Aero Gener Adores

G m b H

Technical Documentation

Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators

DIgSILENT GmbH Heinrich-Hertz-Strasse 9 D-72810 Gomaringen Tel.: +49 7072 9168 – 0 Fax: +49 7072 9168- 88 http://www.digsilent.d e-mail: [email protected]

Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators Published by DIgSILENT GmbH, Germany Copyright 2003. All rights reserved. Unauthorised copying or publishing of this or any part of this document is prohibited.

doc.TechRef, 14 August 2003


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DIgSILENT GmbH Heinrich-Hertz-Strasse 9 D-72810 Gomaringen Tel.: +49 7072 9168 – 0 Fax: +49 7072 9168- 88 http://www.digsilent.d e-mail: [email protected]

Dynamic Modelling of Doubly-Fed Induction Machine Wind-Generators Published by DIgSILENT GmbH, Germany Copyright 2003. All rights reserved. Unauthorised copying or publishing of this or any part of this document is prohibited.

doc.TechRef, 14 August 2003


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The electrical systems of several European countries contain large amounts of embedded wind generation and similar scenarios are foreseen in other parts of the world. This aspect, together with the significant size of new wind farm projects, requires realistic modelling capabilities of wind generators for proper assessment of power system planning and impact analysis of future wind generation. As a result of research and consulting activities of DIgSILENT, generic dynamic dynamic models of different types of wind power generation were developed. These models are now available available in the standard Wind-Power library Wind-Power library of PowerFactory of PowerFactory . This document describes a doubly-fed induction generator wind turbine model including all relevant components. At the same time, this document is a reference to all DFIG-related models of the Wind-Power library. Wind-Power library. The presented models are mainly intended for stability analysis of large power systems. The proper response of the models to network faults was in the centre of interest, but the models can also be used for simulating the impact of wind fluctuations to power systems. There is no wind model included in this description. However, any type of stochastic or deterministic wind model, or measured wind speeds can be connected to the wind speed input of the presented model. The models are intended for balanced and unbalanced unbalanced RMS calculations typically applied in stability studies. However, it is also possible to perform electromagnetic transient simulations with these models. The basic structure of the model is briefly described in this section and more thoroughly analyzed in the following sections.


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DFIG

Prime Mover Grid Side Converter Rotor Side Converter

External Grid

Control

Control

Protection

Figure 1: Doubly-Fed Induction Generator Concept

The general concept of a Doubly-Fed Induction Generator (DFIG) is shown in Figure 1. The prime mover, consisting of a pitch-angle controlled wind turbine, the shaft and the gear-box drives a slip-ring induction generator. The stator of the DFIG is directly connected to the grid, the slip-rings of the rot or are fed by self-commutated converters. These converters allow controlling the rotor voltage in magnitude and phase angle and can therefore be used for active- and reactive power control. In the presented model, the converters and controllers are represented to the necessary extent. Both the rotor- and the gridside controllers are modelled in full detail, including fast current control loops. However, for many applications the fast control loops of the grid side converter can be approximated by steady state models. With the rotor side converter, the situation is different due to protective practices in DFIG. For protecting the rotor-side converter against over-currents, it is usual practice to bypass the rotor-side converter during system faults. Whether the DFIG is totally disconnected from the system or not, depends on the actual deepness of the voltage sag and on the applied protection philosophy. The correct modelling of the rotor bypass, usually called “crow bar protection”, is essential to assess voltage stability of large farms during faults in the transmission- or distribution network. For this reason, it is necessary to model even the fast current controls of the rotor side converter to effectively determine the operation of the crow bar. Other protection functions also found in DFIG such as over/under-speed and over/under-voltage are considered in the proposed model as wel


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T N E L I S g I D

DFIG: speed

Prime Mover pt beta

Pitch Control *

vw

Turbine *

Pwind

Shaft *

omega.

Pref

MPT ElmMpt*

DFIG ElmAsm*

Ifq_ref;Ifd_ref Pfq;Pfd

Pmq ; Pmd

Qref

P;Q Power Measurement StaPqmea

PQ Control ElmGen*

Current Control *

Transformatio.. *

. . h p s o c

bypass

Protection ElmPro*

(From Protection System)

. . I ; q f I

u

psis_.. V meas. StaVmea*

Current Measurement *

iq;id

Irot

(To Protection System)

Figure 2: Complete Scheme of the Doubly-Fed Induction Machine Wind Generator

The complete scheme of a doubly-fed induction machine wind generator is shown in Figure 2. The main components are: •

The prime mover consisting of the pitch angle controller, the wind turbine and the shaft (Pitch-Control, Turbine, Shaft)

•

Doubly-Fed induction generator (DFIG)

•

The control-system regulating active and reactive power of the DFIG through the rotor-side converter applying a maximum power tracking strategy (MPT, Power Measurement, PQ Control, Current Control, Current Measurement)

•

Protection-system (V meas., Protection)


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The models of all major components are described in the f ollowing sections. It is important to point out that these models can be used in combinations that differ from Figure 2, e. g. realizing power-dependent speed control instead of the speed-dependent power control. Additionally, the model can be extended by stochastic or deterministic wind-speed models, more sophisticated voltage and frequency control.

The prime mover of a wind generator model represents the conversion of kinetic energy stored in the air flowing through th e blades into rotational energy at the generator shaft. The prime-mover model is subdivided into three sub-models, which are •

The turbine that transforms the wind energy into rotational energy at the turbine shaft.

•

Blade angle controller.

•

Shaft coupling turbine and generator including t he gear-box.

