of relevant system elements are neglected. Study purpose In general, for systems which are in the planning stage, typical models and parameters could be applied as long as there is no specific additional information available. However, a more detailed representation is necessary for system extensions, where a detailed model representation should form part of the performance specification. Special attention has to be paid to the analysis of operational problems and operation optimization. For these cases, detailed modeling of the relevant components is critically important.

As soon as a detailed analysis and representation representation of system models models is required, the subsequent subsequent questions to be asked are:




 

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How can the structures and parameters of the model be determined? Are IEEE models and additional manufacturers' block diagrams adequate and accurate? How could the available information be used within the power system analysis software?

The approach which is presented here and successfully applied in various projects can be called the "Advanced System Modeling Approach (ASMA)''. Typical applications are:  

 

The analysis of controller problems and relevant malfunctions, especially under disturbance conditions; Optimization of control parameter settings; Modeling of unconventional system structures and control concepts often found in industrial systems; Study applications for the design and specification phase of components and systems (e.g. power system stabil izer, generator and HVDC controllers).

For the ASMA approach, the following steps are critically important: Setup of system models Based on the fundamental equations of engineering and physics, the basic algebraic and differential equations are to be set up according to the required degree of accuracy. In addition, all parameters such as time constants and gains which could be also derived from these basics, are to be calculated with the same degree of accuracy. Performance of system tests In order to define all other parameters and, in pa rticular, non-linear characteristics, system performance tests are the best method. In the majority of cases, frequency response tests will not permit the determination of any non-linear structure and its parameters. Special test procedures, which do not interfere with normal operation, have to be applied to focus on the steady-state characteristics, gains and time constants. These measurements are preferably executed with a highly accurate digital transient performance measurement system. System Identification Non-linear, multi-input and multi-output system identification techniques are applied for system identification procedures. Typically, the mis match between measured and identified data should be smaller than 2%. Comparison of measurements and simulations Besides the analysis of subsystems and components, overall system performance is to be compared with the theoretical model for all relevant operating modes.

Of course, very strict application of the ASMA approach is not necessary for modeling relays and less complex or digital control functions, as these are clearly defined by their appropriate general and acceptance test documentation. documentation. However, independently of the analyzed system, where the system representation cannot be matched to a classical IEEE or any other standard model, there is a substantial need for an easy to use and flexible method for the realization of individual models. 25.8.1: Modeling and Simulation Tools 25.8.2: DSL Implementation: an Introduction 25.8.3: Defining DSL Models


25.8.1 Modeling and Simulation Tools

As already indicated, indicated, the most critical and decisive decisive factor for reliable simulation simulation results is the accuracy accuracy and completeness completeness of system model representation representation for identification and simulation purposes. Methods for solving this task range from the classical and traditional way of using software which allows interfacing of user-defined models at the FORTRAN/C level - typically via connection lists - to the block-oriented approach which is based on the provision of predefined low-level block macros being connected at the case definition level. In addition, most modern commercially available general purpose simulation tools may be used for flexible and specific system representation. Unfortunately, this approach does not adequately cover the special electrical system load flow characteristics characteristics.. In order to provide a very flexible modeling and simulation tool, which forms part of a stability program, a control system based simulation language was developed. The following describes the main features of the DIgSILENT Simulation Language (DSL):  





 

The simulation tool falls into the category of a Continuous System Simulation Languages (CSSL); DSL includes a complete mathematical description of (time-) continuous linear and non-linear systems; The simulation tool is based upon common control and logic diagrams, leading to a non-procedural language, as the sequence of elements can be chosen arbitrarily. In other words, a DSL model can be converted into a graphical representation; Provision of flexible definition of m acros, which could be: algebraic equations, ba sic control elements like PID, PTn or even compl ete physical subsystems like valve groups or excitation systems; Provision of various intrinsic functions such as: "select'', "lim'', "limits'', "lapprox'', "picdrop'' in order to provide a complete control of models; Provision of various forma l procedures for error detection and testing purposes such as: algebraic loop detection, reporting of unused and undefined variables a nd missing initial conditions.


25.8.2 DSL Implementation: an Introduction

The "DIgSILENT Simulation Language" is used to define new dynamic controllers which receive input signals from the simulated power system and which react by changing some other signals. DSL itself can be looked upon as an add-on to the transient analysis functionality of PowerFactory . During the simulation, the model equations of the DSL models are combined with those describing the dynamic behavior of the power system components. These equations are then evaluated together, leading to an integrated transient simulation of the combination of the power system and its controllers. The DSL main interfacing functions are: Signal input and output channels: Any variable defined within the kernel (currently more than than 2500) and in a DSL model, can be accessed in a read-and-write mode. Main and sub-address features are implemented allowing the access of any signal existing in the system or to build up complex structures such as hardware-based modules taking equipment "rack'' and "function card'' structures into account. Events: Conditions evaluated by DSL models may cause events to be sent to the program kernel where they will be scheduled within the event queue. Output and Monitoring: Conditions may trigger user-defined messages to be displayed in the output window.


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Fig. 25.33: Structure of the PowerFactory DSL System

The structure of a DSL model is best explained by an example. This example considers a prime mover unit model of a simple hydro turbine. This DSL model has been defined graphically, and contains one embedded DSL macro. This embedded macro models a single integrator and is defined by programming it. The basic method for designing new DSL models is as follows: 1.

A set of basic DSL models is created. These models implement simple, 'primitive' controllers like a 'first order time lag' or a 'PID' controller. controller. The PowerFactory program PowerFactory program is shipped with a large number of these primitive controller models. New primitives are created by programming their differential equations and signal settings, using the DSL language. The more complex controller is created graphically by drawing its its block diagram. This kind of block diagram normally uses references other DSL models which are thus thus combined into a more complex controller. Controller references may be used to include DSL primitive models into the complex mo del, but may also refer to other graphically defined complex models. Highly complex controllers may thus be designed in a hierarchical way, by designing sub-models and sub-sub-models, where the DSL primitives form the lo west level. Section 25.8.3 Defining DSL Models describes these procedures in detail.

2.

Fig. 25.34: Diagram of a Simple Model of a Hydro Turbine

Figure 25.34 depicts the model definition that was used to define the hydro turbine model. The resulting DSL code, as shown in the output window when a graphical Rebuild ( 1. 2. 3. 4. 5. 6. 7. 8.

) is is pe performed is is:

model Pt = 'pmu_hydro '(At,C;x1;Ti; ) pt_x = 'I.BlkDef'(x e;x1;Ti;) i3 = i1/i2 i1 = At*At i2 = pt_x*pt_x i4 = xe*pt_x xe = i3-C Pt = pt_x-i4

The line numbers have been added for readability. The corresponding block definition shows: Output Signals Input Signals State Variables Parameter Internal Variables

: : : : :

Pt At, C x1 Ti

The example describes a simple hydro turbine model with the input signals A_t and C and the output signal P_t.

Fig. 25.35: Graphical Representation of a DSL Model of an Integrator

Figure 25.35 depicts the graphical representation representation of the embedded primitive DSL model. This primitive model is included in the hydro turbine (in line 2 of the definition of the hydro). The The DSL primitive implements a single integrator and is programmed as follows: 1. 2. 3. 4. 5. 6. 7.

model y = 'I'(xe;x1;Ti;) 'I'(xe;x1;Ti;) [Ti] = 's' limits(Ti) = (0,) inc(x1) = y inc(xe) = 0 x1. = xe/Ti y = x1

Line 1 is generated by clicking on the Equations button in the block diagram dialogue. Lines 2..7 were entered manually. The block definition dialogue was used to set the following: Output Signals Input Signals State Variables Parameter Internal Variables

: : : :

y xe x1 Ti

Parts of a DSL Model Advanced Features Features Parts of a DSL Model

Both example DSL models show the two basic parts of any DSL model, primitive or complex: 1. The inter interfac face e definit definition ionss 2. The DSL DSL model model desc descrip ription tion


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Interface description

The interface defines the model name, names of input and output signals, model parameters and state variables. These are shown in the output window in the model heading. Example (line 1 from the hydro t urbine model):

1. model Pt = 'pmu_hydro'(At,C;x1;Ti;)

The block diagram dialogue further allows for the definition of limiting parameters and input signals, and the classification of the model as a linear model and/or as a DSL macro. Model description

The model description describes the DSL model, based on the signals defined in the interface. The DSL description includes: 

 



Parameter descriptions: name and unit Allowed parameter ranges Initial conditions and functions which are used to calculate initial values. The algebraic relations which define the controller.

Example (the integrator): 2. 3. 4. 5. 6. 7.

[Ti] = 's' ! the unit of Ti is seconds limits(Ti) = (0,) ! Ti > 0 inc(x1) = y ! initially x1=y inc(xe) = 0 ! initially xe=0 x1. = xe/Ti ! equation 1: deltax1 / deltat = xe/Ti y = x1 ! equation 2: y=x1

Advanced Features

The numerical integration of DSL models, interrupt scheduling and input-output signal processing is handled automatically by the program kernel. In addition, if the output of a DSL model is an electric current being added to the appropriate total bus current - which is the case if a load or generator model is created - all Jacobian elements necessary for the iterative simulation procedure will be calculated automatically. Another useful feature of DSL is the algorithm implemented for numerical setup of the system matrix for eigenvalue calculation purposes. Consequently, any model implemented at the DSL level will be automatically taken into consideration when calculating the system eigenvalues or when applying the modal network reduction approach (MRT). Of course, any signal limiting functions will be disabled automatically for this calculation procedure. In addition, inputs and outputs of model parameters, its organization via windows menus etc. is also derived automatically from the DSL model.


25.8.3 Defining DSL Models

A new DSL model is created either by entering the DSL code in the equation part of a "Block Definition'' ( BlkDef ) object, or by creating a new Graphical Block Diagram (see also section Composite Block Definitions on how to create a new block definition). Both methods will result in a Block Definition Object which holds the definition of the DSL model. The block definition objects thus serve two purposes in the process of constructing a DSL model:  

They hold the definitions and parts of a graphically constructed composite block definition, and the diagram graphic which was used to define the model; They provide the surrounding in which a new " DSL primitive '' or 'primitive block definition' can be defined.

Composite Block Definitions Primitive Block Definitions Block Definition Dialogue Composite Block Definitions

To create a new composite block definition: 

Use the main menu entry File −> New or Strg-N and then select the option Block/Frame Diagram from the "New" command dialogue (ComNew ).



Use the Insert New Graphic

icon on the toolbar (of the graphics window) and select the option Block/Frame Diagram .

To access the dialogue of the block definition (BlkDef ), double-click on the frame box surrounding the diagram. Complex block definition objects are conceptually similar to "Grid Folders'' in the PowerFactory database tree. They are defined by graphically defining a controller block diagram of which they will store the graphical information and all logic parts. These parts include signals, small standard components (adders, multipliers, etc.) or DSL primitives. Although a complex block definition object is created graphically, it allows for additional DSL equations to define those aspects of the controller that would be otherwise difficult to enter in a graphical way. The graphical environment in which a complex block diagram is constructed, is not treated here. Please refer to Chapter 10 The Graphics Editor for more information. Primitive Block Definitions

To create a primitive DSL block definition: 

Right-click on or inside a (library) folder in the active project in the data manager and select New... −> Block/Frame - Diagram from the context-sensitive menu;



Use the "New Object"



icon in the database manager and select Block Definition (BlkDef) ;

Double-click an new/empty block reference in an open block diagram and then use the block definition inside the local library.

button to select a block definition. Following this, use the

icon to create a new

DSL primitives are the building blocks from which the more complex controller diagrams are composed. A DSL primitive, for example, might implement a low pass filter, which may then be used to graphically construct more complex controllers which include this kind of filter. Unlike transformers or other power system components, which may be looked upon as 'power system primitives', a DSL primitive is only referred to by a complex block diagram and may thus be used in more than one complex DSL model at the same time. Block Definition Dialogue

When creating a primitive DSL model or by double-clicking on the frame of a composite block definition, a dialogue will appear, where input and output variables, parameters, state variables and limiting signals can be defined. Furthermore, additional equations, initial conditions of variables as well as names and units of parameters can be inserted. Figure 25.36 shows an example dialogue of a PI controller including limiting parameters and a 'switch' signal.


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Fig. 25.36: Dialogue of the Block Definition  





The Name and Title will appear in the library folder, where the model is stored. The Level of the model representation is only important w hen using or changing old models. For new created models "Level 3'' should always be used. For macros, this option does not have any impact, because the level of the highest block is important, i.e. the controller definition. "Automatic Calculation of Initial Conditions'': PowerFactory can calculate the initial conditions automatically. However, if no sequence is found (because of, for example, deadlock situations) there will be an error message. "Classification'':

Linear This option will only effect the graphical representation of the block in the diagram. If this option is enabled, the block will be represented as a linear block, otherwise as a nonlinear block with two lines. Macro This option is used to identify the block definition as a macro inside the library. Matlab Enabling the 'Matlab' tag will show a n input dialogue, where a Matlab (*.m) fil e can be defined with which the block definition can com municate during a simulation. For m ore information about the Matlab interface see Section 25.10 Matlab Integration . 









A constant Limiting Parameter may be defined, which are defined in the common model dialogue, as well as limiting signals, which are similar to input signals. The difference is the graphical representation in the block diagram. Input and output signals have to be defined for internal use inside the block definition. The number and their name will then appear in the graphical dia gram when the block is used. State variables are needed when not only linear, but also differential, equations are used. Then for every first-order derivative one state variable must be specified. The Parameters will appear in the common m odel dialogue and can then be specified. The parameter defined in the block definition w ill automatically be inserted in the block reference. The names of the parameters can be different in the block reference and in the block definition. Only the order must be identical. Internal variables are only used inside the block definition but can not be set from outside.

There are several buttons on the right side of the dialogue: Contents This button will display the (possible) contents of the blo ck definition. This can be the graphically i nserted objects, further block references or the packed macros. This may additionally include, for example, internally-defined events. Equations The "Equations" button will print the DSL equations to the o utput window, regardless of whether they are defined graphically or on the "Additional Equations" page, as well a s variable definitions. Macro Equat. This button prints the current block definition DSL equations (including the equations in the used m acros) to the output window. Check "Check" will verify the model equations and output error messages if errors have occurred. Otherwise the following message will occur: DIgSI/info - Check '\TestUser.IntUser\Windparks.IntPrj\Library \Block Definitions\DFIG\Voltage Control.BlkDef': DIgSI/info - Block is ok.

Check Inc. The initial conditions of the block definition will be printed and checked. Pack Pack will copy a ll used DSL models (macros) of a composite model definition to the folder "Used Macros" inside the block definition. In this way there will now be references to other projects or libraries outside the model. Beware: any further changes in the macro library have no i nfluence; the macros are copied and no longer linked to the li brary. So if there is an error in a certain macro it has to be fixed s eparately in each packed block. Pack-> Macro

This command will reduce the entire model including DSL blocks and additional equations and m acros into one DSL model containing only equations. All graphical information will be lost. It should be noted that this command is irreversible. Encrypt The "Encrypt" button is available when Pack-> Macro is activated before. This command encrypts all equations inside the model, so that the equations can not be seen or output anymore. In this way a model containing sensitive or restricted device equations can be deliv ered without showing the internal equations. It should be noted that this command is irreversible and a decrypt function is not available.

By clicking on the button the second page of the dialogue can be accessed. Here the (additional) equations of the DSL model can be defined. Also further information e.g. the initial conditions of state variables and the name and unit o f parameters can be specified. Figure 25.37 shows the additional equations of the DSL model of the PI controller.

Fig. 25.37: Dialogue of the block definition - Page 2

The next section describes the handling and usage of the DSL language.

DIgSILENT GmbH www.digsilent.de Tel: +49 (0)7072 9168-50 Fax: +49 (0)7072 9168-88


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[email protected]

25.9 The DIgSILENT Simulation Language (DSL) The DSL language is used to program models for the electrical controllers and other components used in electrical power systems. As for any other simulation or programming language, a special syntax is provided for the model formulation. This syntax is explained in the fo llowing order: 25.9.1: Terms and Abbreviations 25.9.2: General DSL Syntax 25.9.3: DSL Variables 25.9.4: DSL Structure 25.9.5: Definition Code 25.9.6: Initial Conditions 25.9.7: Equation Code 25.9.8: Equation Statement 25.9.9: DSL Macros 25.9.10: Events and Messages 25.9.11: Example of a Complete DSL Model


25.9.1 Terms and Abbreviations

The following terms and abbreviations are used to describe the DSL syntax: expr arithmetic expression, not to be terminated with a ';' 

 



arithmetic operators: +, -, *, / constants: all numbers are treated as real numbers standard functions: sin(x), cos(x), tan(x), a sin(x), acos(x), atan(x), sinh(x), cosh(x), tanh(x), exp(x), ln(x), log(x) (basis 10), sqrt(x) (square root), sqr(x) (power of 2), pow (x,y), abs(x), min(x,y), max(x,y), modulo(x,y), trunc(x), frac(x), round(x), ceil(x), floor(x). These standard functions are described in detail in the last chapter. Parenthesis: (arithmetic expression)

All trigonometric functions are based on radians (RAD). Example:

A = x1+2.45*T1/sin(3.14*y)

boolexpr logical expression, not to be terminated with a ';' 

 



Logical relations: <, >, <> (inequality), >=, <=, =. Unary operators: .not. Binary operators: .and. .or. .nand. .nor. .eor. Parentheses: {logical expression}

Example:

A = {x1>0.and..not.x2 <= 0.7}.or.T1=0.0

string anything within '...' (single quotation marks).

Example: A = 'this is a string'


25.9.2 General DSL Syntax Line length: The maximal line length is 80 characters. Longer lines have to be broken by using the '&' sign in the first column of the continuing li ne. A '&' sign in the first column joins the current row and its preceding row. Example: y = lapprox(x, 1.674, 7.367, 2.485, 12.479, 5.457, 18.578 & 6.783, 15.54, 8.453, 12.589, 9,569, 6.478)

Line breaking cannot be used within names or strings. Case sensitivity

All keywords, names, functions, variables, models, macros, etc. are case sensitive. Blanks All blanks are removed when the DSL code is processed. Exception: blanks in strings are kept. Comments The '!' sign causes the remaining line to be interpreted as a comment. Comments are removed when the DSL code is processed.

Example: ! comments may start at the beginning of a line x1. = select(at<> 0, ! comments may be used in broken lines & (1-sqr(x1)/sqr(at))/Tw, 0)


25.9.3 DSL Variables

A DSL model may use five different types of variables: Output signals

Output signal variables are available as input signals to more complex DSL models. Input signals

Input variables may originate from other DSL models or from power system elements. In the latter case, currents and voltages, as well as any other signal available in the analyzed power system, become available to the DSL model. State variables

State variables are time-dependent signals generated and used within the DSL model itself. Parameters Parameters are 'read only' numbers which are set to alter the behavio r of the DSL model. Internal variables

Internal variables are defined and used in the DSL model to ease the construction of a set of DSL equations.

The following rules may be helpful when interpreting warning and error messages: 

 

A state variable may not be simultaneously used as a state variable and an output variable; if required, the use of an assignment like y=x1 is recommended. All parameters are real numbers. A special parameter 'array_iiii' (with up to 4 digits i), with 2*iiii elements is provided to define characteristics (see procedure "lapprox'').




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Only the derivatives of state variables can be assigned an expression.


25.9.4 DSL Structure

DSL models are constructed of three parts:  



The interface part, which states the model name, title, classification and variable set. This part is set in the first page of the block diagram dialogue; Definition code; Equation code.

The definition and equation code form the actual controller network definition and are treated in the next sections.


25.9.5 Definition Code Definition code in the equation part of a DSL model is used to define parameter properties and initial conditions.

Unit and Parameter Description Valid Value Ranges Unit and Parameter Description vardef(varnm) = unitstring;namestring Unit and name for variable varnm.

Examples:

vardef(Ton) = 's';'Pick up time for restart' ! defines unit and name vardef(Ton) = ;'Pick up time for restart' ! only defines name vardef(Ton) = 's'; ! only defines unit

[varnm] = unitstring Unit for variable varnm, maximum 10 characters wide. Remark: A macro call causes error messages if the units of the substituted variables do not match the defined units.

Example:

[Ton] = 's' ! defines unit

Valid Value Ranges limits(varnm) = [/( minimum value, maximum value ]/) Defines the valid interval for variable varnm. Violations of the interval limits during simulation will be reported: limits(yt)=(,1] is equivalent to output(yt>1,'Maximum exceeded: yt=yt>1')

The '(' and ')' braces exclude the minimum or maximum value from the interval; the '[' and ']' braces include them. Examples: limits(x)=[min,max] ! min <= x <= max limits(x)=(min,max] ! min < x <= max limits(x)=(,max] ! x <= max limits(x)=(min,) ! min < x

If required and if possible, the program automatically determines the smallest interval under several intervals of the same variable. Example:

limits(x)=(1,3) and limits(x)=(2,4] results in 2
Macro models often define limits for certain variables. The model which uses the macro might also define limits for the variables which are used in the macro calls. The 'smallest interval' method gives the calling model thus the freedom to redefine parameter limits without violating the internal macro limit definitions.


25.9.6 Initial Conditions

Direct Setting of Initial Conditions Iterative Setting of Initial Conditions Direct Setting of Initial Conditions inc(varnm) = expr

Definition of the initial condition of variable varnm. If inc(varnm) is not defined, the normal assignment expression will be evaluated (only possible if varnm is of the intern or input type). If inc(varnm) is defined, it wi ll be evaluated when the model is reset. inc0(varnm) = expr

Definition of the initial condition of variable varnm, for unconnected output or input variables. This variant of the inc() statement is used only when the variable varnm could not be initialized through the initi al condition of the connected input or output signal. The inc0() statement is thus used to make open input or output terminals possible. incfix(varnm) = expr This variant of the inc() statement is valid only in connection with automatic initialization and is used to determine the initial values in ambivalent situations. With the incfix, one or more variables can be directly initialized so that other variables can be initialized automatically.

Example: An AVR model has two inputs, [ upss , usetp ], and one output, [ uerrs ]. Both inputs cannot both be initialized automatically by the single output value, which is determined by the connected machine. Therefore one of the inputs must be initialized as fixed, e.g. by incfix(upss)=0. The initial value of usetp is now automatically determined, using upss=0. Iterative Setting of Initial Conditions

Three functions are available for determining initial values iteratively: looping, intervalinc, newtoninc. These functions are used to find the initial value for one set o f parameters if the initial values of another set of parameters, which are functions of the first set of parameters, are known. The iterative functions are used to find the (approximated) values for the unknown parameters for which the known parameter take their initial value. loopinc (varnm, min, max, step, eps) Performs a simple linear search for a single value for which the parameter varnm is closest to its known initial value. varnm = target variable, whose initial value is known min = lower limit max = upper limit step = stepsize eps = maximum error Example: inc(a) = loopinc(b, -5, 5, 0.01, 0.001) 

The initial value of variable a is searched for by evaluating parameter b, beginning at a=-5, ending at a=5, with an increment of 0.01.


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

Return value: the value of a for which the deviation of b from its known initial value, takes the smallest value. A warning is given if the smallest deviation is greater than eps.



Restriction: Can only be used on the right side of a n inc() statement

intervalinc(varnm, min, max, iter, eps) Performs an 'interval-division search' for a single value for which the parameter varnm is closest to its known initial value. varnm = target variable, whose initial value is known min = lower limit, max = upper limit iter = maximum number of iterations s = maximum error Example inc(a) = intervalinc(b, -5, 5, 40, 0.001) Explanation: The initial value of the variable a is searched for, within the interval [-5,5] by successively dividing the interval as long as the deviation of the variable b from its initial value is less than eps. The iteration stops if the maxi mum number of iterations is reached, and a w arning is given if the smallest devi ation is greater than eps. Restriction: May only be used on the right side of a n inc() statement newtoninc(initexpr, start, iter, eps) Performs a Newton iterative search for one or more parameters by minimising the errors in a set of coupled equations. initexpr = the expression which must equal the parameters whose initial value is sought start = the starting value for the parameter whose initial value is sought iter = the maximum allowed number of iterations eps = the maximum allowed absolute error between initexpr and the parameter whose initial value is sought. Example: qt0 = 0.5 eps = 0.000001 maxiter = 100

inc(hedr) = newtoninc(hw-sqr(qedr)*(Rds+Rdr), hw, maxiter, eps) inc(qt1) = newtoninc(Pt1/(4*dh*eta1), qt0, maxiter, eps) inc(qt2) = newtoninc(Pt2/(4*dh*eta2), qt0, maxiter, eps) inc(qt3) = newtoninc(Pt3/(4*dh*eta3), qt0, maxiter, eps) inc(qt4) = newtoninc(Pt4/(4*dh*eta4), qt0, maxiter, eps) This example shows a part of the initial value definitions for a model where the initial values of 5 parameters ( hedr ,qt1 ,..,qt4 ) are sought simultaneously by setting up a system of coupled equations and solving that system by the Newton method so that, eventually:

The following guidelines should be considered:   





Add the initial conditions to the complex block, as opposed to each primitive (like a first-order time lag). The general initialisation 'direction' is from right to left, i.e. the outputs are normally k nown and the inputs (or setpoints) have to be determined. If initial conditions are not defined for a certain variable, the simulation equations are used instead. It should be therefore enough to specify the initial conditions of the state variables and input variables. The option Automatic Calculation of Initial Conditions requires configuring, but does not require correct initial conditions for each state/input variable. The initial values are only used to initial ize the iteration process. The incfix-function can be used to determine the initial values in ambiguous situations. Use the option Verify Initial Conditions to check if the initial conditions lea d to the correct result.


25.9.7 Equation Code

Within the equation code, all equations necessary to build up the simulation models are included. The set of equations defines a set of coupled differential equations which describe the transfer functions between the input and output signals. These transfer functions may range from simple linear, single-input single-output functions, to highly complex non-linear, non-continuous, multi-input, multi-output functions. DSL is used to describe the direct relationships between signals and other variables. Expressions may be assigned to a variable, or to the first derivative of a state variable. Higher order differential equations have to be thus split up into a set of single order equations by the introduction of additional state variables.


25.9.8 Equation Statement

The equation statements are used to assign expressions to parameters, thus relating all parameters in a set of differential equations. Syntax: varnm = expr Assigns expression 'expr' to variable 'varnm'. Examples : y = sin(a)+3*x1 y = .not. x1>2 .or. a<=3 varnm. = expr Assigns expression expr to the first order derivative of the variable varnm. Examples: x1. = (xe-x1)/T1 x2. = x1

Remarks   

DSL assignments may occur in any sequence. The sequence does not influence the evaluation of the assignments. All variables are of type floating point, even if assigned to a boolean expression, in which case the value will be 0.0000 or 1.0000. When a variable z is used in a logical expression (i.e. y=.not.z), the logical 1 of z is tested by evaluating (z>0.5): y1 = .not.z is interpreted and equal to y1 = (z=<0.5) There is no warning against mixing logical and non-discrete variables in expressions. Consequently the following code will not cause a message to be emitted: depending on y, z will take the value x1 + 4.0, or just x1:

y = .not. x1>2 .or. a<=3 z = 4.0*y + x1




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The assignment of a value to a variable takes place in an order which recognizes the connections between these variables. In the case of the following example, the second line will be evaluated first, then line 1:

1. a = b+5 2. b = x1 3. x1. = 1 

Algebraic loops are not supported. In the following example, an error message will be displayed:

a = b+5 b = 2*a 

If there is no assignment to a variable varnm, varnm will keep its initial value. The right side expression may not contain derivatives. Derivatives may only appear on the left side of the equal sign. The first example is correct; the second is false.

x1. = asin(a) ! Correct a = sin(x1.) ! Not accepted


25.9.9 DSL Macros

A DSL macro is a predefined DSL model, complex or primitive, which is meant to be included in higher level DSL models. The block diagram edit dialogue offers a 'Macro' classification option which can be set to mark the model as a macro. A DSL macro is included in a higher level DSL model either by creating a block reference in the block diagram graphics or by its explicit inclusion in a DSL equation. Syntax: varnm1, varnm2,... = macroname (i1,i2,... ; s1,s2,... ; p1,p2,... ; i1,i2,...) Assigns the output signals of the DSL macro macroname to the variables varnm1 , varnm2 , ... Assigns the input signals of DSL macro to the variables i1, i2,... The macro uses the state variables s1, s2,... the parameters p1, p2,... and the internal variables i1, i2,... Example: P1,P2 = '\User\I.BlkDef'(i1,i2;s1,s2;T1,T2) This example assigns to P1 and P2 the output of DSL model \ User\ I.BlkDef .

Macro calls are not supported within expressions, even if they only have one output variable. Correct example:

y = my_macro(x1, s1, p1, i1)

!

Incorrect example:

y = 3 * my_macro(x1, s1, p1, i1) + 4

which should be replaced by:

y1 = my_macro(x1, s1, p1, i1) y = 3 * y1 + 4

DSL Internal Macro Handling DSL Models DSL Internal Macro Handling

A preparser substitutes each macro call with the equation code of the macro. The variables of the macro DSL model are then replaced by the variables used in the macro call. The local variable names of macros thus disappear after the preparation process. DSL Models

In general, there are two basic types of DSL models possible: 1.

2.

Models of electrical devices such as generators, loads or HVDC systems. These models are characterized by their principal output signal "complex device current'', which is injected to the electrical grid at a certain busbar. However, in addition to the electrical device currents, there may be any other varia ble defined as an output signal. A summ ary of the available variables can be seen in the corresponding Technical References of the element. Models with output signals which are not directly injected to the electrical network (general devices). Among these types of models are prime mover units, voltage controllers, relays, calculation procedures, etc.


25.9.10 Events and Messages

The DSL language provides procedures for the generation of an interrupt event and for sending messages to the output window: 



The procedure fault(boolexpr, event_string) generates an event and is evaluated at the beginning of each tim e step The procedure output(boolexpr, message_string) outputs a message and is eval uated at the end of each time step.

The "fault" and "output" procedures are evaluated at each time step during the simulation of a model. The first time that boolexpr is found to be true, the string will be processed and a message will be sent to the output window, or an event will be added to the PowerFactory event queue. The '"fault" or "output" procedures will be disabled afterwards until the DSL model is reset, to prevent an avalanche of messages or events. Both procedures are explained in detail in the following paragraphs. output(boolexpr, message_string) fault(boolexpr, event_string) output(boolexpr, message_string)

The message_string may contain variables and the special function num(boolexpr) or num(expr): 

Variable names which appear directly after an '=' sign will be substituted by their actual values; hence, the line of code below may generate the message: maximum exceeded: yt=1.2 > ymax=1.0:

output(yymax,'maximum exceeded: yt=yt > ymax=ymax') 

The num(expr) or num(boolexpr) will be substituted with the calculated value of the expression, e.g.:

value=num(a+b) may produce value=3.5000 fault(boolexpr, event_string)

Each DSL model can add events to the event list. A DSL model of a distance relay, for instance, can open the power switch of a line by adding the correct switch event. 'Adding an event' is done by executing an existing event object in the PowerFactory database. Consequently, all events that may be used by t he DSL model have to be created together with the DSL model. They must all be stored inside the common model ( ElmDsl ). These DSL events will thus form an integrated part of the DSL model. The event_string in the fault expression must refer to the name of one of these events. At evaluation, the event will be thrown onto the event stack if boolexpr is true. As


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soon as the simulation reaches the event, it will execute it. Consequently, a delayed event may be thrown by the DSL model by setting the execution time ahead of the current time. The parameters of the event can be modified in the fault string by assigning a new value. The mechanism is the same as described above in the output procedure. Example:

fault(u>1.1,'name=MySwitchEvent1 dtime=0.15')

If the variable u exceeds 1.1, the event named 'MySwitchEvent1' will be thrown onto the event stack and its variable dtime (relative event time) will be set to 15 milliseconds. The event will thus be delayed for that amount of time, which, in this case, mimics the time needed to open a switch. The actual switch that will open is defined in the event object 'MySwitchEvent1'. Note The events are accessed or created by opening the edit dialogue of the common model (double-click on the DSL model Data Manager), and then pressing the button Events in the dialogue. A list of events already defined inside this model is displayed. The events are not added to the project's global event list unless the event is 'activated' by the DSL model.

in the


25.9.11 Example of a Complete DSL Model Thermal Double Reheat Turbine with Steam Storage

Controller Model:

model pt,ptmw = 'pmu_1'(at,s gn,cosn,ngnu m;x1,x2,x3, x4;Thp, Tip,Tlp,alfl p,Tspi) limits(T1) = [0,) limits(alfhp) = [0,1] vardef(alfhp) = ;'High pressure turbine ratio'; limits(alflp) = [0,1-alfhp] vardef(alflp) = ;'Low pressure turbine ratio'; vardef(Tspi) = 's';'Boiler capacity time constant'; limits(Tspi) = (0,) vardef(Thp) = 's';'High pressure turbine time constant'; vardef(Tip) = 's';'First reheater time constant'; vardef(Tlp) = 's';'Second reheater time constant'; inc(x1) = y/K inc(xe) = y/K inc(x4) = 1.0 inc(at) = pt inc(steamflow0) = pt inc(ylp) = pt x1. = select(T1>0,(xe-x1)/T1,0) y = K*select(T1>0,x1,xe) ! if T1=0 => y=xe steamflow = at*x4 x4. = (steamflow0 - steamflow)/Tspi ! boiler yhp = PT1(steamflow;x1;Thp) ! high pressure part yip = PT1(yhp;x2;Tip) ! medium pressure part ylp = PT1(yip;x3;Tlp) ! low pressure part pt = yhp*alfhp + ylp*alflp+ yip*(1.0-a lfhp-alflp) ptmw = pt*sgn*cosn*ngnum ! only for output purposes

[T1] = 's'

The used macro 'PT1' is defined as:

model y = 'PT1'(xe;x1;K,T1;) x1. = select(T1>0,(xe-x1)/T1,0) y = K*select(T1>0,x1,xe) ! if T1=0 => y=xe inc(x1) = y/K inc(xe) = y/K [T1] = 's' limits(T1) = [0,)


25.10 Matlab Integration Additionally to designing controllers or various electrical and mechanical models using the DIgSILENT Simulation Language, there is also the possibility to use an interface to Matlab . This interface gives the opportunity to model controller or very complex transfer functions using the Matlab environment and insert them as a block definition into a frame in a PowerFactory transient simulation. PowerFactory can correspond to the Matlab program during the simulation. It will transfer the input values of a block to Matlab for every time step, which will then simulate a specified *.m file in its own environment and gives back the results as the outputs of the block definition. Consequently this function needs a installation of the Matlab program including the Simulink package. The implementation of a Matlab file is shown in the next sections. In this example a voltage controller is implemented first using a built-in model ( ElmVco ) and using a definition from Matlab . This example can also be found in the FAQ on the DIgSILENT home page. Implementation of Voltage Controller - Example Implementation with Built-In Model Implementation with Matlab Model The Matlab File Additional notes


25.10.1 Implementation of Voltage Controller - Example

In this example the grid consists of two generators, one load and one line, as shown in Figure 25.38.

Fig. 25.38: Matlab example grid

The simulation event is defined for the lo ad, where the reactive power is increased after 0.5 seconds. The complete example contains three files:


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1. Matlab Example.dz is a PowerFactory file. 2. VCOtype16.m is a Matlab M-file. This file is an interface to the Simulink model, and it is used as a middle layer in the communication between PowerFactory and Simulink. 3. vcotype16mod.mdl is a Simulink model and contains Simulink implementation of VCO type 16.


25.10.2 Implementation with Built-In Model

In the base study case, the voltage controller models are represented by the built-in models VCO type 16 ( ElmVco__16 ). The built-in VCO type 16 inside PowerFactory is one excitation control system with simplified exciter. Both composite models use the AVR inside the IEEE-frame from the global library. The generators have different VCO parameters set. In Figure 25.39 the edit dialogue of the ElmVco with the parameters of the AVR can be seen.

Fig. 25.39: Parameters dialogue of the voltage controller

The model representation of the ElmVco__16 is indicated in Figure 25.40.


The plots resulting from the simulation (Figure 25.45) show busbar voltages and excitation voltage for both generators. The results are stored in result files l ocated under the "Results" folder of the relevant study case.


25.10.3 Implementation with Matlab Model

In the second study case "Matlab'' which is a modification of the base case, VCO type 16 is modelled inside the Simulink package, instead of using a built-in model. The Matlab console is started automatically when running the simulation. To implement a Matlab model into a current project in PowerFactory it has to be included into a frame similar to a DSL model definition. This procedure is described in detail in the Section 25.10 Matlab Integration . First a slot inside the frame has to be created, where the controller model should be inserted. This is done exactly like for implementing built-in models or common models. Then a block definition BlkDef has to be created inside the library. Instead of programming the transfer function using the DSL code, there can now the definition of the Matlab code be imported. This can be done in the dialogue of the block definition. When creating a primitive DSL model in the library by 

right-clicking a or inside a (library) folder in the active project in the data manager and selecting New... −> Block/Frame - Diagram from the context menu.



using the "New Object''



icon in the database manager and selecting Block Definition (BlkDef) .

double-clicking an new/empty block reference in an open block diagram and then use the block definition inside the local library.

button to select a block definition. Then The

icon can be used to create a new

Now open the dialogue of the new BlkDef 

by double-clicking on the frame of a composite block definition



by double-clicking the definition in side the library or o n its icon

Here input and output variables, parameters, state variables and limiting signals have to be defined. Instead of inserting the equations to describe the different function blocks, a Matlab file *.m can be selected, when the option Matlab is activated. The edit dialogue of the block definition including the parameter definition and the selected file can be seen in Figure 25.41 for the mentioned example.


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Fig. 25.41: Composite model using a special frame

The model representation of the ElmVco__16 in the Matlab Simulink package is shown in Figure 25.42.


