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Reactive Power Supplied byWind Energy Converters

Cost-Benefit-Analysis

M. BraunISET

Institut fuer Solare Energieversorgungstechnik e. V.Koenigstor 59, D-34119 Kassel, Germany

Phone +49(0)561/7294-118E-mail: mbraun@iset.uni-kassel.de

Abstract:

This paper provides a cost-benefit-assessment ofreactive power supplied to network operators byWind Energy Converters (WECs). An approach isproposed to estimate the costs of reactive powersupply by WECs with inverter-coupled generators.A cost-benefit-analysis shows the economicattractiveness of reactive power supply in manycases, but also significantly varying costs. An

economic optimisation of both, the WECs and thenetworks operation, must consider these costvariations.

Keywords: Ancillary Services, Economic Analysis,Inverter Losses, Reactive Power, Wind EnergyConverter

1 Introduction

In standard Alternating Current (AC) electrical

networks the voltage and current pulsate with thenetworks frequency (in Europe: 50 Hz). Due to aphase shift between voltage and current twodifferent types of power are distinguished: activepower for the useful work and reactive powerwhich oscillates between electrical storageelements (capacitors and reactors). Many loadsand generators as well as the passive networkelements have a certain reactive powercharacteristic. Different types of compensatingunits can be installed to compensate reactivepower flows in the network. This goes alongsidewith the objectives of network operators who haveto control the grids voltage within allowed limits(e.g. EN50160). Furthermore, network operatorsaim at reducing grid losses and congestions by

use of reactive power control. The distributedsupply of reactive power by Wind EnergyConverters (WECs) is an option to support networkoperation.Presently, WEC have to fulfil grid coderequirements for reactive power (e.g. Germany[1,2] or Spain [3]). This paper analyses the costsand the benefits of this service to provide moreinsights into its economics which allows designingimproved economic frameworks with regard toreactive power supply. Firstly, it describes the

capability and availability of reactive power supplyby WECs. Secondly, the costs are assessed, and,finally, a cost-benefit-analysis shows the economicattractiveness of this ancillary service by WECs.

2 Reactive Power SupplyCapability of WECs

In principle all generators which are coupled to thenetwork either with inverters or with synchronousgenerators are capable of providing reactive power[4]. Principal WEC designs [5] are directly-coupled induction generators (IGs) in

fixed speed or variable slip design withcapacitor banks;

doubly-fed induction generators (DFIGs) witha power electronics converter between thepoint of grid connection and the rotor circuit ofthe IG (designed only with a fraction of therated power);

directly-coupled synchronous generators(SGs) with a dynamic gearbox and excitationcontrol; and

inverter-coupled generators with a full powerelectronics converter (FC) which couplesdifferent designs of induction andsynchronous generators.

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IGs are not considered further on because theircontrol capabilities are limited compared to therequirements of network operation and theircapacitors can be regarded as additional passivenetwork elements (see section 4.1.1). Also SGswith little installation rates are not considered indetail. However, the approach for FCs is

transferable to SGs. The focus of this paper is onthe two market-dominating power electronicdesigns: DFIG and FC with a market share of 50%and 42% respectively (rest: IG) in Germany [6].

2.1 Inverter-Coupled Generators (FC)

Reactive power occurs only in AC networks due toa phase shift between voltage and current. In DCnetworks it is not defined. Consequently, only thegrid-side inverter of the power electronic back-to-back converter needs to be considered as it

defines the phase angle of the current to the mainsgrid.One fundamental limit is the maximum currenttransfer of the inverter or the maximum apparentpower Smax. The phase angle of the current vectorcan be arbitrarily controlled as long as the absolutevalue of the current does not exceed its maximum.The active power transfer Pact is generally handledby the operational control of the WEC with firstpriority so that it limits the maximal possiblereactive power supply Qmax according to

.)((t)Q

22

maxmax tPS act=

(1)

However, also the reactive current faces limitsmostly due to reasons of stability and availability.Figure 1 presents an example of the loadingcapability chart (power domain) of a FC whichtransfers active power and supplies reactive power(practical values see [7]).