In this section all aspects related to the power conversion from kinetic wind energy to rotational energy that are of relevance for the stability model are explained. The kinetic energy of a mass of air m having the speed v w is given by:

E k

=

m 2

⋅ vw

2

(1)

The power associated to this moving air mass is the derivative of the kinetic energy with respect to time.

P 0

=

∂ E k ∂t

=

1 ∂m ⋅

2

∂t

⋅ vw

2

=

1 2

⋅ q ⋅ vw

2

(2)

where q represents the mass flow given by the expression:

q

=

ρ ⋅ vw ⋅ A

(3)

ρ is the air density and A the cross section of the air mass flow. Only a fraction of the total kinetic power can be extracted by a wind turbine and converted into rotational power at the shaft. This fraction of power (PWIND) depends on the wind speed, rotor speed and blade position (for pitch and active stall control turbines) and on the turbine design. It is usually denominated aerodynamic efficiency Cp :


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Figure 3: Typical Cp(β , λ) Characteristic

Cp =

P Wind

(4)

P 0

For a specific turbine design, the values of C p are usually presented as a function of the pitch angle ( β) and the tip speed ratio (λ). The tip speed ratio is given by:

λ =

ω TUR ⋅ R

(5)

vw

R is the radius of the turbine blades and ωTUR is the turbine speed. PowerFactory allows the input of a two-dimensional lookup characteristic (for different values of β and λ) to define Cp. A twodimensional, cubic spline-interpolation method is used for calculating points between actually entered values. The high accuracy of the interpolation method avoids the need of entering a large number of points (see also Figure 3). Alternatively, analytical approaches for approximating the Cp -characteristic could be used but since these data are usually available in tabular formats, no such model was included into the PowerFactory standard Wind-Power-Library. Finally, the mechanical power extracted from the wind is calculated using:

P mech

=

ρ 2

2

⋅ π ⋅ R ⋅ Cp

(λ , β ) ⋅ vw 3


(6)

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The Cp -characteristic can be calculated using special software for aerodynamic designs that is usually based on blade-iteration techniques or it can be obtained from actual measurements. It has to be pointed out that the presented turbine model is based on a steady state approach and is not able to represent stall dynamics. The input/output diagram of the turbine model is depicted in Figure 4 and the input-, output- and parameter definitions are presented in Table 1 to Table 3.

beta

vw

Pwind

Wind-Turbine omega_tur

Figure 4: Input/Output Definition of Wind-Turbine

Table 1:Input Definition of Wind-Turbine Input

Symbol

Description

Unit

beta

β (6)

Blade pitch angle

degrees

vw

vw (5,6)

Wind Speed

m/sec

omega_tur

ωTUR (5)

Turbine Angular Velocity

rad/sec

Table 2: Output Definition of Wind-Turbine Output

Symbol

Description

Unit

Pwind

Pmech (6)

Generated, Mechanical Power

MW

Table 3: Parameter-Definition of Wind-Turbine Output

Symbol

Description

Unit

R

R (5,6)

Rotor Blade Radius

m

rho

ρ (6)

Air Densitiy

kg/m3

Cp

Cp(β,λ) (6)

Cp-Characteristic (2-dim. Lookup-table)


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T N E L I S g I

Blade Angle Control:

D

BLADE ANGLE CONTROLLER

SERVO

ref

Vrmax

speed

-

rate_op

Ymax

beta_ref PI controller Ka,Tr,Ta

beta

-

Time Const T

Vrmin

Limiter

rate_cl

{1/s}

Ymin

Figure 5: Block Diagram of Blade Angle Controller

Adjusting the blade angle allows varying the power coefficient Cp, and hence controlling the power generated by a wind turbine (see also Figure 3). The two common concepts are pitch-control and active-stall control. In a pitch-controlled wind turbine, the blades are turned into the wind for reducing the lift forces at the blades which lowers the power coefficient. Active-stall controlled wind turbines turn the blades out of the wind flow for disturbing the laminar air flow at the blades and hence reducing the generated power. The model presented here is generic and captures the main characteristics of pitch angle controls of existing wind generation technologies. Controller and servomechanism are depicted in Figure 5. The controller has a feedback of the generator speed. Its speed-reference is set to the maximum speed (usually above 20% nominal). The blade angle is at the minimum limit of the controller for all operating conditions below rated rotor speed. This minimum limit corresponds to the optimum blade angle 1. The servomechanism model accounts for the associated time constant, rate-of-change limits and blade angle limitations.

1

Blade-Angle optimization can be realized using a variable minimum blade angle limit


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Blade Angle Controller

speed

beta

Figure 6: Input/Output Definition of Blade Angle Controller

Table 4: Input Definition of Blade Angle Controller Input

Description

Unit

speed

Speed Input (from Generator)

p.u.

Table 5: Output Definition of Blade Angle Controller Output

Description

Unit

beta

Blade Angle (Pitch-Angle)

deg

Table 6: Parameter Definition of Blade Angle Controller Parameter

Description

Unit

Ka

Blade Angle Controller Gain

deg/p.u.

Ta

Blade Angle Controller Time Constant

s

Tr

Lead Time Constant

s

T

Servo Time Constant

s

rate_op

Opening Rate of Change Limit

deg/s

rate_cl

Closing Rate of Change Limit

deg/s

beta_max

Max. Blade Angle

deg

beta_min

Min. Blade Angle

deg

ref_speed

Speed Reference

p.u.


