Minimum Inertia Requiremenyt

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2017.2720621, IEEE Transactions on Power Systems

1

Minimum Synchronous Inertia Requirement of Renewable Power Systems Huajie Gu, Ruifeng Yan, Member, IEEE and Tapan Kumar Saha, Senior Member, IEEE

Abstract—The installed capacity of wind generation and photovoltaics (PV) in many countries is going to dominate generation fleets in a bid to meet growing renewable energy targets. Synchronous inertia has never been problematic as there was more available than needed, but it is being significantly reduced due to the increasing integration of non-synchronous renewable generation. When the low bidding priced generation of wind and PV becomes considerably large, conventional economic dispatch algorithms can result in less online synchronous inertia and put power system security at risk. However, the compromise of power system security due to synchronous inertia shortage is not well studied in literature. This paper develops a synchronous inertia constrained economic dispatch algorithm to satisfy the minimum required synchronous inertia of frequency control. Synchronous condensers and wind reserve are economically allocated to alleviate any shortage of synchronous inertia and frequency control ancillary services (FCAS). A Gaussian particle swarm optimization algorithm is introduced to simultaneously co-optimize the dispatch of synchronous generators and their FCAS, wind reserve and synchronous condensers.

N reg*

N ctg**

NSC N WF

Psync i  t 

Preg* i  t 

Index Terms— Synchronous inertia, economic dispatch, wind turbine, renewable energy, power system. 

Pctg** i  t 

NOMENCLATURE

Pwrsv i  t 

C t  Csync i  Creg* i 

Cctg** i 

Csc i  Cwrsv i  Nsync

Overall power system operational cost in the economic dispatch cycle t in terms of net load Generation cost of the ith synchronous generator Cost of a type of regulation FCAS from the ith registered synchronous generator, where * is R (raise) or L (lower) Cost of a type of contingency FCAS from the ith registered synchronous generator, where ** is R6 (6 second raise) or L6 (6 second lower) or R60 (60 second raise) or L60 (60 second lower) or R5 (5 minute raise) or L5 (5 minute lower) Cost of synchronous inertia provision services from the ith registered synchronous condenser Cost of power reserve from the ith registered wind farm Number of synchronous generators

i    Ii I t  f f cstr

f nom

f cstr1 f ctg

f cstr2 Pctg  t  Perr  t 

Corresponding author: Ruifeng Yan (email: [email protected]). He is with Global Change Institute, University of Queensland, Brisbane St Lucia, QLD 4072 Australia. Huajie Gu and Tapan Kumar Saha are with power and energy systems research group, School of Information Technology and Electrical Engineering, University of Queensland, Brisbane St Lucia, QLD 4072, Australia (emails: [email protected], [email protected]).

vi vmin i

Number of synchronous generators registered for a type of regulation FCAS, where * is R (raise) or L (lower) Number of synchronous generators registered for a type of contingency FCAS, where ** is R6 (6 second raise) or L6 (6 second lower) or R60 (60 second raise) or L60 (60 second lower) or R5 (5 minute raise) or L5 (5 minute lower) Number of registered synchronous condensers Number of wind farms having power reserve Dispatched power output of the ith synchronous generator in the dispatch cycle t Dispatched amount of a type of regulation FCAS from the ith registered synchronous generator in the dispatch cycle t, where * is for R (raise) or L (lower) Dispatched amount of a type of contingency FCAS from the ith registered synchronous generator in the dispatch cycle t, where ** is R6 (6 second raise) or L6 (6 second lower) or R60 (60 second raise) or L60 (60 second lower) or R5 (5 minute raise) or L5 (5 minute lower) Dispatched amount of power reserve from the ith registered wind farm in the dispatch cycle t Penalty coefficient of power reserve unavailability assigned to the ith wind farm Synchronous inertia of the ith synchronous generator or condenser Total synchronous inertia of dispatched synchronous generators and condensers in the dispatch cycle t Rate of change of frequency (RoCoF) RoCoF constraint Normal frequency deviation Normal frequency deviation constraint Contingency frequency deviation Contingency frequency deviation constraint Contingency size in the dispatch cycle t Power mismatch in the dispatch cycle t caused by forecast errors Current wind speed blowing across the ith wind farm Minimum wind speed of the ith wind farm to enable power reserve

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2

ci ki

i

i hi li   

Scale parameter of Weibull distribution for wind speed variation of the ith wind farm Shape parameter of Weibull distribution for wind speed variation of the ith wind farm Mean of Weibull distribution for wind speed variation of the ith wind farm Autocorrelation of two successive wind speeds of the ith wind farm Height above ground of the ith wind farm Turbulence length scale of the ith wind farm Time lag between two successive wind speeds Frequency in wind turbulence spectrum Constant to tune the penalty coefficient I. INTRODUCTION