When the block definition is specified, a DSL model has to be created first. As described in Section 25.7.4 The Common Model , the common model element ( ElmDsl , ) is the front-end object for all user-defined block definitions. This means that all user-defined transient models including built-in elements or Matlab models cannot be used other than through a common model. The common model then combines a model or block definition with specific set of parameter values. The edit dialogue of the DSL element now looks different to the built-in ElmVco. From Figure 25.43 can be seen, that this dialogue is similar to the normal DSL models. All time constants and other parameters are the same as for the built-in VCO models.

Fig. 25.43: Parameters dialogue for the Matlab voltage controller

Figure 25.44 shows the composite model using the special frame with the generator 'G1' and the Matlab-AVR inserted into the slots.


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Fig. 25.44: Composite Model using a special frame

These results from the simulation of the reactive power step using the built-in VCO model (dotted curves) and using the Matlab representation (solid curves) can be seen in Figure 25.45 25.45..

Fig. 25.45: Results of the transient simulation with the Built-In model


25.10.4 The Matlab File

The Matlab file VCOtype16.m is an interface configuration for the Simulink model, stored in the file vcotype16mod.mdl, and the PowerFactory PowerFactory DSL DSL model. There the input and output signals, the parameters and the state variables are defined, as described below. The transfer function is specified. The contents of this file i s listed here: function [t, x, y] = VCOtype16 global U Tvm Usetp Upss Vska Tisp Ur1mx Ur1mn Vsex Efdmx Efdmn ve1 x1 x2 options = simget('VCOtype16mod'); simget('VCOtype16mod'); options = simset('InitialState', simset('InitialState', [x1,x2]); [t, x, y] = sim('VCOtype16mod', sim('VCOtype16mod', [], options);

PowerFactory inserts PowerFactory inserts the following variables into the Matlab workspace:

U, Tvm, Usetp, Upss, Vska, Tisp, Ur1mx, Ur1mn, Vsex, Efdmx, Efdmn, ve1, x1, x2

Those variables are necessary to successfully run t he Simulink model. There are three input signals ( U , Estop , Upss ), ), one output signal Uerrs and two state variables x1 and x2 . In each step of the PowerFactory PowerFactory simulation simulation the Simulink model is completely evaluated. State variables ('InitialState') are assigned to Simulink model in each step of the simulation. For PowerFactory PowerFactory it it is a simple function call: [t, x, y] = VCOtype16.

PowerFactory uses only one Simulink model for both generators. To avoid limitation of Simulink, which allows only one instance of the model running at the same time, PowerFactory uses PowerFactory must PowerFactory must send all parameters in the each step of the simulation. To find appropriate equations for the initial conditions you need to understand the construction of the transfer function blocks in Simulink . To obtain this understanding you can replace the variables with actual numbers in the Matlab Simulink model, set the initial conditions, run it for a few seconds and monitor the outputs of all transfer functions to see whether the model initialized correctly. The Matlab Simulink model (.mdl) and the interface file (.m) file may not have the same name. The order of the state variables in the interface file's statement "options = simset('InitialState', [x1, x2, .......])" is important; the order of the elements in the vector [x1, x2, ...] must be the same as in the state variable vector constructed internally by Matlab. To determine the order of the Matlab state variable vector the user may use the


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command "[sizes,x0,xstring]= ModelName" in the Matlab workspace, where ModelName is the name of the Simulink model (without the .mdl extension and without inverted commas). The output of the string variable xstring contains the names of the dynamic blocks in the Simulink model in the desired order. In the case of the above example the first state variable is in the measurement block and the second state variable is in the integrator: xstring = ...'VCOtype16_model/Mea ...'VCOtype16_model/Measure/State sure/State Space' ...'VCOtype16_model/Integrator'

The names of the variables in the 'Initial conditions' fields in the masks of the Simulink model dynamic blocks is irrelevant. The initial conditions are set within PowerFactory . Also, for the purpose of PowerFactory's PowerFactory's model model checking mechanisms, the state derivatives equal to zero The Simulink solver parameters are set to integrate over one small time step, e.g. start time = 0, end time = 0.01, and step size = 0 .01. The y-matrix returned by MATLAB contains the output variables. If more than one output variable is defined in the DSL model, then those are sorted alphabetically before assigning the outputs from MATLAB . For example, if there are two outputs "uerrs" and "output", then the value from the first column of the y-matrix is assigned to "output" and the value from the second column is assigned to "uerrs".


25.10.5 Additional notes

DIgSILENT PowerFacory calls MATLAB using the programme identification keys "Matlab.Application" and "Matlab.Application.Single". PowerFactory will start that same MATLAB installation which was used last. Additional information on the calling of MATLAB is available on http://www.mathworks.com http://www.mathworks.com..


Chapter 26 Modal Analysis / Eigenvalue Calculation The modal analysis calculates the eigenvalues and eigenvectors of a dynamic multi-machine system including all controllers and power plant models. This calculation can be performed not only at the beginning of a transient simulation but also at every time step when the simulation is stopped. The eigenvalue analysis allows for the computation of modal sensitivities with respect to generator or power plant controllers, reactive compensation or any other equipment. The calculation of eigenvalues and eigenvectors is the most powerful tool for oscillatory stability studies. For its application it is highly recommended to first compute the 'bare natural' system oscillation modes. These are the oscillation modes of the system without taking any controller or power plant model into consideration, i.e. with constant turbine power, constant excitation voltage etc. Starting from these 'bare natural' modes the effects of controllers (structure, gain, time constants etc.) and other additional models can be calculated as the second step. 26.1: Theory of Modal Analysis 26.2: Performing an Eigenvalue Analysis 26.3: Visualization of Modal Analysis Results


26.1 Theory of Modal Analysis After the initial conditions have have been calculated calculated successfully, which means means that all time-derivatives time-derivatives of the state state variables should be zero, zero, or the simulation has has been stopped at a point in time, the modal analysis calculates the complete system A-matrix by means of numerical, iterative algorithms. The representation representation of the electrodynamic network model is equivalent to the representation used for the balanced RMS simulation, except for the general load model, for which the frequency dependencies are neglected. The computation time for the models analysis is approximately proportional to the number of state space variables to the power of three. A multi-generator system exhibits oscillatory stability, if all conjugate complex complex eigenvalues, making making up the rotor oscillations have have negative real parts. parts. This means they they will lie in the left complex half-plane. The individual generator oscillations will then be stable. Assuming that one of the conjugate complex complex pair of eigenvalues is given by:

then the oscillatory mode will be stable, if the real part of the eigenvalue is negative

The period and damping of this mode are given by

where A and A are amplitudes of two consecutive swing maxima or minima respectively. n n+1 The oscillatory periods of local generator oscillations are typically in the range of 0.5 to 5 Hz. Higher frequency of the natural oscillations, i.e. those which are normally not regulated out, are often damped to a greater extent than slower oscillations. The oscillatory period of the oscillations of areas (inter-area oscillations) is normally a factor of 5 to 20 times greater than that of the local generator oscillations. The absolute contribution of an individual generator to the oscillation mode which has been excited as a result of a disturbance can be calculated by:

where generator speed vector i'th eigenvalue i'th right eigenvector magnitude of excitation of the i'th mode of the system (at t=0) (depending on the disturbance) n number of conjugate complex eigenvalues (i.e. number of generators - 1)


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In the following c is set to the unit vector, i.e. c = [1, ..., 1], which corresponds to a theoretical disturbance which would equally excite all generators with all natural resonance frequencies simultaneously. The elements of the eigenvectors Φ then represents the mode shape of the eigenvalue i and shows the relative activity o f a state variable, when a particular mode is excited. i of the generators when an eigenfrequency is excited, whereby those generators with opposite signs in Φ oscillate in opposite phase. They show e.g. the speed amplitudes i The right eigenvectors Φ can thus be termed the "observability vectors''. The left eigenvectors Ψ measures the activity of a state variable x in the i-th mode, thus the left i the "relative contribution vectors''. i eigenvectors can be termed Normalization is performed by assigning the generator with the greatest amplitude contribution the relative contribution factor 1 or -1 respectively. For a n-machine power system, n-1 generator oscillation modes will exist and n-1 conjugate complex pairs of eigenvalues λ will be found. The mechanical speed ω of the n i generators will then be described by:

The problem of using the right or left eigenvectors for analyzing the participation of a generator in a particular mode i is the dependency on the scales and units of the vector elements. Hence the eigenvectors Φ and Ψ are combined to a matrix P of participation factor by: i i

The elements of the matrix p are called the participation factors. They give a good indication of t he general system dynamic oscillation pattern. They may be used easily to ij determine the location of eventually needed stabilizing devices in order to influence the system damping efficiently. Furthermore the participation factor is normalized so that the sum for any mode is equal to 1. The participation factors can be calculated not only for the generator speed variables, but for all variables listed in Table 26.1 26.1.. Name

Unit

Description

s:speed

p.u.

Speed

s:phi

rad

Rotor-angle

s:psie

p.u.

Excitation-Flux

s:psiD

p.u.

Flux in D-winding

s:psix

p.u.

Flux in x-winding

s:psiQ

p.u.

Flux in Q-winding

Table 26.1: Variables accessible for eigenvalue calculation


26.2 Performing an Eigenvalue Analysis A modal analysis can can be started when a balanced steady-state steady-state condition is reached reached in a dynamic calculation. calculation. Normally, Normally, such a state is reached reached by a balanced balanced load-flow calculation, followed by a calculation of initial conditions. However, it is also possible to perform a balanced RMS simulation and start a modal analysis after the end of a simulation or after stopping the simulation. Note The modal analysis can be executed at any point of time in a transient simulation. Nevertheless always keep in mind that the results of the modal analysis are valid on the basis, that the system is in a quasi steady-state operation point. Furthermore the calculated oscillation modes are only valid for "small'' perturbations of the system. If large transient disturbances are applied to the network, the oscillation frequency and damping may change from the results of the eigenvalue analysis.

When a load-flow load-flow is calcula calculated, ted, the the icon to open open the modal modal analysis analysis dialogue dialogue(( calculating the initial conditions used by the modal analysis can be specified.

) becomes becomes active. active. Using Using the Settings button (in the ''Basic Options'' page), the options for

On the ''Advanced Options'' page, the state variable and the result file for the Eigenvalue analysis can be defined. The default state variable is the speed signal of the generators. The default result file is Eigenvalue (s:speed) and is stored inside the active study case. The relative participation factors can be calculated not only for the generator speed variables, but there is also the possibility to select from the variables as shown in table 26.1.. 26.1 Figure 26.1 shows the command dialogue of the modal analysis with the variable s:speed selected as the state variable.

Fig. 26.1: Command dialogue of the modal analysis

When executing the command by pressing Execute, the initial conditions of all elements is calculated first. Then the modal analysis constructs a system matrix from the load-flow and the dynamic data. The eigenvalues and eigenvectors are calculated directly from that matrix. Since eigenvalue calculations require linearized models, PowerFactory automatically PowerFactory automatically performs the linearization of all relevant system elements.


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The following information is printed to the output window, when the eigenvalues are calculated: DIgSI/info (t=-100:000 ms) - Initial conditions calculated. DIgSI/info (t=-100:000 ms) - Starting Modal Analysis. Please wait... DIgSI/info (t=-090:000 ms) - Modal Analysis ready !


26.3 Visualization of Modal Analysis Results 26.3.1: Output Window 26.3.2: Modal Analysis Plots 26.3.3: Data Browser


26.3.1 Output Window

The results of the modal analysis can be outputted in various ways:  



The system eigenvalues and eigenvectors only The relative generator participation factors Detailed information about the eigenvalues and the relative generator participation factors

The results are printed to the output window with the ComSh output command by activating the "Output Calculation Analysis"-icon executed, the ComSh shows the active option Eigenvalues in the LoadFlow/Simulation report selection.

. After a modal analyses has been

Selecting Eigenvalues will then enable the selection Output of Eigenvalues , as shown in Figure 26.2. Either the eigenvalues may be reported, or the participation factors. When the option Eigenvalues is selected all calculated eigenvalues of the system are printed in a report style into the output window. Figure 26.3 shows the results of a small example power system.

Fig. 26.2: Output of eigenvalues with participation factors selected

Fig. 26.3: Output of system eigenvalues

Selecting the option Participations , either detailed or not, will further enable the selection of the state variables and the certain eigenvalues as can be seen in Figure 26.2. For the user convenience, there is also the possibility to define a filter for the eigenvalues (system modes). The filter for eigenvalues is used to show only the participation factors of specific system modes, if Select Eigenvalue(s) is set to Filtered . Otherwise the selected specific eigenvalue will be used and the filter will be ignored. The system modes and participating generators can be filtered by using the following options: Maximal Damping The damping of the system mode will be below the defined value in [1/s]. Maximal Period System modes oscillating below the defined periodic time in [s] will be shown. Min. Participation Only generators with a participation factors above the specified limit will by outputted.


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The results of the participation factors of the generators in the small example power system are shown in Figure 26.4.

Fig. 26.4: Output of participation factors


26.3.2 Modal Analysis Plots

The Eigenvalue Plot (Viseigen) The Mode Bar Plot (VisModbar) Mode Phasor Plot (VisModephasor) The Eigenvalue Plot (Viseigen)

The Eigenvalue Plot displays the calculated eigenvalues in a two axis coordinate system. For the vertical axis, i t is possible to select among the imaginary part, the period or the frequency of the eigenvalue. The horizontal axis shows the real part. An Eigenvalue Plot is generated by clicking on the icon from the 'Select Plot Type' button of the toolbar menu (see Figure 26.5). After cliking on the icon, the edit dialogue of the Viseigen object pops up; there the user can set the figure appearance and the displayed values on the vertical axis. Figure 26.6 shows an example of an Eigenvalue Plot displaying the imaginary part of the calculated eigenvalues.

Fig. 26.5: Selection of the modal analysis plot

Double-clicking on any of the displayed eigenvalues, pops-up the informative dialogue of Figure 26.7. There the oscillation parameters and the coordinates in complex and polar representation are given.

Fig. 26.6: The Eigenvalue plot

Fig. 26.7: IntEigen dialogue The Mode Bar Plot (VisModbar)


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Displays the participation factors of the system generators (according to the state variable selected in the modal analysis command, Figure 26.1) in a selected mode by means of a bar diagram. A new Mode Bar Plot is created by clicking on the

icon from the 'Select Plot Type' button (Figure 26.5).

After the icon has been clicked, the VisModbar dialogue pops up, there the bar diagram options and the displayed mode can be set. Participant generators can be filtered according to the magnitude of the participation factor; also the bar diagram can be restringed to a selected group of generators. Figure 26.8 shows the Mode Bar Plot for the 20th mode of the small power system used for the example of figures 26.3 and 26.4.

Fig. 26.8: The Mode Bar plot

The magnitude and the phase of any participation factor can be visualized by double clicking on a bar. This action opens the so called IntEigstate dialogue from Figure 26.9.

Fig. 26.9: Eigenvalue state dialogue Mode Phasor Plot (VisModephasor)

The Mode Phasor Plot displays the participation factors of the system generators (according to the state variable selected in the modal analysis command, Figure 26.1) in a selected mode by means of a phasor diagram. A new Mode Phasor Plot is created by clicking on the

icon from the 'Select Plot Type' button (Figure 26.5).

Like in the Mode Bar Plots, the participant generators can be filtered according to the magnitude of the participation factor and the diagram can be restringed to a selected group of generators. Figure 26.10 shows the Mode Phasor Plot for the same mode from Figure 26.8. Double clicking on a participation factor phasor will display its IntEigstate dialogue as in Figure 26.9.

Fig. 26.10: The Mode Phasor plot


26.3.3 Data Browser

The calculation results of the modal analysis can be displayed in a data browser by clicking on the icon (toolbar menu). The ComModres dialogue from Figure 26.11 pops up. There the result file containing the defined output variables (see 26.2) and the values to display (eigenvalue or mode data) are selected. Pressing the Execute button in the ComModres dialogue, opens a data browser containing the calculation results as in Figure 26.12.


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Fig. 26.11: Displaying modal analysis results in a data browser (ComModres dialogue)

Fig. 26.12: Modal analysis results in a data browser


Chapter 27 Model Parameter Identification The process of parameter estimation for power system elements for which certain measurements have been made is performed with the "Parameter Estimation" function using the icon

.

The ComIdent command object is a high performance non-linear optimization tool, which is capable of a multi parameter identification for one or more models, given a set of measured input and output signals. This identification is principally performed in the fol lowing way: 









A "Measurement File'' object (ElmFile) is created which maps the raw measured data onto one or more "measurement signals''. These signals may contain measured excitation and response signals. The measurement signals are used as inputs by the mo dels of the power system elements for which one or m ore parameters have to be identified, or they may be used to control voltage or current sources. The output signals of the power system elements are fed into a comparator, just as the corresponding measured signals. The comparator is thus given the measured response on the excitation and the simulated response of the element models. The comparator calculates an objective function, which i s the weighted sum of the differences between the measured and the simulated response, raised to a who le power (by default to the power of 2). The ComIdent command will collect al l objective functions from all comparator objects in the currently active study case and will m inimize the resulting overall objective function. To do this, the ComIdent command is given the list of parameters which are to be identified. The objective functions are minimized by altering these parameters.

This whole process is visualized in Figure 27.1.

Fig. 27.1: The identification Principle

Of course, Figure 27.1 only visualizes the principle of the identification. To connect measurement files, power system models and comparator objects to each other, a composite frame is used. This, and all other details of the PowerFactory identification functions, is described in the following sections. 27.1: Target Functions and Composite Frames


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27.2: Creating The Composite Identification Model 27.3: Performing a Parameter Identification 27.4: Identifying Primary Appliances


27.1 Target Functions and Composite Frames The parameter identification process is performed by minimizing objective functions. These objective functions are calculated by ElmCompare objects from the difference between measured responses and calculated responses of one or more power system elements. To define an objective function, the measured excitation signals must be connected to the component models or to voltage or current sources, and the measured and calculated response signals must be connected to the compare object. All this is done graphically by drawing a Composite Frame, using a block definition ( BlkDef ) with slots. A simple example of an identification block diagram, for the objective function for a voltage controller, is visible in Figure 27.2.

Fig. 27.2: Simple identification block diagram

The block diagram uses slo ts which reserve space for the measurement files, the comparator and the element models. 27.1.1: The Measurement File Slot 27.1.2: Power System Element Slot 27.1.3: Comparison Slot


27.1.1 The Measurement File Slot

The measurement file object ( ElmFile) has the following signals available: 



 

Number of Input Signals: 0 Number of Output Signals: 10 Input Signals Names: Output Signals Names: "y1,..,y10''

The measurement file slot in the example of Figure 27.2 has the following settings: 



Class Name Filter: "ElmFile'' Output Signals: "y1,y2''

The fact that the signal is named "output'' signals in the case of the measurement file does not implicate that the parameter identification only regards measured response signals ("measured outputs'') from power system elements. It only means that the measured excitation signals will be mapped onto ElmFile signals. The ElmFile will reproduce the measured excitation and response signals during the identification process.


27.1.2 Power System Element Slot

Power system element slots are used in the identification block diagram in the same way as they are used to define composite models. As in the case of a composite model diagram, the element slots may use any of the available parameters of the power system element model as input or output. The in- and output signals are defined by stating the exact variable name (see also Section Composite Block Definitions in Section 25.8 User Defined (DSL) Models ). In the case of the example in Figure 27.2, the "Vco1'' slot has the following parameters set: 

 

Class Name Filter: "ElmVco*'' Output Signals: "uerrs'' Input Signals: "u''


27.1.3 Comparison Slot

The comparison object ElmCompare has the following properties: 

  





Number of Input Signals: 21 Number of Output Signals: 0 Measured Response Signal Names: "in1mea,..,in10mea'' Simulated Response Signal Names: "in1sim,..,in10sim'' Weighting Factor: qzpf Output Signals Names: -

The calculated value of the objective function will be multiplied by the weighting factor before it is put out. The weighting factor may be used, for instance, to connect a timewindow to the comparison object which forces the objective function to zero for those moments in time which are n ot to be used in the identification process.


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In the case of the example in Figure 27.2, the Comparison slot has the following parameters set: 



Class Name Filter: "ElmCompare'' Input Signals: "in1meas,in1sim''


27.2 Creating The Composite Identification Model The identification block diagram only defines a generalized 'workbench' that is needed for the identification process. Its function is similar to that of the " Composite Frame'' object. There is also the need to create a composite model, based on the block diagram, to identify particular parameters of particular objects. Suppose having a voltage controller model of which one wants to identify the parameters ka '' and ta . Measurements of the behavior of the physical appliance are available as measured voltage-curves on the input and output of the controller during a disturbance. Assuming the example identification block diagram of Figure 27.2, a composite model ( ElmComp ) has to be created in the active grid folder. Note If the identification process only addresses secondary power system element, which are not directly connected to busbars, the identification process does not require a power system grid. However, all calculation functions like load-flow or EMT simulation require a calculation target in the form of an activated grid of system stage folder. Therefore, a grid folder with at least one 'DUMMY' busbar has to be created when secondary element models are to be identified.

The composite model must be set to use the i dentification block. It will then show the slots that have been defined in that block. In the current example, the composite model dialogue will look like Figure 27.3.

Fig. 27.3: The example composite identification model

In this figure, the three slots have been assigned already. Visible is that the comparison object "Compare Signals'' is selected, as well as a measurement file and the voltage controller of which to find the best possible values for ka and ta . 27.2.1: The Comparison Object


27.2.1 The Comparison Object

The comparison object calculates the objective function from the connected measured and simulated responses. It allows for the use of weighting factors and for other powers to raise to. The example in Figure 27.4 shows the default settings.

Fig. 27.4: The comparison object dialogue

In this figure, the 10 difference signals are listed, with their weighting factor. By default, these are one, but they may be edited freely. The power factor equals 2 by default but may be set to any other positive whole number from 2 to 10. The objective function calculated by the comparison object equals


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where



is the measured response (i.e. "in1mea'')



the simulated response (i.e. "in1sim'')

 

is the weighting factor (i.e. for the difference signal nr.1) p is the power


27.3 Performing a Parameter Identification The identification process is executed by the ComIdent command. This command can be opened by the "Stability'' toolbar which is be accessed by selecting the icon

icon on the main menu. This icon can be found on the

.

The Comident dialogue is depicted in Figurefigure 27.5.

Fig. 27.5: The ComIdent dialogue

This dialogue shows references to the following objects: Composite Model This reference is normally not needed. When left open, the identification process will automatically gather all composite identification models and will minimize all objective functions.When the composite model reference is set, then the identification will only minimize that model's objective function. Load-Flow Settings This reference is automatically set to the load-flow command that will be used during the identification process. Initial Conditions This reference is automatically set to the initial conditions command that will be used during the identification process. Simulation This reference is automatically set to the simulation command that will be used during the identification process.

The identification process allows for the use of load-flow calculations and/or dynamic simulations. The "Load-Flow'' and "Simulation'' pages shows the variables that are to be identified, in case of a load-flow or a dynamic identification. See for example Figure 27.6.

Fig. 27.6: Setting identification parameters

In this example, two parameters of the voltage controller element "vco IEEEX1'' from the Composite Identification Model are listed. The identification process will alter these parameters in order to minimize the objective functions. The "Mode'' field in the parameter list determines the parameter constraints: 0 means not to change the parameter, but to l eave it at its initial conditions. This option may be used to temporarily exclude some parameters from the identification process. 1 mean to optimize the parameter without restrictions 2 means to optimize the parameter, given the constraint that the parameter value must always be greater than zero.

Although the object for which the parameters are optimized in this example is the same object as is used in the Composite Identification Model, it is allowed to enter any other parameter from any other element, as long as that element belongs to the active study case. Such may be used to optimize secondary appliance, where only the behavior of the primary appliance has been measured.


27.4 Identifying Primary Appliances A primary appliance, such as a general load, an asynchronous machine or a static var system, do not have an input signal like a voltage controller or any other secondary appliance. It would therefore not be possible to connect a measured signal directly to a load model in order to simulate its response. To identify a primary element model, a small grid model is used to which one or more controllable voltage sources may be connected. These voltage sources will translate the measured voltage signals from the measurement file into a normal busbar voltage which will be used in the load-flow or simulation calculations. The response of the primary


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element models connected to that busbar may then be compared to a measured response. An example of this method is shown in the following figures.

Fig. 27.7: Identification diagram with primary element

In Figure 27.7, a simple Identification Block Diagram is shown in which the measurement file is no longer connected to the element slot, but to the voltage source slot. The voltage at the busbar at which the voltage source will be connected will thus be forced to the measured values during the identification process.

Fig. 27.8: Primary element and voltage source

In Figure 27.8, a very simple grid is shown to which the load which is to be identified and a voltage source element are connected. As with the normal identification process, a Common Identification Model has to be created which uses the Identification Diagram with Primary Element as shown in Figure 27.7. In the ComIdent command dialogue, the unknown parameters of the load may then be listed. It is of course possible t o mix the identification of both primary and secondary power system elements at the same time.


Chapter 28 Contingency Analysis In general, contingency analysis is performed to ascertain the risks that contingencies pose to an electrical power system. PowerFactory 's contingency analysis module offers two distinct contingency analysis methods: Single Time Phase Contingency Analysis: The non-probabilistic (deterministic) assessment of failure effects under given contingencies, within a single time period. Multiple Time Phase Contingency Analysis: The non-probabilistic (deterministic) assessment of failure effects under given contingencies, performed over different time periods, each of which defines a time elapsed after the contingency occured. It allows the definition of us er defined post-fault actions.

Contingency analyses can be used to determine power transfer margins or for detecting the risk inherent in changed loading conditions. This chapter deals with deterministic contingency analysis. 28.1: Single Time Phase Contingency Analysis 28.2: The Single Time Phase Contingency Analysis Command 28.3: Multiple Time Phase Contingency Analysis 28.4: The Multiple Time Phase Contingency Analysis Command 28.5: Creating Contingency Cases Using Fault Cases and Groups 28.6: Creating Contingency Cases Using the Contingency Definition Command


28.1 Single Time Phase Contingency Analysis The single time phase contingency analysis function performs l oad flow calculations for user-defined sets of contingency cases, which take one or more primary components out of service. The command calculates the initial consequences of the contingencies, but does not regard the operational measures taken to mitigate v oltage band problems or supply interruptions. To access the various contingency analysis related functions within PowerFactory , click on the icon To initiate the contingency analysis command, click on the

on the "Select Toolbar" (shown in Figure 28.1).

icon, which should now be visible in the first row of icons at the top right of the screen.

Fig. 28.1: Contingency Analysis Selection from the Main Toolbar

The single time phase contingency analysis is carried out using the Contingency Analysis command (ComSimoutage , ). When executed, it automatically performs a 'base' load flow calculation to determine the operational point of the network under no-fault conditions. The command contains Contingency Cases (ComOutage objects) which define one or more elements that are taken out of service simultaneously. Following the calculation of the base load flow, for each of these contingencies a contingency load flow is calculated. This calculation considers the post-fault thermal ratings of branch elements (see Section 7.5.7), transformer tap changer controller time constants and automatic shunt compensators (for further information please refer to Section 28.2). In PowerFactory , contingency cases can be generated by two primary means: 

Via the definition and use of Fault Cases and Fault Groups ; and/or




Using the Contingency Definition (ComNmink ) command, either via its toolbar icon ( Calculate --> Contingency Analysis... .

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) or by selecting component(s) in the single-line graphic, right-clicking and selecting

In the first case, contingency cases can be created using references to user defined Fault Cases and Fault Groups (introduced in Section 7.5.3) from the . By means of a topological search, PowerFactory determines which circuit breakers must be operated in order to clear the faults, and generates Operational Library the corresponding contingency cases. Each contingency case is generated with its corresponding interrupted components for each fault case/group. Fault cases and groups reside in the Operational Library folder, and can be reused. Hence there is no need to manually redefine the same contingencies each time a contingency analysis is required. For further information on creating contingencies from fault cases/groups, please refer to Section 28.5. In the second case, contingencies can be created using the Contingency Definition command. This command is available either via the icon on the main toolbar, or by right-clicking on a selection of elements in the single line diagram, and selecting the option Calculate --> Contingency Analysis.... Either an n-1 or an n-2 outage simulation for the selected elements can then be prepared. The Contingency Definition command optionally allows all lines/cables, transformers and/or generators to be selected to create contingencies. For further information on creating contingencies using the Contingency Definition command, please refer to Section 28.6. The raw results of the single time phase contingency analysis correspond to the steady-state operational points of the network being studied, considering each one of the defined contingencies up to the given Post Contingency Time (see Section The Single Time Phase Contingency Analysis Command for further information on this setting). The reporting facilities available in PowerFactory 's contingency analysis function allow the filtering of results of interest to the user; i.e. maximum loading of branch elements, exceeded voltage limits, etc. Refer to Section The Single Time Phase Contingency Analysis Command for further information on configuring the reporting settings; and see Section 13.9 Results Objects for information on using results (ElmRes) objects in PowerFactory . The following sections provide detailled information regarding the settings and features of the contingency analysis command in its single time phase configuration.


28.2 The Single Time Phase Contingency Analysis Command PowerFactory 's contingency analysis command (ComSimoutage

) can be configured to perform single time phase contingency analysis, as displayed in Figure 28.2. In this configuration, it determines the initial operational point of the network by means of a 'base' load flow calculation; then for each of the stored contingency cases, places the interrupted components (see Section 28.2.4) on outage and performs a contingency load flow. The contingency load flow is characterized by the Post Contingency Time parameter (available in the Basic Options tab of the Contingency Analysis command, if either a Contingency Load Flow has been defined, or when the option Consider Specific Time Phase has been selected). This parameter determines the duration of the interval between the occurrence of the fault(s) which define the contingency, and the time when the load flow calculation of the network under the contingency situation is performed. The Post Contingency Time is a key parameter of the single time phase contingency analysis because: 1.

The actions of transformer automatic tap changers and switchable shunt compensators on the faulted network are only regarded if the time constants of their controllers are less than the defined Post Contingency Time (i.e. if the controllers are fast enough to operate during the time phase); and

2.

The operational thermal ratings of branch elements during the contingency (if 'short term' thermal ratings (see Section 7.5.7) have been defined) will depend on the duration of the contingency, i.e. the Post Contingency Time .

Note: The 'base' and the 'contingency' load flow calculations by default use the same load flow command (ComLdf object). However, the user can define different load flow commands for these two calculations by selecting the option `Allow different settings' on the Advanced tab of the contingency analysis command ( ComSimoutage ). The actions of automatic tap changers and switchable shunts are only possible if the corresponding options are selected in the 'Basic Options' tab of the load flow command(s).

The contingency analysis uses a result file object ( ElmRes , see Section 13.9: Results Objects) to store the voltages at terminals, and the loading of certain branch element classes (lines, transformers, series capacitances and series reactances). Recording the loadings for all branches and the voltages for all terminals for every contingency may lead to excessive data storage. Therefore, in order to reduce the amount of data recorded, only significant results are recorded. For contingency analysis, a calculated parameter is considered to be significant if the constraints (voltage and thermal limits) of the corresponding component are violated. Constraints can be set individually for each terminal and branch element (in the Load Flow tab of the element's dialogue) or globally in the Limits for Recording field of the contingency analysis command. A calculated result is stored in the result file whenever one of the constraints (individual or global) is violated.

Fig. 28.2: Basic Options for the Contingency Analysis ( ComSimoutage) Command

The settings of the contingency analysis command are entered using the dialogue shown in Figure 28.2. The following subsections explain each of the available options. 28.2.1: Basic Options 28.2.2: Effectiveness 28.2.3: Advanced Options 28.2.4: Representing Contingency Situations - Contingency Cases


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28.2.1 Basic Options Calculation Method AC Loadflow Calculation The contingency analysis uses an iterative AC load flow calculation to calculate the power flow per contingency case. DC Loadflow Calculation The contingency analysis uses a li near DC load flow calculation to ca lculate the active power flow per contingency case. Calculation Settings Load Flow

Only available when option Use same settings is selected in the Base Case versus Contingency Load Flow section of the Advanced Options tab.This is a reference to the load flow command used to calculate both the network operational point before the simulation of contingencies, and the contingency load flow(s). The settings of this load flow command can be edited by pressing the

button.

Base Case Load Flow Only available when option Allow different settings is selected in the Base Case versus Contingency Load Flow section of the Advanced Options tab. This is a reference to the load flow command used to calculate the network operational point before the simulation of contingencies. The settings of

this load flow command can be edited by pressing the

button.

Contingency Load Flow Only available when option Allow different settings is selected in the Base Case versus Contingency Load Flow section of the Advanced Options tab. This is a reference to the load flow command used to assess the network under contingency situations. It is characterized by the Post Contingency Time, which is defined in the Post Contingency Time field, also located in the Calculation Settings section of the dialogue. The contingency load flow command referred to by the Contingency Load Flow is always stored inside the contingency analysis command itself. The settings of this load flow command

can be edited by pressing the command by pressing the

button. The Contingency Load Flow command settings can be set those currently used by the Base Case Load Flow button.

Note: If no 'contingency' load flow command is defined, the 'base' load flow command is used to asses the network under contingency situations. In this case the action of automatic transformer tap changers and switchable shunt compensators is directly considered (provided that the corresponding options are selected in the 'Basic Options' tab of the assigned load flow command). Consider Specific Time Phase

Only available when option Use same settings is selected in the Base Case versus Contingency Load Flow section of the Advanced Options tab. This option must be enabled to define a post contingency time. Post Contingency Time (End of Time Phase)

This value defines the time phase under consideration for the update of contingencies. This means that all switch-open events with an event time less than or equal to this are considered in the update. The contingency load flow is calculated at the post contingency time. Limits for Recording The parameters in this section set the global constraints used to determine whether a calculated result is recorded in the Results object (i.e. the object pointed to by the Results field in the Basic Data tab of the dialogue). Whenever one of the defined constraints is violated, the calculated result (for the corresponding contingency case

and network component) is recorded. Different limits for Base Case If selected, a different set of limits can be defined for recording the 'base' load flow calculation results. Max. thermal loading of edge element Maximum thermal loading. Va lues exceeding this value will be recorded in the result file for t he corresponding component. Lower limit of allowed voltage Minimum admissible voltage. Voltages lower than this value will be recorded in the result file for the corresponding terminal. Upper limit of allowed voltage Maximum admissible vol tage. Voltages higher than this value will be recorded in the result file for the corresponding terminal. Maximum voltage step change Maximum (+/-) admissible voltage change. Larger voltage changes will be recorded in the result file for the corresponding terminal. Contingencies

The Contingencies section of the Basic Data tab, as shown in Figure 28.3, allows the display, creation and removal of contingencies. These are the contingencies that will be analyzed by the contingency analysis command.

Fig. 28.3: Contingencies Section of Contingency Analysis Dialogue Show

Displays a list of all defined contingencies. Add Cases/Groups

This button is used to create contingency cases ( ComOutage objects) based on fault cases and/or fault groups. A fault case contains events: one for the fault location, and (optionally) others specifying post-fault actions. Fault groups contain a set of references to fault cases. In order to use the Add Cases/Groups option, the fault cases and/or groups must have been previously defined in the Operational Library . If these have been defined, when the Add Cases/Groups button is pressed, a data browser listing the a vailable fault cases/groups pops up. The user can then select the desired fault cases/groups from this browser and press Ok. The corresponding contingencies are then created automatically by PowerFactory . One contingency is created for each selected fault case, and one contingency is created for each fault case referred to within each selected fault group. For further information on creating contingencies from fault cas es/groups, please refer to Section 28.5. Remove All

Removes all contingency cases (ComOutage objects) stored in the contingency analysis command. Results

Reference to the result file object (ElmRes ) where the contingency analysis results are recorded. The results stored in this file are filtered according to the global constraints set in the Limits for Recording section of the Basic Data tab, and also according to the individual constraints defined within each component's respective dialogue (i.e. on the Load Flow tab of the element dialogue). For further information on result objects, see Section 13.9: Results Objects. Additional Functionality

Besides the standard buttons found within a PowerFactory command ( Execute, Close and Cancel), the contingency analysis command provides an additional button: Update

Updates all contingency case objects ( ComOutage ). This occurs before any analysis is executed. The n-k level is detected. For contingencies based on fault cases/groups the list of interrupted components (see Section 28.2.4) is updated. If desired, an Update can be executed before every contingency analysis. Note that topological changes made to the network under study may lead to changes in the contingency cases, in which case it is recommended to execute an Update. Note: Changes made to the network topology or in the settings of the contingency analysis command and its load flow commands, often have an effect on the stored contingency cases. These effects are only visible if an Update is executed. Updates can be made automatically by selecting the option `Update contingencies


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28.2.2 Effectiveness Calculate Quad Booster Effectiveness Show QBs

Shows a list of the transformers for which the effectiveness should be calculated. Add QBs

Adds references to transformers for which the effectiveness should be calculated. Remove All

Removes all references to transformers for which the effectiveness is currently calculated. Calculate Generator Effectiveness Show Gen.

Shows a list of the generators for which the effectiveness should be calculated. Add Gen.

Adds references to transformers for which the effectiveness should be calculated. Remove All

Removes all references to generators for which the effectiveness is currently calculated.


28.2.3 Advanced Options Update contingencies before running a calculation Updates all contingency case objects ( ComOutage ) before any analysis is executed. The n-k level is detected. For contingencies based on fault cases/groups the list of interrupted components (see Section 28.2.4) is updated. Note that topological changes ma de to the network under study may lead to changes in the contingency cases, therefore it is recommended to always enable this option. For further information please refer to Section 28.5.

Base Case versus Contingency Load Flow Use same settings Uses the settings from the base case load flow for the contingency case load flow.

Allow different settings Allows different settings for the base case load flow and the contingency case load flow.