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Jg

ωg

Dtg Jt

ωt

K tg

ω’ g

Dg

Dt

Figure 7: Spring-Mass Model of Second Order

T N E L I S g I D

Shaft Model:

0

0

Pwind

Twind

0

Torque

-

Tmec

omega_tur tdif

Mass_1Torque D_turb,J

0

Spring K,D_shaft

1

0

RatePt Pbase

1

pt

1

1

1

speed_gen

Gear Box RPMnom

omega_gen

Figure 8: Block Diagram of Shaft


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Under normal operating conditions, variable speed generators are “decoupled” from the grid; that is, with appropriate controls, torsional shaft oscillations are filtered by the converters and almost not noticeable as harmonics of the generated power. However, during heavy faults, e.g. short circuits in the network, generator and turbine acceleration can only be simulated with sufficient accuracy if shaft oscillations are included in the model. Shaft characteristics of wind generators are quite different from other t ypes of generation due to the relatively low st iffness of the turbine shaft. This results in torsional resonance frequencies in a range of about 0.5 to 2 Hz. The proposed model approximates the shaft by a two-mass model, represented by turbine- and generator inertia (see Figure 7). The model according to Figure 7 and Figure 8 represents the turbine inertia and the coupling between turbine- and generator. The generator inertia however, is modelled inside the built-in induction machine model. T he generator inertia is specified in the form of an acceleration time constant in the induction generator type. The inertia of the gear-box is not modelled separately but shall be included in the generator inertia. The spring-constant K and the corresponding damping coefficient D are related to the turbine-side. Shaft-models of higher order can easily be implemented by expanding the second order model. For stability analysis however, a second order model provides sufficient accuracy.

Pwind

omega_tur

Shaft speed_gen

pt

Figure 9: Input/Output Definition of Shaft

Table 7: Input Definition of Shaft Input

Description

Unit

Pwind

Turbine Power

MW

speed_gen

Generator Speed

p.u.

Table 8: Output Definition of Shaft Output

Description

Unit

omega_tur

Turbine Speed (Angular Velocity)

rad/s

pt

Mechanical Power at Generator Inertia

p.u.


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Table 9: Parameter Definition of Shaft Parameter

Description

Unit

Pbase

Rated Power of Generator

MW.

D_turb

Turbine Damping

Nms/rad

J_shaft

Turbine Inertia

kgm2

K_shaft

Shaft-Stiffness

Nm/rad

D_shaft

Torsional Damping

Nms/rad

RPMnom

Nominal Rotor Speed

rpm

The electrical characteristics and hence the modelling requirements vary considerably with the different types of generators. In this section the available models for doubly-fed induction machines are presented. Obviously, the equipment characteristics depend on the manufacturer. The models presented here reflect typical equipment and control structures. This section starts with a description of the DFIG including the rotor-side converter. The grid-side converter with controls is described in section 0, followed by a presentation of DFIG protections.

The doubly-fed induction machine model extends the usual induction machine by a PWM converter in series to the rotor impedance as shown in Figure 10. In this figure, Rs and Xs are the resistance and leakage reactance of the sta tor winding; Xm is the magnetizing reactance and Zrot is the rotor impedance. Rs

U

Zrot

Xs

Xm

Ur

Ur'= e

− jω

r t

Ur

UAC

UDC

Figure 10: Equivalent Circuit of the Doubly-Fed Induction Machine with Rotor-Side Converter

The PWM converter inserted in the rotor circuit allows for a flexible and fast control of the machine by modifying magnitude and phase angle of the rotor voltage. It is assumed that a standard bridge consisting of six transistors builds the converter and that sinusoidal pulse width modulation is applied. In contrast to the normal induction machine model, in which the rotor is short-circuited, the winding ratio between rotor and stator is important for calculating actual DC voltages. The nominal rotor voltage that can be measured at the slip rings under open rotor conditions defines this winding ratio.


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For load flow calculations and transients initialization, only active power (AC-side), reactive power and the slip have to be specified. Internally, the corresponding modulation factors of the converter (Pmd, Pmq) are calculated and together with the power balance between the AC and DC side of the converter, DC voltage and DC current are obtained. During time domain simulations the converter is controlled through the pulse width modulation indices Pmd and Pmq which define the ratio between DC voltage and the A C-voltage at the slip rings. The modulation indices Pmd and P mq are defined in a rotor-oriented reference frame. For more details about the built-in DFIG model, please refer to the corresponding Model Description of the Technical Reference Manual .

Pref Ifq_ref;Ifd_ref Pfq;Pfd

Pmq ; Pmd

Qref

P;Q

PQ Control ElmGen*

Current Control *

Transformatio.. *

bypass

(From Protection System)

Ifq;Ifd psis_r;psis_i

Current Measurement * Irot

iq;id

phim

(To Protection System)

Figure 11: Main Components of the Rotor-Side Converter Controller (Composite Model Frame)

The basic diagram (Frame) of the rotor-side converter controllers is shown in Figure 11. The rotor-side converter is controlled by a two stage controller. The first stage consists of very fast current controllers regulating the machine’s rotor currents to reference values that are specified by a slower power-controller (second stage). The rotor-side current-controller operates in a stator-flux oriented reference frame. Hence, rotor currents must first be transformed into a stator-flux oriented reference frame (psis_r, psis_i, see Figure 11).