R

ENEWABLE energy is a promising technology to reduce CO2 emission and therefore to mitigate global warming. Within the next few decades, current power systems predominantly supplied by synchronous generators will gradually witness a structural change of generation portfolios and ultimately may even shift to a 100% renewable power system (RPS). For an RPS with great asynchronous renewable generation, although massive transmission upgrades [1] and demand side management [2] are also crucial, the most basic and challenging problem lies in the electricity supply side. Economic dispatch algorithms proposed in literature have focused on the improvement of algorithm performance [3, 4] and consideration of more operational constraints [5], such as spinning reserve and generator ramp rates. They did not dynamically evaluate the synchronous inertia adequacy of a dispatch result in terms of N-1 contingency [3-5]. This is due to the fact that synchronous inertia adequacy is not a problem for a conventional power system with limited non-synchronous generation. However, synchronous inertia is being materially reduced due to ongoing displacement of synchronous generators by asynchronous ones, such as wind turbine generators and photovoltaic (PV) panels. Electronic inverters used in wind turbines and PV panels lack the synchronous inertia that can help an RPS survive a major disturbance. If comprised of less online synchronous inertia, an RPS may routinely suffer a rapid rate of change of frequency (RoCoF) and a large frequency deviation following a disturbance. A great RoCoF of 6 Hz/s was recorded in the South Australian blackout on September 28, 2016 which was caused by the “lightness” of the South Australian power system [6]. The instantaneous penetration level of wind and PV generation was over 50% before the blackout in South Australia and only three thermal power plants were dispatched [6]. This paper therefore proposes a synchronous inertia constrained economic dispatch to keep the minimum amount of synchronous inertia online. The proposed algorithm introduces a feedback loop to conventional economic dispatch algorithms. The feedback loop is used to evaluate the inertia adequacy of dispatched synchronous generators and to ensure the dynamic security of frequency control for an RPS with high

non-synchronous renewable generation. II. METHODOLOGY Australian energy market operator (AEMO) studied a 100% RPS of the national electricity market (NEM) [1] and proposed generation mixes for that scenario in 2030. One of them is studied in this paper and listed in Table I. Fig. 1 shows the predicted wind/PV generation and load profile of the NEM on a random day in 2030. The prediction is made based on the data from the NEM Review for the Australian power system [7]. Net load is the actual load subtracted by non-dispatchable wind and PV generation [8]. As can be seen in Fig. 1, the net load is significantly light and reaches its minima of 2.2 GW at T0. Consequently, fewer synchronous generators are required to power the net load. The light net load may cause a shortage of synchronous inertia and degrade frequency control. At present, successful frequency control in the NEM requires that RoCoF should not exceed ±0.5 Hz/s [8]. Tolerated frequency deviations for normal events are ±0.15 Hz [8]. Maximum allowed frequency deviations for contingency events are ±0.5 Hz [8]. TABLE I.

A 100% RPS GENERATION MIX PROJECTION OF THE NEM [1] Generation PV, rooftop PV, utility Wind, onshore Geothermal Bagasse Biomass (wood) Concentrating solar thermal (CST) Hydro Pumped hydro Biogas Total Peak demand

Capacity (MW) 10,905 11,000 34,500 1,000 1,010 7,000 11,000 7,330 740 13,500 97,985 43,000

If there is no wind or PV generation in the power system, conventional dispatch algorithms schedule a large amount of synchronous generators to meet the actual load. Consider an N-1 contingency event for the RPS, the largest online synchronous generator is suddenly tripped at T0 as highlighted in Fig. 1. The maximum post-contingency frequency deviation of the RPS is well within its required band (49.5~50.5 Hz) as shown in Fig. 2. The largest RoCoF is 0.09 Hz/s which is less than the threshold of 0.5 Hz/s. Therefore, the frequency control security is conventionally guaranteed by a large fleet of synchronous generators. With a large amount of wind and PV integration, fewer synchronous generators are scheduled by conventional economic dispatch algorithms, especially during the low load condition. For the same contingency event at T0 in Fig. 1, the corresponding maximum frequency deviation rapidly breaches its constraint (49.5 Hz) as in Fig. 2. The largest RoCoF is 1.43 Hz/s which is much larger than the maximum tolerated value of 0.5 Hz/s. Therefore, the inadequacy of synchronous inertia should be taken into account when performing economic dispatch with a large amount of wind and PV generation.



3

Fig. 1. A projected daily wind/PV generation and load profile of the NEM in 2030 [7].

Fig. 2. A frequency control example with the current frequency regulation standard used by AEMO.

In general, a rapid RoCoF may result in the cascading trip of online synchronous generators [8-10]. A faster initial RoCoF generally contributes a larger frequency deviation. A severe frequency deviation can also trip synchronous generators and load shedding is required to restore RPS frequency [8-10]. These two frequency control indices are secured by synchronous inertia and frequency control ancillary services (FCAS) in the NEM of Australia. Synchronous inertia as a large damper is vitally important to slow down frequency dropping so that sluggish droop controllers can correct frequency later. As synchronous generators are coupled with power system frequency, the kinetic energy of their spinning rotors or inertia is instantaneously released to address the power deficit in a fast manner. Governor response of synchronous generators or FCAS take time to further balance the power deficit. A. Current Economic Dispatch and Frequency Control in the NEM AEMO uses a five minute central dispatch cycle consisting

Generation and FCAS Dispatch



...

Load Tracking

... ...

19:40

12:05

Load Tracking

...

19:35

...

12:10

...


of generation and FCAS dispatches to instantaneously balance generation and load in the cheapest manner [11], as illustrated in Fig. 3. Generation dispatch centrally schedules synchronous generators based on their real-time bids to track a five minute ahead load forecast [8].