Output per Contingency Case Short

Displays only the number of iterations required for each contingency case. Detailed

Displays the full load flow output per contingency case. Initialisation of Contingencies If the AC Load Flow Calculation is selected in the Calculation Method section of the Basic Options tab, the user has the possibility to choose between the previous contingency case and the base case to initialize the current contingency load flow. Calculating an Individual Contingency

Click on the Show button in the contingency analysis command dialogue (see Figure 28.2 or 28.3) to open the list of contingencies included in the analysis. From here the user can right-click on a contingency of interest, and select Execute from the context sensitive menu. Additionally, the corresponding element can be marked in the single line graphic by right-clicking on the contingency object in the list and selecting Mark in Graphic from the context sensitive menu.


28.2.4 Representing Contingency Situations - Contingency Cases

Contingency cases (ComOutage objects) are objects used in PowerFactory to define contingency situations within the analyzed networks. A contingency case determines which components are put on outage. When a contingency analysis ( ComSimoutage ) is executed, the contingency analysis command considers each of the contingency cases stored inside it, taking the corresponding components out of service and performing a contingency load flow. As mentioned previously, the contingency cases used by a specific contingency analysis command are stored inside the command itself. Contingency cases are created either by using Fault Cases and/or Fault Groups (see Section 28.5), or via the Contingency Definition command ( , see Section 28.6). The contingency cases can be viewed using the Show button available in the dialogue of the corresponding contingency analysis command (see Figure 28.3). Additionally, the contingency cases within the active study case's contingency analysis command may be viewed by clicking on the Show Contingencies icon (

), located on the main toolbar (only available

when the Contingency Analysis toolbar is selected). In both cases a new data browser listing the defined contingencies is opened, with the contingencies listed inside. By double-clicking on a contingency from the list, the corresponding edit dialogue for that particular contingency is opened (as illustrated in Figure 28.4). The dialogue displayed in Figure 28.4 shows the following fields: Name

Name of the contingency case. Not Analyzed

If enabled, the case is not considered by the contingency anal ysis command. Number

An identification number which is stored in the results. The number can be used for reporting. Fault Case

Reference to the fault case (if any) from where the contingency case o riginated. Fault Group

Reference to the fault group (if any) from where the contingency case originated. This field is only avai lable if the contingency case has an as sociated fault group. Interrupted Components This is a table showing the components put on outage by the contingency case. The table, which is read-only, is automatically generated when the contingency case is created. Fault Type

Displays the fault type and the contingency order. See Figure 28.8. Contingency Analysis Reference to the contingency analysis command where the contingency case is stored.

The Mark in Graphic button highlights the interrupted components in the single line diagram.


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Fig. 28.4: Contingency Cases (ComOutage objects)

Normally, contingency cases ( ComOutage objects) are analyzed by the contingency analysis command ( ComSimoutage ) in which they are stored. However, each contingency case provides the functionality of a command itself, and can be executed individually using the Execute button at the top right of the ComOutage dialogue. In this case the actions taken by the circuit breakers, which must switch to clear the fault, are shown in the single line graphic (only if the contingency case was created using fault cases/groups). Note: The 'Interrupted Components' table is updated by the program each time the Update button from the single time phase contingency analysis command is pressed. Similarly if the option 'Update contingencies before running a calculation' is selected on the Advanced Options page, the tables of all the stored contingency cases are automatically updated before executing the contingency analysis.

For further information about contingency cases generated using fault cases and/or fault groups, please refer to Section Creating Contingency Cases Using Fault Cases and Groups. For information about contingency cases created using the Contingency Definition (ComNmink ) command, please refer to Section Creating Contingency Cases Using the Contingency Definition Command.


28.3 Multiple Time Phase Contingency Analysis PowerFactory provides tools for the analysis of contingencies over multiple time phases, allowing the definition of post-fault actions that can lead to the mitigation of voltage band problems or supply interruptions which are caused by faults in the networks under analysis. Before presenting the multiple time phase contingency analysis itself, it is necessary to introduce two basic concepts used to define the functionality of this tool: 



Contingencies: These are objects of the class ComOutage ( ) which are used to represent contingencies. They are defined by a set of events which represent the occurrence of the originating fault(s) over time and the subsequent fault clearing and post fault actions. It should be noted that in PowerFactory there generally exists one ComOutage object which covers all time phases. This means that the calculation of a contingency considers all time phases defined in the contingency analy sis command. All events which fall within the specific time phase are executed. For further information about the definition and use of contingencies please refer to Section 28.4.5. Time Phases: These represent points in time at which the steady-state operational point of the network under analysis is calculated. Ea ch time phase is defined via a user defined Post Contingency Time (see the Basic Options tab of the Contingency Analysis command). The Post Contingency Time defines the end of a phase, i.e. the point in time at which the steady-state of the network is calculated. For further information regarding the definition of time phases please refer to Section 28.4.4.

The contingency analysis with multiple time phases is executed via the Contingency Analysis command (ComSimoutage , ). Upon execution, it performs a prefault (base) load flow calculation, then for each contingency (stored inside the command), it loops over the list of defined time phases (also stored inside the command), calculating the corresponding post-contingency load flows. For each load flow calculation, the events (faults and post-fault actions) whose time of occurrence is earlier than, or equal to, the corresponding Post Contingency Time, are considered. Similar to single phase contingency analyses, the effect of transformer tap changers and switchable shunts depends on these components' corresponding time constants and the current Post Contingency Time. Controllers are only considered if their time constants are smaller than the current Post Contingency Time. Additionally, the operational thermal ratings of branch elements during the contingency (if 'short term' thermal ratings ( 7.5.7) have been defined) will depend on the duration of the contingency i.e. the current Post Contingency Time. The raw results of the contingency analysis with multiple time phases correspond to the steady-state operational point of the network being analysed, at every Post Contingency Time for each of the defined contingencies. The reporting features included in the function allows the filtering of problematic contingencies, according to maximal loading of branch elements, exceeded voltage limits, etc. The following sections provide detailled information regarding the settings and features of the contingency analysis command in its multiple time phase configuration.


28.4 The Multiple Time Phase Contingency Analysis Command The Contingency Analysis command (ComSimoutage ) can be used to perform contingency analysis with multiple time phases. In this configuration it determines the initial operational condition of the system via a 'base' load flow calculation. Following this, it loops over the defined time phases for each stored contingency (ComContingency object). Load flow calculations are performed which consider the contingency events whose time of occurrence is earlier than, or equal to, the Post Contingency Time set in the corresponding load flow command.


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As a result of the execution of the Contingency Analysis command, the steady-state operational point of the network at the Post Contingency Time, for every contingency, is obtained. The calculated results are filtered according to user defined criteria and recorded in the Results (ElmRes) object referred to by the Contingency Analysis command. When configured to perform contingency analysis with multiple time phases, the Contingency Analysis command stores the contingencies to be analyzed within the command itself. A folder (named Time Phases) is also stored wi thin the command; this folder contains the load flow commands that define the time phases. The user may define as many contingencies and time phases as required, following the procedures explained in this section. The Contingency Analysis command can be accessed via the main toolbar by clicking on the already been selected). The following subsections present the options available in the dialogue.

icon (provided that the Contingency Analysis toolbar

has

28.4.1: Basic Options 28.4.2: Effectiveness 28.4.3: Advanced Options 28.4.4: Defining Time Phases for Contingency Analyses 28.4.5: Representing Contingency Situations with Post-Fault Actions



Fig. 28.5: Basic Options Tab of the Contingency Analysis (ComSimoutage) Command Calculation Method

This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.1. Calculation Settings Load Flow

This is the reference to the load flow command which is used to calculate the network operational point, both prior to the simulation of contingencies and for the contingencies. The settings of this load flow command can be accessed and edited by pressing the button. If the option Allow different settings has been selected on the Advanced Options tab, the Calculation Settings section will be configured as shown in Figure 28.7. Base Case Load Flow

This is the reference to the load flow command which is used to calculate the network operational point prior to the simulation of contingencies. The settings of this load flow command can be accessed and edited by pressing the

button.

Time Phase n

Lists the defined time phase(s). The button

next to each time phase can be used to remove the corresponding time phase. If the option Allow different settings

has been selected on the Advanced Options tab, the Time Phase will have its load flow accessible by pressing the

button next to the defined time phase.

Add Time Phase

Opens an input dialogue to define the new time phase by entering its Post Contingency Time . If the option Allow different settings has been selected on the Advanced Options tab, the previous (i.e. that with the next earlier occurrence in time) loa d flow settings will be used for the new time phase. In the case that there is no previous time phase load f low the base case settings will be used for the new time phase. Use Base Case Settings for All

Copies the settings from the base case load flow to all time phase load flows. Limits for Recording

This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.1. Contingencies

This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.1. Results

This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.1.


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28.4.2 Effectiveness

These options are only available for the Single T ime Phase calculation. Please refer to Section 28.2.2.


28.4.3 Advanced Options Post contingency time for order identification

The order of the contingencies stored inside the command is calculated according to the time defined in this field. Only the events (actions) taking place before this point in time are considered when calculating the contingency order. Note: In PowerFactory a region is defined as a set of topologically connected components. A region is interrupted if it is energized (topologically connected to a network reference bus) before a fault and de-energized afterwards. The order of a contingency corresponds to the number of interrupted regions at the time of its calculation (i.e. the 'Post contingency time for order identification').

Base Case versus Contingency Load Flow

This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.3. Output per Contingency Case This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.3. Initialisation of Contingencies This setting is configured as described for Single Time Phase operation. Please refer to Section 28.2.3.


28.4.4 Defining Time Phases for Contingency Analyses

The time phases of a contingency analysis are defined in the Calculation Settings section of the Basic Data tab of the Contingency Analysis command, by specifying a Post Contingency Time for each defined time phase. A specified Post Contingency Time defines the end of a time phase and is used to determine which events (actions) from the analyzed contingency are considered. If the time of occurrence of an event from a contingency occurs earlier than or equal to the Post Contingency Time, the event will be considered in the corresponding load flow calculation. Each defined time phase uses a corresponding load flow calculation, and by default, this is the same load flow calculation as that used for the base case load flow. In this case, the load flow used for the entire contingency analysis calculation is accessible via the Load Flow field ( ), as shown in Figure 28.6. If the option Allow different settings in the Base Case versus Contingency Load Flow section of the Advanced Options tab is selected, the user can define individual load flow commands for each time phase, as illustrated in Figure 28.7. Access to each load flow command and its settings is again via the

button.

Fig. 28.6: Same Settings for Base Case and Contingency Load Flows

Fig. 28.7: Different Settings for Base Case and Contingency Load Flows

Note: Transformer tap changer controllers and switchable shunts are only considered by a time phase if their time constants are smaller than the current Post Contingency Time. The operational thermal ratings of branch elements during a contingency (if 'short term' thermal ratings (see Section 7.5.7 ) have been defined) will also depend on the duration of the contingency (i.e. the current Post Contingency Time).

The Contingency Analysis time phases are stored within a folder inside the ComSimoutage command and can be accessed via the Data Manager. By clicking on the button next to each defined time phase in the Calculation Settings section of the Basic Data tab, the edit dialogue of the corresponding load flow command pops up. New time phases can be defined in the data browser by clicking on the Add Time Phase button. Existing time phases can be deleted using the that after several time phases have been defined, this list is then scrollable using the up/down arrow buttons (

icon. Note

) available in the dialogue.


28.4.5 Representing Contingency Situations with Post-Fault Actions

Contingency situations which include post-fault actions are represented in PowerFactory via objects called 'Contingencies' (ComOutage , defined by a set of events which represent:

). The contingencies are




 

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Faults on the selected components; The switching actions carried out to isolate the faulty components; The post contingency actions taken in order to mitigate the subsequent voltage band problems and/or supply interruptions.

Contingencies are created based on fault cases defined in the Operational Library . These fault cases define the location of the fault events, and may also define post contingency actions taken to isolate the fault and mitigate the effects of the outage of the component(s). Whenever a new contingency is created, a link from the object to the fault case is set. New contingencies are created in a Contingency Analysis command by clicking on the Add Cases/Groups button in ComContingency the Configuration section of the Basic Data tab (see 28.2). Besides the events which are transferred from the linked fault case during calculation of the contingency case, the user has the possibility to define additional post contingency actions in the contingency by manually creating new events. The contingencies calculated in a Contingency Analysis, are stored inside the command itself and can be accessed using the Show button (see Figure 28.5). Alternatively, the contingencies in the Contingency Analysis command contained in the active study case can be viewed by clicking on the Show Contingencies icon ( ) on the main toolbar. In both cases a new data browser listing the defined contingencies is shown. By double-clicking on a selected item from the list, the edit dialogue of the corresponding contingency (Figure 28.4) pops up. Normally, contingency cases are analyzed by the Contingency Analysis command in which they are stored. However, each case provides the functionality of a command and can be executed individually using the Execute button at the top right of the ComOutage dialogue (see Figure 28.4). In this case, all of the time phases are executed for the selected contingency considering its associated events. The results observed in the single line graphic correspond to those from the last ti me phase, including the final states of the network switches. The events that define a contingency can be displayed in a list format in a new data browser by pressing the Events button in the fault case ( IntEvt) dialogue (as shown in Figure 28.10). This data browser can be used to edit and/or delete the listed events. New events can be created using the New icon at the top of the o pened browser window. It should be noted that events created locally in the contingency object are only considered if the option Use locally defined events (User defined)is selected in the Events Used for this Contingency field. The Start Trace button ( , available on the main toolbar) can be used to follow the behavior of the system over time. When this button is pressed, a dialogue opens allowing the user to select a contingency. Following the selection of a contingency by the user and pressing OK, the contingency dialogue is closed and the base case load flow is executed. The execution of the first event(s) and all subsequent event(s) is initiated by pressing the Next Time Step button on the main toolbar. At each time step the load flow calculation results and the state of the network circuit breakers are displayed in the single line graphic. It should be noted that the Next Time Step evaluates events according to their time of occurrence, and not according to the time phases defined in the Contingency Analysis command. After the last time event (s) are executed, the Next Time Step button becomes inactive. The Stop Trace button ( each ComOutage dialogue can be used to initiate the Trace for that particular contingency.

) can be pressed to clear the calculation. Alternatively, the Trace button in

Note: The 'Trace' functionality can be started directly from the main toolbar by pressing the 'Start Trace' button ( ). In this case a data browser listing all available contingencies (those stored inside the 'Contingency Analysis' command of the active study case) is displayed. After the user selects the desired contingency by double-clicking on it, the 'Base Case' load flow is executed. The subsequent event(s) are then calculated using the 'Next Time Step' button.


28.5 Creating Contingency Cases Using Fault Cases and Groups Contingency cases created from fault cases can be regarded as contingency situations produced in a network as a consequence of the clearing of a fault. Fault cases without switching events (created following the procedure described in Section 15.3: Fault Cases and Fault Groups) are used to automatically generate contingency cases in the contingency analysis command, by pressing the Add Cases button and selecting the desired objects from the data browser that pops up. For every selected fault case, the calculation automatically detects which circuit breakers must open in order to clear the defined fault(s). All components which, after the switching actions that clear the fault(s), lose their connection to the network reference bus, are regarded as 'interrupted' and are subsequently added to the Interrupted Components table of the corresponding contingency case. In other words, these components are put on outage by the contingency case. Depending on the fault defined in the fault case that generates a contingency, the field Fault Type (Figure 28.8) in the contingency case dialogue is regarded as:  

Busbar fault: If the contingency originates from a fault on a busbar n-k fault: With contingency order equal to k (k >= 0). k corresponds to the number of network regions (sets of topologically connected components) which are disconnected during a fault, by the switching actions performed. It should be noted that the switching actions which are considered depend on the post contingency time used by the update (this time differs between single- and multiple time phase analyses).

Fig. 28.8: Fault Type field in the Contingency Case (ComOutage ) dialogue

Note: In PowerFactory an interrupted component is a network primary element that is energized before a fault and de-energized afterwards. A component is considered to be energized if it is topologically connected to a network reference bus. A region is defined as a set of topologically connected components. Like components, regions can have energized, de-energized and interrupted states, depending on their connection to a network reference bus.

Contingency cases can be created from fault cases/groups, which reside in the Operational Library , by pressing the Add Cases/Groups button in the contingency analysis command (see Section 28.2.1 and Figure 28.3). In the case of creating contingencies from fault group(s), a contingency case will be generated for each fault case referred to in the selected fault group(s). Note: The 'topological search' algorithm used by the program to set contingency cases from fault cases requires the explicit definition of at least one reference bus in the analyzed system. A bus is explicitly set as reference if a synchronous generator (ElmSym) or an external network (ElmExtnet) with the option 'Reference Machine' enabled (available in the element's 'Load Flow' tab) is connected to it. 28.5.1: Browsing Fault Cases and Fault Groups 28.5.2: Defining a Fault Case 28.5.3: Defining a Fault Group


28.5.1 Browsing Fault Cases and Fault Groups

There are two types of subfolder inside the Faults folder in the Operational Library : Fault Cases and Fault Groups.


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Fig. 28.9: Contents of the Faults folder in the Operational Library

In order to make a new folder of either of these types, left-click on the Faults folder icon ( ) and then press the "New Object" button ( Manager. In the drop-down list, select whether a new Fault Cases or Fault Groups folder should be created.

) on the toolbar of the Data

The Fault Cases folder holds every contingency (n-1, n-2, or simultaneous) defined for the system, as described in Section Defining a Fault Case. Alternatively, several fault cases can be selected and stored in a Fault Group, as described in Section Defining a Fault Group.


28.5.2 Defining a Fault Case

To define a fault case for an element in the grid, select it on the single-line diagram. Then right-click and choose Define ... --> Fault Case --> Single Fault Case or Define ... --> Fault Case --> Multiple Fault Cases, n-1 (or Multiple Fault Cases, n-2). If Multiple Fault Cases, n-2 is selected, fault cases will be created for the simultaneous outage of each two elements in the selection. It is also possible to specify simultaneous outage of all elements in the selection. Several elements can be selected in the single-line diagram, in which case a fault case will be created for each of these elements in the Fault Cases folder. Alternatively, a filter can be used to list all elements which outages are to be defined for. Highlight these elements, right-click and choose Define ... --> Fault Case.... The Simulation Events/Fault dialogue opens, as displayed in Figure 28.10, where the user can enter the desired name of the fault case in the Name field; create switch events (on the second page

of the Basic Data tab, by clicking on the Create Switch Events button).

Fig. 28.10: Creation of Fault Case (IntEvt)

Fault cases can also be defined by the Contingency Definition command, as explained in Section 28.6. For further background on fault cases, please refer to Section 7.5.3 Faults .


28.5.3 Defining a Fault Group

To define a fault group, left-click on the Fault Groups folder. Then click on the 'New Object' button ( ). A Fault Group dialogue pops up as shown in Figure 28.11. In this dialogue the user can specify the name of the fault group in the Name field, and add fault cases to this new group using the Add Cases button. Click the Cases button to view existing cases (if any) in the fault group.

Fig. 28.11: Creation of Fault Group (IntFaultgrp )

Note: When a fault group is defined and fault cases are added to it, a reference is created to each selected fault case. The fault case itself resides in the Fault Cases subfolder. This means that if an item in the fault group is deleted, only the reference to the fault case is deleted. The fault case itself still exists in the Fault Cases folder.


28.6 Creating Contingency Cases Using the Contingency Definition Command The Contingency Definition command (ComNmink ) is used to generate contingency cases based on selected components. In this case the selected components are directly put on outage (and therefore listed in the Interrupted Components table in the contingency case dialogue) without any switching actions. The Contingency Definition command can be used to generate contingency cases either for (i) a user-defined selection of elements; and (ii) for pre-defined sets of elements. This is described below. To generate contingency cases for a new selection of elements:


 



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Select the components to be put on outage via either the single line graphic or the Data Manager. Right click on the selection and choose Calculate --> Contingency Analysis... This command will create a list with references to the selected objects inside the Contingency Definition command (ComNmink ). The command dialogue shown in Figure 28.12 will pop up. Set the options in the command according to the desired type of contingency cases (see explanation of options below) and click on Execute.

To generate contingency cases for either the complete system or a pre- user defined set:

 

Click on the icon on the main toolbar to open the command; Set the options in the command according to the desired type of contingency cases and the selection of elements (see explanation of options below) a nd click on Execute.

Fig. 28.12: Contingency Definition Dialogue (option: Generate Contingencies for Analysis )

Once the Contingency Definition command is executed, it generates the corresponding contingency cases according to the options selected and the listed objects. The contingency analysis command in the active study case (where the newly-created contingency cases are stored) is then automatically opened. The created contingencies can be analyzed by executing the already-opened contingency analysis command. Note that when a new list of contingencies is created using the Contingency Definition command, the previous content of the contingency analysis command is overwritten. It is also possible to open the Contingency Definition command directly from the Contingency Analysis toolbar ( on the

), without any previous selection, by clicking

icon. In this case, contingencies for all elements within the network (selected according to their class, as described below), can be created.

The Contingency Definition command offers the following options to generate contingency cases from the selected objects: Creation of Contingencies Generate Fault Cases for Library Generates fault cases which are stored in the Operational Library , in a folder named Faults. Generate Contingencies for Analysis Generates contingencies which are stored in the contingency analysis command, and then opens the contingency analysis command ( ComSimoutage) dialogue. Outage Level n-1

Creates single contingency cases for each of the selected components. n-2

Creates contingency cases for every unique combination of two selected components. Lines/cables

Contingency cases according to the selected outage level will be generated for all lines and cables ( ElmLne objects) in the system. Transformers

Contingency cases according to the selected outage level will be generated for all transformers ( ElmTr2 , ElmTr3 objects) in the system. Generators

Contingency cases according to the selected outage level will be generated for all synchronous generators ( ElmSym objects) in the system. The selection of elements to outage in the preparation command can also be created by the use of DPL scripts. Please refer to the Reference manual.

ComNmink methods in the DPL

Note: It is important to note the difference between contingency cases created from fault cases and contingency cases created with the Contingency Definition command. In the former, the cases are regarded as the outage of certain network components as a consequence of fault clearing switching actions, with the fault(s) being defined by the fault case and the switching actions automatically calculated by the program. In the latter, the cases are regarded as contingency situations generated by the outage of a selected group of components.


Chapter 29 Reliability Assessment In general, the assessment of reliability indices for a power system network, or of parts thereof, is the assessment of the ability of that network to provide the connected customers with electric energy of sufficient availability, as one aspect of power quality. The reliability assessment module of PowerFactory offers two distinct calculation functions for the analysis of network reliability under probabilistic scenarios, as described below: Network reliability assessment: The probabilistic assessment of interruptions during an operating period of the power system. Voltage sag assessment: The probabilistic assessment of the frequency and severity of voltage sags during an operation period.

Both of these calculation methods has its own typical applications. Network reliability assessment is used to calculate expected interruption frequencies and annual interruptions costs, or to compare alternative network designs. Voltage sag assessment is used to determine the expected number of equipment trips due to deep sags. This chapter deals with probabilistic Reliability Assessment. For information on PowerFactory 's deterministic Contingency Analysis, please refer to Chapter 28 Contingency Analysis . 29.1: Network Reliability Assessment 29.2: Voltage Sag Analysis


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29.3: Compact Reliability Glossary


29.1 Network Reliability Assessment Reliability analysis is an automation and probabilistic extension of contingency evaluation. The planner is not required to pre-define outage events, but can optionally select that all possible outages are considered for analysis. The relevance of each outage is considered using statistical data about the expected frequency and duration of outages according to component type. The effect of each outage is analyzed in an automated way, meaning that the software simulates the protection system and the network operator's actions to re-supply interrupted customers. As statistical data regarding the frequency of each event is available, the results can be formulated in probabilistic terms. An analytical assessment of the network reliability indices (transmission, sub-transmission or distribution level) is initiated by the following actions within PowerFactory :



Clicking the



Clicking on the

icon on the main toolbar to activate the reliability toolbar (if not already active); and icon.

The Reliability Assessment (ComRel3 ) dialogue will then appear, as shown in Figure 29.4. A reliability assessment will be started when the Execute button is pressed. The calculation time required for a reliability assessment can range from a few seconds for a small network only considering single-order contingencies, to several hours for a large network considering also second-order faults. A reliability assessment calculation can be interrupted by clicking on the Break icon (

) on the main toolbar.

The following sections provide the technical background information required to perform reliability assessment with PowerFactory . 29.1.1: Probabilistic Reliability Assessment - Technical Background 29.1.2: The Reliability Assessment Command 29.1.3: Calculated Results for Reliability Assessment 29.1.4: Failure Models for Reliability Assessment 29.1.5: Load Modeling for Reliability Assessment 29.1.6: System State Enumeration in Reliability Assessment 29.1.7: Failure Effect Analysis in Reliability Assessment


29.1.1 Probabilistic Reliability Assessment - Technical Background

The assessment of reliability indices, also known simply as "reliability analysis'', essentially comprises the following:  

 

 

Failure modeling Load modeling System state production Failure Effect Analysis (FEA) Statistical analysis Reporting

Fig. 29.1: Reliability Analysis: Basic Flow Diagram

The basic reliability analysis calculation flow diagram is depicted in Figure 29.1. The failure models describe the way in which the system components may fail, how often they will fail and how long it takes to repair them. The load models may consist of only a few possible load demands, or may be based on precise load forecast and growth scenarios. The combination of one or more simultaneous faults and a specific load condition is called a 'system state'. The system state production module will use the failure models and load models to build a list of relevant system states. Each of these system states may have one or more faults. It is the task of the FEA module to analyze the faulted system states by imitating the system reactions to these faults, given the current load demands. The FEA will normally take the power system through a number of operational states which may include:  

 

Fault clearance by tripping protection breakers; Fault separation by opening separating switches; Power restoration by closing normally open switches; Overload alleviation by load transfer and load shedding.

The basic task of the FEA functions is to find out whether system faults will lead to lo ad interruptions and if so, which loads will be interrupted and for how long. The results of the FEA are combined with the data that is provided by the system state production module to update the statistics. The system state data describes the expected frequency of occurrence of the system state and its expected duration. The duration of these system states should not be confused with the interruption duration. A system state with a single line on outage (i.e. due to a short-circuit on that line), will normally have a duration equal to the time needed to repair that line. In the case of a double feeder, however, no loads may suffer any interruption. In the case that loads are interrupted by the outage, the power may be restored by network reconfiguration (i.e. by fault separation and closing a back-stop switch). The interruption duration will then equal the restoration time, and not the repair duration (=system state duration). Stochastic Models

A stochastic model describes how and how often a certain object changes. A line, for example, may suffer an o utage due to a short-circuit. After this ki nd of outage, repair will begin and the line will be put into service again following successful repair. If two states for line A are defined (i.e. "in service'' and "in repair''), monitoring of the line could result in a graph as depicted in Figure 29.2.


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Fig. 29.2: Example of a Monitored Component State in Time

Line A in this example fails at time T after which it is repaired and put back into service at T . It fails again at T , is repaired again, etc. The repair durations R =T -T , 1 2 3 1 2 1 R =T -T , etc. are exaggerated in this example. 2 4 3 The repair durations are also called the "Time To Repair'' o r "TTR''. The service durations S =T , S =T -T , etc. are called the "life-time'', "Time To Failure'' or "TTF''. 1 1 2 3 2 Both the TTR and the TTF are stochastic quantities. By gathering failure data about a large group of similar components in the power system, statistical information about the TTR and TTF, such as the mean value and the standard deviation, can be calculated. The statistical information is then used to define a stochastic model. There are many ways in which to define a stochastic model. The so-called "homogenous Markov-model'' is a highly simplified but generally used model. A homogenous Markov model with two states is defined by: 



A constant failure rate lambda ('lambda'); and A constant repair rate mu ('mu').

These two parameters can be used to calculate the following quantities: 

 



mean time to failure, TTF = 1/lambda; mean time to repair, TTR = 1/mu; availability, P = TTF/(TTF+TTR); unavailability Q, = TTR/(TTF+TTR);

The availability gives the fraction of time during which the component is in service; the unavailability gives the fraction of time during which it is in repair; and P+Q = 1.0. For example, if 7500 monitored transformers were to sho w 140 failures over 1 0 years, during which a total of 7360 hours was spent on r epair, then:

These equations also introduce some of the units used in the reliability assessment: 

 



frequencies are normally expressed in [1/a] = "per annum'' = per year; lifetimes are normally expressed in [a] = "annum''; repair times are normally expressed in [h] = "hours"; probabilities or expectancies are expressed as a fraction or as time per year ([h/a], [min/a]).

Of course, it is also possible to define a homogenous Markov model with more than two states. This kind of model may be needed to distinguish between faults that can be repaired reasonably fast, and faults which require a longer time to repair. Two repair states are then needed, each with a different mean repair time. The homogenous Markov model is completely memory-less. This means that if preventive maintenance is performed to improve the reliability of a component, it does not make any change if the last maintenance has been performed one week or 5 years ago, or even if maintenance was performed at all. The probability for the component to fail in the next period of time will be equal in all cases. Effects of changing preventive maintenance can therefore not be calculated when using the homogenous Markov model. The same memory-less quality means that all repairs will behave in the same way, apart from their mean duration. Only mean durations can be determined when using homogenous Markov models. Interruption costs, however, may be dependent on the fraction of repairs that take longer than a certain amount of time. A certain repair may take 2 hours on average, for example, but when compensation has to be paid for interruptions longer than 3 hours, and when such long repairs occur in 20% of all cases, using the mean duration alone will not produce correct results. A realistic assessment of interruption costs is therefore not possible when using the homogenous Markov model. All reliability assessment functions in DIgSILENT PowerFactory are therefore based on the "Weibull-Markov'' model (WM-model). This more advanced stochastic model has the following features: 



 

It uses Weibull distributions for all s tochastic durations. This distribution uses a shape factor and a characteristic time. By setting the shape parameter "beta'' to 1.0, a homogenous Markov model results. The Weibull-Markov model is therefore 100% backwa rds-compatible with the homogenous Markov model, and existi ng 'homogenous Markov data' may be used directly wi thout any need for conversion. It allows addressing the effects of maintenance and a geing of equipment. It allows a fast and correct calculation of interruption costs in all cases.

A Weibull-Markov model with three states is depicted in Figure 29.3.


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Fig. 29.3: A Weibull-Markov model

This example shows all the parameters needed for defining a Weibull-Markov model. The parameters beta ('beta') and eta ('eta') are used to define the stochastic duration of each state, i.e. the stochastic TTF (State S 0) or TTR (State S 2). The "Transition Probabilities'' Prij define the probability of the state to change to another state. In the example of the 7500 monitored transformers, a Weibull-Markov model would result in

The shape factors beta and beta were left at their default values as no data is available for calculating them. The raw data, however, could be analyzed to get more 0 1 realistic values.


29.1.2 The Reliability Assessment Command

In PowerFactory the network reliability analysis is carried out using the Reliability Assessment command (ComRel3 toolbar when the 'Reliability Analysis' toolbar

). It can be accessed from the main

is selected. The configuration options available for the calculation are described in the following subsections.

Advanced OptionsBasic Options

Fig. 29.4: Reliability Assessment (ComRel3 ) Dialogue - Basic Options

The following options can be configured in the Reliability Assessment dialogue shown in Figure 29.4: Analysis Network, connectivity analysis This will start an analysis involving the entire network. A load is assumed to be supplied when it is connected to a source of power. The analysis considers disconnected loads only. A load is considered to be disconnected if it is supplied before a fault a nd is interrupted due to failure effects. Possible overloading of components is not regarded. Network, load flow analysis This will start an analysis during which load flow calculations are made to check for possible overloading. A load might be disconnected or partially shed due to load or voltage constraints. Generator re-dispatch, load transfer and load shedding are used to a lleviate overloads. Start Year Start of the period for consideration of load curves. Stop Year Final year of the period for consi deration of load curves.

Loads Consider Load Curves If this option is checked, characteristics assigned to the active and reactive power of loads will be considered during the analysis. If unchecked, the power demand entered in the dialog the load element (ElmLod ), disregarding any time-based characteristics. Define Load States When considering load curves, the reliability anal ysis is not able to st udy each time interval of the study period. A useful approach i s to aggregate the individual hours of the time to study to representative states, called `clusters'. The procedure used in PowerFactory is adaptive and selects the number of clusters according to the load and generation characteristics. Show Load States

Displays the load characteristics object which con tains the defined load states. Characteristic Load States Sets the time scale for the load state clusters. Possible options are Yearly (creates a load characteristic object for every single year) and Complete Time Range (creates a single load characteristic object for the complete time range). It is recommended to use Yearly only if load characteristics were defined over years. Complete Time Range is recommended when


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there is no load change/development over several years.

Automatic Contingency Definition Selection Commonly in reliability analysis, outages are studied in one specific part of the grid (e.g. at one voltage level), however the consequences of the outages should be analyzed for the entire grid. This option allows the user to define the scope of the outages studied, relative to the entire network. The options are Whole System (consideration of all elements for outages); Single Grid (selection of a single grid contained in the Network Data folder); or User Defined (uses a selection which contains references to the failin g elements). Busbars/Terminals Consideration of busbar/terminal outages. Lines/Cables Consideration of overhead line and cable outages. Transformers Consideration of transformer outages. Common Mode Consideration of Common Mode outages. These are groups of elements which are in topological or functional vicinity. Therefore all elements in this group may be affected by a single outage event. Common Mode outages are treated like single element failures. Independent second failures In addition to n-1 outages, n-2 outages for all combinations of n-1 outages are considered.

Double-earth faults Consideration of double-earth faults. The probability of double-earth faults can be defined on the Earth Fault tab of the Line Type Failures (StoTyplne) dialogue.

Independent/switching failures Consideration of situations where protection devices or circuit breakers refuse to open fo r fault clearance. The Probability of Failure (of refusal to open) can be defined on the Reliability tab of circuit-breaker elements ( ElmCoup , StaSwitch). Maintenance The reliability assessment function in PowerFactory considers not only forced outages, but also s cheduled outages. Scheduled outages are known in advance and are therefore considered separately to forced outages. Even if scheduled outages do not lead to service interruptions, they weaken the structure of the grid and therefore thorough reliability analyses should consider them. Loads disconnected due to scheduled maintenance are not treated as interrupted. Advanced OptionsBasic OptionsOutputs

Fig. 29.5: Output Tab of Reliability Assessment Dialogue

The following options are available on the Outputs tab (see Figure 29.5): Results

This options allows the selection of the result element ( ElmRes ) where the results of the reliability analysis will be stored. Normally PowerFactory will create a result object within the active study case. Perform Evaluation of Result File When a reliability analys is is started, all contingencies studied are written to a database file. Typically the databa se file is analyzed in a second step, where the contingencies can be filtered and the results analyzed in detail. The re-evaluation of the existing database content is carried out when this button is pressed. Output Displays the form used for the output report. Report settings can be inspected and the format selected by clicking on the

button.

FEA

A failure effect analysis (FEA) is made for each system state that occurs during the state enumeration. The configuration options are shown in Figure 29.6 and are explained next.

Fig. 29.6: Reliability Analysis dialogue - FEA options

Switch/Load Events Delete switch events

Removes all switch events associated with the contingencies stored inside the command.


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Delete load events

Removes all load events associated with the contingencies stored inside the command.

Fault Clearance Breakers Use all circuit breakers All switches in the system whose Usage is set to Circuit Breaker can be used for fault clearance.

Use only circuit breakers with protection device All circuit breakers in the system which are controlled by a protection device (fuse or relay) can be used for fault clearance.

Automatic Power Restoration If this option is not selected the FEA will stop after the protection trips and will not perform any remedial actions. All loads disconnected after fault clearance are treated as interrupted. This typically leads to an extreme worst-case analysis, particularly for distribution systems where re-supply by switching is a typical option.

Fault Separation Use all separation switches Normally, any components affected by faults will be isolated so that the remaining healthy part of the grid can be re-connected to the power supply. By selecting this option, the user allows all switches to be used for disconnecting a defective component.

Use only marked separation switches Normally, any components affected by faults will be isolated so that the remaining healthy part of the grid can be re-connected to the power supply. By selecting this option, the user allows only switches with the option Use for fault separation enabled to be used for disconnecting a defective component.

Time to open remote controlled switches The time (in minutes) taken to open remote controlled switches. Switch Actions When set to parallel, it is assumed that the switching actions can be performed immediately following the switching time. However, a switch can be closed for power restoration only after the faulted element was disconnected. When set to serial, it is assumed that all switching actions are performed serially.

Overloading

This option only appears when the Analysis option on the Basic Options page is set to Network, Load Flow Analysis. Load Flow Command Displays the load flow command used for reliability analysis. The load demand is calculated using this load flow. In addition, its settings are used for the overload alleviation calculation. Consider branch if loading exceeds If there are overloaded elements in the system, these overloadings should be removed through overload alleviation. Branches whose loading exceeds this limit, are considered by the overload alleviation algorithm.

Network

Transmission (Gen. Re-dispatch, Load-Transfer/-Shedding) Distribution (Switching Actions, Loading & Voltage Constraints) Advanced Options

Fig. 29.7: Reliability Analysis dialogue - Advanced Options Definition of Colours for the 'Isolated Grids' Colouring Mode The sequence of events during the FEA of a contingency can be visuali zed on the single line diagram. This o ption allows the definition of colors to be used for differentiating areas for resupply. State Enumeration Load States Accuracy Accuracy used for calculating load characteristics. A load is discretized with the accuracy entered here. An accuracy of 5% will divide each load into 20 discrete load steps starting from 0MW up to the maximum demand.

Limited number Used to limit the number of load states. If this option is enabled a maximum number of load states can be defined. In the case that the load characteristic's generation exceeds this number, an error message is displayed and the algorithm stops.

Ignore Load Correlation By default, the time correlation of the load curves is considered when creating the load characteristics. For radial networks this correlation can be ignored. Therefore, to reduce the number of different load states, enable this option.

Failures, correction of forced outage rate Usually the failure rate is determined using historical statistics of failures. A failure is registered only if the element was healthy before the failure occurred. Therefore, the failure rate should consider the probability of the element being healthy. To consider this, enable this option.