Figure 1: Loading capability chart of a FC(Q > 0: capacitive)

Within the active power generation limits Pmin and Pmax (red),

inductive reactive power limit Qmin (blue, left-hand side),

capacitive reactive power limit Qmax (blue, right-hand side), and

apparent power limit Smax (green)

the reactive current of the inverter can becontrolled arbitrarily with response times in theorder of milliseconds.

While the solid blue line in Figure 1 shows oftenpublished reactive power limits even more ispossible as displayed by the dashed blue line. Alsoreactive power can be supplied if no active poweris transferred [8,9]. An extension of the solid to thedashed blue line, given by equation 1, depends onthe power electronic design. The availability is thendependent on the actual active power transfer sothat not 100% availability can be stated but less.As an exemplary database (source: ISET), themeasurements of an Enercon E-66 WEC (withPmax = 1300 kW) in Germany are analysed. Foreach five minute interval, the maximum active

power is measured in the years 2001-2003. Themaximum reactive power Qmax is calculated withequation 1 for different inverter sizes Smax. Thisleads to the availability of a certain reactive powerQ as displayed in Table 1 showing the influence ofoversizing the inverter. With Smax = 1400 kVA =1.077 Pmax it is possible to guarantee 520 kVAr andwith Smax = 1500 kVA = 1.154 Pmax even 748 kVArfor the full active power operation range. Morereactive power can be supplied but the availabilityis less than 100% but still more than 90% up to1000 kVAr.

Availability of Q withQkVAr Smax =

1300 kVASmax =

1400 kVASmax =

1500 kVA100 >99% 100% 100%200 >99% 100% 100%300 >99% 100% 100%400 99% 100% 100%500 97% 100% 100%600 95% >99% 100%700 94% 98% 100%800 94% 95% >99%900 93% 94% 97%1000 92% 93% 94%1100 89% 92% 94%

1200 84% 90% 93%1300 5% 85% 90%1400 0% 5% 86%1500 0% 0% 5%

Table 1: Available reactive power Q of an EnerconE-66 WEC (with Pmax = 1300 kW) in Germany with

different inverter sizing Smax

Also certain overload capabilities for short-termreactive power supply exist, e.g. for fault-ridethrough support. In contrast, active power has nooverload flexibility if not throttled because it is

directly linked with the maximum mechanicalpower due to the wind conditions. However, thepossibilities from these overload capabilities arenot discussed further in this paper.

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2.2 Doubly-Fed Induction Generators(DFIG)

A DFIG is an IG whose rotor windings are coupledby a power electronic converter to the grid. Thisdesign allows an excitation in the rotor coils forspeed regulation and reactive power control of the

IG by the rotor-side inverter as well as reactivepower supply by the grid-side inverter. Three limitsdefine the reactive power capacity of a DFIG [10]:

stator current (heating of stator coils) Smax (green), Qmin (blue, left-hand side),

rotor current (heating of rotor coils) Qmax (blue, right-hand side), and

rotor voltage (limiting the rotor speed).The rotor voltage can be a limit at high slip s,

reducing Qmax further on. Figure 2 shows theloading capability chart at s = 0. At lower slip thedefining circles are extended in direction of the P

axes (and compressed at higher slip). A detaileddiscussion on the functional dependenciesprovides Lund et al. in [10].

Figure 2: Loading capability chart of a DFIG(Q > 0: capacitive)

3 Costs of Reactive PowerSupply by WECs

Costs for reactive power supply can be separatedinto investment costs [/kVAr] and operationalcosts [c/kVArh]. Both costs are very specific andshow large ranges. The purpose here is to give anorder of magnitude and an understanding of thevarious dependencies.Hence, additional minor cost factors are notdiscussed in detail. They tend to be dependent onthe higher currents (often with I) causingelectromagnetic forces (mechanical stress) andhigher temperatures (thermal stress). Theseeffects result in higher maintenance costs andequipment aging as well as higher costs ofunavailability. Due to their I-dependency theseadditional minor costs might be added to theoperational costs (see section 3.2).The following analysis of investment andoperational costs focuses on WECs with FC. It ispossible to transfer this approach to DFIG and SG.