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The block Current Measurement transforms rotor currents from the original, rotor-oriented reference frame to stator-flux orientation. Additionally, the magnitude (in kA) of the rotor-current phasor is calculated and sent to the rotor current protection model. For considering flux-measurement delays (or flux-observer delays), a delay time constant can be entered. This transformation decomposes the rotor currents into a component that is in-phase with stator flux (d-component) and a component that is orthogonal to stator flux (q-component). The q-component of the rotor current directly influences the torque, why the q-axis can be used for t orque- or active power control. The d-axis component is a reactive current component and can be used for reactive power- or voltage control. T N E L I S g I D

Current Control:

Rotor-Side Converter Current Control

bypass

0

MaxPmq 0

Irq_ref

1

yi

non-windup PI Kq,Tq 1

-

MinPmq

q u

Max x3 2

0

Irq

0

module limiter

(1/(1+sT)) Tr

1

1

Pmq Pmd

0

1

d u

MaxPmd 0

Ird_ref

3

yi1

non-windup PI Kd,Td 1

6 1 o

4

MinPmd x4

Ird (1/(1+sT)) Tr

Figure 12: Block Diagram of Rotor-Current Controller

The block-diagram depicted in Figure 12 is the implementation of the rotor-current controller. There are two independent proportional-integral-(P-I-) controllers, one for the d-axis component, one for the q-axis component. The output of the current controller defines the pulse-width modulation indices in stator-flux orientation. For limiting harmonics, the magnitude of the pulse-width modulation index is limited to the parameter Max. Both P-I-controllers are equipped with non-windup limiters. By activating the additional input signal bypass, the pulse-width modulation indices are immediately set equal to zero, which is equivalent to blocking and bypassing the rotor-side converter (“Crow-Bar protection”, see section 3.5). Because the modulation index of the doubly-fed induction machine must be defined in a rotor-oriented reference frame, the outputs of the rotor-current controller have to be transformed back from stator-flux-orientation to rotor-orientation. This transformation is realized by the block Transformation .


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cosphim ifd sinphim

Rotor-Current Measurement

id iq

ifq

psis_r Irot psis_i

Figure 13: Input/Output Definition of Rotor-Current Measurement

Table 10: Input Definition of Rotor-Current Measurement Input

Description

Unit

cosphim

Cosine of rotor angle

sinphim

Sine of rotor angle

id

Rotor-Current (d-axis, in rotor-oriented reference frame)

p.u.

iq

Rotor-Current (q-axis, in rotor-oriented reference frame)

p.u.

psis_r

Stator Flux, real part

p.u.

psis_i

Stator Flux, imaginary part

p.u.

Table 11: Output Definition of Rotor-Current Measurement Output

Description

Unit

ifd

Rotor-Current (d-axis, Stator-Flux Orientation)

p.u.

ifq

Rotor-Current (q-axis, Stator-Flux Orientation)

Irot

Rotor-Current (Magnitude of current-phasor)

kA

Table 12: Parameters of Rotor-Current Measurement Parameter

Description

Unit

Tm

Measurement Delay Time

s

Urrated

Rated Rotor Voltage

kV

Srated

Rated Power of DFIG

MVA


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bypass Pmq Ifq_ref Ifq

Rotor-Current Controller

Ifd_ref

Pmd

Ifd

Figure 14: Input/Output Definition of Rotor- Current Controller

Table 13: Input-Definition of Rotor- Current Controller Input

Description

Unit

bypass

Bypass-Signal

Iq_ref

q-Axis Current Reference

p.u.

Ifq

q-Axis Current

p.u.

Id_ref

d-Axis Current Reference

p.u.

Id

d-Axis Current

p.u.

Table 14: Output-Definition of Rotor-Current Controller Output

Description

Pmq

q-Axis Pulse Width Modulation Index

Pmd

d-Axis Pulse Width Modulation Index

Unit

Table 15: Parameter-Definition of Rotor- Current Controller Parameter

Description

Unit

Tr

Current Measurement Time Constant

sec

Kq

q-Axis Gain

p.u

Tq

q-Axis Time Constant

sec

Kd

d-Axis Gain

p.u

Td

d-Axis Time Constant

sec

MinPmq

Min. q-Axis Pulse-Width Modulation Index

p.u

MinPmd

Min. d-Axis Pulse-Width Modulation Index

p.u

MaxPmq

Max. q-Axis Pulse-Width Modulation Index

p.u

MaxPmd

Max. d-Axis Pulse-Width Modulation Index t

p.u

Max

Max. Magnitude of Pulse-Width Modulation Index

p.u


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cosphim sinphim Pfd Pfq

Rotor-dqTransformation

Pmdd

Pmq psis_r psis_i

Figure 15: Input/Output Definition of Rotor-dq-Transformation

Table 16: Input Definition of Rotor-dq-Transformation Input

Description

Unit

cosphim

Cosine of Rotor-Angle

sinphim

Sine of Rotor-Angle

Pfd

d-Axis Modulation Index (Stator-Flux Orienation)

Pfq

q-Axis Modulation Index (Stator-Flux Orientatin)

psis_r

Stator-Flux, Real Part

p.u.

psis_i

Stator-Flux, Imaginary Part

p.u.

Table 17: Output Definition of Rotor-dq-Transformation Output

Description

Pmd

d-Axis Modulation Index (Rotor-Orientation)

Pmq

q-Axis Modulation Index (Rotor-Orientation)


Unit

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T N E L I S g I D

PQ Control: Active and Reactive Power Control Rotor Side Converter

bypas.

0

MaxIfq 0

Pref 1

1

xP

P 2

-

non-windup PI Kp,Tp MinIfq

x1

(1/(1+sT) Ttr

Max

Active Power Control 0

0

module limiter 1

1

Ifq_ref Ifd_ref

0

1

MaxIfd 0

3

Qref

1

-

non-windup PI Kq,Tq MinIfd

xQ x2 4

Q

Reactive Power Control

(1/(1+sT) Ttr

Figure 16: Block-Diagram of PQ-Controller

D-axis and q-axis component of the rotor current are controlled t o reference values specified by active- and reactive power controllers according to Figure 16. Similar to the rotor-current controller, the power controller regulates active- and reactive power by independent P-I-controllers. The P-I-controllers are equipped with non-windup limiters. The output limits the magnitude of the rotor-current reference. In contrast to the output-limiter in Figure 12, the q-axis-component (active current component) is prioritized. Voltage control can either be realized by connecting a voltage controller behind the reactive power reference or by replacing the reactive power controller by a voltage controller defining the d-axis current reference.

bypass Ifd_ref Pref

PQ-Controller

P Qref

Ifq_ref

Q

Figure 17: Input/Output Definition of PQ-Controller


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Table 18: Input Definition of PQ-Controller Input

Description

Unit

bypass

Bypass-Signal

Pref

Active Power Reference

p.u.