Fig. 3. Current five minute central dispatch in the NEM.

Over periods shorter than five minutes, small power mismatches caused by forecast errors of load, wind and PV generation are controlled by regulation FCAS [8]. Regulation FCAS are split into raise and lower regulation FCAS. Their required amounts in the next five minutes are purchased from registered synchronous generators. Contingency FCAS are used to manage rapid and large frequency deviations arising from sizable load-generation unbalances caused by a sudden loss of large generation or a load [8]. The contingency FCAS are split into six categories: 6 second raise (R6), 6 second lower (L6), 60 second raise (R60), 60 second lower (L60), 5 minute raise (R5) and 5 minute lower (L5). The required amount of each of them in the next five minutes is purchased from registered synchronous generators with different ramp rates [8]. Regulation and contingency FCAS are required to restore frequency to the normal frequency range within a dispatch cycle. Therefore, the frequency control of every dispatch cycle is relatively independent. The blue dashed line in Fig. 2 illustrates a frequency control example with the current frequency regulation standard used by AEMO. A contingency event occurs at time zero, resulting in a rapid drop in frequency. Synchronous inertia as a measurement of stored rotational kinetic energy is instantaneously released to slow down frequency dropping speed, in other words to reduce RoCoF. When frequency further leaves the normal frequency operating range at T1, R6 contingency FCAS are activated to rapidly but temporarily balance the power deficit [11]. Then R60 contingency FCAS start at T2 (T1 + 6s) to bring frequency back to the normal frequency range [11]. Next, R5 contingency FCAS as a delayed service enter at T3 (T1 + 60s) to further restore the frequency to around the nominal value – 50 Hz [11]. B. Synchronous Inertia Constrained Economic Dispatch The flow chart of the proposed economic dispatch algorithm is shown in Fig. 4. A feedback loop highlighted in red is added to conventional economic dispatch. The feedback loop is introduced to evaluate the synchronous inertia adequacy of a



4

C t  

Nsync

C i 1



N regR

C i 1



sync i

regR i

 P  t     C

N ctgR6

C

ctgR6 i

regR i

C

N ctgR5

C i 1

ctgR5 i

NSC

 P  t  

i 1

Dispatch result

Proposed algorithm: a feedback loop to evaluate synchronous inertia adequacy

Yes

Output dispatch result

Fig. 4. Synchronous inertia constrained economic dispatch algorithm.

C. Minimum Synchronous Inertia For the dispatch cycle t, the total synchronous inertia of dispatched synchronous generators and condensers is Nsync  NSC



Ii

(2)

the penalty coefficient proposed to

t    i 1

CctgL60 i  PctgL60 i  t  

N ctgL5

ctgR5 i

 t     CctgL5 i  PctgL5 i  t   i 1

i 1

 is

N-1 contingency rapid dynamic simulation

Initial RoCoF is the largest after a contingency event, though RoCoF is gradually reduced through the provision of R6 contingency FCAS. The largest RoCoF is only determined by the contingency size and synchronous inertia. The largest RoCoF of the dispatch cycle t can be derived as [15] Pctg  t  (4) f max  t    f cstr 2I t  If only considering the RoCoF constraint, then the required minimum synchronous inertia according to (4) is

ctgR60 i

N WF



Frequency response safe?

(1)

i 1

  Csc i  I i    Cwrsv i  Pwrsv i  t    i  vi  vmin i   where i vi  vmin i

No

i 1

regL i

 t     CctgL6 i  PctgL6 i  t   N ctgL60

 P

 P

Economic dispatch via DLGPSO

I t  

N ctgL6

ctgR6 i

ctgR60 i

regL i

Forecasted net load

The minimum amount of the total synchronous inertia should ensure that RoCoF and frequency deviation meet their constraints in case of a contingency event. They are f cstr  f  f cstr  (3) f cstr1  f nom  f cstr1 f  f  f cstr2 ctg cstr2 

i 1

 P

N ctgR60 i 1



sync i

N regL

i 1



 P t 

cost of its power reserve in the cost function. Therefore, power reserve from a wind farm with greater uncertainty is less favored by the dispatch algorithm for sourcing FCAS. Wind reserve price will not be out of control in the future, because FCAS market is a demand-driven and free-bidding market. Many individual wind farms will partake in FCAS market and they will compete for selling their power reserve. Whoever offers the cheapest wind reserve will be chosen. PV theoretically can provide power reserve to support frequency control. However, the problem is its price. Levelised cost of electricity (LCoE) for PV is around 170 AUD/MWh, whilst for wind energy is 80-100 AUD/MWh [14]. Wind reserve is more financially attractive than PV reserve. Therefore, the power reserve capability of PV is not taken into account in this paper.