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29.1.3 Calculated Results for Reliability Assessment

The network reliability assessment produces two sets of indices: 



Load point indices System indices

Load point indices are calculated for each individual load point, and are used in the calculation of many system indices. This section provides the principle equations for the various reliability indices, however it should be noted that the actual reliability assessment calculations use somewhat more complex calculation methods. Nevertheless, the principle equations shown here can be used for hand calculations or for gaining a better understanding of the reliability assessment results. In the definitions for the various reliability indices, the following parameters are used: The number of customers supplied by load point i The number of affected customers for an interruption at load poi nt i The frequency of occurrence of contingency k The probability of occurrence of contingency k C The number of customers A The number of affected customers

The total connected kVA interrupted, for each interruption event, m Duration of each interruption event, m

The total connected kVA served Load Point Frequency and Expectancy Indices: ACIF: Average Customer Interruption Frequency ACIT: Average Customer Interruption Time LPIF: Load Point Interruption Frequency LPIT: Load Point Interruption Time

These indices are defined as follows:

, Unit: 1/a

, Unit: h/a , Unit: 1/a , Unit: h/a

where i is the load point index, k is the contingency index, and frac_i,k is the fraction of the load which i s lost at load point i , for contingency k. For unsupplied loads, or for loads that are shed completely, frac_i,k=1.0. For loads that are shed only partly, 0.0 <= frac_i,k < 1.0. For the Analyzed System: SAIFI System Average Interruption Frequency Index , in units of [1/C/a], is the mean interruption frequency found by dividing by the total number of customers in the

analyzed system. CAIFI Customer Average Interruption Frequency Index , in units of [1/A/a], is the mean interruption frequency found by dividing by the total amount of affected customers.

i.e. customers that will s uffer interruptions, in the analyzed system. ASIFI Average System Interruption Frequency Index , in units of [1/a], is the equivalent of SAIFI, but scaled by load. SAIDI System Average Interruption Duration Index , in units of [h/C/a], is the mean time per year that customers are interrupted, by dividing by the total number of customers

in the analyzed system. CAIDI Customer Average Interruption Duration Index , in units of [h], is the mean duration per interruption. ASIDI Average System Interruption Duration Index , in units of [h/a], is the equivalent of SAIDI but scaled by load. ASAI Average Service Availability Index, is the probability of having one ore more loads interrupted. ASUI Average Service Unavailability Index , is the probability of having all loads supplied.

, Unit: 1/C/a

, Unit: 1/A/a

, Unit: h/C/a

, Unit: h

, Unit h/a


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, Unit 1/a Load Point Energy Indices: LPENS Load Point Energy Not Supplied LPES Load Point Energy Shed

These indices are defined as follows:

in MWh/a

in MWh/a

in MWh/a Where Pd_i is the weighted average amount of power disconnected Pr_i is the weighted average amount of power at risk Ps_i is the weighted average amount of power shed at load point i. For the Analyzed System: ENS Energy Not Supplied , in units of [MWh/a], is the total amount of energy which is expected not to be delivered to the loads. SEAR System Energy At Risk , in units of [MWh/a], is the total amount of energy at risk for the system. SES System Energy Shed , in units of [MWh/a], is the tota l amount of energy which is expected to be shed in the sys tem. AENS Average Energy Not Supplied , in units of [MWh/C/a], is the average amount of energy not supplied, for all customers. ACCI Average Customer Curtailment Index , in units of [MWh/A/a], is the average amount of energy not supplied, for all affected customers.

in MWh/a

in MWh/a

in MWh/a

in MWh/C/a

in MWh/A/a Load Point Interruption Cost: LPEIC is defined as

in M$/a where LPEIC_i,k is the average interruption cost for load point i and contingency case k, considering the load point interruption costs function and the a ssessed distribution of the durations of the interruptions at this load point for contingency case k. The interruption costs are calculated differently for different cost functions. All costs functions express the costs as a function of the interruption duration. For cost functions expressed in money per interrupted customer, the number of interrupted customers is estimated for each i nterruption as the highest number of customers interrupted at any time during the whole interruption duration. For the analyzed system EIC Expected Interruption Cost , in units of [M$/y], is the total expected interruption cost. IEAR Interrupted Energy Assessment Rate , in units of [$/kWh], is the total expected interruption cost per not supplied kWh.

in M$/a

in $/kWh Additional Calculated Indices for Load Points : AID Average Interruption Duration [h] Additional Calculated Indices for Busbars/Terminals: AID Average Interruption Duration [h] LPIF Yearly Interruption Frequency [1/y] LPIT Yearly Interruption Time [h/y]


29.1.4 Failure Models for Reliability Assessment

Failure models are available for the following PowerFactory objects: 

 

Busbars and terminals Lines and cables Transformers

In addition to the line o r cable failure model, a common mode failure model is available. All failure models define how often a component will suffer an active failure. All active failures must be cleared by protection. When a failure cannot be separated from all generators or external networks by protection, a warning message will be issued. Repair of the faulted component is assumed to start directly after the fault has been cleared. The repair duration (which is also defined in the failure models) is the time needed to restore the functionality of the component. The time needed to begin the repair (i.e. if spare parts need to be ordered first) and all other delays are therefore to be included in the total repair time. Busbar and Terminal FailuresBusbar and Terminal Failures

The failure model for busbars and terminals is normally specified on the Reliability tab of a bar type ( TypBar ). This busbar type is then assigned to a busbar or terminal element ( ElmTerm ) via the Type in the Basic Data tab of the busbar or terminal element. The bar type model ( TypBar ) has a reference to a failure model (StoTypbar ), as shown in Figure 29.8.


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Fig. 29.8: Busbar Type Failures (StoTypbar )

The bar failure model defines a failure frequency for the busbar itself and an additional failure frequency for each connection to the busbar. The repair duration is independent of the number of connections. The total failure frequency for a triple busbar system with six feeders, for example, is calculated as: F_tot = 3 * F_bar + 6 * F _connection [1/a] which would total 0.24 per year for the failure model shown. The bar or terminal elements will show the total outage rate, outage expectancy and mean outage duration on their respective Reliability tabs. See Figure 29.9.

Fig. 29.9: Reliability Data for the Busbar/Terminal

The busbar or terminal element can be made to overrule its assigned Type model by selecting an Element model. The terminal element also provides fields for user defined voltage limits and switch access times. Line Failures

The line and cable failure model is normally specified on the Reliability tab of a line type ( TypLne). This is a reference to a li ne failure model ( StoTyplne) as shown in Figure 29.10.

Fig. 29.10: The Line Type Failure Model (StoTyplne)

Depending on the options selected, the line failure model uses a failure frequency or expectancy per unit length. The repair duration is independent of the length. Both the time to failure and the repair duration have a shape factor Beta. The Outage Expectancy equals the Mean repair duration multiplied by the Failure Frequency and is therefore also defined in units of per 100 km length. The frequency, outage expectancy and mean outage duration are displayed on the Reliability tab of the line/cable element, as depicted in Figure 29.11. The failure data


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can be defined in the line type data and used by different line elements.

Fig. 29.11: Reliability Data for Line/Cable

The line or cable element can be made to overrule its assigned Type model by selecting an Element model. The line element offers an additional user defined parameter on its Reliability tab: Load Shedding/Power Restoration Constraints Settings valid for emergency loading situations. Max. Loading This is the admissible lo ading during contingencies. Typically this value depends on the thermal i nertia of the element (cable or line) as this emergency loading wil l only occur for a l imited time. Reasonable values may be between 120% and 140%. If the loading of the element exceeds this limit the reliability analysis will start load-shedding. Transformer Failures

A single transformer failure model is available for both two- and three-winding transformers. The transformer failure model is normally specified on the Reliability tab of a transformer type ( TypTr2, TypTr3 ). This is a reference to a failure model as depicted in Figure 29.12.

Fig. 29.12: The Transformer Failure Model ( StoTyptrf )

Depending on the selected options, the transformer failure model has a Failure Frequency or Expectancy and a Repair duration distribution. Both the time to failure and the repair duration have a shape factor Beta. The Outage Expectancy equals the Mean repair duration multiplied by the Failure Frequency .

Fig. 29.13: Reliability Data for a Transformer

The frequency, outage expectancy and mean outage duration are displayed on the Reliability page of the transformer element, as depicted in Figure 29.13. The transformer element can be made to overrule its assigned Type model by selecting an Element model. All transformer failures are assumed to be active failures. Like the line element, the transformer element Reliability tab also offers an additional parameter to be defined. Load Shedding/Power Restoration Constraints Settings valid for emergency loading situations. Max. Loading Admissible loading during contingencies. For transformers, a value may be entered up to 140%. Maintenance


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Maintenance is included in the reliability assessment by defining one or more maintenance blocks. A maintenance block consists of: 



A list of objects to maintain; A maintenance schedule.

All objects in the list of objects will be taken simultaneously out of service for maintenance by this maintenance block. See Figure 29.14 for an example.

Fig. 29.14: Defining a Maintenance Block

The maintenance schedule is a list of deterministic moments in time at which the maintenance will start. For each planned maintenance activity, the duration must be given. See Figure 29.15 for an example.

Fig. 29.15: Defining a Maintenance Schedule Common Mode Failures

All component failure models are independent models. Two or more objects may share the same failure model, but their failure behavior will be independent. From the failure models, the outage expectancy can be calculated as the average fraction of time, or the average time per year, during which the component is not available. Two parallel lines on the same tower or two cables in the same trench will normally share the same failure data. The probability of both lines on outage at the same time will be the product of the individual outage probabilities, because the failures that lead to the outages are independent. The following example illustrates this.  

Suppose each line suffers an outage once every 5 years, for 10 hours. Their outage expectancy is therefore 2 h/y and their individual outage probability is 2.3CDOT 10^-4. The probability of the overlapping events which result in both li nes on outage is 5.2CDOT 10^-8, and the outage expectancy is thus only 1.6 SECONDS per year. The overlapping outage occurs on average once every 21900 y ears.

The double outage, however, may be much more frequent due to causes that effect both lines. Examples of such causes are dredging, lightning, storms, cars hitting poles, etc. The common mode object which is used to model such common mode causes is depicted in Figure 29.16 and Figure 29.17.

Fig. 29.16: Common Mode Failure: Basic Data


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Fig. 29.17: Common Mode Failure: Failure Data

The Basic Data page of the common mode model shows a list where all objects that are outaged by the common cause can be entered. The failure data is entered in the Failure Data page. The example shows a common cause which outages two lines once every 5 years on average, for an average of 52 hours. Common mode failure models can be defined for lines or cables and for line or cable routes. The common mode failures will not cancel the individual failure models, but w ill cause additional (simultaneous) outages of all listed components. Common mode failure models are created as: 

  

In the database manager, open the grid folder in which the elements for which a common mode failure is to be defined are located Create a new StoCommon object in this grid folder (click on the icon) Add two or more lines in the model and select the elements that will fail Enter the failure frequency etc., as described above.


29.1.5 Load Modeling for Reliability Assessment Stochastic Load Models

A power system may include independent stochastic loads, such as large industrial loads, pumping stations, etc. For most applications, however, the behavior of the loads can be modeled by historic characteristics. The settings for load characteristics can be entered in the Reliability tab of the load element ( ElmLod ) dialogue. In addition to the parameters displayed, load characteristics (e.g. 24h-load curve, annual load growth rate) can also be considered in the reliability evaluation. The Reliability tab of the load element is shown in Figure 29.18. The following section describes the options available.

Fig. 29.18: Stochastic Load Model Number of connected customers In addition to the load's active and reactive power, the number of connected customers also impacts on the ca lculation of some load point and system indices (e.g. SAIFI, SAIDI). The number of individual customers connected to this particular load element is specified here. Interruption costs

A characteristic of interruption cost (given in currency units per kW of installed power) can be referred to. This possibility is discussed in detail in the next section of this chapter. Time dependent rate A characteristic describing the interruption costs per (for example) kWh, over interruption time.

Scaling factor

This factor is used to scale the cost characteristic and adapt it to a specific customer's damage cost. Unit

The following units can be selected: $/kW, $/customer, or $. Load Shedding/Transfer Load Priority If load shedding is required, the Load Priority is used for discriminating between more important loads a nd less important loads. The priority v alue is proportional to the importance of the load; i.e. the higher the priority value, the more important the load. It should be noted that this value is only used as a guide within the reliability calculation; the algorithm will try to shed lower priority loads first, but may ultimately (or al ternatively) shed higher or highest priority loads depending on system conditions. Shedding Steps

Number of steps for load shedding. For example, a value of 4 steps means that the load can be shed in steps of 25%. An infinite number of steps means a load that can be shed exactly as required. Transferable

This percentage indicates the extent to which a load can be su pplied by an external source, i.e. by a connection to a neighboring network which is not shown in detail in the grid. Alternative Supply Node Node which delivers the transferred power. If this node is no t given, it is assumed that the transferred supply comes f rom outside the modeled grid. Interruption Cost Functions

Interruption cost functions are defined as one-dimensional vector characteristics ( ElmVec ) with time scales ( TriTime). An example is shown in Figures 29.19 and 29.20. The time scale is freely definable, but must be monotonically rising. More than one interruption cost function may be used at the same time for different loads, and each


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function may use a different time scale.

Fig. 29.19: Customer Damage Function - Time Intervals

Fig. 29.20: Customer Damage Function - Cost per Time Interval

Interruption costs functions are not interpolated in any way. The interruption costs used for a certain interruption duration will remain constant between durations. This means that an interruption functions such as:

means that:

Selecting an interruption cost function for a particular load is done by setting the Time dependent rate reference on the Reliability tab of the load element dialogue, as depicted in Figure 29.21. The type (parameter name: Unit) of the interruption cost function must be set in the load element. Three types of interruption cost functions can be used: $/kW Cost per interrupted power (kW), versus the interruption duration. $/customer Cost per interrupted customer, versus the interruption duration. $ Cost versus the interruption duration. The selected interruption cost function will be interpreted according to the selected Unit .


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Fig. 29.21: Load with Interruption Cost Load Shedding and Transfer

Load transfer and load shedding are performed for the express purpose of overload alleviation. If overloading is detected in the post-fault system condition, a search is begun for the loads contributing to these overloads. The overloads are then alleviated by either:  

Transferring some of these loads, if possible; or Shedding some of these loads, starting with the lowest priority loads.

Each load model uses three values to define the load transfer and load shedding possibilities: 





The number of load shedding steps (parameter name: Shedding steps ) defines the minimum amount of loa d that can be shed. Four shedding steps means that the loa d can only be shed to 25%, 50%, 75% or 100%. A value of zero shedding steps means that the load can be shed up to any amount. The Load priority is used to determine which loads to shed. The algorithm will always try to shed the loads with the lowest priority first. However, should system conditions require it, higher priority loads may be shed instead, o r they may be shed following the shedding of lower priority loads. The load transfer percentage (parameter name: Transferable) defines the amount of load that can be transferred away from the current network. The network that picks up the transferred load is not considered. A transfer percentage of 30% would mean that the load can be transferred away, by up to 30%. A percentage of zero means that no transfer is allowed.

A distinction should be made between load transfer for overload alleviation, and load transfer for power restoration. Load transfer by isolating a fault and closing a back-stop switch is already considered during the fault separation and power restoration phase of the failure effect analysis.


29.1.6 System State Enumeration in Reliability Assessment

The enumeration method analyses all relevant possible states of the system one by one. A fast "topological'' state enumeration method is used which ensures that each possible system state is only analyzed once. Realistic state frequencies (average occurrences per year) are calculated by considering only the transitions from a healthy situation to an unhealthy one and back again. This is important as the individual system states are analyzed one by one, and the (chronological) connection between them is therefore lost. The enumerated calculation method has the advantage that is fast enough for quick investigation of large distribution networks, but does not compromise accuracy. Exact analytic averages are calculated. Distributions of reliability indices, however, cannot be calculated. For example, the average annual unavailability in hours/year can be calculated, but the probability that this unavailability is less than 15 minutes for a certain year cannot be calculated. The state enumeration algorithm may include independent, overlapping failures as well as common mode failures and maintenance schedules. The use of the Weibull-Markov model means that annual interruption costs can also be assessed accurately. The principle flow diagram for the entire reliability assessment by state enumeration is depicted in Figure 29.22.

Fig. 29.22: Principle Flow Diagram for Reliability Assessment by State Enumeration

After the termination of the State Enumeration, the analyzed cases are available for verification. An example can is given in Figures 29.23 and 29.25.


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Fig. 29.23: Reliability Assessment - Contingency Cases

Fig. 29.24: Contingency Case (ComContingency ) Dialogue


29.1.7 Failure Effect Analysis in Reliability Assessment

Of central importance in the reliability assessment calculation is the analysis of the reaction of the system to specific contingencies. This analysis is performed by the failure effect analysis (FEA) function. The FEA function is a stand-alone function which can also be started separately. Basically, a FEA analysis consists of 4 steps:   



Fault clearance; Fault isolation; Power Restoration; Overload alleviation.

The failure effect analysis for the network assessment may be carried out with or without overload alleviation. Overload alleviation is performed by calculating an AC load flow, searching for overloaded branches and performing load transfer and load shedding. Disabling the overload alleviation for networks where overloads due to contingencies are not expected to occur may speed up calculations considerably. The failure effect analyses will be performed for each failure. For every failure a contingency is created. Should the calculation be using load characteristics, a contingency is created for every failure and load state. The general sequence of actions is illustrated in Figure 29.25. For each of the system states, one or more failures are present in the system. All failures are assumed to be active, i.e. they will cause an intervention by the protection system. The system is assumed to react to these short-circuits by immediately opening one or more protection switches (breaker B2), followed by manual or automated separation of the faulted equipment (disconnectors D2A, D2B) and the restoration of power to the remaining part of the protected area (restoration switch R12).


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Fig. 29.25: Fault Clearance and Power Restoration

Fault Clearance Fault Clearance

The fault clearance functions assume 100% selectivity of the protection. Therefore it is assumed that the relays nearest to the failure will open. In the case that protection/switching failures are considered in the FEA, it is assumed that the next protection device has a 100% selectivity. Failure of either the protection system or of circuit breakers is not considered in the present version of PowerFactory . In the pre-processing phase of the reliability assessment, all breakers in the system that can be tripped by an overcurrent or distance relay, fuse, or any other kind of relay, are marked as "protection breakers''. Figure 29.26 shows a simple network containing four loads, a breaker and a back-stop switch. The current system state to be analyzed for possible load interruptions is the one with a short-circuit on line "LR2''.

Fig. 29.26: Short-Circuit on Line

At fault clearance, a topological search is started at all faulted components. This search will find the smallest network area around each faulted component which is confined by protection breakers only. This smallest area will be isolated f rom the rest of the network if these protection breakers are opened. This set of protection breakers is further reduced by regarding only those breakers which would actually interrupt a fault current. Breakers further down a feeder past the fault position, i.e. breakers that would not see a fault current, will not be opened. The fault clearance phase is ended by opening the minimum set of protection breakers found earlier. If it is impossible to isolate the faulted component from all synchronous generators or external networks by protection breakers only, then an error message will be issued and the reliability assessment will terminate. The area around the faulted components which is isolated by the protection breakers is referred to as the "protected area''. Figure 29.27 shows the example network after the fault clearance functions have opened the protection breaker. The protected area is the whole bottom line feeder; and loads 1, 2, and 3 are interrupted.

Fig. 29.27: Protected Area Fault Isolation

If the option Automatic Power Restoration has been enabled in the FEA tab of the Reliability Assessment command dialogue, and one or more separation and one or more power restoration switches have been found, an attempt is made to minimize the effects of the faults by re-connecting as many loads as possible back to the healthy part of the system. After the protected area and the tripped breakers have been determined during the fault clearance phase, a search is started for the minimum separated area. The fault separation and power restoration both make use of the same topological search for switches as has been used to find the protection breakers during the fault clearance phase. The fault separation phase starts a topological search at the faulted components for the smallest area around these components which is confined by separating breakers. This smallest area will be isolated from the remaining network by opening these separating switches. Either all closed switches qualify as separators, or only those switches which have the option Use for fault separation selected in the switch elements' Reliability tab (when the option Only use marked separation switches was selected on the FEA tab of the reliability command dialogue). The result of the search for the separation switches is a set of separating switches which will, when opened, isolate the smallest possible area around the faulted elements from the rest of the network. This area is called the "separated area''. The separated area is smaller than, or equal to, the protected area. It will never extend beyond the protected area. The area between the protected and the separated area is called the "restorable area'' because, in principle, power may be restored to those areas. Figure 29.28 shows the example network with the opened separation switches. The separated area now only contains the faulted line. Two restorable areas result from the fault separation; the area which contains load 1, and the area which contains loads 2 and 3. Power to load 1 is restored by (re)closing the protection breaker. The left-most separation switch is remote-controlled and has a switching time of 3 minutes. The protection breaker is also remote controlled, and load 1 is therefore restored in 3 minutes (=0.05 hours). Load 2 and 3 are still to be restored.

Fig. 29.28: Fault Isolation and Power Restoration


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Power Restoration

If the option Use Power Restoration Switches has been enabled in the command dialogue, then a search will be started for the minimum number of restoration switches needed to restore as large a part of the protected area as possible. During this search, only the opened protection switches and the normally open switches that have the option Use for power restoration selected, are considered. The power restoration phase uses a topological search for all power restoration switches along the borders of the restorable areas. Each of these switches that are connected to an area that is still supplied are marked as possible candidates for power restoration. For each restorable area, only the fastest candidate switch is closed. Each restorable area that is reconnected to the supplied network is called a "restored'' area. Figure 29.29 shows the example network in which power to load 1 is restored by (re)closing the protection breaker. Power to load 2 and 3 is restored by closing the back-stop switch. Because the back-stop switch has a switching time of 30 minutes, loads 2 and 3 are restored in 0.5 hours. The network is now in the post-fault condition.

Fig. 29.29: Power Restoration by Back-Stop Switch

All loads and busbars in a separated area are considered to be interrupted for the duration of the repair, which is normally in the order of hours. All loads and busbars in a restored area are considered to be interrupted for the time needed to open all separators and to close all power restoration switches. Each switch can have an individual actuation time defined. Effects of automation and remote control can thus be analyzed by lowering the actuation times for the remote controlled switches. In order to enhance the transparency of the network reliability assessment, the system response to user selected faults can be made visible in the single line diagram. The different areas and the protection, separation and restoration switches can be colored differently. This gives a quick insight into the possible impact of certain faults or fault combinations. Click on the Colour Representation icon (

) on the main toolbar to select the appropriate colouring mode.

Overload Alleviation and Power at Risk

Many reliability calculations in radial distribution systems may be carried out assuming that overloading of lines due to the outage of one or more components seldom occurs. In such cases, the overload verification may be disabled, thereby increasing the calculation speed. A connection algorithm is used to check if a certain busbar or load is still physically connected to a generator or external network. When this is the case, the load or busbar is considered to be supplied. In meshed structures, or in cases where overloading is important (i.e. when there is a risk that increasing loads would lead to overloading), an overload verification must be used. For all contingencies which are analyzed in the reliability assessment, an AC load flow is carried out for the post-fault system state. The post-fault system state is reached after the fault clearance, fault separation and power restoration processes have finished. Figure 29.30 shows a line overload in the post-fault condition in the example network: line "LnA'' i s loaded to 122%.

Fig. 29.30: Overloaded Post-Fault Condition Load Transfer

In many distribution systems, it is possible to transfer loads from one feeder to the other. If both feeders are being considered in reliability assessment, and when the normally-open switch between them is marked for power restoration, the transfer will be automatically performed in the power restoration phase. In some cases, however, the transfer switch and/or the alternative feeder are not included in the network model for which the reliability assessment is made. This may be the case when a (sub-)transmission network is analyzed, where the connected distribution networks are modeled as single lumped loads. In this scenario, transfer switches that connect two distribution networks will not be visible. Therefore, the possibility of transferring parts of the lumped load model to other feeders can be modeled by entering a transfer percentage at each lumped load. This transfer percentage defines the portion of the lumped load that can be t ransferred 'away' from the analyzed network, without specifying to which feeder(s) the portion is transferred. The use of the load transfer percentage (parameter name: Transferable on the load element's Reliability tab) is only valid when load transfer is not expected to result in an overloading of the feeders which pick up the transferred loads. Load transfer is used in the overload alleviation prior to the calculation of power at risk (see following section for further information). The power at risk is considered to be zero if all overloads in the post-fault condition can be alleviated by load transfers alone. Load Shedding

In the example network shown in Figure 29.31, loads 2, 3 and 4 all contribute to the line overload. As a result, some of these loads must be shed. There are three basic variations of shedding that can be used:   

Optimal load shedding Priority optimal load shedding Discrete optimal load shedding

Optimal load shedding presumes that all loads can be shed to any amount. The target is then to find a shedding variation in which as little load as possible is shed. In the example network it does not matter which load is shed, as a MW reduction of any load will result in equal reduction of the line overloading. In more complex (meshed) networks, with more than one overloaded branch, the reduction of one particular load may have a greater impact on the total overloading than the reduction of another load. The reliability assessment functions use linear sensitivity indices to first select those loads with any contribution to overloading. A linear optimization is then started to find the best shedding variation for alleviating all overloading, which will minimize the total amount of shed load. The resulting minimum amount of shed load is called the "Power at Risk'', because it equals the minimum amount of load that has to be shed in case of the initial network fault occurring. The power at risk is multiplied by the duration of the system state to get the "Energy at Risk''. The total energy at risk for all possible system states is reported after the reliability assessment has finished, and is referred to as the "System Energy At Risk'' (SEAR). Figure 29.32 shows the calculated energy at risk. Because the line was overloaded by 0.53 MW and the faulted line has an outage


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expectancy of 0.15 h/a, the energy at risk is 0.08 MWh/a.

Fig. 29.31: Energy at Risk

The priority load shedding is performed after the power at risk has been determined. The priority optimal load shedding considers the load priorities defined for each load. The overload alleviation functions use the load sensitivity indices to calculate the lowest possible shedding priority. This is done such that when all loads which have equal or lower priority would be shed, then all overloads would be alleviated. From this, it is clear that loads with higher priorities do not need to be shed to alleviate the overloading. The priority load shedding is performed by repeating the linear optimization for the lower priority loads only. Figure 29.32 shows that when load 4 is set to a higher priority, load 2 is shed instead.

Fig. 29.32: Priority Load Shedding

Discrete optimal load shedding is performed together with priority load shedding. Mixing discrete and priority load shedding does not require additional calculations. The discrete load shedding variation uses the fact that each load can only be shed over a fixed number of steps. The number of possible steps is entered in each load element (Reliability tab, parameter Shedding steps). The discrete shedding variation is calculated by transforming the linear optimization problem into a discrete optimization problem. Solving this linear optimization problem results in a higher or equal total shed power. Figure 29.33 shows the example network where all loads can only be shed completely. As the demand at load 3 is only 0.35 MW, and the overload is 0.53 MW, it cannot contribute to overload alleviation. Shedding load 2 therefore leads to the minimum amount of shed load.

Fig. 29.33: Discrete Load Shedding


29.2 Voltage Sag Analysis 29.2.1: Calculation Options 29.2.2: Performing a Voltage Sag Table Assessment


29.2.1 Calculation Options

Voltage sag analysis has a lot in common with probabilistic reliability analysis. Both use fault statistics to describe the frequency of faults and then use these statistics to weight the results of each event and to calculate the overall effects of failures. Reliability analysis looks for sustained interruptions as one aspect of quality of supply, whereas voltage sag analysis calculates the voltage drop during the fault until the protection system has disconnected the defective component.


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An assessment of voltage sag tables for a selection of load points can be started as follows: 

Select one or more busbars/terminals and/or loads in the single line diagram or the data manager, right-click the selection and select "Calculate... --> Voltage sag table..." ; or



Click on the

icon on the main toolbar to activate the Additional Tools toolbar (if not already visible), and then click the Voltage sag table assessment icon (

).

In both cases, the voltage sag table command dialogue will open, as shown in Figures 29.34 and 29.35.

Fig. 29.34: Voltage Sag Table Assessment - Basic Options

Basic Options Load selection Reference to the set of load points. A load po int can be defined by a busbar, terminal or l oad. Short-circuit command Displays the short-circuit command that is used. The options for the short-circuit type will be changed during the voltage sa g calculation, depending on the Advanced Options specified

in the ComVsag dialogue. However, other settings may be inspected or changed by clicking on the

button.

Results Reference to the result file that is used for storage of results. Exposed area limit This defines the minimum remaining voltage for the voltage sag calculation to continue calculating short-circuits at busbars which are further away from the selected load points. If shortcircuits at all busbars (at a certain distance away from all load points) result in voltages at the load points being higher than this limit, then no further short-circuit will be analyzed.

Advanced Options

The Advanced Options shows the various short-circuit ty pes that can be analyzed by the voltage sag assessment command. All components for which a failure model has been defined use the same short-circuit frequency. It is not possible to define frequencies of occurrence for single phase, two-phase or three-phase short-circuits independently for each component. The relative frequency for each type of short-circuit is entered for all components in a uniform way.

Fig. 29.35: Voltage Sag Table Assessment - Advanced Options

The voltage sag analysis simulates various faults at all relevant busbars. It starts with the selected load points, and proceeds to neighboring busbars until the remaining voltage at all load points does not drop below the defined Exposed area limit. The remaining voltages and the short-circuit impedances for all load points are written to the result file specified by the Results parameter. After all relevant busbars have been analyzed, the sag table assessment continues by analyzing short-circuits at the midpoint of all lines and cables that are connected between the relevant busbars. Again, the remaining voltages and short-circuit impedances for all load points are written to the result file. After the complete exposed area has been analyzed in this way, the result file contains the values for Z_F1, Z_F2, Z_F0, Z_S1, Z_S2, Z_S0 and ura, uia, urb, uib, urc, uic for the two ends of all relevant lines and cables and at their midpoints. The written impedances are interpolated between the ends of a line and the middle with a two-order polynomial. From them, and from the written remaining voltages, the various source impedances are estimated. These estimated impedances are also interpolated between the ends and the midpoint. The interpolated impedances are then used to estimate the remaining voltages between the ends and the midpoints of the li nes or cables. This quadratic interpolation gives very good results also for longer lines, and also for long parallel or even triple parallel lines. The main advantage is a substantial reduction in computation and an increase in the overall calculation speed.


29.2.2 Performing a Voltage Sag Table Assessment

A voltage sag table assessment is performed in two phases: 1.

A result file with remaining voltages and short-circuit impedances is created by executing the ComVsag command. This can be done by selecting one or more nodes, right-clicking

2.

and executing the Calculate... --> Voltage sag table... option, or by initiating the command directly from the main toolbar by clicking on the icon. A voltage sag plot is created by selecting one or more of the nodes for which the ComVsag command was executed, right-clicking and executing the option Show --> Voltage Sag Plot...

Alternatively, 



The Load selection in the ComVsag dialogue can be filled manually with a set of objects. A load point is defined by a terminal, a busbar, or by a single-connection element (a load, motor, generator, etc.). These kinds of elements can be multi-selected from the single-line diagram or data ma nager. Once selected, right-click on them and select Define... --> General Set from the context-sensitive menu. This set can then be selected as the Load selection . A voltage sag plot can be created on a virtual instrument page manually, and the load points can then be selected from the list of analyzed load points.


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If several objects are selected which are all connected to the same busbar, then that busbar will be added only once to the set of lo ad points. The Load selection parameter in the voltage sag assessment command should be set to use the SetSelect which has the Used for: Voltage sag table flag set. However, any other selection may be assigned to the Load selection. The voltage sag tables are not calculated until a voltage sag plot is constructed. Upon reading the remaining voltages, short-circuit frequencies and short-circuit impedances from the result file, a voltage sag table is constructed for each selected load point. Figure 29.36 shows the voltage sag plot dialogue.

Fig. 29.36: Voltage Sag Plot Dialogue

Because there is no single definition of a voltage sag, the plot offers a selection of sag definitions:   



Minimum of Line-Neutral Voltages Minimum of Line-Line Voltages Minimum of Line-Line and Line-Neutral Voltage Positive Sequence Voltage

Secondly, the x-variable against which the sag frequency will be shown has to be selected. Possible x-variables are: 

 



Remaining Voltage Nom. Voltage at Shc-Busbar Fault Clearing Time Short-Circuit Type

Additionally, the x-variable can be sub-divided according to a split-variable (parameter name: Split Bars in). Possible split variables are: 



no split any of the possible x-variables

the same parameter cannot be selected for the x-variable and the split-variable. An example of the resulting voltage sag plot, in accordance with the settings shown in Figure 29.36 is shown in Figure 29.37.

Fig. 29.37: Example Voltage Sag Plot

The voltage sag plot always shows the annual frequency of occurrence on the y-axis. The example plot shows a bar for each load point for each x-variable, which is the Remaining Voltage. All three loads can be seen to suffer either deep sags (remaining voltage less than 0.4 p.u.), or very shallow sags, although the values at 0.8 p.u. are also significant. Each bar is subdivided to the nominal voltage at SHC-Busbar. The shallow sags are caused by the low voltage network, as well as the very deep sags. The high voltage network seems to cause moderate voltage sags. This is caused by the fact that the low vo ltage networks in this example are radially operated and the higher voltage networks are meshed. More detailed information about a specific value in the voltage sag plot can be obtained by placing the mouse over a bar or part of a bar (without clicking) and allowing the balloon help to pop up. The voltage sag plot dialogue has a Report button, which outputs the voltage sag plot data to the output window. A table for each selected load point will be written in accordance to the selected Voltage Sag definition, x-Variable and Split Bars in selection. An example of a voltage sag table is shown below. The reported voltage sag tables also show the totals for each row and column. DIgSI/info - 'Grid\TA2.ElmTerm' col : Remaining Voltage (Volt.Sag) [p.u.] row : Nom. Voltage at Shc-Busbar (Unom Shc) [kV] val : Frequency of Shc (Sag Freq.) [1/a] ---------------------------------------------------------------------| 0.20 0.50 0.60 0.80 0.85 0.90 0.95 1.00 |


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-------|-------------------------------------------------------|-----10.0 | 1.56 0.94 0.00 0.00 0.00 0.00 2.25 6.75 | 11.50 50.0 | 1.45 1.52 0.00 0.83 0.09 0.12 1.08 5.57 | 10.66 150.0 | 3.50 2.32 1.67 0.00 0.00 0.00 0.00 0.00 | 7.50 380.0 | 0.00 1.25 0.00 1.25 0.00 0.00 0.00 0.00 | 2.50 -------|-------------------------------------------------------|-----| 6.52 6.04 1.67 2.08 0.09 0.12 3.33 12.32 | 32.16 ----------------------------------------------------------------------


29.3 Compact Reliability Glossary Lost load Shed load Stochastic Statistic Outage Forced Outage Scheduled Outage Maintenance Spare Unit Failure Hidden Failure Active Failure Passive Failure Repair Interruption Contingency Adequacy Security Availability Redundant Unit Base State (n-1) system (n-k) system Distribution Function Probability Density Function Hazard Rate Function Lost load

A system load that is disconnected from the supply as a direct result of one or more system failures by intervention of automatic protection devices. A system load cannot be partly lost. Shed load

A system load that is disconnected from the supply as a result of one or more system failures by intervention of a system operator. A system load may be shed up to a certain percentage. Stochastic

A quantity is said to be stochastic when its value is random and therefore unknown. The range of possible values is known, however, as is the respective likelihood of these values. The number of eyes thrown with a dice is random, the possible outcomes are {1,2,3,4,5,6} and the likelihood is frac16 for each outcome. For a continuous range of possible outcomes, the likelihood is a continuous function, which is called the Probability Density Function or "PDF''. Statistic

Statistical calculation methods are used to analyze stochastic quantities Stochastic. A simple example is the method for calculating a mean repair duration by dividing the total time spend repairing by the number of repairs performed. Information obtained using statistical methods on measured data can be used to build stochastic models of the observed equipment. Outage

The removal of a primary component from the system. Forced Outage

The unplanned removal of a primary component from the system due to one or more failures in the system. A failure does not have lead to lead to an outage, for instance the failure of a transformer tap changer. Scheduled Outage

The planned removal of a primary component from the system. Maintenance

The planned removal of one or more primary components from the system. Spare Unit

A reserve component, not connected to the system, which may be used as a replacement for a component on outage by switching or replacing. Failure

The event in which a component does not operate as intended or stops operating as intended. An example of the former is a circuit breaker that fails to trip; an example of the latter is a transformer that is tripped by its Buchholz relay. Hidden Failure

An undetected change in a component which will lead to the failure of the component the next time it is required to operate, unless it is inspected and repaired first. Active Failure

The failure of a component which activates the automatic protection system. Active failures are always associated with short-circuits. Passive Failure

The failure of a component which does not activate the automatic protection system. Repair

The restoration of the functionality of a component, either by replacing the component or by repairing it. Interruption

An unplanned zero-voltage situation at one or more load points due to outages in the system. Contingency


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The state of a system in which one or more primary components are on outage. The level of a contingency is determined by the number of primary components on outage. A "k-Level'' contingency is thus the state of a system in which exactly k primary components are on outage. Adequacy

The ability of the electrical power system to meet the load demand under various steady state system conditions. Security

The ability of the system to meet the load demand during and after a transient or dynamic disturbance of the system. Availability

The fraction of time a component is able to operate as intended, either expressed as a real fraction or in hours per year. Redundant Unit

A component whose o utage will never lead to an interruption in the base state which cannot be restored by normal switching actions (i.e normal network reconfiguration) alone. Base State

The state of the system where all components are able to operate as intended. (n-1) system

A system for which all relevant components are redundant unitsRedundant Unit. (n-k) system

A system for which the outage of any k or less components will never lead to an interruption which cannot be restored by normal switching actions (i.e normal network reconfiguration) alone. Distribution Function

The distribution function for the stochastic quantity X equals the cumulative density function CDF(x). CDF(x) = the probability of X to take a value smaller than x. Probability Density Function

The function PDF(x), describing the probability of the stochastic quantity to take a value from an interval around x, divided by the length of that interval. The PDF(x) is the derivative of the distribution functionDistribution Function. Hazard Rate Function

The function HRF(x) describes the probability of a stochastic quantity to be larger than x+dx, given the fact that it is larger than x, divided by dx. Therefore, the hazard rate may describe the probability of the failure of an element in the upcoming time period, given the fact that it is still functioning properly. The hazard rate is often used to describe equipment ageing and wear. A well-known example is the "bath-tub'' function which describes the probability of a device failing in the next period of time during wear-in, normal service time and wear-out.