P

q-Axis Current

p.u.

Qref


p.u.

Q

d-Axis Current

p.u.

Table 19: Output-Definition of PQ-Controller Output

Description

Unit

Ifq_ref


p.u.

Ifd_ref


p.u.

Table 20: Parameter Definition of PQ-Controller Parameter

Description

Units

Ttr

Measuring time constant

sec

Kp

Active Power Control Gain

p.u

Tp

Active Power Control Time Constant

sec

Kq

Reactive Power Control Gain

p.u

Tq

Reactive Power Control Time Constant

sec

MinIfq

Min. q-axis current reference

p.u

MinIfd

Min. d-axis current reference

p.u

MaxIfq

Max. q-axis current reference

p.u

MaxIfd

Max. d-axis current reference

p.u

Max

Max. current magnitude reference

p.u

According to the classical control strategy the active power dispatch of wind-turbines is permanently optimized. Hence, the wind turbine operates with maximum possible active power output, depending on actual wind speed. As shown in Figure 3 there is, for every wind speed, an optimum mechanical speed (optimum λ). Assuming that the wind turbine always operates at this optimum point, the actual wind speed and hence the maximum possible active power can be calculated from the mechanical speed, without the necessity of wind-speed measurements. Calculating the table of max. power versus mechanical speed and applying the maximum power as active power reference to the PQ-controller drives the wind turbine into the optimum point. In the PowerFactory model, the power vs. speed characteristic (or MPT-characteristic) is defined using a linearly interpolated table. Alternatively, many doubly-fed induction machines are operated using a slightly different control-scheme, in which active power is measured and mechanical speed is calculated by the inverse MPT-characteristic. In this case, the calculated speed is sent as


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speed-reference to a speed-controller. Replacing the active power controller according to Figure 16 by a speed-controller and connecting an inverse MPT table to the speed-reference point realizes this alternative control scheme.

speed

MPT-Characteristic

Pref

Figure 18; Input/Output Definition of MPT-Characteristic

Table 21: Input Definition of MPT-Characteristic Input

Description

Unit

speed

Mechanical Speed

p.u.

Table 22: Output Definition of MPT-Characteristic Output

Description

Unit

Pref

Active Power Reference

p.u.

Table 23: Parameter Definition of MPT-Characteristic Parameter

Description

Unit

array_MPT

Array of Power Reference Points

p.u.


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3

1 L

PWM U1 1 C

Figure 19: Grid-Side Converter

The grid-side converter consists of a 6-pulse bridge (PWM U1 in Figure 19), the AC-inductance (L1) and the DC -capacitance (C1). Like the rotor-side converter, the grid-side PWM converter is modelled using a fundamental frequency approach. The input variables Pmr and Pmi, together with the DC -voltage, define magnitude and phase angle of the AC-voltage at the PWMconverter’s AC-terminal. The pulse-width modulation indices Pmr and Pmi are referred to the so-called global reference frame , which is in EMT-simulations a steady state reference frame and which rotates with reference frequency (mechanical speed of the reference machine) in case of an RMS simulation. However, the reference frame has no influence to t he system’s performance, as long as all quantities are given in the correct reference frames. More information about the PWM-controller, the AC-inductance and the DC -capacitance can be found in the corresponding Model Descriptions . The basic diagram of the grid-side controller is shown in Figure 20. The modulation indices of the Converter are imposed from a Current Control through a reference frame transformation ( ph- transf ). The Current Control operates in an AC-voltage oriented reference frame. It contains two current control loops: direct (active-) and quadrature (reactive-) axis current components ( id and iq ). The reference of the direct axis current component (id_ref ) is set by DC voltage control . The reference of the quadrature axis current component (id_ref ) is, kept constant (const. reactive power) in this case. For defining the AC-voltage oriented reference frame, a PLL (phase-locked-loop) is required measuring the voltage angle. The PLL-output is used for transforming the current measurement into the voltage-oriented reference frame ( dq- transf) and for transforming the controller outputs (pulse-width modulation indices) back to the global reference frame ( ph-transf ).


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T N E L I S g I D

Grid Side Converter:

udc_ref

udc

DC Voltage measurement StaVmea*

iq_ref

id_ref

DC Voltage Control ElmDc *

ir Current Measurement StaImea*

Current Control ElmCur*

ii

iq

Pmq

id

Pmd

Pmr

cosph.. PLL ElmPll*,ElmPhi*

dq transf ElmDq-*

ph-transf ElmDq-*

Converter ElmVsc*

Pmi

sinph..

Figure 20: Grid-Side Converter- Frame

T N E L I S g I D

Current Control:

Grid-Side Converter Current Control

Max_Pmd id_ref

0

{K (1+1/sT)} Kd,Td

-

Min_Pmd 1

id

Max

x3

(1/(1+sT)) Tr

0

0

module limiter 1

1

Pmd Pmq

0

1

Max_Pmq iq_ref

2

-

{K (1+1/sT)} Kq,Tq Min_Pmq

3

iq (1/(1+sT)) Tr

x4

Figure 21: Block Diagram of Grid-Side Current Controller


22

3

The grid-side controller (Figure 21) is very similar to the rotor-side current controller (Figure 12). However, since it operates in a voltage-oriented reference frame and not in a flux-oriented reference frame the role of d- and q-axis is inverted: the d-axis component defines active-current and the q-axis component defines reactive current.