Conventional economic dispatch

dispatch result via rapid dynamic simulation of an N-1 contingency event. If the post-contingency frequency response of an RPS cannot satisfy the constraints of RoCoF and frequency deviation, the dispatch algorithm will find a new solution until the simulated frequency response is acceptable. Synchronous generators and their FCAS are the only resources available in the conventional economic dispatch. However, frequency control is compromised by the shortage of synchronous inertia and FCAS in an RPS with high wind and PV penetration. Synchronous condensers and wind reserve are therefore introduced to the proposed dispatch algorithm. Wind reserve is dispatched to maintain the minimum amount of power reserve needed by the studied power system to satisfy frequency control. Meanwhile, synchronous condensers are scheduled to keep the adequacy of synchronous inertia. The proposed economic dispatch algorithm schedules wind reserve and synchronous condensers simultaneously with conventional FCAS from synchronous generators. The economic dispatch problem in this paper is optimized by a Gaussian particle swarm optimization algorithm with differential evolution local search (DLGPSO) [12, 13]. The DLGPSO optimizer offers a self-tuning capability based on Gaussian distribution so as to avoid the parameter sensitivity of the original PSO algorithm. Furthermore, it is used with differential evolution to boost the algorithm performance. Wind and PV generation is not dispatchable and the net load should be powered by synchronous generators. The adequacy of synchronous inertia and FCAS should also be maintained. For the dispatch cycle t, the dispatches of synchronous generators and their FCAS, synchronous condensers and wind reserve are simultaneously co-optimized to minimize the total cost of the next five minute RPS operation. The cost function is the sum of the cost of synchronous generation and their FCAS, the cost of synchronous inertia provision services from synchronous condensers and the cost of wind reserve. Therefore, the cost function to be minimized is formulated as

describe the power reserve uncertainty from the ith wind farm. It is further explained in Section II-D. A wind farm with larger power reserve uncertainty is assigned with a bigger penalty coefficient. This penalty coefficient intentionally scales up the



5

I t  

Pctg  t 

(5)

2f cstr As can be seen in Fig. 5, the relevant minimum required synchronous inertia is determined proportionally by the contingency size and RoCoF constraint. For example, in order to ensure RoCoF is not larger than 0.5 Hz/s, the minimum required synchronous inertia is 35 GWs for the contingency size of 700 MW. However, such a level of synchronous inertia alone is not enough to prevent the maximum frequency deviation from violating its constraint.

unlikely to reduce to a level below 6 m/s for the same period of time. As a result, WF B has a better capability to provide power reserve, and should be favored by the economic dispatch algorithm. Meanwhile, if the wind speed variability is the same for both wind farms, the higher the current wind speed of WF A is, the more secure its power reserve will be in the next dispatch interval. Consequently, WF A is more preferable under this situation. Therefore, the probability of wind reserve unavailability is related to two factors – the location of a wind farm and its current wind speed. The location determines wind variability calculated based on long-term historical wind speed profile. The current wind speed is associated with the ability of a wind farm during a dispatch interval to contribute a certain amount of power reserve.

Fig. 5. Minimum required synchronous inertia with respect to contingency size (RoCoF constraint only).

Frequency deviations also depend on the amount and ramp rate of contingency FCAS. A rapid dynamic security model of RPS frequency control is developed in Section III-A to quantify frequency deviations with respect to different amounts of online synchronous inertia and FCAS. It is therefore used to quickly evaluate the synchronous inertia adequacy for every economic dispatch result. D. Wind Reserve Uncertainty The variation of nationwide wind generation may be relatively smaller as more wind turbines are being installed over a larger geographical area. However, the power output variation of a single wind farm within a day can be considerably large as shown in Fig. 6. Its power output can become zero for hours during a day. Power reserve of an individual wind farm is not as reliable as that of a conventional power plant. A minimum wind speed is required to enable power reserve, otherwise a wind turbine may stall. In order to maintain promised power reserve, the incoming wind speed of a wind farm should be greater than a required minimum level, e.g. 6 m/s in the next dispatch cycle. Therefore, the availability of wind reserve is determined by wind speed variation. For instance, both Wind Farm A (WF A) and Wind Farm B (WF B) are facing the same wind speed of 8 m/s. According to the wind speed variability from historical data, the wind speed of WF A has a high probability to become less than 6 m/s in the next dispatch cycle. On the contrary, the wind speed of WF B is

Fig. 6. Daily generation of Boco Rock wind farm in NSW Australia [7].

The variation of wind speeds over a certain time interval on the ith wind farm is conventionally assumed to be subject to Weibull distribution with scale parameter ci and shape parameter ki [12, 16, 17]. Scale and shape parameters are derived from historical wind statistics. They are different for wind farms in different locations. The probability density function (PDF) of bivariate Weibull distribution describing two successive wind speeds on the ith wind farm is given by [16] 

1 f ws i  v1 , v2  

4 1  i

2

e



1

2 1 i2



x

2 2 1  x2  2 i x1 x2

2 2 1  x2

 x

2

1

  x   x   ki 1  erf  1  1  erf  2   2  ci   2  ln  2  ln  2 2 ki2        x    x   1  erf  1  1  erf  2    2    2  

1

(6)

where v  i    1  c  x1  2erf 1  2e  i    k

1

   

(7)



6 and

   x2  2erf 1 1  2e (8)      i is the autocorrelation of two successive wind speeds on the same wind farm at time lag  . So f ws i  v1 , v2  is the PDF of the event that wind speed v1 changes to v2 after  seconds. The autocorrelation  i can be estimated from a turbulent spectrum of wind speeds as [18] v    2   ci 

ki



i   Speci    cos  2   d

penalty coefficient is proportional to the probability of wind reserve unavailability. A wind farm is given a larger penalty coefficient if it has a higher probability that its power reserve is going to be unavailable.