Chapter 30 Optimal Power Flow PowerFactory 's Optimal Power Flow (OPF) module optimizes a certain objective function in a network whilst fulfilling equality constraints (the load flow equations) and

inequality constraints (i.e. generator reactive power limits). The user can choose between interior point and linear optimization methods. In the case of linear optimization, contingency constraints can also be enforced within OPF. An OPF calculation in PowerFactory can be initiated by one of the following means: 

By going to the main menu and selecting Calculation --> Optimal Power Flow... ; or



By clicking on the OPF icon

on the main toolbar.

In both cases, the calculation is started by pressing the Execute button in the OPF command dialogue. 30.1: AC Optimization (Interior Point Method) 30.2: DC Optimization (Linear Programming)


30.1 AC Optimization (Interior Point Method) If the AC Optimization method is selected, the OPF performs a non-linear optimization based on a state-of-the-art interior-point algorithm. The following sections explain the selection of objective function to be optimized, the selection of control variables, and the definition of inequality constraints. The OPF command in PowerFactory is accessible by going to the main menu and selecting Calculation --> Optimal Power Flow... , or via the OPF icon

on the main toolbar.

30.1.1: Basic Options 30.1.2: Initialization 30.1.3: Advanced Options 30.1.4: Iteration Control 30.1.5: Output



The Basic Options tab of the OPF dialogue (AC optimization method) is shown in Figure Basic Options Tab of OPF Dialogue (AC Optimization Method).


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Fig. 30.1: Basic Options Tab of OPF Dialogue (AC Optimization Method) Method To perform an AC optimization OPF study, the Method must be set to AC Optimization (Interior Point Method) as shown in Figure 30.1 . Objective FunctionObjective Function

The OPF command object ( ComOpf ) dialogue is shown in Figure 30.2. For AC optimization, a selection of three distinct objective functions is available, namely:   

Minimization of Losses Minimization of Costs Minimization of Load Shedding

Fig. 30.2: Objective Function Selection for OPF (AC Optimization Method) Minimization of Losses Minimization of Losses

When this objective function is selected, the goal of the optimization is to find a power dispatch which minimizes the overall active power loss. Minimization of Costs

When this objective function is selected, the goal o f the optimization is to supply the system under optimal operating cost. More specifically, the aim is to minimize the cost of power dispatch based on non-linear operating cost functions for each generator and on tariff systems for each external grid. For this purpose, the user needs to introduce, for each generator, a cost function for its power dispatch; and for each external grid, a tariff system. Cost Functions for Generators

Imposing an operating cost function on a generator element is done as follows: on the Optimization tab of each synchronous machine ( ElmSym ) element's dialogue (see Figure 30.3), it is possible to specify the operating costs of the unit with the aid of the Operating Costs table (which relates active power produced (in MW) to the corresponding cost (in $/h)). This data is then represented graphically beneath the Operating Costs table, for verification purposes (see Figure 30.3). The number of rows that can be entered in to the table is unlimited. To add or delete table rows, right-click on a row number in the table and select the appropriate command (i.e. Copy, Paste, Select All; Insert Rows, Append Rows, Append n Rows, Delete Rows, etc.). Tariff Systems for External Grids

An external grid contributes to the overall cost function by a predefined tariff system. On the Optimization tab of each external grid ( ElmXnet) element's dialogue (see Figure 30.4), the tariffs can be edited via the Incremental Costs table. This table relates the cost (in $/MWh) over a certain range of active power exchange. The input data is represented graphically beneath the Incremental Costs table. In addition, the user can enter a monthly no load cost (in $/month), which can be interpreted as a vertical shift of the cost function. This input parameter is called No load costs (monthly) and can be seen in Figure 30.4. In contrast to a synchronous machine, where the cost curve is directly expressed in $/h, the cost curve of an external grid is defined by means of a tariff which holds within certain intervals. Mathematically speaking, the cost curve of a synchronous machine is calculated as the interpolation of predefined cost points, whereas the cost curve of an external grid is a piecewise linear function with predefined slopes in each interval.


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Fig. 30.3: Editing the Operating Costs of a Synchronous Machine (ElmSym )

Fig. 30.4: Editing the I ncremental Costs of an External Net (ElmXnet)

Note that this piecewise linear function is not differentiable at the interval limits. Since non-differentiable functions might cause problems within the optimization routine, PowerFactory smooths the cost function slightly over a small range around the non-differentiable points. The width of this range can be defined by the user through the Smoothing Cost Function factor (also shown in Figure 30.4). A value of 0% corresponds to no smoothing of the curve, whereas a value of 100% corresponds to full interpolation. The default value is 5%. It is recommended to leave this value at its default setting. Minimization of Load Shedding

The goal of this objective function is to minimize the overall cost of load shedding, such that all constraints can be fulfilled. A typical application for this objective function is "Infeasibility Handling". For the above mentioned objective functions, it may occur that the constraints imposed on the network are such that no feasible solution exists. This can be seen by lack of convergence of the optimization. In such cases, it is highly likely that not all loads can be supplied due to constraint restrictions. Hence it is recommended in these situations to firstly perform a Minimization of Load Shedding . In this (and only this) optimization scenario, all load elements which have the option Allow load shedding enabled will act as controls. This option is enabled in the load (ElmLod ) element's dialogue on the Optimization tab in the Control section. All loads without this option enabled will behave as they would in a conventional load flow calculation. In order to minimize the overall load shedding, for each individual load, the user must specify the cost of shedding (in $ per shed MW). For each load that participates as a control in the optimization, the scaling factor will be optimized. The optimization is such that the overall cost of load shedding is minimized. Additionally, the user can specify the range over which the load may be scaled (options Min. load shedding and Max. load shedding ), as shown in Figure 30.5.

Fig. 30.5: Editing a Load Element ( ElmLod ) for Minimization of Load Shedding Controls

The global control parameters can be selected on the Basic Options tab of the OPF ( ComOpf ) dialogue (see Figure 30.6). The user can specify which parameters might serve as potential degrees of freedom for the OPF algorithm; i.e. which parameters will contribute as controls. The set of potential controls can be grouped into four categories:


1. 2.

Generator Active Power Dispatch (ElmSym ) Generator Reactive Power Dispatch (ElmSym )

3.

Transformer Tap Positions (for 2- and 3-winding transformers): 2-Winding Transformer ( ElmTr2):

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

Tap Position (continuous or discrete) 3-Winding Transformer ( ElmTr3 ): HV-Tap Position (continuous or discrete) LV-Tap Position (continuous or discrete) MV-Tap Position (continuous or discrete) 4. Switchable Shunts (ElmShnt):  



 



Number of steps (continuos or discrete)

It should be noted that the load scaling factors will only be taken into account for the Minimization of Load Shedding objective function. In this case, all loads which allow load shedding are automatically used as controls. These global controls determine which element controls will be considered in the optimization. The general rule is as follows: a parameter will be considered as a control if the corresponding flag is set on the Optimization page of the element's dialogue and if, in addition, the corresponding global parameter is set on the Basic Options tab of the OPF command dialogue (see Figure 30.6). For example, if the control parameter Tap Position HV-Side of a 3-winding transformer is enabled (as shown in Figure 30.9), it will only be included in the OPF as a control parameter if the corresponding option Transformer Tap Positions (parameter name: iopt_trf ) is enabled in the ComOpf dialogue (as shown in Figure 30.6). If enabled, the above mentioned control parameters serve as variable setpoints during the OPF. However, if a parameter is not enabled as a control parameter, the OPF will treat this parameter according to the load flow settings.

Fig. 30.6: Global Controls for OPF (Ac Optimization Method)

For example, if the Tap Position HV-Side parameter of a 3-winding transformer is selected as an OPF control, the optimization algorithm will adjust it in such a way that it contributes optimally to the objective function. On the other hand, if the user decides that this tap position shall not be a control parameter, the OPF will calculate the correct tap position according to the load flow settings. This could be a fixed position or a position found due to the option Automatic Tap Adjust of Transformers being selected in the load flow command. In this mode, the transformer tap position could be found in order to control the voltage of a certain node, or to be a slave that is externally controlled by some other transformer tap. Setting Individual Model-Based Controls Setting Individual Model-Based Controls

Each control can be individually selected to take part in the optimization. Specifically, for each generator ( ElmSym ), each transformer ( ElmTr2, ElmTr3 ), and each shunt (ElmShnt), the user can check the corresponding Control flag on the optimization page of the element's dialogue. Synchronous Machines

A synchronous machine may contribute two possible setpoints, namely active and reactive power control (see Figure 30.7).

Fig. 30.7: Active and Reactive Power Controls of a Synchronous Machine ( ElmSym ) 2- and 3-Winding Transformers

If a transformer has the T ap Position option selected, the user can further select the associated Control Mode to be used. This determines whether the tap position will be treated as a continuous or a discrete control parameter in OPF. Note that a 3-winding transformer has up to three tap changers which may individually be used as either continuous or discrete control parameters in OPF. Figure 30.8 shows the Controls section of the dialogue for a 2-winding transformer and Figure 30.9 shows the Controls section of the dialogue for a 3-winding transformer.


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Fig. 30.8: Tap Position Control (and Loading Constraint) for a 2-Winding Transformer

Fig. 30.9: Tap Position Control for a 3-Winding Transformer Shunts

In a similar fashion to transformers, the number of steps for a shunt may serve as either a continuous or a discrete optimization parameter (see Figure 30.10).

Fig. 30.10: Control Parameter for a Shunt ( ElmShnt) Constraints

The user can formulate various inequality constraints for certain system parameters, such that the OPF solution lies within t hese defined limits. Since all inequality constraints are considered as "hard constraints", setting constraints may result in no feasible solution being found. The handling of OPF constraints in PowerFactory is very flexible, and various categories of constraints exist. A constraint is considered in the OPF if and only if the individual constraint flag is checked in the element and the corresponding global flag is enabled in the OPF dialogue. Figure 30.11 shows the Constraints available for the AC optimization formulation of OPF in PowerFactory .

Fig. 30.11: Constraints Settings for OPF (AC Optimization Method)


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The optimization uses further constraints that are automatically imposed as soon as the corresponding parameter is used as a control. Examples of such constraints are tap position limits and the number of steps for switchable shunts. Network elements and their available constraints are listed below: 

Busbars and Terminals (StaBar , ElmTerm ):



Minimum Voltage Maximum Voltage Lines (ElmLne ):  



Maximum Loading 2- and 3-Winding Transformer ( ElmTr2, ElmTr3 ): Maximum Loading Tap Position range (if corresponding tap is a designated control parameter) Shunts ( ElmShnt):



Controller Steps range (if switchable steps are designated control parameters) Generator ( ElmSym ):













Minimum Active Power Maximum Active Power Minimum Reactive Power Maximum Reactive Power Secondary Controller ( ElmSecctrl): Minimum Total Active Power Maximum Total Active Power Station Controller ( ElmStactrl):



Minimum Total Reactive Power Maximum Total Reactive Power Boundary ( ElmBoundary ):

 

 







 

 

 

Minimum Active Boundary Flow Maximum Active Boundary Flow Minimum Reactive Boundary Flow Maximum Reactive Boundary Flow

Branch Flow Limits (max. loading) Branch Flow Limits (max. loading)

Branch flow limits formulate an upper bound on the loading of any branch ( ElmLne, ElmTr2, ElmTr3 , etc). The user has to specify a maximum value for the loading (see Figure 30.12). If specified as in Figure 30.12, this constraint is only taken into consideration if the corresponding flag ( Branch Flow Limits (max. loading) ) in the OPF dialogue is also ticked. Loading limits are supported for li nes and 2- and 3-winding transformers.

Fig. 30.12: Constraint on the Max. Loading of a Line Element (similar for 2- and 3-Winding Transformers) Active and Reactive Power Limits of Generators

For each synchronous machine ( ElmSym ), the user may impose up to four inequality constraints: namely a minimum and maximum value for active power generation; and a minimum and maximum value for reactive power generation (see Figure 30.13). Active power limits are specified as MW values; reactive power limits may be specified as either absolute values or as per unit values (i.e. referred to the type's nominal apparent power). Alternatively, it is possible to directly use the reactive power limits specified in the synchronous machine's type ( TypSym ). Again, the user is free to select any number and combination of the available constraints.

Fig. 30.13: Active and Reactive Power Constraints of a Synchronous Machine ( ElmSym ) Active Power Limits of Secondary Controllers

A secondary controller (ElmSecctrl) may impose an upper and lower active power constraint on the sum of the participating synchronous machines (see Figure 30.14). For practical purposes, this may serve as a reserve constraint for the total active power generation of various synchronous machines, in order to cover an outage of one of the machines. Suppose, for example, that a secondary controller is defined for three machines with maximum active power limits of 15MW, 20MW, and 25MW, respectively. Then a maximum total active power constraint of 35 MW on these three generators would cover an outage of the highest rated generator, and accordingly, an outage of any single one of the generators.


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Fig. 30.14: Total Active Power Sum Limit Constraint of a Secondary Controller ( ElmSecctrl) Reactive Power Limits of Station Controllers

Similar to the secondary controller (however with the roles of active and reactive power exchanged), a station controller ( ElmStactrl) may hold an upper and a lower limit on the total sum of the reactive powers of the participating generators (see Figure 30.15).

Fig. 30.15: Total Reactive Power Sum Limit Constraint of a Station Controller ( ElmStactrl) Voltage Limits of Busbars/Terminals

The maximum and minimum allowable voltages for each terminal or busbar element ( ElmTerm ) can be specified in the corresponding element's dialogue (see Figure 30.16). Therefore, each terminal or busbar may contribute at most two inequality constraints to the OPF. Maximum and minimum voltage limits may be imposed individually; i.e. it is possible to specify an upper limit without specifying a lower limit.

Fig. 30.16: Voltage Constraints for a Terminal/Busbar ( ElmTerm ) Boundary Flow Limits

PowerFactory boundary elements ( ElmBoundary , icon ) define topological regions in a power system by a user-specified topological cut through the network. Constraints can be defined for the flow of active and reactive power in a network (between defined boundaries), and this constraint can then be enforced in OPF. For detailed information on defining boundaries, please refer to Section Boundaries.

Fig. 30.17: Defining Boundary Flow Limits ( ElmBoundary ) ResultsMathematical BackgroundResultsMathematical Background

The non-linear optimization is implemented using an iterative interior-point algorithm based on the Newton-Lagrange method. Recall that the goal of the optimization is to minimize an objective function f subject to the equality constraints imposed by the load flow equations and also to the inequality constraints defined for various power system elements. This is summarised mathematically as follows:

subject to:

where g represents the load flow equations and h is the set of inequality constraints. Introducing a slack variable for each inequality constraint, this can be reformulated as:

We then incorporate logarithmic penalties and minimize the function:

where µ is the penalty weighting factor. In o rder to change the contribution of the penalty function:

to the overall minimization, the enalt wei htin factor

will be decreased from a user-defined initial value

to a user-defined tar et value

.


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The smaller the minimum penalty weighting factor, the less the applied penalty will be for a solution which is close to the constraint limits. This may result in a solution that is close to the limiting constraint bounds (if necessary). On the other hand, a smaller minimum penalty weighting factor will result in a higher number of iterations required. Results

The presentation of the OPF results is integrated into the user interface, in that the solution of the non-linear optimization OPF is available via the complete set of variables available for conventional load flow calculations. These can be viewed in the single line diagram of the grid, or through a data browser. The inclusion of the following variables in the Flexible Data tab (for synchronous machines and grids) is suggested, as shown in Figure 30.18. The actual variable names are given in parentheses. Synchronous machines: 

 



Active Power (Calculation parameter P:bus1; this parameter is highlighted in Figure 30.18) Reactive Power ( Calculation parameter Q:bus1) Apparent Power (Calculation parameter S:bus1) Voltage Magnitude (Calculation parameter u:bus1)

Fig. 30.18: Definition of Flexible Data for Synchronous Machines ( ElmSym )

Grids: 

 

 

Total Production Cost, including costs through external grids ( Calculation parameter c:cst_disp; see this parameter highlighted in Figure 30.19). It should be noted that the production costs are expressed in the same units utilized in the production cost tables of the individual generator elements. Active Power Losses (Calculation parameter c:LossP) Reactive Power Losses (Calculation parameter c:LossQ) Active Power Generation (Calculation parameter c:GenP) Reactive Power Generation ( Calculation parameter c:GenQ)

Fig. 30.19: Definition of Flexible Data for Grids ( ElmNet)

Besides these results, the complete set of variables from conventional load flow calculations is available. For further information on defining F lexible Data in PowerFactory , please refer to Section The Flexible Data Page Tab in the Data Manager . A text report is also available and can be generated by clicking on the Output Calculation Analysis result documentation.

icon on the main toolbar. This offers various templates for detailed


30.1.2 Initialization

The non-linear optimization requires initialization to generate an initial starting condition. The Iteration tab of the OPF dialogue as shown in Figure 30.20 allows the user to select the initialization method.

Fig. 30.20: Initialization Settings for OPF (AC Optimization Method) Initialization of Non-Linear Optimization Load Flow

Displays the load flow command which is used for initialization in the case that no flat start is used. Initialize by Flat-Start

The user may choose whether the initialization is performed by a load flow calculation or by a flat start. If it is known in advance that the final solution of the optimization is close to a valid load flow solution, initialization using a load flow calculation results in faster convergence. No Flat Initialization (Use Load Flow Result) If this option is selected, the OPF checks w hether an "OPF-initializing" load flow result has been calculated prior to the OPF. Here, "OPF-initiali zing" means that the flag iopt_initOPF was enabled in the load flow command dialogue before execution. This flag is labelled Use this load flow for initialization of OPF and can be found on the second page of the Advanced Options tab in the ComLdf dialogue. The result of this load flow is then used as a starting point fo r the iterative OPF interior-point algorithm. If no va lid OPF-initializing load flow result is found, the OPF will recalculate a new load flow.




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Penalty Weighting Factor

The penalty weighting factor determines the amount by which the penalty is applied. For example, the smaller the specified penalty weighting factor, the less that the penalty will be applied for solutions which are close to constraint limits. Initial Value Initial value of the penalty weighting factor.

Target Value Target value of the penalty weighting factor.

Reduction Factor A factor by which the current penalty weighting factor will be divided by between the iterations.

Fig. 30.21: Penalty Weighting Factor Settings for OPF (AC Optimization Method)



PowerFactory offers the user flexibility in configuring of the number of iterations and the convergence criteria for OPF. The available options o n the Iteration Control tab of the OPF dialogue are shown in Figure 30.22.

Fig. 30.22: Iteration Control Settings for OPF (AC Optimization Method)

The implementation of the Lagrange-Newton method means that t he OPF will internally minimize the resulting Lagrange function:

with the Lagrange multipliers

.

The following parameters can be used to alter the stopping criteria for this iterative process. The algorithm stops successfully if the following three criteria are f ulfilled: 1. 2.

The maximum number of iterations has not yet been reached. All load flow constraint equations g(x)=0 are fulfilled to a predefined degree of exactness (i.e. within an allowable tolerance), which means: all nodal equations are fulfilled. all model equations are fulfilled. 3. The Lagrange function L converges. This can be achieved if: either the objective function itself converges to a stationary point, or the gradient of the objective function converges to zero.  



The following parameters are used to configure these stopping criteria. The alteration of the default values for these parameters is recommended only for advanced users. Maximum Number of Iterations Interior-Point Algorithm (Inner Loop) Maximum number of iterations for the interior-point algorithm. Control Loop (Outer Loop) Maximum number of iterations of the outer loop. Convergence Criteria Max. Acceptable Error for Nodes The maximum allowable error for the nodal equations (in kVA).

Max. Acceptable Error for Model Equations The maximum allowable error for the model equations (in %).

Max. Change of Objective Function Used when Convergence of Objective Function option values of objective function become constant is selected. The user enters a value (in %), below which the Lagrangian is considered to have converged. Max. Value for Gradient of Objective Function

Used when Convergence of Objective Function option gradient of objective function converges to zero is selected. The user enters an absolute value, below which the Lagrangian is considered to have converged. Convergence of Objective Function Options relating to the convergence criteria for the Lagrangian function: either the value of the function itself is required to converge to a stationary point, or the gradient of the Lagrangian


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is required to converge, as described below. values of objective function become constant If this option is selected, the user is asked to enter a value for the Max. Change of Objective Function . If the change in value between two consecutive iterations fal ls below this value, the Lagrangian is considered to have converged. gradient of objective function converges to zero If this option is selected, the user is asked to enter a value for the Max. Value for Gradient of Objective Function . If the gradient falls below this value, the Lagrangian is consi dered to have converged. For reasons of mathematical exactness, it is strongly recommended to select the latter option, gradient of objective function converges to zero . If the underlying Jacobian matrix is numerically instable, this often results in oscillatory behaviour in the last iterations. Therefore, the latter method provides assurance that the result is in fact a minimum.


30.1.5 Output

Prior to the non-linear o ptimization, the OPF informs the user (in the output window) of the total number of constraints and controls that will be considered in the subsequent calculation. This information is detailed in that the imposed constraints and the participating controls are counted for each constraint and control categories separately. Two options are available to select the level of detail contained in output messages. These options are available in the Output tab of the OPF dialogue and are shown in Figure 30.23 and are described below.

Fig. 30.23: Output Settings for OPF (AC Optimization Method)

Show Convergence Progress Report Show Convergence Progress Report If this flag is checked on the Output page of the OPF dialogue, the user will get a detailed report on the convergence of the non-linear optimization. For each step of the iteration, the following figures are displayed in the output window: 

 

 

 

 

The current error of the constraint nodal equations (in VA) (Err.Nodes); The current error of the constraint model equations (Err. ModelEqu) ; The current error of the inequality constraints ( eInequ) ; The current value of the gradient of the Lagrangian function ( gradLagFunc) ; The current value of the Lagrangian function ( LagFunc) ; The current value of the objective function f to be minimized ( ObjFunc) ; The current value of the penalty function f pen (PenFunc) ; The current values of the relaxation factors (Rlx1, Rlx2) for the primal and dual variables; The current value of the penalty factor µ (PenFac ).

Show Max. Nodal and Model Equation Error Elements

If this flag is checked, the algorithm outputs per iteration, the components which have the largest error in the equality constraints (i.e. mismatch in the load flow equations). An outer loop is wrapped around the central non-linear optimization algorithm. This outer loop is required to perform rounding and optimization of the evaluated tap and shunt positions to discrete values (if desired by the user). The maximum number of outer loops is defined on the Iteration Control tab of the dialogue. However, if no convergence is reached with the defined number of outer loops, the user will be informed via a message in the output window that further outer loop iterations are required.


30.2 DC Optimization (Linear Programming) The following describes the configuration of the DC optimization formulation of OPF in PowerFactory . Internally, from the settings provided, a linear programming (LP) formulation of the problem is derived. The load flow is calculated using the linear DC load flow method. For general information about DC load flow please refer to Section 22 Load Flow Analysis . PowerFactory uses a standard LP-solver (based on the simplex method and a branch-and-bound-algorithm) which ascertains whether the solution is feasible. The result of the linear optimization tool includes calculated results for control variables, such that all imposed constraints are fulfilled and the objective function is o ptimized. Provided that a feasible solution exists, the optimal solution will be available as a calculation result. i.e., the algorithm will provide a DC load flow solution, where all generator injections and tap positions are set to optimal values. The DC load flow solution includes the following calculated parameters: 

For terminals: Voltage Angle (phiu [deg]) Voltage Magnitude (u [p.u.]; assumed to be 1.0 p.u. in DC calculation) Voltage Magnitude (upc [%]; assumed to be 100 % in DC calculation) Line-Ground Voltage Magnitude (U [kV]) Line-Line Voltage Magnitude (U1 [kV]) For branches: Active Power Flow (P [MW]) Active Power Losses (Ploss [MW]; assumed to be 0 MW in DC calculation) Reactive Power Flow (Q [Mvar]; assumed to be 0 MVAr in DC calculation) Reactive Power Losses (Qloss [Mvar]; assumed to be 0 MVAr in DC calculation) Loading [%] (Loading with respect to continuous rating)  

 





 

 



The following parameters are calculated in addition to the results found by the DC load flow:




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For generators:

c:avgCosts The fixed cost factor [$/MWh] used in the objective function (i.e. average cost considering the costs at the generator's active power limits). c:Pdisp Optimal power dispatch for generator. c:cst_disp Production costs in optimal solution: cst_disp = costs * Pdisp 

For Transformers:

c:nntap Optimal tap position. 

For loads:

c:Pdisp Optimal load shedding for load. 30.2.1: Basic Options 30.2.2: Initialization 30.2.3: Advanced Options 30.2.4: Iteration Control 30.3.5: Output



The Basic Options tab of the OPF dialogue (DC optimization method) is shown in Figure 30.24.

Fig. 30.24: Basic Options Tab of OPF Dialogue (DC Optimization Method) Method To perform a DC optimization OPF study, the Method must be set to DC Optimization (LP) as shown in Figure 30.24. Objective FunctionObjective Function

The user can select a linear optimization objective function using the list box as shown in Figure 30.25. These objective functions are now described.

Fig. 30.25: Objective Function Selection for OPF (DC Optimization Method) Feasibility Check Performs a feasibility check of the network considering the specified controls and constraints (i.e. performs a constrained load flow). Minimization of Costs The objective is to minimize generation costs. To perform a cost minimization calculation for each generator, a cost factor needs to be entered: Cost curve $/MWh per generator ( ElmSym , see Figure 30.3) The (linear) algorithm uses a fixed cost-factor [$/MWh] per generator. This cost factor is the average cost considering the costs at the generator's activ e power limits. Min. Generator Dispatch Change Minimizes the change in generator dispatch from the generators' initial value. Controls

The Controls section of the OPF Basic Options tab is highlighted in Figure 30.26. The basic role of each control is as described for the AC optimization method in Section Basic Options


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Fig. 30.26: Controls Selection for OPF (DC Optimization Method)

The user can select from the following control variables: 



Generator Active Power Dispatch (ElmSym ) In generator optimization, for each selected generator a single control variable is introduced to the system. The total number of generator controls in this case equals the number of selected generators. Transformer Tap Position (ElmTr2, ElmTr3 )

In tap optimization, for each selected transformer a single control variable is introduced to the system. The total number of tap controls in this case equals the number of selected transformers. 

Allow Load Shedding (ElmLod ) A separate control variable is introduced to the system for each selected load. The total number of load controls in this case equals number of selected loads. This control variable can be selected in conjunction with any objective function.

Note At least one type of control variable in the Controls section of the OPF dialogue must be selected. Constraints

The three constraints as shown in Figure 30.27 are as described for the AC optimization method in ConstraintsSection Basic Options.

Fig. 30.27: Constraints Selection for OPF (DC Optimization Method)

For DC optimization the following constraint is imposed: Transformer Tap Constraints (implicitly imposed) Minimum and maximum tap positions (ElmTr2, ElmTr3 ) for transformers are considered. These constraints are implicitly imposed when transformer tap positions are specified as controls in the Controls section of the dialogue (see Figure 30.27). This leads to 2 constraints introduced to the LP for the base case tap position calculation. Handling

Active power dispatch constraints can be chosen on an individual basis (by a checkbox) per generator. Please see Figure 30.13 for setting min/max constraints for generators for optimization. It should be noted that generator constraints are not implicitly imposed when active power dispatch is selected as a control. Tap position constraints will be implicitly imposed whenever the corresponding tap is a designated control variable, as in Figure 30.8. Loading constraints can be chosen on an individual basis (by a checkbox) per line element ( ElmLne), as shown in Figure 30.12. If loading constraints are included, the


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maximum loading limits will be calculated with respect to the type of the element, or with respect to a thermal rating object ( IntThrating , as shown in Figure 30.28 . If a thermal rating object is selected, the limits will be calculated with respect to the Continuous Rating value.

Fig. 30.28: Thermal Rating Object (IntThrating ) Ratings Tab for Setting Rating Values

Boundary flow constraints can be chosen on an individual basis per boundary ( ElmBoundary), as shown in Figure 30.17.



The OPF calculation is initialized by a load flow, which is displayed by the Load Flow parameter on the Initialization tab of the OPF dialogue. The user can inspect the load flow settings by clicking on the button, as illustrated in Figure 30.29. The load flow command contained in the current study case is set here automatically. Within the load flow command, the Calculation Method will be automatically set to DC Load Flow (linear) for use by OPF (when Method is set to one of the LP variants).

Fig. 30.29: Initialization Settings for OPF (DC Optimization Method)



The Advanced Options tab of the OPF dialogue is shown in Figure 30.30.

Fig. 30.30: Advanced Options for OPF (DC Optimization Method) Load Shedding OptionsLoad Shedding Options

If Allow Load Shedding is among the selected Controls (see Section Basic Options) on the Basic Options tab, an additional term will be added to the objective function. This weight of this term can be controlled using the Penalty Factor in the Load Shedding Options section of the dialogue. The following term will be added to the objective function, where ω is the specified Penalty Factor :

Transformer Tap Deviation Control

If tap positions are to be optimized, different solutions can yield the same optimal value for the objective function. One can therefore impose a term to the objective function, which forces the solution to be as close as possible to the initial transformer tap positions.


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Use Penalty Factor for Tap Deviation If enabled, the following additional term is added to the objective function:

Penalty Factor Specifies the weighting factor for the additional objective function term above. Calculation of Transformer Tap Positions Discrete controls (Using direct method) This method calculates discrete tap position values within the LP (known as the "direct method"). Thi s method may provide better accuracy however will yield fewer solutions. Continuous controls (Using outer loop rounding) This method calculates continuous tap positio n values and then rounds these values to discrete values in the outer loop of the calculation. This method may be faster but the values may not be optimal.



Two outer loop settings are available: (i) control of the number of iterations of the algorithm; and (ii) definition of a constraint tolerance. These settings are shown in Figure 30.31 and are described below.

Fig. 30.31: Iteration Control Settings for OPF (DC Optimization Method) Outer Loop

Following the solution of the LP problem, it may be the case that loading constraints are not within their boundaries. This can occur for tap position controls and/or generator controls (and in the latter case, only when the generators use non-linear cost curves). The reason is that for taps, the algorithm uses tap sensitivities which assume a linear change in MW flow per tap step. Since these tap sensitivities depend on the initial tap position, the result becomes inaccurate if the optimal tap position is far from the i nitial tap position. This inaccuracy can be remedied by an additional outer loop. At each iteration, this outer loop starts with the optimized tap positions which were calculated in the previous loop. The same principle applies for the use of generators with non-linear cost curves. The following Outer Loop settings can be entered on this tab: Max. Number of Iterations Maximum number of outer loop iterations until all constraints are fulfilled (within a defined tolerance). Max. Acceptable Error for Constraints Maximum relative error (in %) by which a constraint can be violated while still being considered a feasible solution.

It should be noted that when Max. Number of Iterations is set to one, the LP is solved without outer loops.


30.3 Contingency Constrained DC Optimization (LP Method) This performs an OPF using DC optimization (as described in Section DC Optimization (Linear Programming)), subject to various user defined constraints and also to the constraints imposed by a set of selected contingencies. In addition to the variables available for viewing for DC optimization, contingency constrained OPF offers the following result variables (in addition to those found by the DC load flow, as described in Section DC Optimization (Linear Programming)): 

For generators:

c:Pdisp Optimal generation for each contingency case. The optimum generation for each contingency case is stored as a parameter event object in the corresponding contingency object ( ComOutage). Thus, each contingency object will hold parameter events for each selected generator (the name of the parameter event is the name of the generator). The parameter event reflects the optimal generation for that generator in the given contingency case. 

For Transformers:

c:nntap Optimal tap positions for each contingency case. The optimum tap positions for each contingency case are stored as a parameter event object in the corresponding contingency case object ( ComOutage). Thus, each contingency object ( ComOutage) will hold parameter events for each selected transformer (the name of the parameter event is the name of the transformer). The parameter event reflects the optimal tap position for that transformer in the given contingency case. c:mxTpChng (_l, _m, _h) mxTapChng is the maximum tap change devia tion between the optimal base case tap position and the optima l tap position considering all contingencies. For 3-winding transformers, HV-, MV- and LV-side tap changes are calculated individually. 

For loads:

c:Pdisp Optimal load shedding for each contingency case. The optimum load shedding for each contingency case is stored as a parameter event object in the corresponding contingency case object ( ComOutage). Thus, each contingency object will hold parameter events for each selected load (the name of the parameter event is the name of the loa d). The parameter event reflects the optimal load shedding for that load in the given contingency case.



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The Basic Options tab of the OPF dialogue (contingency constrained DC optimization method) is shown in Figure 30.32.

Fig. 30.32: Basic Options Tab of OPF Dialogue (Contingency Constrained DC Optimization Method) Method

To perform a contingency constrained OPF study, the Method must be set to Contingency Constrained DC Optimization (LP) as shown in Figure 30.32. Contingency Analysis

This is a reference to the Contingency Analysis (ComSimoutage) command to be used during the contingency constrained OPF. The user can select and set this contingency analysis command via the

button, and view or edit the ComSimoutage command settings using the arrow button

.

Objective Function

The selection of objective function for Contingency Constrained DC Optimization includes the same objective functions as those provided for DC Optimization (see Section Basic Options). Two additional objective functions are provided, which are shown in Figure 30.33 and described below.

Fig. 30.33: Objective Function Selection for OPF (Contingency Constrained DC Optimization Method) Min. (Pre-to-Postfault) Generator Dispatch Change Minimizes the sum of the generator dispatch changes between the base case and each contingency case.

Min. (Pre-to-Postfault) Transformer Tap Change Minimizes the sum of the tap position changes between the base case and each contingency case. Controls

The definition of control variables for the contingency constrained DC optimization method differs slightly from the DC optimization method, however the basic fundamental role of each control is as described for the AC optimization method in Section Basic Options. The Controls section of the OPF dialogue is highlighted in Figure 30.34.


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Fig. 30.34: Controls Selection for OPF (Contingency Constrained DC Optimization Method)

The user can select from the following control variables: 

Generator Active Power Dispatch (ElmSym ) Dispatch in Contingencies 





Use base case dispatch: For all contingency cases, use the generator dispatch from the base case. Using this setting, a si ngle control variable is introduced to the system for each selected generator. The total number of generator controls in this case equals the number of selected generators. Allow different dispatch: For each contingency case, allow a generator dispatch different to that used in the base case. Using this setting, for each selected generator, a control variable is i ntroduced for the base case and for each contingency case. This option must be selected from the drop-down box when the objective function Min. (Pre-to-Postfault) Generator Change has been selected. The total number of generator controls in this case equals: (number of selected generators) * (1 + number of selected contingencies)

Transformer Tap Positions (ElmTr2, ElmTr3 )

Tap Positions in Contingencies 



Use base case tap positions: For all contingency cases, use the transformer tap positions from the base case. Using this setting, a single control variable is introduced to the system for each selected transformer. The total number of tap controls in this case equals the number of selected transformers. Allow different tap positions: For each contingency case, allow ta p positions different to those used in the base case. Using this setting, for each selected transformer, a control variable is introduced for the base case and for each contingency case. This option must be selected from the drop-down box when the objective function Min. (Pre-to-Postfault) Transformer Tap Change has been selected. The total number of tap controls in this cas e equals: (number of selected transformers) * (1 + number of selected contingencies)

Allow Load Shedding (ElmLod ) A separate control variable is introduced to the system for the base case and for each contingency case. This control variable can be selected in conjunction with any objective function. The total number of load controls equals: (number of selected loads)*(1 + number of selected contingencies) Constraints

The Constraints section of the OPF dialogue is shown in Figure 30.35, for the contingency constrained DC optimization method. This formulation of OPF performs a contingency analysis for a predefined set of contingencies ( ComOutage objects; i.e. a set of interrupted components per contingency case). The Max. Loading (parameter: maxload ) for lines and transformers (ElmLne, ElmTr2, ElmTr3 ; (one constraint per bus)) for each contingency case is considered in the calculation. For each loading constraint, the number of constraints added to the LP will be: 2*(number of contingencies). In addition to the constraints provided for DC optimization (see Section Basic Options for further information), the contingency constrained DC optimization method offers additional constraints: Maximum Number of Tap Changes per Contingency If this checkbox is ticked, then for each contingency, no more than the maximum tap position change steps from the base case to the contingency case are allowed over all transformers (i.e. for a given contingency, a constraint is enforced on the sum of all max. difference of base case to contingency case taps, over all transformers).

Transformer Tap Constraints (implicitly imposed) Minimum and maximum tap positions ( ElmTr2 , ElmTr3 ) for transformers are considered. These constraints are implicitly imposed when transformer tap positions are specified as controls in the Controls section of the dialogue (see Figure 30.35). This leads to two constraints in LP formulation for the base case tap position calculation, and to: 2 x ( 1 + number of contingencies) constraints for contingency case calculations.


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Fig. 30.35: Constraints Selection for OPF (Contingency Constrained DC Optimization Method) Handling

Active power dispatch constraints can be chosen on an individual basis (by a checkbox) per generator. Please see Figure 30.13 for setting min/max constraints for generators for optimization. Tap position constraints will be implicitly imposed whenever the corresponding tap is a designated control variable, as illustrated in Figure 30.8. Loading constraints can be chosen on an individual basis (by a checkbox) per line element ( ElmLne). Once a loading constraint for a specific line is imposed, it will be considered by all contingencies contained in the contingency list. See Figure 30.12. If loading constraints are included, the maximum loading limits will be calculated with respect to the type of the element, or with respect to a thermal rating object ( IntThrating, as shown in Figure 30.28). If a thermal rating object is selected, the limits w ill be calculated with respect to the Continuous Rating value.

