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Apparent Power Loss Based Equivalent Model ofWind Farm Collector System

Akhilesh Prakash Gupta, Student Member, IEEE, A. Mohapatra, Member, IEEE, and S. N. Singh, Fellow, IEEEDepartment of Electrical Engineering

Indian Institute of Technology Kanpur, Kanpur, India 208016.Email: apgupta@iitk.ac.in; abheem@iitk.ac.in; snsingh@iitk.ac.in

Abstract—Recent expansion of utility-scale wind farms haslead to increased concern and interest in studying the interac-tion of wind farm and the power system network. A suitableequivalent/ aggregated model eliminates the need to develop thefull detailed model of the wind farm which makes the analysisfast and reliable. Within a wind farm, the wind turbines areinterconnected by an electrical network also known as collectorsystem. While aggregating the wind farm, aggregated model ofcollector system also plays an important role. This paper presentsan effective apparent power loss based equivalent model for windfarm collector system while considering the reactive power limitsof each wind turbine and wake effect in the wind farm. Theproposed approach compares the total apparent losses in padmount transformer, trunk lines and feeder lines of the detailedand equivalent models. Based on this comparison, values ofparameters in equivalent model have been calculated. Test systemof HornsRev offshore wind farm has been simulated in PSS/Esoftware and it is found that the equivalent model obtained withthe proposed method has the highest accuracy over other methodssuggested in the literature.

Index Terms—Aggregation, wind farm, collector system, equiv-alent model, wake effect, PSS/E.

I. INTRODUCTION

Wind power is considered as one of the fastest growingrenewable energy technology and it has crossed 500GWinstallation milestone around the world [1]. India ranks at 4th

position in extracting maximum power from wind. With a totalinstalled capacity of 34.13GW till March 2018, wind powergeneration has increased more than 5 times since 2005. InIndia, wind energy currently contributes to 58.50% of totalrenewable energy capacity (58.30GW ) [2]. Compared to largeconventional power plants, wind turbines (WTs) are individualunits of low power rating but installed in large numbers.Moreover, due to dependency on the weather conditions, thepower generated by a WT has non-controllable stochasticcharacter. Hence, in order to compensate for any randomchange in wind power and to balance the total generationand demand, reserve capacity of conventional power plantsare required [3]. Typical wind power plants consist of aninterconnected substation, collector system, reactive powercompensators, step-up transformers and wind turbine generatorsystems. Proper modeling of all these components is verycrucial for the stability analysis, operation and control of thepower system. With the existing practice of disconnecting WTsduring a disturbance, WTs never take part in voltage and

frequency control. However, with high grid penetration andnew grid code requirements, the WTs will also influence theoverall behavior of power system [4].

A modern wind farm usually consists of hundreds of WTinterconnected through underground cables or overhead lines.This poses a dimensionality challenge in modeling of allWTs in a large wind farm. One possible solution to thisdimensionality issue is the model reduction by maintainingthe dominant characteristics of the overall system. This fieldof equivalent modeling of wind farms has been studied earlier[5]–[8] and is broadly divided into three categories: equiva-lent wind, equivalent turbine-generator system and equivalentcollector system. Wind speed signal of a wind farm consistsof four components: mean wind speed, ramp, wind gustand turbulence. The equivalent wind speed model gives atime-domain signal to the WTs to accurately represent theactual dynamic behavior of the wind [4], [9]. An exhaustivevalidation of the turbine-generator equivalencing technique hasbeen done in [10]. It has been shown that some types of WTscan be aggregated together and wind farm with a single ormulti-machine model can be used in fast transient analysisor load flow studies. A probabilistic clustering approach todetermine the equivalent number of WTs and their parametershas been proposed in [7]. The advantage of this approach isthat it can be used for a wind farm with arbitrary layoutsand it takes into account the variation in the wind speed. Anequivalent model of WTs with identical incoming wind speedshas been proposed in [11], [12].