(9)

0

where Speci   is the Kaimal spectrum for wind turbulence of the ith wind farm and is defined as [18]

0.164 Speci   

i   0 i

(10) 5   3         1  0.164  i  0 i         where i    hi / i and 0 i  0.041 hi / li . Over a time period of  , the cumulative distribution function of a wind speed ramp starting in the range vs1 to vs 2 and ending in the range ve1 to ve 2 for the ith wind farm is [18]

Fig. 7. Probability of power reserve unavailability of a wind farm over the next five minutes for different Weibull distribution parameters.

The penalty coefficient changes the competitiveness of wind farms in FCAS market. Boco Rock and Gullen Range wind vs 2 ve 2 Fws i  vs1  v1  vs 2 , ve1  v2  ve 2     f ws i  v1 , v2  dv1dv2 (11) farms in NSW Australia [7] are used as examples for further vs1 ve1 Therefore, the probability of current wind speed vi decreases explanation. Assume that at the beginning of one economic dispatch cycle, they are offering the same amount of 1 MW to less than the minimum one vmin i can be estimated by power reserve at the same price of 150 AUD/MWh. Boco Rock Fws i vi  0.5  v1  vi  0.5, 0  v2  vmin i (12) wind farm has a penalty factor of 1.3 and its power reserve Since the integration at one point is zero, a range of price is lifted to 150×1.3=195 AUD/MWh in the cost function  vi  0.5, vi  0.5 is introduced to facilitate the probability of the proposed economic dispatch algorithm. Meanwhile, Gullen Range wind farm has a penalty factor of 1.2 and its calculation. power reserve price is increased to 150×1.2=180 AUD/MWh in The probability of power reserve unavailability of a wind the cost function. The proposed economic dispatch algorithm farm for the next five minutes (an economic dispatch cycle) is prefers the power reserve of Gullen Range wind farm because it shown in Fig. 7. The minimum required wind speed is set to be is cheaper and more reliable in comparison with that of Boco 6 m/s. In general, the probability of wind reserve becoming Rock wind farm. Note that the increased price is only used to unavailable is increasing when mean wind speed is dropping. quantify the wind reserve uncertainty for the cost function. The The probability is further affected by Weibull scale and shape actual price paid to a wind farm is the same as its bid. parameters. According to the probability of wind reserve unavailability E. Forecast Errors for the next five minutes, a penalty coefficient is introduced to Forecast errors of load, wind and PV generation can be quantify the impact of wind reserve uncertainty on economic experienced at all times. Forecast systems used by AEMO are dispatch decision making. Since one objective of the proposed required to have a target that five minute ahead normalized economic dispatch algorithm is to simultaneously minimize the mean absolute errors should not exceed tolerated thresholds [8]. cost of FCAS, whoever offers the cheaper wind reserve will be Regulation FCAS are used to correct small power mismatches favored. If the original price of power reserve from the ith wind caused by forecast errors. farm is multiplied by a penalty coefficient larger than one, then The amount of regulation FCAS should not be less than the the price of this wind reserve is increased. Consequently, the worst power mismatch caused by forecast systems, though it opportunity of this wind reserve being chosen for sourcing may not be fully activated due to the fact that the sum of wind FCAS is disadvantageous. and PV generation may change less as compared with The penalty coefficient assigned to the ith wind farm for its individual wind or PV generation. For instance, an unexpected power reserve uncertainty is defined as increase of wind generation over a dispatch cycle occurs along vi  0.5 vmin i i  vi  vmin i   1    f ws i  v1 , v2  dv1dv2 (13) with an unpredicted decrease of PV generation. For this case, vi  0.5 0 the overall variation of wind and PV generation is smaller, and where  is a constant to tune the penalty coefficient. The







7 the amount of regulation FCAS is always enough to compensate power mismatches due to forecast errors. III. FREQUENCY CONTROL DYNAMIC MODELLING A. Frequency Control The RPS frequency control dynamic model is shown in Fig. 8. Simulated power unbalances are caused by both forecast errors and the sudden loss of the largest online synchronous generator. Regulation and contingency FCAS can be provided by hydro, bio-fueled gas, steam power plants and wind farms. Details of FCAS modelling can be found in [11]. Electrically decoupled wind turbines can participate in frequency regulation via emulated inertia (EI) and active power control (APC). EI extracts kinetic energy from a spinning rotor by means of reducing its speed. APC enables wind turbines to have a governor type response similar to synchronous generators.

Perr (t)

Pctg  t 

 

Power system

they are the source of synchronous inertia provision services. B. Variable-speed Wind Turbine EI Frequency deviation [21] or its combination of RoCoF [22] can be used to trigger EI response. Considering the susceptibility of a derivative controller to noise, the frequency deviation triggered EI controller proposed by General Electric (GE) is used in this paper [21]. However, an EI controller is a replaceable component for a fast dynamic RPS model. Since the aim of this paper is to develop a synchronous inertia constrained economic dispatch algorithm, other EI controllers can also be chosen. As shown in Fig. 9, frequency is the input of the EI controller and it contains information of both frequency deviation and RoCoF. Frequency is first passed through a dead band. When frequency deviation is larger than the preset threshold, EI response is activated. Furthermore, a washout filter is applied to ensure the inertia response will be ceased after the required support period. As a result, the washout filter can generate an aggressive power surge signal to counter faster RoCoF. Therefore, EI response is affected by both frequency deviation and RoCoF.

f

pmxwi Wind farms

f



dbwi

f0

∑

Hydro power plants

Gas power plants

Steam power plants Fig. 8. RPS frequency control dynamic model.