Boundary flow constraints can be chosen on an individual basis per boundary ( ElmBoundary ), as shown in Figure 30.17. Once a boundary constraint for either the maximum total active power limit or min total active power limit is imposed, it wi ll be considered by all contingencies in the contingency list. The list of contingencies to be considered by the OPF is selected by choosing a specific contingency analysis command (parameter Contingency Analysis in the OPF dialogue, Basic Options tab), which contains in its folder the contingency objects ( ComOutage) to be considered.



As described for DC optimization. Please refer to Section Initialization.



As described for DC optimization. Please refer to Section Advanced Options.



As described for DC optimization. Please refer to Section Iteration Control.


30.3.5 Output

Contingency Analysis ResultsLimits for RecordingFor contingency constrained OPF, one can choose to record the results of those branches which exceed a selected limit value. This can be done for both the non-optimized results and the optimized results. For each recording of results (i.e. with optimized or non-optimized values) a separate result file must be chosen.


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Fig. 30.36: Output Settings for OPF (Contingency Constrained DC Optimization Method) Contingency Analysis Results

Results (non-optimized) The result file in which to store the non-optimized results. Results (optimized) The result file in which to store the calculated (optimized) results. Limits for Recording

The limits displayed here are set in the selected Contingency Analysis command on the Basic Options tab of the ComSimoutage dialogue. They define the limits outside of which results will be written to the result file(s). Please refer to Section Basic Options for further information.


Chapter 31 Optimization Tools for Distribution Networks The objective of this chapter is to present the tools implemented in PowerFactory for the optimization of distribution networks. By means of simple command edit dialogues it is possible to calculate the optimal placement, type and size of capacitors in radial distribution networks; the optimal separation points of meshed networks and the optimal type of reinforcement cables and overhead lines. Each section introduces a different tool, presenting a general description, the objective function, the optimization procedure and the command dialogues. 31.1: Optimal Capacitor Placement 31.2: Open Tie Optimization 31.3: Cable Size Optimization


31.1 Optimal Capacitor Placement The idea for optimal capacitor placement is to determine the location, type and the size of capacitors to be installed in the nodes of the radial distribution network. The economic benefits due to energy loss reduction are weighted against the cost of installation of such capacitors while keeping the voltage profile of the system within defined limits. The pre-configured commands related to optimal capacitor placement become available at the button bar on the main menu after selecting the These commands are:



Setup of Optimization and execution



Showing and setting up the list of available capacitor types



Result output for nodes with new capacitors installed



Result output for new capacitors recommended for installation



Result output as a pre-configured text report

icon in flexible tool bar.

(see Section 31.1.3 and 31.1.4). .

. .

.

31.1.1: Objective Function 31.1.2: Optimization Procedure 31.1.3: Basic Options Page 31.1.4: Advanced Options Page 31.1.5: Results


31.1.1 Objective Function

The optimization algorithm minimizes the annual total network cost (which is a sum of three parts: cost of grid losses, cost of all installed capacitors and fictitious penalty cost of voltage violations) according to:

with:








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CLosses corresponds to the anual cost of grid losses. Ccap corresponds to the annual cost of capacitors (investment, maintenance, insurance), as indicated on the description page of the capacitor type. m is the number of installed capacitors. CVoltViol corresponds to a fictitious cost used to penalize the bus vol tage violation. n is the number of feeder buses.

The voltage violation cost is calculated according to voltage limits and penalty factors. The voltage limits are defined in the 'Basic Options' tab ('Allowed Voltage' field, see Section 31.1.3: Basic Options Page) of the Optimal Capacitor Placement dialogue. The penalty factors are defined in the 'Advanced Options' tab ('dv < dvmax' and 'dv > dvmax' fields, see Section 31.1.4: Advanced Options Page). The penalty values are applied for voltages inside the admissible voltage band (parameter 'weight': Penalty Factor 1) and for voltages outside for voltages the admissible band (parameter 'weight2': Penalty Factor 2). 

If the voltage U of a busbar is within the allowed limits, its penalty cost corresponds to:

with: ∆U is the absolute deviation from the nominal voltage in p. u. (

).

w1 is the penalty factor 'dv < dvmax' (para meter 'weight') inside the admissible voltage band in $/% from the 'Advanced Options' tab. 

If the voltage U is outside the allowed band, its penalty cost corresponds to:

, i. e. voltage higher than max. limit:

or , i. e. voltage lower than min. limit:

with: ∆U absolute deviation from the nominal voltage U in p. u. n U + ∆U higher voltage limit in p. u. n max U - ∆U lower voltage limit in p. u. n min w1 is the penalty factor 'dv < dvmax' (para meter 'weight') inside the admissible voltage band in $/% from the 'Advanced Options' tab. w2 penalty factor 'dv > dvmax' (parameter 'weight2') outside the admissible voltage band in $/% from the 'Advanced Options' tab.

The algorithm can be summarized in two sentences: 

If the voltages are inside the admissible band the penalty cost applied is equal to



If the voltages are outside the admissible band the penalty cost applied is equal to the penalty inside the band (

) plus the factor

, with

being either the maximum or the minimum limit value of the admissible band.

Figure 31.1 ilustrates the concept of the voltage band violation cost.

Fig. 31.1: Fictitious cost assigned by voltage band violations

Note If no penalty costs are to be applied within the admissible band, w1 ('dv < dvmax' , parameter 'weight') should be set to zero. In case this value is greater than zero, the program will add additional costs to all busbar with voltage different from 1.0 p.u. Note The values for the penalties w1 (parameter weight) and w2 (parameter weight2) should be carefully chosen since the target function is a sum of three objective functions. If these values are high, it can make the algorithm not consider the other two objectives. Otherwise, if there are very low, the algorithm may not take the voltage violations into account in the optimal capacitor placement algorithm.


31.1.2 Optimization Procedure

To find the optimal configuration of capacitors, PowerFactory applies 2 different steps: 1. 2.

Sensitivity analysis to select the candidate buses for capacitor installation Optimization step to determine the actual locations and sizes of the shunt capacitors

The optimization is not only performed for a single load level, but for all load levels described in a discrete scale that is handed over to PowerFactory . For each of these load levels the voltage at the buses must be k ept within the allowed bandwidth. An additional vectorial characteristic describes the probability of each of these load levels in hours/year, so that the cost of losses can be calculated accordingly. The final result of the optimization process are the locations for the installation of capacitors, the types and sizes of capacitors to be installed and the capacitor switch positions f or the different load levels. Sensitivity Analysis

In this step test capacitors are installed at all busbars in t he system and the effect of the installation on the total annual system cost is evaluated. The size of the test capacitors used to evaluate the cost benefit can be selected according to 4 different options:  



Minimum available capacitor size is used. Maximum available capacitor size is used. The capacitor size is determined by the peak reactive power requirements of the load.




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The capacitor size best fitting to the reactive energy consumption of the load is used.

Final optimization step

This step implements 2 different optimization procedures to determine the optimum l ocation of capacitors: a. Gradient search - this search is fast and mostly will find a solution that performs well - even if not the mathematically exact global optimum. b. Tabu Search - this search finds the exact optimum, but may be more time-consuming.


31.1.3 Basic Options Page

Fig. 31.2: Basic Options page Feeder

Please select the feeder for which the optimum capacitor placement should be performed. The feeder is a special PowerFactory element which has to be created before selecting it in this dialogue (for information about feeders refer to 7.3.3 Network Data ). Optimization Level

The Optimization Level List offers 4 o ptions:  

 

Remove previous solution - deletes any capa citors placed in the network during the previous run of the optimization function Sensitivity only: Performs the sensitivity analysis and shows the result in the text output window, but does not place any capacitors Fix Capacitors: Optimizes the network for fix capacitors, that is capacitors without any voltage control Switched Capacitors: Optimizes the network for switched capacitors performing voltage control.

Sensitivity Analysis 

  

Min Shunt: the minimum available capacitor size is used Max. Shunt: the maximum available capacitor size is used Best fit to load: the capacitor size best fitting to the reactive energy consumption of the load is used Depend on load: the capacitor size is determined by the reactive power requirements of the loa d

Optimization Approach 



Gradient Search: Newton-Raphson-Optimization to detect local optimum Reactive Tabu Search: Tabu search to detect global optimum of reactive power installation

Max. Number of Iterations

Max. number of iterations as criterion for interrupting before termination of optimization process. Max. Execution Time

Max. duration until interrupting before termination of optimization process. Connect Candidate Shunts

The optimization always generates a report describing the proposed capacitor locations. If this field is checked, the capacitors are added to the data of the network. Do not consider Energy Cost

If this option is checked, the cost of losses are not considered in the t arget function. Energy Cost

Energy cost applied (in specific cost per kWh). Constraints - Allowed voltage

Voltage band, defined by lower limit (min. voltage) and upper limit (max. voltage) in %. Different penalty cost apply for voltages within the allowed band and outside. Constraints - Reactive Power of all capacitors

If the sum reactive power of all capacitors is limited, the value is entered in this fi eld. Available Capacitors

When pushing this button, the list appears with all capacitor types available for the optimization. The recommended way of entering types to this list is by copy/paste from type libraries.



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31.1.4 Advanced Options Page

Fig. 31.3: Advanced Options page Discrete Scale and Trigger

Scale with discrete steps of the loading.The correct consideration of the load levels makes it necessary to have defined a vectorial characteristic with scaling factors for each load during the defined load level. It is good practise to refer to this characteristic in the scaling factor o n the load-flow page of each load. Figures 31.4 and 31.5, show an example of a discrete scale and a load characteristic. Further information on scales and vector characteristics is given in 7.7 Parameter Characteristics and Parametric Studies .

Fig. 31.4: Example of discrete scale for loading level

Fig. 31.5: Example of load characteristic Time Vector

Vectorial Characteristic to describe the probability of each discrete loading level (in hrs/yr). Further information on scales and vector characteristics is given in 7.7 Parameter Characteristics and Parametric Studies .


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Fig. 31.6: Example of load curve (time vector) Candidate Buses

Percentage of all candidate buses from the sensitivity analysis that are used for the actual optimization process. Fix number of capacitors

If checked, each capacitor type in the list is used once only. Penalty factor 1: dv < dvmax

Penalty cost for buses with voltage values inside the admissible band (see Section 31.1.1). Note If no penalty costs are to be applied within the admissible band, 'dv < dvmax' should be set to zero. In case this value is greater than zero, the program will add additional costs to all busbar w ith voltage different from 1.0 p.u. Penalty factor 2: dv > dvmax

Penalty cost for buses with voltage values outside the admissible band (see Section 31.1.1). Note The values for the penalties dv < dvmax' and dv > dvmax' should be carefully chosen since the target function is a sum of three objective functions. If these values are high, it can make the algorithm not consider the other two objectives. Otherwise, if there are very low, the algorithm may not take the voltage violations into account in the optimal capacitor placement algorithm.


31.1.5 Results

The last three tool-bar buttons give access to the o ptimization results. Result output for nodes with new capacitors installed

When pressing the icon

, a list appears with all nodes named where capacitors are listed.

Result output for new capacitors recommended for installation

Pressing the icon

generates a list of capacitors distributed in the grid.

Result output as a pre-configured text report

This icon (

) generates a report with the results of the sensitivity analysis and the final optimization procedure.


31.2 Open Tie Optimization The open tie optimization is started when selecting the general tools



Open-Tie-Optimization

in the flexible toolbar and pressing the icon for open tie-point optimization:

.

31.2.1: Optimization Procedure 31.2.2: Options Page



Input data for the optimization algorithm is a network with - in general - a meshed topology. The optimization algorithm will proceed in the following way:




 

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A search is started for possible meshes in the network. Each found mesh is closed first by closing all open switches in the loop. A load-flow calculation is then made, after which the loop is opened at the position with the l owest current. Normally, the switch with the lowest current is opened, but alternatively, the element with the lowest current can be taken out of service when that current is lower than the lowest switch current. When opening a loop at the optimum locatio n for active losses leads to an overload on any line i n the network, the algorithm will open a different line instead. This is continued until no more closed loops can be found.

A final optimization step is following to search for further improvement. The impact of opening disconnectors on voltage band violations is not checked. The typical case in open-tie optimization however is that the open-tie-location optimum for loss reduction also performs best for keeping the defined voltage band.


31.2.2 Options Page

Fig. 31.7: Basic Options page Feeding points

The section of the network where the optimum open-tie points should be determined is defined by a set of "feeding points". Such feeding points can be  

 



External grids. The source-side switchbay of Lines (Overhead lines and cables). The source-side switchbay of transformers (if the complete transformer is selected, the HV side is considered the feeding side). The combination of a busbar/terminal and a branch, in which case the feeding direction towards the branch. A feeder object.

The feeding points are the positions where power is assumed to flow into the network. Only meshes between the feeding points will be optimized. Meshes connecting points in already optimized meshes are optimized also. Update Database

If this box is unchecked, the proposals for opening disconnectors are listed in the output report. If the box is checked, the status of the respective disconnectors is also modified in the data of the network. Force elements on outage when not switchable

The search for the position with the lowest current, which is to be opened, can be extended by allowing the command to force and opening by setting an element out of service, when no switch is available at the specific location. Selection

The possible options are:  



Whole System: the complete system fed by the feeding points is radialized; One Grid: If the network is composed of several grids (e.g. transmission and distribution), the grid to be optimized can be selected; User-defined: an user defined set is selected, the lines in this set are used for radializing the network. The selection can be used to further limit the area which is to be optimized. The first limitation is by defining feeding points. Only meshes for which all elements are in the selection will be optimized.

Load-Flow Command

Reference to the load-flow settings used by the optimization. Output On

If this box is checked, the result report is directly written to the message window. Output

Reference to the configuration dialogue of the output available after termination of the optimization routine.


31.3 Cable Size Optimization The cable size optimization can be selected using the general tools



Cable Size Optimization

31.3.1: Objective Function 31.3.2: Optimization Procedure 31.3.3: Basic Options Page 31.3.4: Advanced Options Page

and pressing the icon for cable size optimization:


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31.3.1 Objective Function

The objective function for the optimization are the annual cost for the reinforced lines. This includes investment, operational cost and insurance fees. The following constraints are considered in the optimization process, where the implementation is based on fictitious penalty cost: Maximum admissible line loading An admissible overloading percentage may be defined by the user to avoid over-rating of the lines. Typically any overloading can be avoided by selecting the appropriate type of conductor for cables and overhead lines. The penalty factor for these lines therefore is fix and cannot be defined by the user. Maximum voltage drop Depending on the system topology, on the loads a nd on the length of the feeder, it may not be possible to a void voltage band violations of some nodes due to voltage drop. This ma y be mitigated by the installation of a capacitor during a post-processing optimization.

The specific penalty cost of the optimization therefore is a parameter that can be defined by the user to weight the voltage loss against the line investments.



The optimization process minimizes the annual cost of the network. As constraints for the optimization it uses the admissible voltage band (in terms of max. voltage drop along the feeder) and loading limits for the planned network. The optimization does not need a load curve or a load forecast, as the impact of the conductor type on the cost of losses is not considered within the function. Input data for the reinforcement optimization is a network model that is complete for load-flow calculation. In addition to the network model, the planner has to provide the following information: 



A library section with standard line types (cable or overhead line) that are available for the new type assignment. A value for the max. voltage drop that is allowed for the new network topology.

The result of the optimization is a report about the recommended new cable/overhead types for the lines in the network and the cost evaluated for t he recommended upgrading.


31.3.3 Basic Options Page

The basic parameter page for the Cable Reinforcement function is shown in Figure 31.8. Its options are explained in the following. Feeder Specific Feeder element that supplies the network region where the cables have to be reinforced. Cable Types Reference to folder that contains the allowed new types for overhead lines and cables. Load-Flow Parameter set for the load-flow performed to analyze overloading and voltage band violations. Cable Overloads Defines how to deal with cable overloads detected during the optimization. Consider Cable Overloads Flag to allow overloading of cables and overhead lines for peak load situation. Max. Loading Limit for the admissible loading in the case that overloading of overhead lines and cables is allowed.

Fig. 31.8: Basic Options page Check Consistency Additional plausibility check that can be performed for the final solution. Several settings are possible: Off No plausibility check performed Sum of feeding cables >= sum of leaving cables very strict condition Smallest feeding cable >= biggest leaving cable less strict criterion) Voltage Profile Criteria for dealing with voltage band violations.


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Consider Voltage Profile Flag to force that voltage band v iolations should be included into the optimization of the line types. Maximum Voltage Drop Limit value (in %) to define the max. voltage drop admissi ble at the end of the feeder. Output Various output options for the optimization results are possible. Report Only Proposed new types for cables and overhead lines are listed in a report of pre-defined form Automatic Type Replacement If this option is selected, the Report will be generated and additionally the network database will be update with the proposed types. Report Format Selection of the format of the generated report.


31.3.4 Advanced Options Page

The advanced parameter page for the Cable Reinforcement function is shown i n Figure 31.9.

Fig. 31.9: Advanced Options page Voltage Profile The voltage profile is treated as a constraint of the optimization process. A plane wi th two slopes at the lower and upper limits adds penalty cost to the optimization result in case of violations. The options are as follows: Penalty Factor 1 Penalty cost for voltage drop lower or equal than admissible limit defined on the basic parameter page (typically this value is set to 0). Penalty Factor 2 Penalty cost for voltage drop higher than the admissible limit defined on the basic parameter page. The value entered here describes the weight of the voltage band limit in comparison to the investment cost for the cable/OHL reinforcement. Consistency Verification/Voltage Drop Additional plausibility check that can be performed for the final solution if voltage drop optimization is applied Cross Section Type selection for reducing the voltage drop is based on cable/OHL cross section. Nominal Current Type selection for reducing the voltage drop is based on rated current of cable/OHL.


Chapter 32 Protection The PowerFactory protection modeling features have been implemented with the following philosophy in mind.  

 

The protection modeling should be as realistic as possible The user must be able to create new complex protection devices or alter existi ng ones Although the protection models may show high complexity, their use must be kept easy All protection models will act on switches.

These specifications led to the following principles.  

A fuse is modeled as a time-overcurrent relay acting on a switch A distinction is made between defining or altering new relay models, which is described in the Technical References, and the use of those models, which is described in this chapter.

32.1: Creating a Protection Device 32.2: Basic Protection Devices 32.3: Path Definitions 32.4: Protection Analysis Results 32.5: Short-Circuit Sweep 32.6: Time-Overcurrent Plot 32.7: The Time-Distance Diagram 32.8: Relay Plot 32.9: The Protection Coordination Wizard


32.1 Creating a Protection Device Protection devices are normally stored in the object which they act upon, but they may be stored elsewhere when needed. Recommended, and by default, is that 

protection devices which act upon a single switch a re stored in the cubicle which contains that switch (highly recommended)




 

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protection devices which act upon two or more switches connected to the same busbar are stored in that busbar protection devices which act upon two or more switches connected to the same busbar system, are stored in the station containing that busbar system protection devices which act upon switches connected to more than one busbar sys tem are stored in the station containing those busbar systems, or in the power system grid folder if more than one station is involved

As a rule, the relay is best stored in the same folder as the voltage and/or current transformers which it uses. Editing or creating protection devices in a cubicle can be done in several ways: 

by right-clicking a switch-symbol in the single line graphic. This will bring a pop up menu with the options Edit Protection Devices and New Protection Devices



by editing the object which is connected to the cubicle (line, transformer, load, etc.) and pressing the Relays will bring a list of all protection devices in the cubicle. New devices may be then created with the

button at the cubicle field. See Figure 32.1 for example. The option Edit icon.

Fig. 32.1: Editing line protection devices

In all cases, selecting the option to create a new protection device will bring a list with the f ollowing options: 

 



Relay Model (ElmRelay ) Fuse (RelFuse) Current Transformer ( StaCt) Voltage Transformer (StaVt)

Each of these options will open a dialogue to specify the device that is to be created or to select the one that is to be edited. Example: a Time-Overcurrent Relay Editing the Relay Elements


32.1.1 Example: a Time-Overcurrent Relay

Protection devices form a group of highly complex and non-uniform power system devices. This places any program for modeling them for a difficult dilemma. On the one hand, the relay models should be as flexible and versatile as possible, to ensure that all types of protection relays can be modeled with all of their features. On the other hand, the relay models should be as simple as possible in order to reduce the amount of work and knowledge needed to define power system protection devices. This dilemma is solved by PowerFactory by separating the process of definition a protection type definition from the process of creating a specific protection element. Although the definition of a new protection type asks for a good understanding of composite frames, DSL, time overcurrent plot definitions, etc., the use of a protection element is more or less a 'take o f the shelf' process. This separation between defining new or using existing relay types led to the global relay object hierarchy as shown in Figure 32.2.

Fig. 32.2: Global relay object hierarchy

The relay frame is a graphically defined composite frame which defines the functional parts of the relay and their connections. The relay frame can be compared with an empty printed circuit board. The relay type is based on the relay frame and defines the type of parts which are allowed to be put in the relay slots. The relay type can be compared with a printed circuit board with specific, but still empty, chip or r elay sockets. The relay itself models a specific protection element, based on the relay frame and the relay type. The relay model uses specific functional elements where the relay type defines only the allowed type of elements. These specific elements must be based on those element types. The relay object can be compared with a finished printed circuit board, where specific relays and chips have been inserted in the sockets. Figure 32.2 also shows that most of the work of defining a protection device is done by the Relay Type Designer. A large set of common relays types is available in the database and these types are ready for use. How to use a relay type, that is: how to create a relay element, how to add it to the power system, how to adjust the relay settings, how to perform calculations, etc., is


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shown by the example of a simple time-overcurrent relay. This relay measures the currents in three phases, but calculates a single maximum current Imax. The relay trips a breaker when Imax violates either the time-overcurrent or the instantaneous overcurrent conditions. The Relay Frame The Relay Type Creating a Relay Model The Relay Frame

The example relay frame is shown in Figure 32.3. This is not a symbolic representation of the relay, but the selected composite frame which defines the relay type. The design of these relay frames is described in the Technical References manual. The block diagram is only shown here to explain the example relay.

Fig. 32.3: Composite frame of a time-overcurrent relay

In the relay frame, the following slots can be distinguished: 



 

A current transformer slot (StaCt), which outputs are the real and ima ginary parts of the three phase currents (IrA, IiA, IrB, etc.) and the real a nd imaginary parts of the zero sequence current (I0x3r,I0x3i). A measurement unit slot (RelMeasure), which output is Imax, w hich is the maximum of the three phase currents. A slot for a time-overcurrent relay unit ( RelToc) and one for an instantaneous overcurrent relay unit ( RelIoc), with the tripping signals as outputs. A logic unit slot (RelLogic ), which combines the tripping signals in a logical way to produce a single tripping signal.

The Relay Type

The example relay type that is defined on the basis o f the time-overcurrent relay frame is shown in Figure 32.4.

Fig. 32.4: The relay type dialogue

The "Relay Definition'' field points to the relay frame. The slot definition list will automatically show all slots defined by that relay frame. In the example, these are the five slots described in the previous section. The "Category'' field is only used to help selecting a relay type. An object type is normally selected for each slot, except for the slots f or the current and voltage transformers. A relay based on the relay type may not use elements other than such which are based on the given object types. The fact that, in t he example, no type is specified for the current transformer, means that all current transformers may be used. Normally, relay types are only selected but not changed or edited. The PowerFactory relay database offers a wide variety of relay types. Creating a Relay Model

This is where we leave the domain of the relay designer enter that of the relay user. As soon as a new relay is inserted in the power system, which is normally done by rightclicking a switch and selecting New Protection Device - Relay Model , an empty relay model ( ElmRelay appears. The example relay model is depicted in Figure 32.5.


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Fig. 32.5: Relay model dialogue

The relay model has a reference to a relay type, a location, a device number and a list of slots. The location is normally set automatically when a relay is defined in the single line graphic by right-clicking a cubicle. The cubicle then defines the location. The device number is only relevant for the device documentation. The slot list is defined by the relay type. As is shown in Figure 32.5, the relay model should define objects for all the slots in the relay type. Each of these 'slot elements' must use the corresponding 'slot type', when such a type is defined in the relay type. Luckily, the tedious work of creating the correct elements, selecting the correct type and assigning the element to the correct slot, is performed by the relay element itself. The whole process of creating a specific relay model thus only asks for selecting a relay type from the database. What follows then can best be compared by an automatic assembly process:  



as soon as a new relay type is selected, the slot definition list is updated all slot elements for which a slot type has been defined will be created automatically. No elements will be created for those slots f or which no slot type has been defined. Normall y, these are only the voltage and current transformer slots. However, if already existing and valid objects are found in the relay model or the cubicle in which it resides, they will be assigned to the slots automatically. the created slot elements are inserted in the slot definition list

The result is a new and complete relay model with all slots filled (except maybe for the transformer slots). Of course, all relay settings are still set to their default values. All slot elements created by the relay model are stored in the relay model itself. Figure 32.6 shows the database tree with the example relay model.

Fig. 32.6: Example relay model with slot elements

The current transformer in the example is not stored in the relay model but in the cubicle. When, again, a new relay type is selected, the slot elements created for the previous relay type will in most cases not be suited for the new type. However, the 'automatic assembly process' will try to reuse as much data as possible from the old settings:  

 

Slot elements that are also suited for the new rely type will be reused as they are Slot elements which are correct except for their type will be assigned the correct slot type Slot elements which cannot be reused will be deleted Missing slot elements will be created automatically

Pressing the Cancel button after the Relay Type has been changed will not restore the old slot elements.

Normally, the relay type will not define any current and/or voltage transformer types. The corresponding transformer element will thus not be created automatically. However, if these measurement transformers were created prior to creating the relay element, they will be assigned to the correct slot automatically. This is the recommended practice. If the measurement transformers were not created yet, they may be created by pressing the Create VT or Create CT buttons. That will create a new transformer in the cubicle were the relay element is stored.


32.1.2 Editing the Relay Elements

After a relay element has been defined and all slot elements have been created, the editing of the relay settings may be started by editing the slot elements. In the example settings have to be enter for    



The CT "Current Transformer 0'' The Measurement object "Measurement'' The time overcurrent relay "Toc'' The instantaneous overcurrent relay "Ioc'' The logic object "Logic''

For the current transformer, the tap settings and the connection type have to be selected. The possible tap range is limited by the type. See Figure 32.7.


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Fig. 32.7: A current transformer dialogue

The measurement object only needs the Nominal Current and Nominal Voltage. Their range is limited by the measurement type. The nominal values are only needed if the relay uses p.u. values. In the example, the measurement object needs no data at all. See Figure 32.8.

Fig. 32.8: A measurement object

The time overcurrent relay allows for setting 

 

The time overcurrent characteristic The pickup current The time dial

All three settings are limited by the relay type: only those characteristics available for this type of relay can be selected and not every possible values for the pickup current or time dial may be entered. See Figure 32.9.

Fig. 32.9: A time overcurrent relay

The instantaneous overcurrent relay allows for setting the pickup current. See Figure 32.10.


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Fig. 32.10: An instantaneous overcurrent relay

The logic unit dialogue shows a list of all switches that will be opened as soon as the logic unit trips. The logic unit combines the tripping signals of the sub relays (the Toc and Ioc relays in this example), in an AND/OR expression (Toc OR Ioc in this example). All switches in the list will be opened. If the relay to which the logic unit belongs is stored in a cubicle, the three-phase breaker in that cubicle will be opened by default if no switches are been specified. See Figure 32.11.

Fig. 32.11: A logic relay object


32.2 Basic Protection Devices As has been explained in the introduction of this chapter, the whole hierarchy of objects that is used to build protection devices can be divided into  

objects which are needed to define new types of protection devices objects which are needed to define specific relay models.

The first group of o bjects are treated in detail in the Technical References manual. The second group of objects are treated in this section. The Current Transformer The Voltage Transformer The Relay Model Directional Relay The Frequency Measurement Unit The Frequency Relay The Fuse Model The Instantaneous Overcurrent Relay The Logic Unit The Measurement Unit The Time Overcurrent Relay Under-/Overvoltage Relay


32.2.1 The Current Transformer

A new current transformer (CT) can be created by right-clicking a cubicle in the single li ne diagram and selecting "New Protection Device - Current Transformer'' . The dialogue as depicted in Figure 32.12 will then pop up.


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Fig. 32.12: The Current Transformer dialogue

A thus created CT will be stored in the cubicle that was right-clicked. The "Location'' fields "Busbar'' and "Branch'' will be set automatically in that case. A current transformer always needs a current transformer type. The top "Location'' field is used either 



to select a cubicle when the CT is created from outside the cubicle, to select the preceding CT in the case of an auxiliary CT.

After selecting the type and the setting of the current transformer, its set ratio is shown in the dialogue ( Ratio ). In very special cases CTs may be connected in series, that is the output of one CT is used as the input of the second CT. In this application the second CT will show a Ratio (the actual ratio of the CT) and a Complete Ratio , (the ratio between the primary branch flow and the secondary CT current, which is the overall ratio of all CTs connected in series). In the example of Figure 32.12, the CT is directly connected to the primary component (which is the standard) and both Ratio and Complete Ratio show the same value of 1000 A to 1 A. The primary connection type is only available in the case of an auxiliary CT. The number of phases can be set to 3, 2 or 1. For a 3- or 2-phase CT, the secondary connection type can be set to D or Y. For a 1-phase CT, the phase can be set to   

a, b or c phase current N = 3*I 0 I =I 0 0

The primary and secondary tap settings are limited to the values defined in the current transformer type. The Current Transformer Type

The current transformer type dialogue, as depicted in Figure 32.13, defines the single phases of a CT. The information about the connection of these phases (Y or D) is defined in the CT element that uses the CT t ype.

Fig. 32.13: The Current Transformer Type dialogue

The current transformer type defines the primary and secondary taps of the transformer. The "Additional Data page'' is used only when saturation is considered, to set the accuracy parameters:  



The accuracy class The accuracy limit factor either The apparent power (acc. to IEC) The burden impedance (ANSI-C) The voltage at the acc. limit (ANSI-C) 

 


32.2.2 The Voltage Transformer

A new vol tage transformer (VT) can be created by right-clicking a cubicle in the single line diagram and selecting "New Protection Device - Voltage Transformer'' . The dialogue as depicted in Figure 32.14 will then pop up.


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Fig. 32.14: The Voltage Transformer dialogue

A thus created current transformer will be stored in the cubicle that was right-clicked. A voltage transformer always needs a voltage transformer type. The "Location'' field is used either  

to select a cubicle when the VT is created from o utside the cubicle to select the preceding VT in the case of an auxili ary VT

After selecting the type and the setting of the current transformer, its set ratio is shown in the dialogue ( Ratio ). In the example of Figure 32.14, the shown VT has a ratio of 5000 V to 100 V. The primary winding is defined by selecting a tap and a connection type. The available tap range is defined in the voltage transformer type. The secondary winding is defined by the secondary winding type, the tap setting and the connection type. The available tap range is defined in the secondary winding type. A voltage transformer requires at least one secondary winding. More windings can be defined by pressing the button Additional Secondary Windings. This will bring a list of all previously defined secondary windings. New windings can be created by pressing the

icon.

The connection type "O'' for the secondary windings is the "Open Delta'' connection, as depicted in Figure 32.15.

Fig. 32.15: The open delta (O) winding connection

The connection type "V'' for the primary and secondary windings is depicted in Figure 32.16. Selecting a "V'' connection for the primary winding automatically sets the secondary winding to a "V'' too.

Fig. 32.16: The "V'' winding connection The VT Secondary Winding

A secondary winding element is needed when a voltage transformer with two or more secondary windings has to be modeled. The edit dialogue for the voltage transformer provides parameters to define the first secondary winding.


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Fig. 32.17: The VT secondary winding dialogue

The secondary winding element requires a type and a reference to the voltage transformer. The tap settings range is defined by the windings type. The VT Secondary Winding Type

The secondary winding type, as depicted in Figure 32.8, defines the burden and tap range for one phase of a voltage transformer. The phase connection type (Y, D, etc.) is defined in the secondary wi nding element.

Fig. 32.18: The VT secondary winding type dialogue

The secondary tap settings defined in the secondary winding type determine the available tabs for the secondary winding element. The Voltage Transformer Type

The voltage transformer type, as depicted in Figure 32.19 defines the primary winding of the voltage transformer.

Fig. 32.19: The voltage transformer type dialogue

The secondary windings are defined i n the voltage transformer element.


32.2.3 The Relay Model

The relay model ( ElmRelay ) is a general 'frame-object' which consists of a relay frame with slots and one or more elements which occupy those slots. All protection relays, except for the fuse models, are modeled as relay models.


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Fig. 32.20: The relay model dialogue

The relay element is defined by selecting a relay type. The relay type defines the relay frame and the slot types which may be used with that frame. After a relay type has been selected, the "Slot Definition'' list will be filled automatically with the correct slot elements. The current and voltage transformers, however, are not created automatically, although available CT's and VT's are selected automatically. Editing the settings of the relay model is done by editing the settings of the listed slot elements. Double-clicking a slot element in the "Slot Definition'' list will open the dialogue of that element. For more information about slot elements, see Directional Relay The Frequency Measurement Unit The Frequency Relay The Fuse Model The Instantaneous Overcurrent Relay The Logic Unit The Measurement Unit The Time Overcurrent Relay Under-/Overvoltage Relay


32.2.4 Directional Relay

The directional relay cannot be used 'as-is', but is always a part of a relay model. For more information about relay models, see 32.2.3 The Relay Model The directional relay calculates the angle between a 'polarization' voltage or current and an 'operating' current. The polarization current or voltage is rotated to the amount of the expected angle first. The relay trips if the remaining angle is smaller than 90° and if both the polarization and the operating voltage/currents are large enough. This principle is shown in Figure 32.21.

Fig. 32.21: Directional relay principle diagram

The polarization quantity A is rotated over the angle M , which is the "Max. Torque Angle'' set in the relay edit dialogue. The rotated polarization quantity A' defines a pol current half plane which forms thepol first tripping condition. FurtherTconditions are the projection of the operating quantity on A' , which must be larger than the operating pol setting, and the polarization quantity, which must be larger than the polarization setting. More details about the polarization methods and the tripping conditions can be found in the basic Technical References manual. The choice for the type of operating and polarization quantity is made in the Directional Relay Type object. The relay object itself allows for the setting of the tripping direction, the polarization method when both methods (voltage and current) are available, and the polarization criteria. See Figure 32.22.


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Fig. 32.22: Directional relay

Selecting a 'Reverse Tripping Direction' will invert the used operating current. The voltage or current polarization allow for setting the "Operating Current'', the "Polarization Voltage/Current'' and the "Max.Torque Angle''.


32.2.5 The Frequency Measurement Unit

The frequency measurement unit cannot be used 'as-is', but is always a part of a relay model. For more information about relay models, see 32.2.3 The Relay Model ). The frequency measurement unit is used to calculate the electrical frequency for the given "Measured Voltage''.

Fig. 32.23: Frequency Measurement

The Nominal Voltage is needed for per unit calculations. The Frequency Measurement Time defines the time used for calculating the frequency gradient.


32.2.6 The Frequency Relay

The frequency relay cannot be used 'as-is', but is always a part of a relay model. For more information about relay models, see 32.2.3 The Relay Model . The frequency relay either trips on an absolute under-frequency (in Hz), or on a frequency gradient (in Hz/s). Which condition is used depends on the selected relay type. The relay type also defines the reset time, during which the frequency condition must be met again for the relay to reset. The time delay set in the relay element defines the time during which the frequency condition must be violated for the relay to trip. See Figure 32.24.

Fig. 32.24: Frequency


32.2.7 The Fuse Model

The fuse model is implemented as a special instantaneous overcurrent relay which does not need a current transformer. A fuse is always located in a cubicle and will trip the phase which current exceeds the melt curve. Optionally, all three phases will be tripped if one of the phase currents exceeds the melt curve.


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Fig. 32.25: The Fuse model dialogue

The calculation of the trip time is either based on the minimum melt curve or on the total clear curve. An example of these curves are shown in Figure 32.26.

Fig. 32.26: Fuse melt characteristics


32.2.8 The Instantaneous Overcurrent Relay

The instantaneous overcurrent relay cannot be used 'as-is', but is always a part of a relay model. For more information about r elay models, see the reference documents). The instantaneous overcurrent relay allows for the setting of the pickup current and the time dial. Both entries are limited by the r elay type. See Figure 32.27.

Fig. 32.27: Instantaneous Overcurrent

The instantaneous overcurrent relay is a combination of a direct overcurrent relay and an optional time delay. The pickup time Ts is the minimum time needed for the relay to react. Additionally, a time dial Tset may be specified. The relay will not trip unless the current exceeds the pickup current Tsetr for at least Ts+Tset. See Figure 32.28.

Fig. 32.28: Instantaneous overcurrent tripping area


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The relay will not reset until the current drops under the reset level, which is specified by the relay type in percent of the pickup current: Ireset=IpsetKr/100%. See Figure 32.29 for a typical timing diagram.

Fig. 32.29: Instantaneous overcurrent timing diagram


32.2.9 The Logic Unit

The logic unit is the fro nt end part of a relay configuration. It combines all internal trigger signals by successive AND and OR o perations and produces one single output. The logic unit type specifies the logical operation, the logic unit itself specifies the switches which will be opened when the r elay trips. See Figure 32.30.

Fig. 32.30: Relay logic

If the relay is located in a cubicle and no switch has been specified, the breaker in the cubicle will be opened by default.


32.2.10 The Measurement Unit

The measurement unit uses the 'raw' signals produces by the current or voltage transformers to calculate 'measured signals'. Which signals are being calculated depends on the measurement unit type. The measurement unit allows for setting the nominal current and voltage. Both are limited by the measurement unit type. If a relay does not need a nominal voltage (i.e. in the case of an overcurrent relay), the nominal voltage field will normally be disabled.