Majority of large wind power plants have a radial feederconfiguration and the WTs are placed optimally to harvestmaximum wind power from wind energy. Collector systemlayout ranges widely in function and features, depending onseveral factors including terrain reliability, expected climateconditions, turbine placement, economics and minimum sys-tem power losses. Muljadi et al. have proposed an analyti-cal approach based on the apparent power losses to derivethe equivalent wind power plant collector system [13], [14].However, there are assumptions in [13], [14] such as identicalcurrent injections from all WTs, voltage of 1pu at all busesand with no reactive power limits considered for individualWTs. These assumptions make the equivalent model highlyinaccurate especially during high wind speed variation andwith consideration of wake effect. This method is useful toutility planners to get a quick and simple estimation of systemlosses. An approach based on the voltage difference between978-1-5386-6159-8/18/$31.00 c© 2018 IEEE

Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India

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the access point of one WT and the point of common coupling(PCC) has been proposed in [15] to calculate the parametersof the equivalent model. However, due to neglect of reactivepower flows and reactive power limits of individual WT, theequivalent model suffers from poor accuracy. In [10], a setof generic WT parameters are suggested which can be usedfor preliminary system studies of large wind farms. Thesevalues are based on the samples of 17 wind power plantsused in [10]. Even though, it has been shown that a smallset of four generic equivalent collector system parameters areadequate, it fails in making proper consideration for windfarm with and without overhead conductors. It also limits therange of wind farm within 50MW − 300MW with which itwould perform satisfactorily. Hence, an accurate equivalent oraggregated model of WTs in wind farm with collector systemis still missing in the literature. There is still scope to improvethe accuracy of equivalent/ aggregated model of wind farmcollector system as compared to actual farm.

This paper, thus, presents a modeling technique of equiv-alent wind farm collector system by comparing the apparentpower loss in the detailed and equivalent models. The wakeeffect and reactive power limits of each WT have beenconsidered so that the accuracy of the proposed equivalentimproves as compared to [10], [13], [15]. This is also realisticas the power output varies across the whole wind farm. Theremainder of this paper is organized as follows: in sectionII, the proposed method for the equivalent model of windfarm collector system is described. Test systems and caseshave been presented in section III and comparison of resultsfrom this method with methods in [10], [13], [15] are given insection IV. Section V concludes the paper and also presentsthe scope of future work.

II. EQUIVALENT MODEL OF COLLECTOR SYSTEM

The mechanical energy from wind after getting convertedinto electrical energy through turbine and generator, enters intothe collector system of the wind farm. The collector systemcomprises of pad-mount transformers, trunk conductors, feedercables and PCC. The collector system or the feeder topologyvaries widely depending on several factors such as reliability,turbine placement, terrain, climate condition and economics,etc. Modern utility size WT has 8kW to 8MW rating andgenerates electrical power typically at 575V or 690V . EachWT is provided with a pad-mount transformer to step up thisvoltage to medium voltage level (typically 35kV ).

Several WTs are connected to the trunk line at this voltagelevel and form a string or ”daisy chain” configuration. Thesetrunk lines then connect to the feeder line. Both feeder andtrunk lines can be overhead lines or underground cables. Allfeeder lines finally connect to PCC through which wind poweris fed to the high voltage grid.

The proposed approach for evaluating equivalent of windfarm collector system is done in two phases. First, equivalentparameters are calculated at the trunk line level. Then, in thesecond phase, equivalent parameters are evaluated at the windfarm level. This method is based on the fact that the apparentpower loss of both the detailed and reduced models should be

equal. Also, with consideration of equal apparent power lossesin other parameters like impedance of pad-mount transformer,etc., equivalent series impedance and shunt admittances attrunk line and wind farm levels are calculated.

A. Equivalent model at trunk line level

Let n WTs be connected in a string or daisy chain con-figuration as shown in fig. 1. Here S(.), V(.) and I(.) are theapparent power, voltage and current phasors at WT terminals,respectively. VPCC is the voltage phasor at the PCC. Zse(.)and Ysh(.) are the series impedances and half line chargingshunt admittances of the offshore cables, respectively. ZTF (.)is the impedance of the individual WT pad mount transformer.

Fig. 1. Detailed model of wind farm at trunk line level

The model of the wind farm collector system shown infig. 1 can be reduced to an equivalent wind turbine with padmount transformer connected to PCC through an equivalentline as shown in fig. 2. Variables Seq , Veq , Ieq , Zse eq , Ysh eq

Fig. 2. Equivalent model of wind farm at trunk line leveland ZTF eq refer to the corresponding equivalent parameters.Equivalent apparent power injection Seq , current injection Ieqand voltage Veq are given by

Seq =

n∑i=1

Si (1)

Ieq =

(SeqVeq

)∗(2)

where, Veq is the weighted average voltage given by

Veq =

n∑i=1

ViSi

n∑i=1

Si

(3)

Evaluation of equivalent impedances and shunt admittancebased on apparent power loss are discussed next.

Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India

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1) Equivalent impedance of pad-mount transformer: Fromfig. 1, apparent power loss in ith transformer is given by

SlossTFi =| Ii |2 ZTFi (4)

Thus, total loss in all transformers of a string can be calculatedas

StotallossTF =

n∑i=1

| Ii |2 ZTFi (5)

From fig. 2, power loss in equivalent transformer is given by

SeqlossTF =| Ieq |2 ZTFeq (6)

On comparing the total apparent power loss of detailed modeland power loss in equivalent model, i.e. (5) and (6), theimpedance of equivalent pad-mount transformer in fig. 2 is

ZTFeq =

n∑i=1

| Ii |2 ZTFi

| Ieq |2(7)

where Ieq is as obtained in (2).2) Equivalent series impedance: From fig. 1, current flow-

ing through ith series impedance Zsei is given by

IZsei =

n∑i=1

Ii −n−1∑i=1

[V′

i (Yshi + Yshi+1)]− V′

nYshn (8)

where, V′

i = Vi −(SiVi

)∗ZTFi. Hence, total apparent power

loss in all line series impedances is calculated as

Stotalloss Zse =

n∑i=1

| IZsei |2 Zsei (9)

From fig. 2, current flowing through equivalent seriesimpedance Zse eq and associated power loss are given by

IZse eq = Ieq − V′

eqYsh eq (10)

Seqloss Zse =| IZse eq |2 Zse eq (11)

On comparing the apparent power losses in (9) and (11), theequivalent series impedance can be given by

Zse eq =

n∑i=1

| IZsei |2 Zsei

| IZse eq |2(12)

3) Equivalent shunt admittance: From fig. 1, apparentpower loss in shunt admittance Ysh1 can be given by

Sloss Y sh1 = Ysh1 | V′

1 |2 +Ysh1 | VPCC |2 (13)

Similarly, loss in shunt admittance Ysh2 is given by

Sloss Y sh2 = Ysh2 | V′

1 |2 +Ysh2 | V′

2 |2 (14)

Thus, the total apparent power loss in all shunt admittancescan be given by

Stotalloss Y sh =

n∑i=2

[Yshi( | V′

i−1 |2 + | V′

i |2)]

+ Ysh1(| V′

1 |2 + | VPCC |2)(15)

From fig. 2, apparent power loss in equivalent shunt admit-tance Ysh eq is given by,

Seqloss Y sh = Ysh eq(| V′

eq |2 + | VPCC |2) (16)

On comparing the apparent power losses of detailed andequivalent models, i.e. (15) and (16), the equivalent shuntadmittance is given by

Ysh eq =Stotalloss Y sh

|V ′eq|2 + |VPCC |2(17)

B. Equivalent model at wind farm level

The reduced model of wind farm at trunk line level (asshown in fig. 2) is connected to the PCC through a feederoffshore cable. Let np number of equivalent wind farms beconnected to the PCC as shown in fig. 3. Then, the complete

Fig. 3. Equivalent model of wind farms at feeder line levelreduced model can be obtained by equating the apparent powerlosses as shown in fig. 4, where, SWF , VWF , IWF , Zse WF ,

Fig. 4. Reduced model of wind farmYsh WF and ZTF WF are the analogous corresponding equiv-alent parameters as compared to the same in fig. 2. SWF , IWFand VWF are given by

SWF =

np∑i=1

Seq i (18)

IWF =

(SWFVWF

)∗(19)

Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India

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where, VWF is the weighted average voltage given by

VWF =

np∑i=1

Veq iSeq i

np∑i=1

Seq i

(20)

Evaluation of other equivalent parameters are as follows.1) Equivalent impedance of pad-mount transformer: From

fig. 3, total apparent power loss in all transformers can becalculated as

Stotalloss TF eq =

np∑i=1

| Ieq i |2 ZTF eq i (21)

Power loss in equivalent transformer of fig. 4 is

Seqloss TF WF =| IWF |2 ZTF WF (22)

On comparing (21) and (22), the equivalent impedance of pad-mount transformer at wind farm level is

ZTF WF =

np∑i=1

| Ieq i |2 ZTF eq i

| IWF |2(23)

2) Equivalent series impedance: From fig. 3, current flow-ing through ith equivalent series impedance at trunk line level,i.e. Zse eq , is

IZse eq i = Ieq i − V′

eq iYsh eq i (24)

Hence, total power loss in all series impedances is given by

Stotalloss Zse eq =

np∑i=1

| IZse eq i |2 Zse eq i (25)

From fig. 4, current flowing through Zse WF and associatedpower loss are given by

IZse WF = IWF − V′

WFYsh WF (26)

SWFloss Zse WF =| IZse WF |2 Zse WF (27)

From (25) and (27), the equivalent series impedance is givenas

Zse WF =

np∑i=1

| IZse eq i |2 Zse eq i

| IZse WF |2(28)