EI and APC both respond to under-frequency contingency events. APC can de-load wind turbines to provide power reserve at the expense of profit losses. APC is also used to reduce power output of wind turbines for over-frequency events. Wind reserve comes with a cost whilst EI response for a short period around ten seconds raises negligible financial problems. EI and APC can effectively reduce RoCoF and frequency deviation in cooperation with the governor response of conventional hydro, gas and steam turbine generators [19]. Synchronous generators equipped with synchronous condensing clutches can be decoupled from their driving turbines and temporarily run as synchronous condensers at the expense of small parasitic load [20]. Such an operation mode can cost-effectively increase the synchronous inertia of an RPS. All gas power plants in the studied generation mix are assumed to be retrofitted with synchronous condensing clutches, and

1 1  sTlpwi

K wi

sTwowi 1  sTwowi

urlwi drlwi

pwi

pmnwi Fig. 9. Variable-speed wind turbine EI control model [21].

Although an EI controller is designed to respond to under-frequency events, it is technically capable of responding to over-frequency events as well. It can be done by modifying the dead band highlighted in red in Fig. 9. EI response of a single wind turbine with respect to different wind speeds is shown in Fig. 10. Fig. 10(a) shows the simulated RPS frequency variation. As can be seen in Fig. 10(b), when wind turbine generation is less than 20% of rated at a low wind speed, power surge from EI response is limited to prevent rotor stall. Above this power output level, the net power increase of EI response is comparatively similar. Initial power surge in Stage 1 of EI response is beneficial to frequency control but following underproduction in Stage 2 is detrimental since it can result in a second frequency drop [19]. When wind speed is over the rated, temporal overproduction can be provided by decreasing pitch angle and power recovery is not required [23]. However, rapid EI response of wind turbines cannot be replaced by such governor like response through reducing pitch angle. It takes more time to change pitch angle due to pitch rate limitations, so the resultant power surge is slower as compared with that of the EI response. C. Variable-speed Wind Turbine APC A wind turbine can be de-loaded either by raising pitch angle [19, 21, 24] or controlling rotor speed [25, 26]. A combination of speed and pitch control has the advantage of eliminating EI



8 power recovery period and delivering more energy upon calling [26]. It is used in this paper to enable the wind turbine with power reserve.

Fig. 10. EI response of a single wind turbine with respect to different wind speeds. (GE 2.5 MW wind turbine [21, 23]).

When rotor speed is below the rated, over-speeding is implemented to de-load a wind turbine as well as to store extra kinetic energy. The reserved power and stored kinetic energy can later be released to address RPS disturbances. After rotor speed reaches the rated, the pitch angle is increased to further curtail power output [26]. As shown in Fig. 11, much more energy is available from a wind turbine using the over-speeding control for the same RPS frequency drop shown in Fig. 10(a). Meanwhile, there are no power recovery periods for the wind turbine. As a result, the wind turbine can contribute significantly more energy to frequency regulation with less wind spillage.

PV generation is treated as negative load but they can be curtailed for security concerns [1]. Geothermal, biomass (wood) and bagasse power plants have slow ramp up capabilities and they are dispatched close to their maximum output [1]. They are suitable for baseload operation. Turbines designed for hydro, pumped hydro, CST and biogas have a faster ramp up capability and they are suitable for supplying rapid demand growth during peak times [1]. Based on predicted load profile and wind/PV generation of a random day as shown in Fig. 1, the proposed economic dispatch algorithm is performed to show that online synchronous inertia should not be less than a certain amount in order to ensure the security of frequency control. The proposed algorithm offers a framework to address the shortage of synchronous inertia caused by the integration of a large amount of renewable energy. It can be directly applied to other power systems. A. Synchronous Inertia As shown in Fig. 12, when net load is dramatically small between 12:00 and 15:00 as in Fig. 1, the synchronous inertia of dispatched synchronous generators based on conventional economic dispatch is significantly light. Such a dispatch cannot guarantee frequency control security as illustrated in Fig. 2.

Fig. 12. Synchronous inertia of the studied RPS.

Fig. 11. EI and APC response of a wind turbine (GE 2.5 MW wind turbine [21], wind speed 8 m/s).

IV. SIMULATION RESULTS The generation mix of studied 100% RPS is listed in Table I and is divided into three categories. Non-dispatchable wind and

The proposed dispatch algorithm gives another curve of online synchronous inertia depicted by the blue dashed line shown in Fig. 12. The minimum amount of synchronous inertia is maintained to ensure frequency control security. To achieve this goal, synchronous condensers are scheduled together with wind reserve and other FCAS to satisfy N-1 contingency frequency control. As a result, the frequency response of the same N-1 contingency event at T0 is now acceptable as shown in Fig. 13. The maximum frequency deviation is now within its band (49.5 Hz). The largest RoCoF is 0.49 Hz/s and it is less than the limit of 0.5 Hz/s. When the proposed dispatch algorithm requires that there is a need to prepare wind reserve or synchronous condensers in the next dispatch cycle, the dispatched amount of wind reserve or the dispatched capacity of synchronous condensers is not zero.