Fig. 32.31: Measurement


32.2.11 The Time Overcurrent Relay

The time-overcurrent relay cannot be used 'as-is', but is always a part of a relay model. For more information about relay models, see 32.2.3 The Relay Model . The time-overcurrent relay allows for the selection of one of the I-t curves ('characteristic') which are available for the selected relay type. The I-t curve i s further specified by the pickup current and the time dial. Both values must be in the range specified by the I-t curve definition. See Figure 32.32 for an example.


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Fig. 32.32: The time overcurrent relay dialogue

The time dial settings will scale the I-t curve in the Time vs. I/Ip plot, according to the curve definition. See Figure 32.33 for example.

Fig. 32.33: I-t curves for different time dials

The pickup current defines the nominal value Ip which is used to calculate the tripping time. The I-t curve definition states a minimum and a maximum per unit current. Lower currents will not trip the relay (infinite tripping time), higher currents will not decrease the tripping time any further. These limits are shown in Figure 32.34.

Fig. 32.34: I-t curve limits

The pickup current may be defined by the relay type to be a per unit value, or a relay current. The nominal current defined by the measurement unit (see Measurement Unit ) is used to calculate Ip in the case of a per unit value. The relay current value already equals Ip.

32.2.10 The

Altering the pickup current will thus not change the I-t curve, but will scale the measured current to different per unit values. The following example may illustrate this: 

 



Suppose the minimum current defined by the I-t curve is imin=1.1 I/Ip. Suppose the measurement unit defines Inom=5.0 rel.A. Suppose pickup current Ipset=1.5 p.u. −> relay will not trip for I<1.1*1.5*5.0 rel.A = 8.25 rel.A Suppose pickup current Ipset=10.0 rel.A −> relay will not trip for I<1.1*10.0 rel.A = 11.0 rel.A


32.2.12 Under-/Overvoltage Relay

The under- or overvoltage relay cannot be used 'as-is', but is always a part of a relay model. For more information about relay models, see 32.2.3 The Relay Model . The under-/overvoltage relay type may define the relay to trip on either 

 

 

Either one of the three phase line to line voltages One particular line to line voltage The ground voltage U . 0 The positive sequence voltage U 1 The negative sequence voltage U


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The relay element allows only for setting the pickup voltage and the time delay. See Figure 32.35.

Fig. 32.35: Under-/Overvoltage


32.3 Path Definitions A path in a single line diagram is defined by selecting a chain of two or more busbars or terminals and inter-connecting objects. The pop-up menu which opens when the selection is right-clicked will show a Path... option. This menu option has the following sub-options: New this option will create a new path definition Edit this option is enabled when an existing path is right-clicked. It opens a dialogue to alter the color and direction of the path Add To this option will add the selected objects to a path definition. The end or start of the selected path must include the end or start of an existing path. Remove Partly This will remove the selected objects from a path definition, as long as the remaining path is not broken in pieces Remove This will remove the firstly found path definition of which at least one of the selected objects is a member

Editing, adding objects to or removing objects from path definition is only possible when the option coloring "Path Definitions'' was chosen in the Color Representation of Graphic dialogue ( SetColgr). This dialogue is opened by pressing the icon

on the graphics toolbar.

A path may be used as a selection for a calculation by selecting one or more objects from the path definition. This will select the whole path.


32.4 Protection Analysis Results Reports Results in Single Line Graph Plots


32.4.1 Reports

The icon "Output Calculation Analysis'' ( ) in the main menu, will open the "Output'' dialogue (ComSh). The results of the lo ad-flow or short-circuit analysis, for a range of relays, can be generated in the output by selecting the options 



Results Relays

To generate a report for one or more relays, or for one or more previously defined paths, the data manager may be used to select one or more relays or paths and rightclicking the selection. The menu will show the option Output-Results if at least one relay was fo und amongst the selected objects or in one of the selected paths. If a busbar was selected, then all relays in connection with that busbar are selected too.


32.4.2 Results in Single Line Graph

The names of the relays or the tripping times may be made visible in the single line graphic by selecting the following options in the main menu. 1. 2.

Output - Results for Edge Elements - Relays Output - Results for Edge Elements - Relay Tripping Times

The first option ("Relays'' ), which is always available, will show the names of the relays in all cubicles. The second option will show the tripping times of the relays after a load-flow or short-circuit calculation has been made. If a relays does not trip, then a tripping time of 9999.99 s is shown.


32.4.3 Plots

The time-overcurrent plots offer many features for displaying the settings of relays and the results of short-circuit or load-flow calculations. The time-overcurrent plots may also be used for changing the settings of relays and fuses, by simply moving the tripping characteristics. Especially the possibility of changing the curves in combination with a short-circuit or load-flow result, and with the help of transformer or line damage curves, ensures a clear and comprehensible setting of the relay parameters.


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The following section explains the special features of the time-overcurrent plots.


32.5 Short-Circuit Sweep The "Short-Circuit Sweep'' command as depicted in Figure 32.36 is used to calculate a short-circuit sweep along a defined path. Short-circuits are calculated along a given path and the results at each short-circuit location are written to a Results object. The position in km relative to the beginning of the path is always written to the results. The sweep command is used e.g. by the Time-Distance Diagram (see 32.7) to record the trigger times of distance relays.

Fig. 32.36: The short-circuit sweep dialogue

Options Advanced Options


32.5.1 Options

Path Additional Relays Results Frame Results Locations Short-Circuit Frame Path

Short-Circuits are calculated along this path. Path is set automatically and grayed out if the command is called by the "Time Distance Plot''. Additional Relays

If the option "Iterate Tripping Times'' on the advanced page is set, the positions where a relay trips is interpolated and written to the results. The relays whose tripping times are checked are the relays found in the path and, in addition, the relays given by the selection referenced in "Additional Relays''. Additional relays is grayed out and set if the command is called by the "Time Distance Diagram''. Results Frame

The variables written to the results object can either be defined by the user or by the "Time Distance Diagram''. If the results are defined by the "Time Distance Diagram'' all "Monitor Variable Sets'' in the results object are ignored. Otherwise the variables found in the "Monitor Variable Sets'' stored in the results object are written. The result frame is grayed out if the command is accessed through the time-distance diagram. Results

Reference to result object, see also Result Frame, grayed out i f the sweep dialogue is accessed through the time-distance diagram. Locations

A short-circuit is calculated on each busbar/terminal found in the path. If "Buses and Branches'' is selected short-circuits on the branches between the busbars are calculated. Short-Circuit Frame

"Command'' is a reference to the short-circuit command. Except the short-circuit location the short-circuit settings are not changed by the sweep. The type of failure, the method of calculation and other settings can be modified there. "Calculation'' is just displaying the "Fault Type'' set in the short-circuit command.



Step Size Precision and Step Size Step Size

The relay tripping positions in the path can either be iterated or calculated with a continuous step size. In the constant mode a short-circuit is calculated at the beginning of the branch. The distance between the following short-circuits on the branch is "Continuous Step Size''. There is always a short-circuit calculated at the end of the branch. In the "Iterate Tripping Times'' method the relay tripping positions are iterated. If the tripping time of a relay changes continuously (like overcurrent relays) the sweep changes to continuous mode automatically. Iteration mode is used again when the tripping time remains unchanged at the next short-circuit position. The step size frame is grayed out if the command is accessed by the time-distance diagram. Precision and Step Size


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The "Precision (Steps)'' defines the maximum iteration error at the relay tripping position. The "Continuous Step Size'' defines the step size for the sweep with constant steps. "Precision and Step Size'' is unused (hidden) if location is set to buses.


32.6 Time-Overcurrent Plot The plot VisOcplot is showing different relay and fuse characteristics in one time-overcurrent plot. Additionally the damage curve and characteristic currents of electrical equipment in the network can easily be shown. This will help to set the relay tripping times and current settings and the selecting of fuses for a good and thorough protection of the equipment. There are several ways to create a time-overcurrent plot ( VisOcplot): 







The easiest way to create and show a VisOcplot is to select one switch, where overcurrent relays or fuses are installed. Right-click the switch to open the context sensitive menu. This will show the options Create Time-Overcurrent Plot and Add to Time-Overcurrent Plot . PowerFactory will then create a new diagram showing the time-overcurrent plot for all relays selected. Another way is to right-click an path element and select Path...−> Time-Overcurrent Plot from the context sensitive menu. Also a relay element ElmRelay can be chosen from the list of calculation-relevant objects or in the data manager. Ri ght-click the relay on the right side of the data mana ger or in the list of relays. Then select Show −> Time-Overcurrent Plot to create a new plot or Show −> Add to Time-Overcurrent Plot to add the characteristic to an existing plot. Additionally other elements like one or more transformers, cables or motors can be selected and right- clicked. The context sensitive menu will show the options Show −> TimeOvercurrent Plot to create a new plot and Show −> Add to Time-Overcurrent Plot to add the characteristic to an existing plot.

Note To show the relay locations and thus to visualize the switches with relays definitions these can be highlighted by setting the color representation of the single-line diagram to "Relay Locations''. By right-clicking these elements the option Show −> − > − > Time-Overcurrent Plot is available and can be chosen.

In all these cases, it is also possible to select the option Add to Time-Overcurrent Plot . This will pop up a list of previously defined over current plots from which one has to be selected. The overcurrent plot shows 

  

the time-overcurrent characteristics of relays the damage curves of transformers or lines motor starting curves the currents calculated by a short-circuit or load-flow analysis and the resulting tripping times of the relays

See Figure 32.37 for an example.

Fig. 32.37: A time-overcurrent plot with short-circuit results

The time-overcurrent plot shows the results of the short-circuit or load-flow analysis as a vertical ' x-value' line across the graph. Because the currents differ for each particular relay, a current line is drawn for each relay. The intersection of the calculated current with the time-overcurrent characteristic is labelled with the tripping time. A 'grading margin' line, which shows the difference between the tripping times, may be added by right-clicking the plot and selecting "Show Grading Margins''. It is also possible to create an user defined 'x-value' by right-clicking the graph and selecting the Set Constant −> x-value option. The vertical line will show the values at the intersections of all displayed characteristics. To move the line left, drag it with the mouse. Changing Tripping Characteristics


32.6.1 Changing Tripping Characteristics

The time overcurrent plots may also be used to change the relay characteristics graphically. Because a relay characteristic is normally the minimum of two or more subcharacteristics, it has to be split first in order to change the sub-characteristics. A characteristic is split by  

right-clicking the characteristic enable the split option

The relay characteristics can also be split by opening the edit dialogue of the plot and enabling the option Split Relay in the table Relay , where all relays are listed. The sub-characteristics are now visible. Each of them can be left clicked and dragged along the time-overcurrent plot area. However, they cannot be dragged outside the allowed range which has been defined for the relay type. After the relay sub-characteristics have been changed, they can be combined again into one single characteristic by disabling the split option again. The plot option dialogue, which is opened by right-clicking the plot area and selecting Options , has an option for showing the grading margins when the time overcurrent characteristics are dragged. The grading margin may be set to a fixed time. The grading margins are shown as two lines, plus and minus the grading margin above and below the dragged tripping characteristic. See Figure 32.38 for an example: the original characteristic is labelled "1'', the new position as "2'', and the grading margins are labelled "a''.


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Fig. 32.38: Moving a characteristic with grading margins

Conductor/Cable Damage Curve Transformer Damage Curve Motor Start Curve Overcurrent Plot Settings Conductor/Cable Damage Curve

The conductor and cable damage curves are used to evaluate a protection coordination variation and as guides for positioning the time-overcurrent characteristics.

Fig. 32.39: Conductor/Cable damage curve

To add a damage curve to a time-overcurrent plot, right-click the plot area and select Add...−> Conductor/Cable Damage Curve. The Rated Short-Circuit Current and time of the cable can be inserted. Also typical Cable Parameters for the conductor, insulation factor, K, are given in figures 32.40 and 32.41. These tables show the temperature range for the cables: 



T1 = maximum operating temperature in º C T2 = maximum short-circuit temperature in º C

2 2 and the K factor for a cross section in mm , CM, MCM and inch .

Fig. 32.40: Typical damage parameters for copper conductor cables


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Fig. 32.41: Typical damage parameters for aluminium conductor cables Transformer Damage Curve

The transformer damage curves are used to evaluate a protection coordination variation and as guides for positioning the time-overcurrent characteristics.

Fig. 32.42: Transformer damage curve

To add an ANSI/IEEE C57.109 damage curve to a time-overcurrent plot, right-click the plot area and select Add...−> Transformer Damage Curve. An example of a timeovercurrent plot with two relay characteristics and a transformer damage curve is shown in Figure 32.43.

Fig. 32.43: Transformer damage curve

To add the damage curves of specific transformers in the power system, right-click the transformer object in the single line graphic or the database manager and select the option Show −> Add to Time-Overcurrent Plot. This will pop up the list of defined overcurrent plots from which one has to be selected. A damage curve will then be calculated from the electrical transformer data, according to the ANSI/IEEE C57.109 standard, and added to the selected time over-current plot. It is also possible to add a two-winding or three-winding transformer object to the graph manually. This i s done by editing the graph and adding the transformer object to the list of displayed relays. Motor Start Curve

The motor start curves are used to evaluate a protection coordination variation and as guides for positioning the time-overcurrent characteristics.


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Fig. 32.44: Motor start curve edit dialogue

The characteristic currents and durations given in the edit dialogue result in a step wise motor start current plot, as depicted in Figure 32.45.

Fig. 32.45: The motor start curve Overcurrent Plot Settings

The time-overcurrent plot settings can be accessed by selecting the Options from the context-sensitive menu. The dialogue shows the following options: Current Unit The current unit may be set to either primary or secondary (relay) ampere. Show Relays This option is used to display only certain types of relay characteristics. Recloser Operation

The different recloser stages can be shown simultaneously or switched off in the diagram. Display automatically This option is used to select how the ca lculated load-flow or short-circuit currents will be displ ayed. Either the current lines, the grading margins, both or none may be selected. Voltage Reference Axis More than one current axis may be shown, based on a different voltage level. All voltage levels found in the path when a time overcurrent plot is constructed are shown by default. An user defined voltage level may be added. Optionally, only the user defined voltage level is shown. Cut Curves at normally the curves of different relay zones cut at the same tripping current. Show Grading Margins while Drag&Drop When dragging the curves up and down resp. right and left, the grading margins of the curve will be shown according to the ma rgin entered.

Fig. 32.46: Overcurrent Plot Settings

The advanced options are: Drag & Drop Step Sizes These are used to set the step change in the relay settings when a tim e-overcurrent plot is dragged with a continuous time dial or pickup current. Time Range for Step Sizes Enter the tripping time range for the y-axis. 'Color for Out of Service' Units The characteristics for units that are out of service are drawn invisible by default. However, a visible color may be selected. Brush Style for Fuses This defines the fill style for fuse curves Nr. of points per curve


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The number of points can be changed to either refine the plotted curves for more detail, or to speed up the drawing of the diagram.


32.7 The Time-Distance Diagram The time-distance plot VisPlottz shows the tripping times of the relays depending on the short-circuit location. It is normally calculated by the short-circuit sweep command. See short-circuit sweep command (Section 32.5) for more information. It is directly connected to a path definition described in Section 32.3 Path Definitions , so it can only be created if a path is already defined.

Fig. 32.47: A time-distance plot

To create a time-distance diagram: 





The easiest way to create and show a VisPlottz is to right-clicked an element, which is already added to a path definition. From the context sensitive menu the option Show −> Time-Distance Diagram can be selected. PowerFactory will then create a new object VisPlottz showing the time-distance plot for all distance relays in the path. Another way is to right-clicked an path element and select Path...−> Time-Distance Diagram from the context sensitive menu. Like above this will create a new object VisPlottz. Also path object SetPath can be chosen in the data manager under Database \ Projectname \ Paths . Select the "Paths'' folder and right-click the path object on the right side of the data manager. Then select Show −> Time-Distance Diagram from the context sensitive menu.

Note To show the path definition and thus to visualize the elements contained in the path can be highlighted by setting the color representation of the single-line diagram to "Path Definitions''. By right-clicking these elements the option Show −> − > − > Time-Distance Diagram is available and can be chosen.

The time-distance plot in Figure 32.47 is separated in two different diagrams. The forward diagram shows all relays at the beginning of the line in path direction. The reverse diagram shows the relays at the beginning of the line in reverse path direction. The upper diagram is in forward direction, the lower one in backward direction. There are three different styles for the time-distance plot.These are: Forward/Reverse

Both diagrams are shown. Forward Only forward direction diagram Reverse Only reverse direction diagram

The Path Axis Methods for calculation of tripping times Short-Circuit Calculation Settings The x-Unit The Reference Relay Double-Click Positions The Context Sensitive Menu Set Relays Buttons


32.7.1 The Path Axis

Fig. 32.48: A path axis

The path axis in Figure 32.48 shows the complete path with busbar and relay locations. Busbars/Terminals are marked with a tick and the name. The boxes above and below the line show the relay locations in forward and in backward direction. The reference relays in both directions are marked with an arrow.


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32.7.2 Methods for calculation of tripping times

There are several methods to calculate the tripping times shown in the plot. To change the method, select the Method option in the context sensitive menu or double-click the plot to access the time-distance plot dialogue and edit Methods option on the Relays page. The methods differ in exactness and speed. The set of possible units for the x-Axis depends on the method used. The methods are: Short-Circuit Sweep Method The short-circuit sweep method is the most accurate method for calcula ting the short-circuit locations. A short-circuit sweep is calcula ted over the branches between the first and the last busbar in the path. At each sh ort-circuit location the relay tripping times are established. The disa dvantage of this method is it's low speed. Whenever the rebuild button of the graphics window is pressed the sweep is recalculated. The possible units for the short-circuit location are position in km or reactance in primary or relay ohm. Kilometrical Method This method is the fastest but most inaccurate one. Tripping time and location are determined with the intersection of the impedances and the relay characteristic. The impedances used for calculation are the impedances of the device. If there is more than one intersection at the same im pedance the smallest tripping time is used. The possible units for the short-circuit location are position in km or reactance, resistance a nd impedance, each in primary or relay o hm.

Fig. 32.49: The Time-Distance plot edit dialogue

The kilometrical method is applicable only for the following paths  

There are no parallel branches in the path. The path is fed from only one side or there is no junction on the path.


32.7.3 Short-Circuit Calculation Settings

If the method for the calculation of the time-distance plot is set to "Short-Circuit Sweep'', the short-circuit sweep command object ComShcsweep is used. There is either the option Shc-Calc... in the context menu of the plot or the Shc-Calc... button in the "Time Distance Plot'' edit dialogue to access the sweep command. Some of the settings in the command are predefined by the time-distance plot. These settings are grayed out when the sweep command is accessed through the plot. The short-circuit command for the calculation is set in the sweep command. To change the short-circuit method, e.. "IEC'' o r "Complete'', open the sweep command and edit the short-circuit dialogue.

Note The easiest way to calculate the short-circuit sweep for the time-distance plot is by simply pressing the button . Mind that this is only needed when using the Short-Circuit Sweep method. The Kilometrical method does not need the short-circuit sweep command.

See Section 32.5 Short-Circuit Sweep for more information.


32.7.4 The x-Unit

There is a set of possible x-units depending on the method used. See the methods description for details. The short-circuit sweep method needs a relay to measure the impedance, named the reference relay. If there is no reference relay selected the first relay in the diagram's direction is used as reference relay. The options available for the x-unit are: Length x-axis is shown depending on the line/cable length from the reference relay in"k m''. Impedance (pri.Ohm) x-axis is shown depending on the impedance from the reference relay. Reactance (pri.Ohm) x-axis is shown depending on the reactance from the reference relay. Impedance (sec.Ohm) Here the impedance from the reference relay is measured on the secondary side. Reactance (sec.Ohm) Here the reactance from the reference relay is measured on the secondary side.


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32.7.5 The Reference Relay

The x-Axis positions or impedances are calculated relative to the beginning of the path. If a reference relay was set the positions/impedances are relative to the reference relay. The sweep method needs always a reference relay. If no reference relay was set the first relay in the diagram's direction is taken for reference relay. The busbar connected to the reference relay is marked with an arrow pointing in the diagrams direction. The reference relay is set either using the graphic or by editing the "Time Distance Diagram'' dialogue. Changing the reference relay graphically is done by clicking with the right mouse button on the relay symbol and selecting "Set reference relay'' in the context menu. If there is more than one relay connected to the selected busbar PowerFactory prompts for the relay to use. In the dialogue of the "Time Distance Relay" the "Reference Relay'' frame is located on the bottom. Change the "Relay'' reference to set or reset the reference relay.


32.7.6 Double-Click Positions

The following positions can be double-clicked for a default action: Axis Edit scale Curve Edit step of relay Relay box Edit relay(s) Path axis Edit Line Any other Open the "Time Distance'' edit dialogue


32.7.7 The Context Sensitive Menu

If the diagram is right-clicked at any position, the context sensitive menu will pop up similar to the menu described in Section 20.1.2 Plots for the virtual instruments. There are some additional functions available in addition to the basic VI-methods for the time-distance plot. Grid Shows the dialogue to modify the grid-lines. Edit Path Opens the dialogue of the displayed path definition ( SetPath). Method Set the used method for calculating the tripping times. x-Unit Set the unit for the x-Axis, km impedances,... Diagrams Select diagrams shown forward, reverse or both. Consider Breaker Opening Time Report This option prints out a report for the position of the relays, their tripping time as well as all calculated impedances in the o utput window. Shc-Calc... Show "Short-Circuit Sweep'' command dialogue.


32.7.8 Set Relays Buttons

The Set Relays button in the dialogue of the time-distance plot fills the table with the relays in forward or reverse direction of the path automatically.


32.8 Relay Plot The relay or R-X plot VisDraw is showing the impedance characteristics of different distance protection relays in one or several R-X plots. Additionally the impedance of connected lines and transformers in the network nearby the protection equipment can easily be shown. Thus the impedances of the different zones of the relay and the tripping time can easily be adjusted and checked for a good and thorough protection of the equipment. There are several ways to create a relay plot ( VisDraw): 





The easiest way to create and show a VisDraw is to select one cubicle, where a distance relay is installed. Right-click the sw itch to open the context-sensitive menu. This will show the options Create R-X Plot and Add to R-X Plot . PowerFactory will then create a new diagram showing the R-X plot for all relays in the selected cubicle. Another way is to right-clicked an element which is belonging to a defined protection path and select Path...−> R-X Plot from the context-sensitive menu. Also a distance relay element ElmRelay can be chosen from the list of cal culation-relevant objects or in the data manager. Right-click the relay on the right side of the data manager or in the list of relays. Then select Show −> R-X Plot to create a new plot or Show −> Add to R-X Plot to get a selection of already created plots to add the characteristic to an existing plot.

Note To show the relay locations and thus to visualize the switches with relays definitions these can be highlighted by setting the color representation of the single-line diagram to "Relay Locations''. By right-clicking these elements the option Show −> − > − > R-X Plot is available and can be chosen.

The R-X plots show 

   

the impedance characteristics of selected distance relays including the different zones. impedance curve of the lines and transformers near the relay location. the location of other distance relay nearby. the short-circuit impedance depending on the location and the fault impedances. the tripping time of the relay.


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Fig. 32.50: A R-X plot with short-circuit results and two relays

In Figure 32.50 an example is shown for the R-X plot, where two relay characteristics and the transmission line impedances are displayed. Furthermore shows the location of the short-circuit or load-flow calculation as a equivalent impedance point in the plot. For every relay displayed in the graph also a legend is shown containing the relevant information regarding the short-circuit calculation of each relay: 

 

 

name of the relay, measured impedances seen from the relay location, the fault type, the actual tripping time of the relay, which zone is tripped.

The information shown may be changed in the relay plot settings. For details please refer to Section 20.1.2 Plots . Modifying the Relay Settings


32.8.1 Modifying the Relay Settings

From the R-X plot the characteristics of the relays shown can easily be changed according to the impedances of the electrical equipment, which is to be protected. By double-clicking the characteristic of a relay zone the settings dialogue of the zone will be opened and can be modified. Here the relay specific information of the impedance characteristic can be entered. Also the information of the line branch connected to the relay in "forward'' direction is shown in the dialogue. If the OK button is selected the characteristic of the relay will be updated. It is also possible to edit the lines or transformer elements shown in the plot. Holding still the mouse arrow over the element for a second a balloon help box will appear and show the name of the element. If one of the lines is double-clicked, the edit dialogue of the element pops up like in the single-line graphics. In this way the line impedances can easily be accessed. Relay Plot Settings

The R-X plot settings can be accessed by selecting the Options from the context-sensitive menu or by pressing the Options button in the edit dialogue of the plot. Basic Options:

The dialogue shows the following options: Unit The current unit may be set to either primary or secondary (relay) ampere. Relays Units This option is used to display only certain types of relay characteristics. Zones Here the zone can be selected which is to be shown. Also All zones of the relays can be displayed in one graph (default). Display This option is used to select how the calculated load-flow or short-circuit current/equivalent impedance will be displayed. Either as an short-circuit arrow, a cross or none may be selected. Show Impedance Color out of service units Zones being out of service can be shown as well in a different color.


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Fig. 32.51: R-X-Plot Setttings

Additionally, the show/hide option for the starting, overreach zones, power swing units and the complete shape of the diagrams can be selected in the dialogue. Branch Impedances:

There are special options to modify the appearance of the branch impedances: Number of Relay Locations Only the branches are shown up to the x-th next relay location. If zero, no branches are shown at all. Branches, max. Depth Maximum number of branches shown from each relay location. If zero, no branches are shown at all. Ignore Transformers Transformer impedances are ignored when activated. Method Method for determining the line impedances. Show Branch Options Here the line style and width can be selected. Legend:

In the legend belonging to each relay different information and calculation results is displayed. Here the user can choose, which results are to be shown.


32.9 The Protection Coordination Wizard The Protection Coordination Wizard for automatic overcurrent protection relay settings calculation has the purpose to: 



Verify that the settings (thresholds, time delays and curve shapes) of the overcurrent devices satisfy the requirements to achieve the protection of the circuit respecting the selectivity constrains and guarantying the "normal operation" of the system, Calculate the settings (thresholds, time delays and curve shapes) to satisfy protection, selectivity and "normal o peration".

It's possible to run the verification process without running the calculation process. The calculation process is using the verification phase to validate the results and generate a report of the achieved results. The Protection Coordination Wizard has the ability to verify/calculate the selectivity for each protective device using the settings of one phase inverse element, two phase definite time elements, one phase ground inverse element and two ground definite time elements. To protect the system the rules implemented in the wizard are calculating the relay settings of one phase inverse element, two phase definite time elements and one ground time definite element. The Protection Coordination Wizard requires that protective devices have been created on each side of a line or of a transformer. Motors, generic loads, capacitors must be protected by a protective device located on the motor, generic load, capacitor feeder itself. Please keep in mind that the coordination process is flexible but cannot manage any possible "circuit" configuration: some of them cannot be protected in a perfect way due to the circuit characteristics and to the protective device characteristics. Example: A relay protecting two transformers in parallel, the relay trip threshold should be at least two times the single transformer rated current. To manage the CT errors and the relay measurement error a 110% (or greater) safety factor is added to the threshold. The threshold value we obtain doesn't guarantee to fully protect the single machine. So it appears clear that not always coordination process is able to achieve a perfect coordination of the protective devices and protection of the protected items. Many times the results we get are an acceptable compromise between the protection and coordination needs using the available protective devices characteristics. In this case a full report showing the current ranges where the coordination or the protection isn't achieved will be made available. Starting the Protection Coordination Wizard The Protection Coordination Wizard Dialogue Window


32.9.1 Starting the Protection Coordination Wizard

Before you can use the Protection Coordination Wizard you have to: 



Define protection devices in the grid (according to Section 32.1: Creating a Protection Device). Define a feeder for the section of the grid, in which you want to ccordinate the protection devices. For informations a bout feeders please refer to Section 12.5 Feeders .

With these elements available in your grid, you can use t he Protection Coordination Wizard. To start the wizard, either: 



Select the Protection toolbar in the main icon bar of PowerFactory . Press the 'Protection Coordination Wizard' button as shown in Figure 32.52.

or: 



Click with the right mouse button on an element in the single-line diagram, which is part of the feeder, i. e. the part of the grid, for which you want to coordniate the protection devices. Select Calculate -> Protection Coordination Wizard from the context sensitive menu as depicted in Figure 32.53.


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Fig. 32.52: The Protection Coordination Wizard button in the Protection toolbar

Fig. 32.53: Starting the Protection Coordination Wizard from the context sensitive menu

The dialogue of the Protection Coordination Wizard pops up (see Figure 32.54). Configure the Coordiniation Wizard for meeting your requirements. Afterwards press the Execute button to run the coordination process.


32.9.2 The Protection Coordination Wizard Dialogue Window

Normally you just have to select the options on the 'Basic Options' tab. Advanced users may use the 'Configuration' tab as well. On the 'Output' tab you can select the output format.

Fig. 32.54: The Protection Coordination Wizard dialogue - Basic Options


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Fig. 32.55: The Protection Coordination Wizard dialogue - Output Options


Chapter 33 Network Reduction A typical application of network reduction is a project where a specific network has to be analyzed, but this network cannot be studied independent of a neighboring network of the same or a higher/lower voltage level. In such cases, one option is to model both networks in detail for calculation purposes. There may, however, be situations when it is not desirable to perform studies with the complete model. Such situations may include, for example, cases when the calculation times would increase significantly or when the data of the neighboring network is confidential and cannot be published in detail. In these cases it is common practise to provide a representation of the neighboring network, which contains the interface nodes (connection points) that may be connected by equivalent impedances and voltage sources. PowerFactory 's network reduction algorithm produces an equivalent representation of the reduced part of the network and calculates its parameters. This equivalent

representation is valid for both load flow and short-circuit calculations, including asymmetrical faults (i.e. single-phase faults). 33.1: Network Reduction Example 33.2: Executing the Reduction Process 33.3: Network Reduction Command 33.4: Technical Background


33.1 Network Reduction Example The example configuration used in this chapter to illustrate the network reduction function is a transmission system as shown in Figure 33.1 feeding a distribution system. The distribution network is fed by two busbars, "Bus 5'' and "Bus 6 '', in the center of the transmission system. It is represented by Load A and Load B and the corresponding two transformers. The distribution system is to be studied in detail, however the transmission system will be represented only by its equivalent model. The transmission system has a connection to another transmission system, which is represented by the External Grid and t he connecting line. This second transmission system shall remain asis, as we want to reduce only one transmission system. The "Boundary" defines which part shall be reduced.

Fig. 33.1: Example System with Original Network

The result of the network reduction is shown in Figure 33.2. The transmission network has been reduced to an equivalent representation by three AC voltage sources (ElmVac ) and three common impedances (ElmZpu) connecting the remaining busbars. A load flow calculation or a short-circuit calculation in the reduced network gives the same results for the distribution network as for the original (non-reduced) network.


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Fig. 33.2: Example System with Reduced Network


33.2 Executing the Reduction Process The grid boundary, which divides the network into a part which shall remain in its original detailed representation (the retained grid) and a part that is to be reduced (i.e. that which shall be represented by a simplified equivalent grid), is defined by means of a boundary element ( ElmBoundary ). A boundary element is essentially a set of cubicles, each one defined with a given orientation to distinguish the two portions of the network separated by the boundary as "interior" and "exterior". The cubicles in the boundary element have to be orientated in order to have the part of the grid which shall be reduced as "interior". For more information regarding boundaries, please refer to Section 12.3 Boundaries . To reduce the network, please proceed as follows: 

The Network Reduction function, by default, retains the original network data. It will only destroy the original data if the associated o ption for this is set accordingly (see Section 33.3.2: Outputs). However, to be absolutely sure of avoi ding any data loss, even when a ccidentally selecting the option which will delete the original grid during the reduction procedure, please first either: make a copy of the whole project and paste/store it with a name different to that of the original project; or export the project as a *.dz- or *.pfd file (for information regarding exporting data please refer to Section 9.1.4: Exporting and Importing of Projects ); or activate the project and create a new Version of the project. For information about Versions please refer to Section 21.1 Project Versions .   

 



Activate the base Study Case. This loads the original network. If you have migrated your project from PowerFactory version 13.2 or another previous PowerFactory version, please ensure that either there is a Variations folder in your current project (located inside the Network Model folder) or that there are already existing System Stages (located inside the Grid folders). For further information, please refer to Section 33.3.2 Outputs . Define the boundary necessary to split the grid into the part to be reduced, and the part to retain i ts detailed representation. Ensure that the boundary splits the network into two regions by using the Check Split button in the ElmBoundary dialogue. For more information about boundaries, please refer to Section 12.3 Boundaries .



Select the Additional Tools icon (

) from the main toolbar.



Press the Network Reduction icon (

) from the Additional Tools icon bar (Figure 33.3). This opens the dialogue for Network Reduction (ComRed ).

 

Choose the settings according to Section 33.3 Network Reduction Command . Click on the Execute button to start the reduction procedure.

Fig. 33.3: The Network Reduction Button in the Additional Tools Icon Bar

Depending on the option selected on the Outputs tab (Section 33.3.2: Outputs), the network r eduction procedure may automatically create a new variation/system stage to represent the original grid. If the original system is represented with multiple grids (or system stages of multiple grids), a new system stage will be created in each one. In the new system stage(s), the part of the grid which shall not be reduced retains its full representation, whereas the part that shall be reduced is erased and the new simplified grid representation is added, with the connections to the other part of the grid (i. e. to the part which is not reduced). The new system stage(s) will therefore represent the combined grid (retained grid and reduced equivalent). The new system stages will be automatically activated in the active study case. In the event that one or more single line graphic diagrams were available in the system stage(s) within the original grid, these graphics will also be available in the new system stage(s) within the combined (partly retained and partly reduced) grid. The first time that the new study case is activated (automatically, at the end of network reduction procedure), the graphics will be displayed. The elements contained in the part of the grid which was reduced (if any of them were previously shown), will appear grey in colour, as "ghost" elements. Deactivating and re-activating the project will make them disappear permanently (they are graphic elements only, and have no corresponding elements in the database in the new system stage(s)). The elements contained in the equivalent grid (equivalent branches, equivalent shunts, equivalent injections, etc) are stored in the database but have no graphic image as yet. These elements can be easily drawn by making use of the PowerFactory tool "Draw Existing Net Elements", which is explained in Section 10.4 Drawing Diagrams with already existing Network Elements .


33.3 Network Reduction Command In this section, the Network Reduction command options are explained.


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33.3.1: Basic Options 33.3.2: Outputs 33.3.3: Advanced Options 33.3.4: Verification



Fig. 33.4: Network Reduction Command ( ComRed ) Basic Options Boundary

The part of the grid which shall be reduced must be defined by a boundary. The project Boundaries folder may contain many defined boundaries, so the user has to select the boundary corresponding to the division which separates the original grid into two parts: (i) the part that shall be reduced; and (ii) the part that shall retain its full representation. Only one boundary can be used in the network reduction calculation. For more info rmation about boundaries, please refer to Section 12.3 Boundaries . Load Flow Calculate load flow equivalent

With this option enabled, the load flow equivalent will be created. If this option is disabled, the load flow equivalent will not be created. This option is normally enabled. Equivalent Model for Power Injection

The load flow equivalent is co mposed of mutual impedances among boundary nodes a nd power injections (and shunt impedances) at boundary nodes. This kind of power injection can be represented by different models. For the load flow equivalent there are three options (models) available: Load Equivalent: a load demand

 

Ward Equivalent: an AC voltage source which is configured as a Ward Equivalent



Extended Ward Equivalent: an AC voltage source which is configured as an Extended Ward Equivalent

Short-Circuit Calculate short-circuit equivalent

This option is used to specify whether the short-circuit equivalent shall be calculated (option enabled) or not (option disabled). Currently, only the complete shortcircuit calculation method is supported. Asymmetrical Representation This option is used to specify whether an unbalanced short-circuit equivalent will be created. If this option is disabled, only a balanced short-circuit equivalent will be created, valid for the calculation of 3-phase short-circuits. If this option is enabled, an unbalanced short-circuit equivalent is created as well, valid for the calculation of singlephase and 2-phase short-circuits. This means the network representation must include zero sequence and negative sequence parameters, otherwise the unbalanced calculation cannot be performed.


33.3.2 Outputs

The Outputs tab is used to specify whether the reduced grid parameters shall be reported only, or whether the reduced grid shall be stored in a new variation. Calculation of Parameters Only

The equivalent parameters are calculated and reported, and no new varia tion will be created. Create a New Variation for Reduced Network

The equivalent parameters are calculated and a new var iation will be automaticall y created, to store the reduced network representation. If the project still includes system stages (from PowerFactory version 13.2 or earlier versions) a new system stage will be created instead of a variation. Reduce Network without Creating a New Variation

The reduced network will be stored directly in the Grid folder inside the Network Data folder. No variation will be created. The part of the grid to be reduced will be deleted and replaced by its reduced representation. To avoid losing the original grid data, save the data before executing the network reduction with this option. To do this, either (i) create a revision manuall y; or (ii) create a version of the project; or (iii) ma ke a copy of the entire project; or (iv) export the project.


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Fig. 33.5: Network Reduction Command - Outputs


33.3.3 Advanced Options Mutual Impedance

Enter here the value for the maximum equivalent branch impedance to be considered. The reduced network will be comprised of, among other elements, equivalent branches that join each pair of boundary nodes (a boundary node is identified for each boundary cubicle). The number of these branches will therefore be N*(N-1)/2, where N is the number of boundary nodes. (Note that this number can be very high in the case of ma ny boundary nodes). It frequently occurs that some (or many ) of these equivalent branches have a very large im pedance value, and therefore that their associated power flows are negligible: hence they are not represented as branches. Therefore, the user is given the possibility to define an impedance limit value, above which branches will be neglected (i.e. not represented) in the reduced network equivalent. Calculate Equivalent Parameters at All Frequencies

With this option the calculation of frequency-related parameters can be enabled or disabled. By default the short-circuit equivalent parameters are calculated at a ll frequencies relevant to short-circuit analysis (equivalent frequencies for calculating the d.c. component of the short-circuit current):  

 

 

f f f f f f

= f n / f n = / f n = / f n = / f n = / f n =

0.4 0.27 0.15 0.092 0.055

f n is the nominal frequency of the grid (usually 50 Hz or 60 Hz). If only transient and sub-transient short-circuit currents are being considered in the calculation, the calculation of frequency-related parameters can be skipped by unchecking this option.