3) Equivalent shunt admittance: From fig. 3, the totalapparent loss in all shunt admittances is given as

Sloss Y sh eq =

np∑i=1

Ysh eq i(| V′

eq i |2 + | VPCC |2) (29)

From fig. 4, loss in equivalent shunt admittance is

Sloss Y sh WF = Ysh WF (| V′

WF |2 + | VPCC |2) (30)

On equating losses in (29) and (30), the equivalent shuntadmittance is

Ysh WF =

np∑i=2

Ysh eq i(| V′

eq i |2 + | VPCC |2)

| V ′WF |2 + | VPCC |2(31)

III. TEST SYSTEMTo validate the accuracy of the proposed wind farm collector

system equivalent method, HornsRev1 offshore wind farm isused as the test system. It is a test system in Denmark andconsists of 80 “Vestas V80” WTs, each of 2MW capacityat rated wind speed [16]. Layout of the wind farm andlength of the cables are shown in fig. 5. Collector systemoperating voltage is 33kV which is connected to grid througha 33/150kV , 160MVA step-up transformer at an offshoresubstation. Parameters of collector system [17] and “VestasV80” WT are given in table I

Fig. 5. Layout of HornRev1 wind farm

TABLE INETWORK PARAMETERS OF HORNSREV1 OFFSHORE WIND FARM

Element description R at 90oC X C

(Ω/km) (Ω/km) (µF/km)150mm2, 3 core 0.16 0.12252 0.19XLPE-Cu Trunk cables

400mm2, 3 core XLPE-Cu 0.063 0.10681 0.28Feeder cables (to Bus 81)630mm2, 3 core XLPE-Cu 0.3679 0.00038 0.19

21km offshore cableOff-shore transformer impedance (pu) 0.0093784+0.0491167j

The reactive power generation of a doubly fed inductiongenerator based WT is in general, limited by the rotor voltageat low speed and by rotor current at high speed. However, themaximum reactive power limits are imposed by stator current[18], [19]. In the present problem of aggregation/ equivalentmodel evaluation of wind farm collector system, the limitson the reactive power output of each WT are calculated fromcapability curve [18].

In the case of wake effect (i.e. decrease in wind speed dueto shadowing effect from upstream WT on other downstreamWT), net active power outputs from all WTs are not equal

Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India

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but depend on the shadowing pattern. In [20], wake effectfor HornsRev1 wind farm planning has been carried out asshown in fig. 6. The shadowing pattern as suggested in [20]is used in this work. Fig. 6 shows the shadowing pattern foreach WT for the incoming wind speed of 1pu and direction of210o − 220o. It can be observed that the last WTs (accordingto wind direction) get lower wind speed and are marked inlight colors.

Fig. 6. Wind farm wake effect patternFrom the wake model when the input wind speed at each

WT is known, wind power output is calculated from the powercharacteristic curve of WT. Power characteristic curve for“Vestas V80” WT is given in [21]. Finally, after estimatingthe net output of each WT from the wake effect shadowingpattern, the reactive power output limits of each turbine arecalculated from the capability curve. In the present work, twodifferent cases of wind speed are considered

1) Case A: Wind direction between 210o−220o with max-imum speed of 10m/s and total wind power generationPWF being 79.725MW .

2) Case B: Wind direction same as in Case A but maximumwind speed being 4.6m/s. In this case due to wakeeffect, wind speed falling on some WTs will be belowthe cut-in speed [21] and hence power output from theseWTs is zero. The total wind power PWF generated is5.567MW .

IV. RESULTS AND DISCUSSIONThe active power output of each WT of HornsRev1 wind

farm and the corresponding reactive power limits for bothcases have been calculated and are given in table II fordifferent wind speeds. These wind speeds refer to the speedsin the wind farm wake effect as in fig. 6. Values of parametersof equivalent wind farm collector system obtained by the pro-posed method, Muljadi et al. method [13], voltage difference

TABLE IIACTIVE POWER GENERATION AND REACTIVE POWER LIMITS OF WTS AT

DIFFERENT WIND SPEEDS

Wind speed Active power Reactive power limits(m/s) (MW ) (max/min, MVAr)

Case A Case B Case A Case B Case A Case B10 4.6 1.2939 0.0963 1.2/-1.8

2/-2.4

8.72 4.01 0.9243 0.088

1.4/-28.7 4.0 0.9185 0.087

8.67 3.98 0.9099 08.66 3.98 0.907 08.64 3.96 0.9013 0

based method [15] and generic values [10] are given in tableIII. The data for pad-mount transformers are unavailable and