Id_ref Id Iq_ref

Grid-Side Current Controller

Pmd

Pmq Iq

Figure 22: Input/Output Definition of Grid-Side Current Controller

Table 24: Input Definition of Grid-Side Current Controller Input

Description

Unit

Id_ref


p.u.

Id

d-Axis Current

p.u.

Iq_ref


p.u.

Iq

q-Axis Current

p.u.

Table 25: Output Definition of Grid-Side Current Controller Output

Description

Pmd

d-Axis Pulse Width Modulation Index

Pmq

q-Axis Pulse Width Modulation Index

Unit

Table 26: Parameter Definition of Grid-Side Current Controller Parameter

Description

Units

Kd

d-axis proportional gain

p.u.

Td

d-axis integral time constant

Sec

Kq

q-axis proportional gain

p.u

Tq

q-axis integral time constant

Sec

Tr

Current measurement time constant

Sec

Min_Pmd

Min. d-axis modulation factor

p.u.

Min_Pmq

Min. q-axis modulation factor

p.u.

Max_Pmd

Max. d-axis modulation factor

p.u.

Max_Pmq

Max. q-axis modulation factor

p.u.


23

3

T N E L I S g I D

PLL:

sinphi sin(x) 0

vr

K Kp

rr

i h p p K

dphi

dom dommax

1

vi

ii

0

m o n _ m o

om

i h p i K

K/s_lim K

1/s

i y

cosphi cos(x)

1

dommin

1/(2pi)

Fmeas

2

Figure 23: Block-Diagram of PLL

Figure 24: Basic-Data-Page of PLL Showing Node-Reference

The reference angle of the current controller is provided by a PLL (phase locked loop). The PLL is a PowerFactory built-in model that refers directly to a bus-bar or terminal. The block-diagram is shown in Figure 23, however, the input voltage is not defined by a composite model but directly by a node-reference in the input-dialogue box of the PLL, as shown in Figure 24.


24

3

Fmeas

PLL

sinphi cosphi

Figure 25: Input/Output Definition of PLL (Built-In Model)

Table 27: Output Definition of PLL Output

Description

Unit

Fmeas

Measured Frequency

Hz

sinphi

Sine of Voltage Angle

cosphi

Cosine of Voltage Angle

Table 28: Parameter Definition of PLL Parameter

Description

Unit

Kp

Controller Gain

Ki

Integration Gain

1/a

ommax

Upper Frequency Limit

p.u.

ommin

Lower Frequency Limit

p.u.

The input/output definition of the transformation blocks carrying out the transformation from the global reference system to the AC-voltage oriented reference system and back are shown in Figure 26.

ir ii sinphi

Grid-dqTransformation

id iq

cosphi

Figure 26: Input/Output Definition of Grid-dq-Transformation


25

3

Table 29: Input Definition of Grid-dq-Transformation Input

Description

Unit

ir

Real Part of Input Signal in Global Reference System

p.u.

ii

Im. Part of Input Signal in Global Reference System

p.u.

sinphi

Cosine of Reference Angle

cosphi


Table 30: Output Definition of Grid-dq-Transformation Output

Description

Unit

id

d-Axis Current

p.u.

iq

q-Axis Current

p.u.

id iq sinphi

PhaseTransformation

ir ii

cosphi

Figure 27: Input/Output Definition of Phase-Transformation

Table 31: Input Definition of Phase-Transformation Input

Description

Unit

id

d-Axis Component of Input Signal

p.u.

iq

q-Axis Component of Input Signal

p.u.

sinphi


cosphi


Table 32: Output Definition of Phase-Transformation Output

Description

Unit

ir

Real Part of Output Signal

p.u.

ii

Im. Part of Output Signal

p.u.


26

3

T N E L I S g I D

DC Voltage Control:

0

udc_ref

Max_idref

1

udc

-

dudc

id_ref

{K (1+1/sT)} Kudc,Tudc

Min_idref

xidref

Figure 28: DC-Voltage Controller

The P-I-controller shown in Figure 28 controls the DC -voltage and sets the d-axis current reference. Time constant and gain of the controller must be set in accordance with the DC-capacitance (see Figure 19).

udc_ref

DC-Voltage Controller

udc

id_ref

Figure 29: Input/Output Definition of DC-Voltage Controller

Table 33: Input Definition of DC-Voltage Controller Input

Description

Units

udc_ref

DC-Voltage, Reference Value

p.u.

udc

DC-Voltage

sec


2 7

3

Table 34: Output Definition of DC-Voltage Controller

Ouput

Description

Units

id_ref


p.u.

Table 35: Parameter Definition of DC-Voltage Controller Parameter

Description

Units

Kudc

Proportional Gain

p.u.

Tudc

Integral Time Constant

sec

Min_idref

Min. d-axis current reference

p.u.

Max_idref

Max. d-axis current reference

p.u


28

3

T N E L I S g I D

Protection:

Irot

0

Rotor Bypass MaxIrotor, tbypass

CrowBar

0

TripSpeed

speed

1

SpeedProt MaxSpeed1,ttripMaxS1, Ma..

1

bypass Max

2

u

2

TripVoltage VoltageProt MaxVoltage1,ttripMaxV1, ..