Fig. 33.6: Network Reduction Command - Advanced Options


33.3.4 Verification Check Equivalent Results

If the option Check load flow results after reduction is enabled, the load flow results a t the boundary nodes will be checked against the original network results. A warning message will be given if the results do not match (within a user defined tolerance). Check Deviation of Working Point If the option Save original operating point to result file is enabled, the operating point where the network reduction takes place will be automatically saved to two result files. These two created files are:  

LdfResultforNR.ElmRes: voltage magnitudes and angles of all boundary nodes; and ShcResultforNR.ElmRes: short-circuit level at all boundary nodes, including I k'' (Ikss), I k' (Iks), ip (ip), ib (ib), I b (Ib), Xb /R b (XtoR_b), and X/R (XtoR).


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Fig. 33.7: Network Reduction Command - Verification


33.4 Technical Background For an improved understanding of PowerFactory 's Network Reduction function, some technical background is provided in the following sections. 33.4.1: Network Reduction for Load Flow 33.4.2: Network Reduction for Short-Circuit 33.4.3: Handling of Slack Bus


33.4.1 Network Reduction for Load Flow Network reduction for load flow is an algorithm based on sensitivity matrices. The basic idea is that the sensitivities of the equivalent grid, measured at the

connection points in the retained grid, must be equal to the sensitivities of the grid that has been reduced. This means that for a given (virtual) set of ∆P and ∆Q injections in the branches, from the retained grid to the grid to be reduced, the resulting ∆u and ∆ϕ (voltage magnitude and voltage phase angle variations) in the boundary nodes must be the same for the equivalent grid, as those that would have been obtained for the original grid (within a user defined tolerance).


33.4.2 Network Reduction for Short-Circuit Network reduction for short-circuit is an algorithm based on nodal impedance/nodal admittance matrices. The basic idea is that the impedance matrix of the

equivalent grid, measured at the connection points in the retained grid, must be equal to the impedance matrix of the grid to be reduced (for the rows and columns that correspond to the boundary nodes). This means that for a given (virtual) additional ∆I injection (variation of current phasor) in the boundary branches, from the retained grid to the grid to be reduced, the resulting ∆u (variations of voltage phasor) in the boundary nodes must be the same for the equivalent grid, as those that would have been obtained for the original grid (within a user defined tolerance). This must be valid for positive sequence, negative sequence, and zero sequence cases, if these are to be considered in the calculation (unbalanced short-circuit equivalent).


33.4.3 Handling of Slack Bus

If the slack bus is located in the grid which is to be reduced, a neighbourhood around this slack will be automatically defined. This neighbourhood will be excluded from the grid to be reduced. That means the neighbourhood of the slack bus w ill remain after the Network Reduction procedure. The neighbourhood is defined based on a search from the slack element towards each connection, until a non-zero impedance element is passed. This means that the neighbourhood contains all elements encountered up to and including the non-zero impedance element.


Chapter 34 State Estimation The State Estimator (SE) function of PowerFactory provides consistent load flow results for an entire power system, based on real time measurements, manually entered data and the network model. Before any further analysis, such as contingency analysis, security checks etc. can be carried out, the present state of a power system must be estimated from available measurements. The measurement types that are processed by the PowerFactory State Estimator are:    

 

Active Power Branch Flow Reactive Power Branch Flow Branch Current (Magnitude) Bus Bar Voltage (Magnitude) Breaker Status Transformer Tap Position

Unfortunately, these measurements are usually noisy and some data might even be totally wrong. On the other hand, there are usually more data available than absolutely necessary and it is possible to profit by redundant measurements for improving the accuracy of t he estimated network state. The states that can be estimated by the State Estimator on the base of the given measurements vary for different elements in the network: 

Loads Active Power, and/or Reactive Power, or Scaling Factor, as an alternative Synchronous Machines Active Power, and/or Reactive Power Asynchronous Machines Active Power Static var System Reactive Power 2- and 3-winding transformers Tap Positions (for all but one taps). 

 



















Objective Function Components of the PowerFactory State Estimator State Estimator Data Input


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Running SE Results


34.1 Objective Function The objective of a state estimator is to assess the generator and load injections, and the tap positions in a way that the resulting load flow result matches as close as possible with the measured branch flows and bus bar voltages. Mathematically, this can be expressed with a weighted square sum of all deviations between calculated ( calVal ) and measured ( meaVal) branch flows and bus bar voltages:

The state vector

contains all voltage magnitudes, voltage angles and also all variables to be estimated, such as active and reactive power injections at all bus bars.

Because more accurate measurements should have a higher influence to the final results than less accurate measurements, every measurement error is weighted with a weighting factor w to the standard deviation of the corresponding measurement device (+transmission channels, etc.). i In this setting, the goal of a state estimator is to minimize the above given function f under the side constraints that all load flow equations are fulfilled.


34.2 Components of the PowerFactory State Estimator The State Estimator function in PowerFactory consists of several independent components, namely: 1. 2. 3. 4.

Preprocessing Plausibility Check Observability Analysis State Estimation (Non-Linear Optimization)

Figure 34.1 illustrates the algorithmic interaction of the different components. The first Preprocessing phase adjusts all breaker and tap positions according to their measured signals.

Fig. 34.1: Variation of the PowerFactory state estimator algorithm

The Plausibility Check is sought to detect and separate out, in a second phase, all measurements with some apparent error. PowerFactory provides various test criteria for that phase of the algorithm. In a third phase, the network is checked for its Observability . Roughly speaking, a region of the network is called observable, if the measurements in the system provide enough (non-redundant) information to estimate the state of that part of the network. Finally, the State Estimation itself evaluates the state of the entire power system by solving the above mentioned non-linear optimization problem. PowerFactory provides various ways for copying with non-observable areas of the network. In order to improve the quality o f the result, observability analysis and state estimation can be run in a loop. In this mode, at the end of each state estimation, the measurement devices undergo a so-called "Bad Data Detection": the error of every measurement device can be estimated by evaluating the difference between calculated and measured quantity. Extremely distorted measurements (i.e. the estimated error is much larger than the standard deviation of the measurement device) are not considered in the subsequent iterations. The process is repeated until no bad measurements are detected any more. In the following, the distinct components of the PowerFactory state estimator are explained in detail. Plausibility Check Observability Analysis State Estimation (Non-Linear Optimization)



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34.2.1 Plausibility Check

In order to avoid any heavy distortion of the estimated network-state due to completely wrong measurements, the following Plausibility Checks can be made before the actual State Estimation is started. Every measurement that fails in any of the listed Plausibility Checks will not be considered.  

 

 

Check for consistent active power flow directions at each side of the branch elements. Check for extremely large branch losses, which exceed their nominal values. Check for negative losses on passive branch elements. Check for large branch flows on open ended branch elements. Check whether the measured branch loadings exceed the nominal loading value of the branch elements. Node sum checks for both, active and reactive power.

Each test is based on a stochastic analysis which takes into account the measurement's individual accuracy. The strictness of the above mentioned checking criteria can be continuously adjusted in the advanced settings. The result of the Plausibility Check is reported, for each measurement, on a detailed error status page (see Section 34.5).


34.2.2 Observability Analysis

A necessary requirement for an observable system is that the number of available measurements is equal or larger than the number of estimated variables. This verification can easily be made at the beginning of every state estimation. But it can also happen that only parts of the network are observable and some other parts of the system are not observable even if the total number of measurements is sufficient. Hence, it is not only important that there are enough measurements, but also that they are well distributed in the network. Therefore, additional verifications are made checking for every load or generator injection whether it is observable or not. The entire network is said to be observable if all load or generator injections can be estimated based on the given measurements. PowerFactory does not only solve the decision problem whether the given system is observable or not: If a network is not observable, it is still useful to determine the islands in the network that are observable. The Observability Analysis in PowerFactory is not purely based on topological arguments; it heavily takes into account the electrical quantities of the network. Mathematically speaking, the Observability Check is based on an intricate sensitivity analysis, involving fast matrix-rank-calculations, of the whole system. The result of the Observability Analysis can be viewed using t he data manager. Besides, PowerFactory offers a very flexible color representation both for observable and unobservable areas, and for redundant and non-redundant measurements (see Section 34.5.4). Observability of individual states Redundancy of measurements Observability of individual states

The Observability Analysis identifies not only, for each state (i.e., load or generator injections) whether it is observable or not. It also subdivides all unobservable states into so-called "equivalence-classes". Each equivalence-class has the property that it is o bservable as a group, even though its members (i.e., the single states) cannot be observed. Each group then can be handled individually for the subsequent state estimation. Redundancy of measurements

Typically, an observable network is overdetermined in the sense that redundant measurements exist, which-for the observability of the system-do not provide any further information. During the Observability Analysis, PowerFactory determines redundant and non-redundant measurements. Moreover, it subdivides all redundant measurements according to their information content for t he system's observability status. In this sense, PowerFactory is even able to calculate a redundancy level which then indicates how much reserve the network measurements provide. This helps the system analyst to precisely identify weakly measured areas in the network. It should be remarked that the non-linear optimization part of the State Estimator may highly profit from these "redundant" measurements; thus, redundant measurements will not be neglected in the state estimation.


34.2.3 State Estimation (Non-Linear Optimization)

The non-linear optimization is the core part of the State Estimator. As already mentioned in the introduction, the objective is to minimize the weighted square sum of all deviations between calculated and measured branch flows and bus bar voltages whilst f ulfilling all load flow equations. PowerFactory uses an extremely fast converging iterative approach to solve the problem based on Lagrange-Newton methods. If the Observability Analysis in the previous step indicates that the entire power system is observable, convergence (in general) is guaranteed. In order to come up with a solution for a non-observable system, various strategies can be followed: One option is to reset all non-observable states, such that some manually entered values or historic data is used for these states. An alternative option is to use so-called pseudo-measurements for non-observable states. A pseudomeasurement basically is a measurement with a very poor accuracy. These pseudo-measurements force the algorithm to converge. At the same time, the resulting estimated states will be of correct proportions within each equivalence-class. In the remaining sections of this guide of use, the instructions related to Data Entry, Options and Constraints, and Visualization of Results are presented.


34.3 State Estimator Data Input The main procedures to introduce and manipulate the State Estimator data are indicated in this section. For applying the PowerFactory State Estimator, the following data are required additional to standard load flow data: 

Measurements Active Power Branch Flow Reactive Power Branch Flow Branch Current (Magnitude) Bus Bar Voltage (Magnitude) Breaker Status Transformer Tap Position Estimated States Loads: Active Power (P) and/or Reactive Power (Q), or the Scaling Factor, as an alt ernative. Synchronous Machines: Active Power (P) and/or Reactive Power (Q) Asynchronous Machines: Active Power (P) Static var Systems: Reactive Power (Q) Transformers: Tap Positions  

   



 

 



For the measurements listed above, PowerFactory uses the abbreviated names P-measurement , Q-measurement , I-measurement , V-measurement , Breaker-measurement , and Tap position-measurement . Similarly, as a convention, the four different types of estimated states are shortly called P-state , Q-state , Scaling factor-state , and Tap osition-state .


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Measurements Activating the State Estimator Display Option Editing the Element Data


34.3.1 Measurements

All measurements are defined by placing a so-called "External Measurement Device" inside a cubicle. For this purpose, select the device in the single-line graphic and choose from the context menu (right mouse button) "New Devices" and then "External Measurements..." (see Figure 34.2). Then, the new object dialogue pops up with a predefined list of external measurements. Please select the desired measurement device among this list (see Figure 34.3).

Fig. 34.2: External Measurements that are located in a cubicle

Fig. 34.3: Defining new external measurements

The following measurement devices are currently supported 

 



(External) P-Measurement ( StaExtpmea) (External) Q-Measurement ( StaExtqmea) (External) I-Measurement, current magnitude ( StaExtimea) (External) V-Measurement, voltage magnitude ( StaExtvmea)


 

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(External) Breaker Signalization Breaker Status ( StaExtbrkmea) (External) Tap-Position Measurement Tap Position ( StaExttapmea)

Any number of mutually distinct measurement devices can be defined in the cubicle. Branch Flow Measurements Current Measurements Voltage Measurements Breaker and Tap Position Measurements Branch Flow Measurements

Any branch flow measurement (StaExpmea , StaExtqmea ) is defined by the following values (see figures 34.4 and 34.5): 

 

 

Measured value ( e:Pmea or e:Qmea, respectively) Multiplicator (e:Multip) Orientation ( e:i_gen) Accuracy class and rating (e:Snom and e:accuracy) Input status (to be found on the second page of the edit object, see Figure 34.5): E.g., tele-measured, manually entered, read/write protected, . . . ( e:iStatus). It is important to note that the state estimator takes into account only measurements, for which the "read"-Status is explicitly set and for which the "Neglected by SE"-Status is unset.

Fig. 34.4: Dialogue for an external P-measurement

The accuracy class and the rating are used for weighting the measurement element. In case of redundant measurements, a more accurate measurement will be higher weighted than a less accurate measurement. Using the flag "orientation", it is possible to define the meaning of the active or reactive power sign. Load orientation means that a positively measured P or Q flows into the element, generator orientation defines a positive flow as flowing out of an element. With the "multiplicator", a measured quantity can be re-rated. E.g., if a measurement instrument indicates 150kW (instead of 0.15MW), the "multiplicator" can be set to 0.001 and the measured value is set to 150 resulting in a correct value. It is important t o note, that External P- and Q-measurements have the additional feature to possibly serve as a so-called (externally created) pseudo-measurement. This feature is activated by checking the corresponding box ( e:pseudo). Pseudo-measurements are special measurements which are ignored during the regular calculation. They are activated in a selective manner only if the observability check found unobservable states in the network (see Section 34.4.1 Basic Setup Options for details). Current Measurements

The External I-measurement ( Staextimea) plays a special role and slightly differs from the External P- and Q-measurements (see Figure 34.6): Besides specifying the measured current magnitude ( e:Imea), the user is asked to enter an assumed (or measured) value for the power factor cos ϕ (e:cosphi and e:pf_recapr).

Fig. 34.5: Second page "Status" of the dialogue for an external P-measurement


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Internally, the measured current magnitude is then additionally transformed into two further measurements, namely an active and a reactive current. This is due to the fact that current magnitude does not provide information on the direction of t he flow, which - on the other hand - is essential to avoid ambiguous solutions in the optimization. In this sense, an external I-measurement may play the role of up to three measurements: 1. 2. 3.

as a current magnitude measurement. as a measurement for active current. as a measurement for reactive current.

The decision which of these measurements shall participate in the state estimator is left to the user by checking the boxes ( e:iUseMagn,e:iUseAct, and/or e:iUseReact). In any case, the corresponding ratings for the used measurement types need to be specified. This is done ( accordingly to the flow measurements) by entering the pairs of fields (( e:SnomMagn,e:accuracyMagn), (e:SnomAct,e:accuracyAct), and (e:SnomReact,e:accuracyReact), respectively). Voltage Measurements

Voltage measurements (StaExvmea) need to be placed in cubicles as well. The measurement point then is the adjacent terminal.

Fig. 34.6: Dialogue for an external I-measurement

A voltage measurement basically has the same properties as a flow measurement, except, for the rating, only a single value for the accuracy needs to be specified. The corresponding internal reference is the nominal voltage of the terminal which serves as measurement point. Breaker and Tap Position Measurements

Both breaker and tap position measurements are assumed to measure the corresponding discrete breaker status and tap position signal accurately. Hence, no ratings needs to be specified. Tap position measurements have a conversion table as extra feature. The conversion table allows any discrete translation mapping between external tap positions (Ext. Tap) and tap positions used by PowerFactory (PF Tap).


34.3.2 Activating the State Estimator Display Option

To access and enter data for State Estimator calculations in the appropriate elements of the grid, the pertinent "Display Options" must be selected as foll ows: a) Click the icon , or select from the main menu "Options User Settings". Change to the tab page "Functions". The window shown in Figure 34.7 will appear. b) Enable the Display Function "State Estimator" as shown below. c) Exit the window clicking the OK button.


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Fig. 34.7: User Settings for State Estimation

With this display function enabled, a new tab called "State Estimator" appears in the State Estimator related elements of the grids in the activated project. The State Estimator data manipulation of the different elements is indicated below.


34.3.3 Editing the Element Data

In addition to the measurement values, the user has to specify which quantities shall be considered as "states to be estimated" by the SE. Possible states to be optimized whilst minimizing the sum of the error squares over all measurements are all active and/or reactive power injections at generators and loads and all tap positions. Loads Synchronous Machines Asynchronous Machines Static var Systems Transformers Loads

For each load (ElmLod), the user can specify whether its active and/or reactive power shall be estimated by the state estimator. Alternatively, the state estimator is able to estimate the scaling factor (for a given P and Q injection). The specification which parameter shall be estimated, estimated, is done by checking corresponding boxes on the "State Estimator" page of the load (see Figure 34.8 34.8). ). When these options are disabled, the load is treated as in the conventional load flow calculation during the execution of the SE.

Fig. 34.8: Editing element data for loads Synchronous Machines

Similarly, for synchronous machines (ElmSym), the active and reactive power can be selected as a control variable for being estimated by the state estimator. Again, the user will find corresponding check boxes on the "State Estimator" page of t he element. If the corresponding check box(es) are disabled, the synchronous machine behaves as in the conventional load flow calculation. Asynchronous Machines

For asynchronous machines (ElmAsm), the active power may serve as a state to be estimated. Once again, again, the corresponding box has to be checked on the "State Estimator" page. If the corresponding check box is disabled, the asynchronous machine behaves as in the conventional load flow calculation. Static var Systems

For static var systems ( ElmSvs ), the reactive power may serve as a state to be estimated. Again, the corresponding box has to be checked on the "State Estimator" page. If the corresponding check box is disabled, the static var system behaves as in the conventional load flow calculation. Transformers

In the 2-winding transformer elements (ElmTr2), the tap position can be specified as a state to be estimated by the State Estimator (see Figure 34.9 34.9). ). Tap positions will be estimated in a continuous way (without paying attention to the given tap limits). For 3-winding transformers, any two of the three possible tap positions (HV-, MV-, and LV-side) can be selected for estimation (see Figure 34.10 34.10). ). The corresponding check boxes are found on the "State Estimator" page of the transformers. If the check box is disabled the State Estimator will treat the tap position of the transformers as in the conventional load flow calculation.


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Fig. 34.9: Editing element data for 2-winding transformers

Fig. 34.10: Editing element data for 3-winding transformers


34.4 Running SE The following steps should be performed to execute the State Estimator: 

Start from a case where the conventional power flow converges successfully.



Make sure that in the toolbar selection, the icon

  

is chosen.

Execute the SE by clicking the icon . Select the desired options for the State Estimator run (see below). Select EXECUTE.

Basic Setup Options Advanced Setup Options Options for the Plausibility Check Check Advanced Setup Options Options for the Observability Observability Check Advanced Setup Options Options for Bad Data Detection Detection Advanced Setup Options Options for Iteration Control


34.4.1 Basic Setup Options

Recall that the State Estimator in PowerFactory PowerFactory consists consists of three dif ferent parts (Plausibility Check, Observability Analysis, State Estimation (no n-linear optimization)) and an additional precedent Preprocessing step (see Figure 34.1 34.1). ). This variation is reflected in the Basic Options dialogue (see Figure 34.11 34.11). ).

Fig. 34.11: Editing the basic options page of the ComSe


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Preprocessing Plausibility Check Observability Analysis State Estimation (Non-Linear Optimization) Preprocessing

The algorithm distinguishes between breaker- and tap position-measureme position-measurements nts on the one hand, and P-,Q-,I-, and V-measurements on the other hand. Breaker- and tap position-measurements position-measuremen ts are handled in the preprocessing step, whereas the latter types are processed in the subsequent parts o r the state estimator. Adapt breaker measurements If this check box is ma rked, all measured breakers statuses will be set to the corresponding measured signal values. Adapt tap position measurements If this check box is ma rked, all measured tap positions wil l be set to the corresponding measured values. Plausibility Check

The algorithm offers various kinds of plausibility checks to validate measurements. Each measurement undergoes the checks selected by the user. If a measurement fails any of the required tests, it will be marked as erroneous and will be neglected in all subsequent steps. A complete error report can be obtained via the error status page of each measurements (see Section 34.5 34.5). ). The following checks can be enabled by marking the corresponding check boxes. Consistent active power flow direction at each branch Checks for each passive branch, whether all co nnected P-measurements comply with a consistent power flow direction. More precisely, i f some flow out of a passive element is measured while, at the same time, no flow into the element is measured, then all P-measurements connected to this element fail this test. For this check,

a P-measurement is said to measure a "non-zero" flow if the measurement value is beyond a value of , where σ and rating are the accuracy and the rating, respectively, of the measurement. Branch losses exceed nominal values Checks for each passive branch, whether the measured active power loss exceeds the nominal loss of the branch by a factor of 1 + ε. This check only applies to passive branches which have P-measurements Pmea , . . . ,Pmea in each of its r connection devices. The threshold ε, by which the nominal loss shall not be 1 r

exceeded, is given by:

, where σ and rating are the accuracy and the rating, respectively, of measurement Pmea . i i i

Negative losses on passive branches Checks for each passive branch, whether the measured active power loss is negative, i.e., if a passive branch is measured to generate active power. This check only applies to passive branches which have P-measurements Pmea , . .. , Pmea in each of its r connection devices. The measured power loss of the branch is said to be 1 r

negative if it is below the threshold (

).

Large branch flows on open ended branches Checks for each connection of the element, whether the connection is an open end (i.e., switch is open, or it is connected to only open detailed switches). If the connection is open and there exists a (P-, Q-, or I-) measurement which measures a "non-zero" fl ow, then the corresponding measurement fails the test. Again, a measurement is said to measure a "non-zero" flow if the measurement value is beyond a value of σ rating. Branch loadings exceed nominal values Checks for each connection of the element, if the measured complex power (which is computed by the corresponding P- and/or Q-measurements) exceeds the rated complex power value by a fa ctor of 1 + s. Here, s is the accuracy of the P- and/or Q-measurement(s). Node sum checks for active and reactive power This check applies to P- and/or Q-measurements. Checks, for each node of the network, if the node sum of the measured values in the adjacent branches is zero. If this is not the case, i.e., if the P- and/or Q-sum exceeds a certain threshold value, all adjacent P- and/or Q-measurements fail the test. Again, "not being zero" means

that the sum of the measured values of the adjacent P-measurements Pmea , ... , Pmea has magnitude below the threshold 1 r

(similarly for Q-

measurements). Observability Analysis

The Observability Analysis is an optional component of the State Estimator. If activated, it checks whether the specified network is observable, i.e., whether the remaining valid P-, Q-, V-, and I-measurements (which successfully passed the plausibility checks) suffice to estimate the selected P-, Q-, Scaling Factor-, and Tap position-states. In addition, the Observability Analysis detects redundant measurements. Redundancy, in general, yields more accurate results for the following state estimation. Moreover, if the Observability Analysis detects non-observable states, upon user selection, it tries to fix this unobservability by i ntroducing further pseudo-measurements. pseudo-measurements. Check for observability regions If the corresponding check box is marked by the user, the execution of the State Estimator will run the Observability Analysis (prior to the state Estimation optimization). Treatment of unobservable areas In case of unobservable states, the user has different options to cope with the situation: Stop if unobservable regions exist . The algorithm terminates with the detection of unobservable states. The Observability Analysis groups all n onobservable states into different "equivalence classes". Each equivalence class consists of states tha t carry the same observability information through the given measurements. In other words, the given measurements can only distinguish between different equivalence classes, but not between various states of a single equivalence class. The results can be viewed by the user (see Section 34.5 Results ). Use P-, Q-values as specified by model . If this option is selected, the algorithm internally drops the "to be estimated" flag of each no n-observable state and uses the element specifications of the load flow settings instead. For example, if a P-state of a load is unobservable, the algorithm will use the P-value as entered on the load flow page. Hence, the network is made observable by reducing the number of control variables. Use predefined pseudo-measurements pseudo-measurements . Using this option, the algorithm "repairs" the unobservability of the network by increasing the degrees of freedom. For that purpose, at the location of each non-observable state, the algorithm tries to activate a pseudo-measurement of the same kind. Hence, if a P- (Q-)state is non-observable in some element, the algorithm searches for a P-(Q-)pseudo-measurement in the cubicle of the element carrying the non-observable state. In case of a non-observable scaling-factor both, a P- and a Q-pseudo-measurement are required. The introduced pseudo-measurements remain active as long as needed to circumvent unobservable areas. Use internally created pseudo-measurements pseudo-measurements . This option is similar to the previous one, except the algorithm automatically creates and activates a sufficient number of internal pseudo-measurements to guarantee observability. More precisely, internal pseudo-measurements are created at the locations of all elements that have non-observable P-(Q-, scaling factor-)state. For each such element, the pseudo-measurement value for P (Q, P and Q) is taken from the element's load flow specification. All internally created pseudo-measurements use a common setting for their rating and acc uracy, which can be specified on the advanced setup options page for the observability check. Use predefined and internally created meas . This mode can be considered as a mixture of the latter two options. Here, in case of a non-observable state, the algorithm tries to activate a predefined pseudo-measurement of the same kind. If no corresponding pseudo-measurement has been defined, then the algorithm automatically creates an internal pseudo-measurement. State Estimation (Non-Linear Optimization)

The non-linear optimization is the central component of the State Estimator. The underlying numerical algorithm to minimize the measurements' overall error is the iterative Lagrange-Newton method. Run state estimation algorithm Check this box to enable the non-linear optimization. Note that after convergence of the method,-upon user settings on the advanced state estimation option pa gePowerFactory performs PowerFactory performs a bad data check which eliminates the worst P-,Q-,V-, and I-measurements among all bad data. Observability Analysis and State Estimation are run in a loop until no further bad measurements exist (recall the algorithm variation as shown in Figure 34.1 34.1). ).


34.4.2 Advanced Setup Options for the Plausibility Check

Each Plausibility Check allows for an individual strictness setting. Note that all checks rely on the same principle: namely, the given measurement values are checked against


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some threshold. Recall, for example, that the "node sum check for P" tests whether the active power sum at a node is below a threshold of . The user has the possibility to infl uence the strictness of this threshold. Therefore, the settings provide to enter so-called "exceeding factors" fac > 0 such that the new threshold is fac  ε instead of ε. E.g., in the case of the node sum check for P, the user may define the corresponding factor fac_ndSumP. The higher the exceeding factor, the less strict the plausibility test will be. Similar exceeding factors can be specified for any of the given t ests.


34.4.3 Advanced Setup Options for the Observability Check

Rastering of sensitivity matrix Settings for internally created pseudo-measurements Rastering of sensitivity matrix

Internally, the Observability Check is based on a thorough sensitivity analysis of the network. For that purpose, the algorithm computes a sensitivity matrix that takes into account all measurements, on the one hand, and all estimated states on the other hand. This sensitivity matrix is discretized by rastering the continuous values. The user can specify the precision of this process by defining the number of intervals into w hich the values of the sensitivity matrix shall be rastered ( SensMatNoOfInt), the threshold below which a continuous value is considered to be a 0 ( SensMatThresh) in the discrete case, and the mode of rastering ( iopt_raster). It is highly recommended to use the predefined values here. Settings for internally created pseudo-measurements

If, on the basic option page, the mode for the treatment of unobservable regions is set to "use only internally created pseudo-measurements" or to "use predefined and internally created pseudo-measurements", the user may specify a default power rating ( SnomPseudo) and a default accuracy class ( accuracyPseudo). These default values are used for all automatically created internal pseudo-measurements.


34.4.4 Advanced Setup Options for Bad Data Detection

Recall that the state estimator loops Observability Analysis and State Estimation as long as no further bad measurement is found (see Figure 34.1). The following settings allow the user to control the number of iterations performed by the loop. Maximum number of measurements to eliminate Tolerance factors for bad measurement elimination Maximum number of measurements to eliminate

The variable iBadMeasLimit specifies an upper limit on the number of bad measurements that will be eliminated in t he course of the State Estimation. Tolerance factors for bad measurement elimination

A measurement is declared to be bad, if the deviation of measured against calculated value exceeds the measurement's accuracy, i.e., if

Eqn 34.1: where calVal and meaVal are the calculated value and the measured value, respectively. The user may modify this definition by adjusting tolerance factors for bad measurements. More precisely, a measurement is declared to be bad, if the left-hand side in equation (34.1) exceeds . Here facErr > 0 is a factor which can be specified by the user for each group of measurements individually. Use the factors facErrP, facErrQ, facErrV, facErrIMagn, facErrIAct, and facErrIReact for P-, Q-, V-measurements, and the three types of the I-measurements (magnitude measure, active current measure, reactive current measure).


34.4.5 Advanced Setup Options for Iteration Control

Initialization Initialization of non-linear optimization Load Flow Stopping criteria for the non-linear optimization Iteration Control of non-linear optimization Convergence of Load Flow Constraint Equations Convergence of Objective Function Output Initialization

The non-linear optimization requires an initialization step to generate an initial starting configuration. Initialization of non-linear optimization

The user may specify whether the initialization shall be performed by a load flow calculation or by some flat start. If it is kn own in advance that the final solution of the optimization part is close to a valid load flow solution, initializing by a load flow calculation pays off in a faster convergence. Load Flow

Specifies the settings of the load flow command which is taken for initialization in case no flat start is used. Stopping criteria for the non-linear optimization

The non-linear optimization is implemented using an iterative Newton-Lagrange method. Recall that the goal of the optimization is to minimize the objective function f (i.e., the square sum of the weighted measurements' deviations) under the constraint that all load flow equations are fulfilled. Mathematically speaking, the aim is to find

under the constraint that

where

is the set of load flow equations that need to be fulfilled. By the Lagrange-Newton method, we thus try to minimize the resulting Lagrange function


with the Lagrange multipliers

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.

The following parameters can be used to adapt the stopping criteria for this iterative process. The algorithm stops successfully if the following three issues are fulfilled: 1. The maximum number of iterations has not yet been reached. 2. All load flow constraint equations (a) all nodal equations are fulfilled. (b) all model equations are fulfilled.

are fulfilled to a predefined degree of exactness, which means:

3. The Lagrange function itself converges. This can be achieved if (a) either the objective function itself converges to a stationary point, or (b) the gradient of the objective function converges to zero.

The following parameters serve to adjust these stopping criteria. The user unfamiliar with the underlying optimization algorithm is urged to use the default settings here. Iteration Control of non-linear optimization

The user is asked to enter the maximum number of iterations. Convergence of Load Flow Constraint Equations

The user should enter a maximal error for n odal equations (where the deviation is measured in kVA), and, in addition, a maximally tolerable error for the model equations (in %). Convergence of Objective Function

The user is asked choose among the following two convergence criteria for the Lagrangian function: Either the function itself is required to converge to a stationary point, or the gradient of the Lagrangian is expected to converge. In the first case, the user is asked to enter an absolute maximum change in value of the objective function. If the change in value between two consecutive iterations falls below this value, the Lagrangian is assumed to be converged. In the latter case, the user is asked to enter an absolute maximum value for the gradient of the Lagrangian. If the gradient falls below this value, the Lagrangian is assumed to be converged. It is strongly recommended-due to mathematical preciseness-to use the criterion on the gradient. The other option might only be of advantage if the underlying Jacobian matrix behaves numerically instable which then typically results in a "toggling" of the convergence process in the last iterations. Output

Two different levels of output during the iterative process can be selected.


34.5 Results The presentation of the State Estimator results is integrated into the user interface. The solution o f the non-linear optimization in the State Estimator is available via the complete set of variables of the conventional Load Flow calculations. It can be seen in the single line diagram of the grid or through the browser. Output Window Report External Measurements Estimated States Color Representation


34.5.1 Output Window Report

The PowerFactory State Estimator reports the main steps of the algorithm in the o utput window (see Figure 34.12). For the Plausibility Checks, this implies the information on how many models failed the corresponding checks. For the Observability Analysis, the report contains the information on how many states were determined to be o bservable, and-in addition-how many measurements were considered to be relevant for observing these states.

Fig. 34.12: Report in the output window

Non-linear optimization reports, in each iteration step, the following figures:  



The current error of the constraint nodal equations (in VA) ( Error Nodes). The current error of the constraint model equations ( Error ModelEqu). The current value of the gradient of the Lagrangian function ( Gradient LagrFunc).


 

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The current value of the Lagrangian function ( LagrFunc). The current value of the objective function f to be minimized ( ObjFunc).


34.5.2 External Measurements

Deviations Error Status Deviations

Each branch flow measurement ( StaExtpmea , StaExtqmea ) and each voltage measurement ( StaExtvmea) offers parameters to view its individual deviation between measured value and computed value by the State Estimation. The corresponding variables are: 

e:Xmea : measured value as entered in StaExt*mea



e:cMeaVal: measured value (including multiplier)



e:Xcal : calculated value



e:Xdif : deviation in % (based on given rating as reference value)



e:Xdif_mea: deviation in % (based on the measured value as reference value)

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e:Xdif_abs: absolute deviation in the measurement's unit

Here X is a placeholder for P, Q, or U in the case of a P-, Q-, or V-measurement. Recall that a StaExtimea plays a special role, since a current measurement may serve as up to three measurements (for magnitude, for active current, and/or for reactive current). Hence, a current measurement has the above listed variables (with X being replaced by I) for each of the t hree measurement types. In order to distinguish between the three types, for a StaExtimea , the variables carry the suffixes Magn (for magnitude measurement), Act (for active current measurement), and React (for reactive current measurement).

Fig. 34.13: For description page for external measurements (StaExtvmea, StaExtqmea, StaExtvmea). Error Status

All measurements ( StaExt*meas) which possibly participate in the Plausibility Checks, the Observability Analysis, or the State Estimation provide a detailed error description page (see figures 34.13 and 34.14) with the following information: 

General Errors: Is unneeded pseudo-measurement ( e:errUnneededPseudo) Its input status disallows calculation, i.e., input status does not allow "Read" or is already marked as "Wrong Measurement" ( e:errStatus) Measurement is out of service ( e:errOutOfService)  

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Plausibility Check Errors: Fails test: Consistent active power flow direction at each side of branch ( e:errConsDir) Fails test: Large branch losses (e:errExcNomLoss) Fails test: Negative losses on passive branches (e:errNegLoss) Fails test: Large branch flows on open ended branches ( e:errFlwIfOpn) Fails test: Branch loadings exceed nominal values ( e:errExcNomLoading) Fails test: Node sum check for P ( e:errNdSumP) Fails test: Node sum check for Q ( e:errNdSumQ)   

   

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Observability Analysis Errors: Measurement is considered to be redundant for observability of the network, i.e., observability is already guaranteed even without this measurement. Nevertheless redundant measurements are used in the non-linear optimization since, in general, they help to improve the result ( e:errRedundant). For redundant measurements, also the redundancy level is indicated on this page ( e:RedundanceLevel). The higher the redundancy level, the more measurements with a similar information content for the observability analysis exist. State Estimation Errors: Measurement is detected to be bad, has been removed and was not considered in las t non-linear optimization loop ( e:errBadData) 

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This detailed error description is encoded in the single parameter e:error that can be found on the top of the error status page. Again, we have the convention that, for a StaExtimea, the variables e:errRedundant, e:RedundanceLevel and e:errBadData carry the suffixes Magn (for magnitude measurement), Act (for active current measurement), and React (for reactive current measurement).


34.5.3 Estimated States

Which states participated as control variables? Observability of individual states Which states participated as control variables?


Page 167 of 168

Recall that -depending on the selected "treatment of unobservable regions"- not all states that were selected for estimation (see Section 34.3.3 Editing the Element Data ) will necessarily be estimated by the algorithm: In case of non-observability, it may happen that some control variables need to be reset. To access the information which states were actually used as control variables, PowerFactory provides a flag for each possible state. These flags are called c:i {P,Q,Scale,Tap}Setp for P-, Q-, Scaling factor-, and Tap-states, respectively. They can be accessed through the Flexible Data Page as Load Flow calculation parameters for the following elements: ElmLod , ElmAsm , ElmSym , ElmSvs , ElmTr2 , and ElmTr3 . Observability of individual states

The Observability Analysis identifies, for each state, whether it is observable or not. Moreover, if the network is unobservable, it subdivides all unobservable states into "equivalence-classes". Each equivalence-class has the property that it is observable as a whole group, even though its members (i.e., the single states) cannot be observed. The equivalence classes are enumerated in ascending order 1, 2, 3, . ...

Fig. 34.14: Detailed error description page for external current measurements (StaExtimea).

For this purpose, the Observability Analysis uses the flags c:i{P,Q,Scale,Tap}obsFlgfor P-, Q-, Scaling factor-, and Tap-states, respectively. These parameters exist for all elements which carry possible states ( ElmLod , ElmAsm , ElmSym , ElmSvs , ElmTr2 , ElmTr3 ). The semantics is as follows:   

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a value of -2 means that the correspond state is not estimated at all. a value of -1 means that the correspond state is unsupplied. a value of 0 means that the corresponding state is observable. a value of i > 0 means that the correspond state belongs to equivalence-class i.


34.5.4 Color Representation

In addition, PowerFactory provides a special coloring mode "Observability" for the single line diagram which takes into account the individual measurement error statuses and the states to be estimated (see Figure 34.15). The coloring can be accessed by clicking the icon

on the task bar.

The color representation is valid as soon as an Observability Analysis has been performed successfully. The color representation paints the location of measurements (of a specific type) and the location of states (of a specific type) simultaneously.

Fig. 34.15: Coloring of measurement error statuses and estimated states.

Estimated States External Measurement Locations

03_Power System Analysis Functions

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