9 Such a need comes from the result of N-1 contingency rapid dynamic simulation as shown in Fig. 4. If this dynamic simulation conveys the dispatch algorithm that the current solution cannot ensure frequency control security, then the dispatch algorithm will find a new solution to satisfy frequency control requirements.

Fig. 14. Dispatched R6/R60/R5 contingency FCAS from synchronous generators and the minimum amount of required wind reserve.

Fig. 13. Frequency response of N-1 contingency event at T0.

B. Wind Reserve De-loading operation of wind farms with abundant wind resources is assumed to be compulsory in this paper. Wind farms should support frequency control as they are the largest energy supplier in the studied generation mix. Fig. 14 shows the dispatched R6/R60/R5 contingency FCAS from synchronous generators and the minimum amount of required wind reserve. Simulation results show that wind reserve is scheduled during the period when there is a shortage of R6 contingency FCAS. The reason why there is such a shortage is that scheduled synchronous generators cannot offer enough rapid power reserve and it is not economical to turn on extra synchronous generators. Therefore, the raise contingency FCAS have to be sourced from more expensive wind reserve.

D. Cost Comparison A 100% RPS is assumed to be subsidy free in this paper. The LCoE of each type of generation is shown in Table II. The pricing of synchronous inertia provision services from power plants running on synchronous condenser mode should consider the investment of synchronous condensing clutches and O&M cost. The cost of synchronous inertia provision services is assumed to be 2 AUD/MWs per hour in this paper [20]. Wind reserve cost is assumed to be 150 AUD/MWh [27]. The daily RPS five minute operational cost is shown in Fig. 16. The opportunity cost of FCAS is only paid when there is an actual contingency event. The normal RPS operational cost based on the proposed economic dispatch algorithm is slightly lifted during the period when synchronous condensers are run to address the shortage of synchronous inertia. As highlighted in Fig. 16, the additional cost of the activation of synchronous condensers is economically acceptable to maintain frequency regulation security.

C. Synchronous Condenser Simulation results show that synchronous condensers are scheduled during the period when the net load is significantly light as can be seen in Fig. 15. When scheduled synchronous generators can provide enough synchronous inertia, the capacity of scheduled synchronous condensers is zero. Because the synchronous inertia from synchronous generators is naturally available with their power dispatch, and the running of synchronous condensers increases the cost of power system operation.

Fig. 15. Minimum capacity of required synchronous condensers.



10 TABLE II.

LEVELISED COST OF ELECTRICITY (LCOE)

Generation type

Prime mover

Energy source

Asynchronous

Non Wind turbine

Solar [14] Wind [14] Geothermal [14] Bagasse [14] Biomass (wood) [14] CST [14] Biogas [14] Hydro [28] Pumped hydro [29]

Steam turbine Synchronous Gas turbine Hydro turbine

Cost (AUD/MWh) 170 100 150 120 125 200 180 20 250

Fig. 16. Studied RPS five minute operational cost during a day.

V. DISCUSSION With less synchronous inertia, frequency variation of an RPS following disturbances can be radical, especially at times of light load. However, hydro, steam and gas turbines and their paired synchronous generators have instability problems and cannot stay synchronized when facing a high RoCoF up to 2 Hz/s [30]. A design improvement of conventional turbines and synchronous generators may be needed so as to tolerate higher RoCoFs in the future. VI. CONCLUSION Conventional economic dispatch algorithms schedule synchronous generators to follow load variation without considering the compromised dynamic security of frequency control caused by a high penetration level of wind and PV generation. An RPS cannot be safely run without enough synchronous inertia so as to survive potential contingency events. This paper developed a synchronous inertia constrained economic dispatch algorithm that guarantees the dynamic security of frequency control all the time. The requirement of synchronous inertia is determined by both RoCoF and frequency deviation constraints. The largest RoCoF is solely decided by synchronous inertia and contingency size, whilst the maximum frequency deviation is further affected by the provision of contingency FCAS. This paper introduces wind reserve and synchronous