Figure 30: Block Diagram of DFIG-Protection

The following protective functions are implemented in the block diagram according to Figure 30: 1. Under-/Over-Voltage 2. Under-/Over-Speed 3. Rotor-Over-Current (“Crow-Bar Protection”)

The Under/Over-Voltage unit supervises the voltage at the HV side of the transformer and has four voltage levels, two for under-voltage and two for over-voltage. If this protective unit triggers the machine breaker is opened. The Under/Over-speed protection unit supervises the generator speed and consists of four levels, two for under-speed and two for over-speed. If this protective unit triggers the machine breaker is opened.

Rs

U

Zrot

Xs

Xm

Ur

Ur'= e

− jω

r t

Ur

Additional Impedance

Figure 31: Equivalent Circuit Diagram of DFIG During Crow-Bar Protection


29

3

The Crow-Bar protection is specific to doubly-fed induction generators and protects the rotor-side converter against overcurrents. When the rotor current exceeds a threshold value, the converter is blocked and bypassed through an additional impedance (see Figure 31). This additional impedance reduces the amount of reactive power absorbed by the machine and improves the torque characteristic during voltage sags. While the Crow-Bar is inserted, the integral actions of the rotor-side controllers are set to zero (see Figure 12 and Figure 16) for minimizing discontinuities in the rotor current when the Crow-Bar is removed. Those discontinuities would eventually lead to subsequent operations of the Crow-Bar protection. When the Crow-Bar is released, the rotor side converter is unblocked. For simulating cases, in which doubly-fed induction generators remain in the system during faults, as recommended by the latest E.ON. guidelines, the operation of the Crow-Bar protection does not open the machine breaker. For simulating synchronous operation of Crow-Bar protection and machine breaker, the model can easily be modified.

Irot speed

DFIG-Protection bypass

u

Figure 32: Input/Output Definition of DFIG-Protection

Table 36: Input Definition of DFIG-Protection Input

Description

Units

Irot

Rotor Current Magnitude

kA

speed

Generator Speed

sec

u

Bus-Bar Voltage

p.u

Table 37: Output Definition of DFIG-Protection Output

Description

bypass

Bypass-Signal (for Crow-Bar Insertion)

Units


30

3

Table 38: Parameter Definition of DFIG-Protection Parameter

Description

Units

MaxIrotor

Rotor Current for Crow Bar Insertion

kA

tbypass

Crow Bar Insertion Time

sec

MaxSpeed1

Overspeed Setting step 1

p.u

ttripMaxS1

Overspeed Time Setting step 1

sec

MaxSpeed2

Overspeed Setting step 2

p.u

ttripMaxS2

Overspeed Time Setting step 2

sec

MinSpeed1

Underspeed Setting step 1

p.u

ttripMinS1

Underspeed Time Setting step 1

sec

MinSpeed2

Underspeed Setting step 2

p.u

ttripMinS2

Underspeed Time Setting step 2

sec

MaxVoltage1

Overvoltage Setting step 1

p.u

ttripMaxV1

Overvoltage Time Setting step 1

sec

MaxVoltage2

Overvoltage Setting step 2

p.u

ttripMaxV2

Overvoltage Time Setting step 2

sec

MinVoltage1

Undervoltage Setting step 1

p.u

ttripMinV1

Undervoltage Time Setting step 1

sec

MinVoltage2

Undervoltage Setting step 2

p.u

ttripMinV2

Undervoltage Time Setting step 2

sec


31

4

In this section the behaviour of t he proposed DFIG model under different types of system faults is presented.

In this case, a three phase fault cleared after 200 ms causing a voltage depression of about 25% is simulated. The results are presented in Figure 33 to Figure 35. T N E L I S g I D

1.000 0.00 -1.000 -2.000 -3.000

0.00

1.000 PQ Control: Total Reactive Power (Q)

2.000

3.000

..

4.000

0.00

1.000 PQ Control: Total Active Power (P)

2.000

3.000

..

4.000

0.00

1.000 T3WT1: AC Voltage at HV side (u)

2.000

3.000

..

4.000

1.200 0.80 0.40 0.00 -0.400 -0.800

1.200 1.00 0.80 0.60 0.40 0.20 0.00

DIgSILENT

Doubly-fed Induction Generator - Example

Plot-1 Date: 5/26/2003 Annex: /1

Figure 33: Three-Phase Fault Far from Wind Generation, Connection Point


32

4

5.500

T N E L I S g I D

7.500

5.000

5.000

2.500 4.500 0.00 4.000 -2.500 3.500

3.000

-5.000

0.00

1.000 2.000 G1d: Stator Active Power

3.000

..

4.000

0.50

-7.500

0.00

1.000 2.000 G1d: Stator Reactive Power

3.000

..

4.000

0.00

1.000 2.000 3.000 PWM U1: Grid Side Converter Reactive Power

..

4.000

0.00

0.25 -0.100 0.00 -0.200 -0.250 -0.300 -0.500

-0.750

0.00

1.000 2.000 3.000 PWM U1: Grid Side Converter Active Power

..

4.000

-0.400


DIgSILENT


Figure 34: Three-Phase Fault Far from Wind Generation, Stator- and Grid-Side Results T N E L I S g I D

1.000 0.99 0.98 0.97 0.96 0.95 0.94

0.00

1.000

2.000

3.000

..

4.000

1.000 Prime Mover: Blade pitch Angle

2.000

3.000

..

4.000

1.000

2.000

3.000

..