TABLE IIIPARAMETERS OF EQUIVALENT COLLECTOR SYSTEM BY DIFFERENT

METHODS

Parameters

Muljadi VoltageProposed et al. based Genericmethod method method values [10]

[13] [15]

Zse WF0.00597 0.0048 0.0020 0.0160

+0.007256i +0.0064i +0.0023i +0.0130iYsh WF 0.049319i 0.0501i 0.0501i 0.0315i

hence, these transformers are considered as part of the WT-generator system. With the input wind signal as per the wakeshadowing pattern, power flow analysis of the complete windfarm is performed and the total apparent power losses and linecharging are calculated. Associated apparent power losses andline charging of the detailed model and the equivalent modelsby the proposed method, Muljadi et al. method [13], voltagedifference based method [15] and generic values [10] are givenin table III. The test system is the same as in section IIIand the results are shown for this system with PCC assumedat 33kV bus and PCC assumed at 150kV bus on the gridside. Percentage errors in the line losses and line charging

TABLE IVLOSSES AND LINE CHARGING IN DETAILED AND EQUIVALENT MODELS

OBTAINED WITH DIFFERENT METHODS

PCC at PCC atTest 33kV bus 150kV bus

Model Line Line Line LineCase losses charging losses charging

(kV A) (kV Ar) (kV A) (kV Ar)Detailed Case A 758.94 4931.9 4382.78 33490.3model Case B 11.12 4935.5 86.19 33423.6

Proposed Case A 713.9 4921.3 4421.22 33479.7method Case B 12.31 4934.0 85.19 33422.1

Muljadi et al. Case A 602.34 5001.4 4294.0 33559.8method [13] Case B 15.94 5012.9 84.7 33501.8

Voltage based Case A 211.07 5005.4 3884.66 33564.1method [15] Case B 6.25 5010.8 84.66 33498.9

Generic Case A 1694.75 3128.1 5546.74 31685.4values [10] Case B NA NA NA NA

of equivalent model as compared to the detailed model arecalculated as ∆X% = abs

(Xi

R−XiFXiF

)where, XiR and XiF

are the line losses and charging of equivalent and detailedsystem, respectively. Percentage error in the these values areshown in table V. As the power output of wind farm in Case B

Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India

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TABLE VPERCENTAGE ERROR IN LINE LOSSES AND LINE CHARGING OF

EQUIVALENT MODELS

Model

33kV Full collectorTest subsystem systemCase ∆Sloss ∆Qcharg ∆Sloss ∆Qcharg

(%) (%) (%) (%)Proposed Case A 5.93 0.2 0.877 0.032method Case B 10.7 0.03 1.16 0.004Muljadi Case A 20.63 1.41 2.03 0.21et al.method Case B 43.35 1.55 1.73 0.24[13]Voltage Case A 72.2 1.41 11.37 0.21basedmethod Case B 43.79 1.53 1.76 0.22[15]Generic Case A 123.3 36.6 26.56 5.4

values [10] Case B NA NA NA NA

is below 50MW so, equivalent model from generic values [10]can not be calculated and thus corresponding entries in tabularform are mentioned as not applicable (NA). It can be observedfrom table V that percentage error in the proposed equivalentmodel is within 5%−10%, while equivalent model from othermethods have high degree of inaccuracy. This is due to the factthat the proposed method does not make any assumptions onpower injections or voltages and also considers the reactivepower flow in the network while calculating the equivalentvalues. The close agreement between the losses obtained fromthe detailed and equivalent model of wind farm verifies theaccuracy of the proposed equivalent model. In addition, thismethod eliminates the calculation of equivalent wind speed byconsidering the actual power injections based on input windspeed for each WT.

V. CONCLUSION

In this paper, an accurate and generic approach to findthe equivalent model of wind farm collector system hasbeen discussed. The proposed aggregation method is basedon simple load flow analysis and equating the line lossesin detailed and aggregated model. This method assures highdegree of accuracy than any other methods presented before byincorporating the reactive power capability of individual WTsand shadowing effect on the wind farm due to wake effect.It has the advantage of being suitable for collector system ofany size or configuration. The implementation of the methodin a large-scale HornsRev offshore wind farm is presented andresults are compared with the other models presented in theliterature. This method is intended to help the power systemoperators to obtain a simple and accurate equivalent model ofthe large wind farm for fast and real-time dynamic simulation.In the present work the equivalent model is tested for staticanalysis which can be used for dynamic analysis like shortcircuit, generator outage, etc. in the external power systemgrid. This method can be further investigated for dynamicsimulation with equivalent model of wind farm connected topower system network.

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Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India