condensers into the economic dispatch of power systems with high penetration of non-synchronous renewable generation. The proposed algorithm economically dispatches wind reserve to address the deficit of conventional FCAS from synchronous generators. Meanwhile, power plants retrofitted with synchronous condensing clutches are scheduled to cover the shortage of synchronous inertia. REFERENCE [1] Australian Energy Market Operator. (2013). 100 percent renewables study modelling outcomes report. Available: https://www.environment.gov.au/climate-change/publications/aemo-mod elling-outcomes [2] J. A. Short, D. G. Infield, and L. L. Freris, "Stabilization of grid frequency through dynamic demand control," IEEE Transactions on Power Systems, vol. 22, pp. 1284-1293, Aug 2007. [3] P. Jong-Bae, L. Ki-Song, S. Joong-Rin, and K. Y. Lee, "A particle swarm optimization for economic dispatch with nonsmooth cost functions," IEEE Transactions on Power Systems, vol. 20, pp. 34-42, 2005. [4] T. Ding and Z. Bie, "Parallel augmented lagrangian relaxation for dynamic economic dispatch using diagonal quadratic approximation method," IEEE Transactions on Power Systems, vol. 32, pp. 1115-1126, 2017. [5] C. Wang and S. M. Shahidehpour, "Effects of ramp-rate limits on unit commitment and economic dispatch," IEEE Transactions on Power Systems, vol. 8, pp. 1341-1350, 1993. [6] Australian Energy Market Operator. (2016). Black system South Australia 28 September 2016 third preliminary report. Available: http://www.aemo.com.au/-/media/Files/Electricity/NEM/Security_and_R eliability/Reports/Integrated-Third-Report-SA-Black-System-28-Septem ber-2016.pdf [7] NEM Review. (2016). Australian national electricity market review. Available: http://www.nem-review.info/ [8] Australian Energy Market Operator. (2013). Integrating renewable energy wind integration studies report. Available: http://www.aemo.com.au/Electricity/Planning/~/media/Files/Electricity/ Planning/Reports/Integrating%20Renewable%20Energy%20-%20Wind %20Integration%20Studies%20Report%202013.pdf.ashx [9] Siemens. (2011). Global blackouts – lessons learned. Available: http://m.energy.siemens.com/ru/pool/hq/power-transmission/HVDC/Glo bal_Blackouts.pdf [10] Australian Energy Market Operator. (2014). Renewable Energy Integration in South Australia. Available: http://www.aemo.com.au/Electricity/Planning/~/media/Files/Electricity/ Planning/Reports/Renewable_Energy_Integration_in_South_Australia_ AEMO_Electranet_Report_Oct_2014.ashx [11] Intelligent Energy Systems. (2010). Raise contingency FCAS-price control mechanism. Available: http://www.energyregulator.tas.gov.au/domino/otter.nsf/LookupFiles/10 3252_IES_Final_Report_Raise_Contingency_FCAS_Price_Control_Me chanism_28_July_2010.pdf/$file/103252_IES_Final_Report_Raise_Con tingency_FCAS_Price_Control_Mechanism_28_July_2010.pdf [12] H. Gu and J. Wang, "Irregular-shape wind farm micro-siting optimization," Energy, vol. 57, pp. 535-544, 8/1/ 2013. [13] C. Wan, J. Wang, G. Yang, H. Gu, and X. Zhang, "Wind farm micro-siting by Gaussian particle swarm optimization with local search strategy," Renewable Energy, vol. 48, pp. 276-286, 12// 2012. [14] AECOM Australia. (2014). Australia's off-grid clean energy market research paper. Available: https://arena.gov.au/files/2014/12/ARENA_RAR-report-20141201.pdf [15] A. Ulbig, T. Rinke, S. Chatzivasileiadis, and G. Andersson, "Predictive control for real-time frequency regulation and rotational inertia provision in power systems," in IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, pp. 2946-2953. [16] D. Villanueva, A. Feijóo, and J. Pazos, "Multivariate Weibull distribution for wind speed and wind power behavior assessment," Resources, vol. 2, p. 370, 2013. [17] H. Gu, J. Wang, Q. Lin, and Q. Gong, "Automatic Contour-Based Road Network Design for Optimized Wind Farm Micrositing," IEEE Transactions on Sustainable Energy, vol. 6, pp. 281-289, 2015.



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Huajie Gu received the B. Eng. degree in Automatic Control from Nanjing Technical University, Nanjing, China, in 2011, and the M. Eng. degree in Control Theory and Control Engineering from Tongji University, Shanghai, China, in 2014. Currently, he is a PhD student in the Power & Energy Systems Research Division at the School of Information Technology and Electrical Engineering, the University of Queensland, Australia. His research interests include wind turbine control and renewable power systems. Ruifeng Yan (S’2009, M’2012) received the B. Eng. (Hons.) degree in Automation from University of Science and Technology, Beijing, China, in 2004, the M. Eng degree in Electrical Engineering from the Australian National University, Canberra, Australia, in 2007, and Ph.D. degree in Power and Energy Systems from the University of Queensland, Brisbane, Australia, in 2012. His research interests include power system operation and analysis, and renewable energy integration into power networks. Tapan Kumar Saha (M’93, SM’97) was born in Bangladesh in 1959 and immigrated to Australia in 1989. He received his B. Sc. Engineering (electrical and electronic) in 1982 from the Bangladesh University of Engineering & Technology, Dhaka, Bangladesh, M. Tech (electrical engineering) in1985 from the Indian Institute of Technology, New Delhi, India and PhD in 1994 from the University of Queensland, Brisbane, Australia. Tapan is currently Professor of Electrical Engineering in the School of Information Technology and Electrical Engineering, University of Queensland, Australia. Previously he has had visiting appointments for a semester at both the Royal Institute of Technology (KTH), Stockholm, Sweden and at the University of Newcastle (Australia). He is a Fellow of the Institution of Engineers, Australia. His research interests include condition monitoring of electrical plants, power systems and power quality.


Minimum Inertia Requiremenyt

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