4.000

G1d: Generator Speed 3.000 2.000 1.000 0.00 -1.000

0.00

4.500 4.400 4.300 4.200 4.100 4.000 0.00 Prime Mover: Wind Power

DIgSILENT



Figure 35: Three-Phase Fault Far from Wind Generation, Mechanical Variables


33

4

Figure 33 shows that the total active and reactive power at the connection point is quickly restored. The active power of the stator has an oscillatory component due to torsional oscillations that is almost perfectly damped by the active power controller of the grid-side converter (Figure 34). The speed deviations are not large enough to cause a variation of the blade angles the pitch control.

In this case, a three phase fault cleared after 400 ms causing a voltage depression of about 85% is simulated assuming that the under-voltage protection is set to avoid the disconnection from the grid under these circumstances. The results are presented in Figure 36 to Figure 38. In this case, it takes longer to restore total active and reactive power than in the previous case, due to the operation of the crow bar (Figure 36). The total reactive power is almost zero during the fault and is negative during the time between clearing the fault and removing the crow bar protection at t=0.5s. In this case, the speed deviation is larger than in the previous case and the blade angle is increased to reduce the power extracted from the wind. The reactive power absorbed by the generator during the time that the crow bar is inserted may have a negative impact on the voltage stability of the system when a significant number of units are connected. The modelling of the operation of this protective function should be particularly considered in the design of transmission systems c onnecting large wind farms to utility grids. T N E L I S g I D

1.000 0.00 -1.000 -2.000 -3.000

0.00

1.000 PQ Control: Total Reactive Power (Q)

2.000

3.000

..

4.000

0.00

1.000 PQ Control: Total Active Power (P)

2.000

3.000

..

4.000

0.00

1.000 T3WT1: AC Voltage at HV side (u)

2.000

3.000

..

4.000

1.200 0.80 0.40 0.00 -0.400 -0.800

1.200 1.00 0.80 0.60 0.40 0.20 0.00

DIgSILENT



Figure 36: Three-Phase Fault Close to Wind Generation, Connection Point


34

4

6.000

8.000

4.000

4.000

2.000

0.00

0.00

-4.000

-2.000

-8.000

-4.000

0.00


3.000

..

4.000

1.200

-12.00

T N E L I S g I D

0.00


3.000

..

4.000

0.00


..

4.000

4.000

0.80

3.000

0.40 2.000 0.00 1.000 -0.400 0.00

-0.800

-1.200

0.00


..

4.000

-1.000


DIgSILENT


Figure 37: Three-Phase Fault Close to Wind Generation, Stator- and Grid-Side Results

T N E L I S g I D

1.140 1.100 1.060 1.020 0.98 0.94

0.00

1.000

2.000

3.000

..

4.000

1.000 Prime Mover: Blade pitch Angle

2.000

3.000

..

4.000

1.000

2.000

3.000

..

4.000

G1d: Generator Speed 0.30 0.20 0.10 0.00 -0.100

0.00

4.400 4.300 4.200 4.100 4.000 3.900 0.00 Prime Mover: Wind Power

DIgSILENT



Figure 38: Three-Phase Fault Close to Wind Generation, Mechanical Variables


35

4

In this case, a single phase fault cleared after 400 ms causing a total voltage depression in phase A at the HV side of the machine transformer is simulated assuming that the under-voltage protection is set to avoid the disconnection from the grid under this circumstances. The results are presented in Figure 39 to Figure 41. In this case, the total active power does not decrease during the fault as in the previous case due to the fault type. However, the increasing rotor current causes the Crow-Bar protection to trip. Consequently, the total reactive power absorption significantly increases until the crow bar protection is removed at t=0.5s. The speed deviation is less than in the previous case and the blade angle is kept constant. In contrast to the previous cases, this case was simulated using an instantaneous-value representation of the AC-system (EMTsimulation). This more accurate model uses fifth-order generator models, including stator transients and differential equations for all network components. T N E L I S g I D

2.00 1.00 -0.00 -1.00 -2.00

-0.00 0.25 PQ Control: Total Reactive Power (Q)

0.50

0.75

[s]

1.00

-0.00 PQ Control: Total Active Power (P)

0.50

0.75

[s]

1.00

0.50

0.75

[s]

1.00

2.00

1.00

-0.00

-1.00

0.25

2.00 1.00 -0.00 -1.00 -2.00

DIgSILENT

-0.00 0.25 T3WT1: Phasenspannung L1/OS-Seite in p.u.


Results at Connection Point Date: 8/11/2003 Annex: 1 /1

Figure 39: Single-Phase Fault Close to Wind Generation, Connection Point


36

4

7.50

9.00

5.00

6.00

2.50

3.00

0.00

0.00

-2.50

-3.00

-5.00

-0.00


0.75

[s]

1.00

-6.00

3.00

3.00

2.00

2.00

1.00

1.00

0.00

0.00

-1.00

-0.00


[s]

1.00

-1.00

T N E L I S g I D

-0.00


0.75

[s]

1.00

-0.00


[s]

1.00


DIgSILENT

Active/Reactive Power Date: 8/11/2003 Annex: 1 /2

Figure 40: Single Phase Fault Close to Wind Generation, Stator- and Grid-Side Results T N E L I S g I D

1.14 1.10 1.06 1.02 0.98 0.94

-0.00 G1d: Generator Speed

0.25

0.50

0.75

[s]

1.00

-0.00 Pitch Control: Blade pitch Angle

0.25

0.50

0.75

[s]

1.00

-0.00 Turbine: Wind Power

0.25

0.50

0.75

[s]

1.00

0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15

4.40 4.30 4.20 4.10 4.00 3.90

DIgSILENT


Mechanical Results Date: 8/11/2003 Annex: 1 /3

Figure 41: Single-Phase Fault Close to Wind Generation, Mechanical Variables


3 7

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