3.1 Investment costs

In principle, grid-side inverters can control reactivepower without the need of additional investmentsdue to the described power electronicfunctionalities. However, additional investmentcosts have to be considered if the inverters rated

capacity is extended for higher capabilities andavailabilities of reactive power supply. Inverters aregenerally oversized by WEC manufacturers tocomply grid code requirements.Assuming inverter costs of 150-300 /kVA leads toadditional investment costs as listed in Table 2 anddepicted in Figure 3. Also the annual costs aregiven in Table 2 with a lifetime of 20 years and 5%discount rate. If 0.5 MVAr should be available froma WEC with FC of 1 MW it has to be oversized by12%. This oversizing generates investment costsof 36-71 /kVAr. A general finding is that theadditional investment costs are low at small

secured reactive power capacities. Other ways ofassessing capacity costs are discussed in [11,22].

Q [MVAr]Additional Costs

[/kVAr]Annual Costs

(20 a, 5%) [/kVAra]

0.1 8-15 0.6-1.20.2 15-30 1.2-2.40.3 22-44 1.8-3.50.4 29-58 2.4-4.70.5 36-71 2.9-5.7

Table 2: Additional investment costs for securedreactive power supply Q of a 1 MW WEC with

inverter costs of 150-300 /MVA

Figure 3: Additional investment costs for securedreactive power supply capacity

3.2 Operational Costs

WECs have low variable operational costs[/MWh] because no primary energy costs have tobe paid for the wind. However, similar to all otherpower plants they have a certain self consumption.The additional self consumption due to reactivepower supply corresponds to the additional lossesof the grid-side inverter.

The following operational cost estimation approachhas been introduced in [12] for photovoltaicinverters. It is further developed, adjusted andapplied to determine the costs of reactive power

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supply by WECs. It can be divided into two mainsteps:

1) Reactive power supply in addition to activepower supply increases the losses of the grid-side inverter of WECs.

2) These additional losses need to becompensated by active power

a. by reducing the amount of active powergeneration resulting in operationalopportunity costs, or

b. by network purchase if no active power isfed into the mains (at low wind conditions).

The determination of the self consumption ofinverters starts with the available data on theinverters efficiency

lossAC

AC

DC

AC

PP

P

P

Peta

'+==

(2)

depending on the active power output PAC on theAC side and the active power input PDC on the DCside. The difference between PDC and PAC definethe losses Ploss of the inverter.The losses of an inverter can be approximated bya second-order polynomial function of the apparentpower supply S [12]

( ) ( )2ScSccSP RlossVlossselfloss ++= (3)

with self losses (standby losses) cself, voltagedependent losses over the power electroniccomponents cVloss (proportional to I), and currentdependent losses over the impedances cRloss(proportional to I2).

An exemplary efficiency curve and thecorresponding loss curve are used for the followingcalculations (Figure 4).

90%

92%

94%

96%

98%

100%

0 20 40 60 80 100

Apparent Power (%Smax)

Efficienc

y

0

1

2

3

Losses

[%S

max

]

Figure 4: Efficiency (red) and losses (blue) of anexemplary grid-side inverter of a WEC

The considered grid-side inverter has a maximalefficiency etamax = 98%. The values of active powerlosses and apparent power are given in percent of

the maximal apparent power Smax for furthergeneralisation.

We can then calculate the additional losses Plossby taking the difference of the inverters losses withreactive power supply Q(t) 0 and without Q(t*) =0 for the same DC link power PDC at time t and at

reference time t* respectively:( )

( ) ( )( )

( ) ( ) ( )( )0*,*

0,

==

=

tQtPtPP

tQtPP

tP

DCDCloss

DCloss

loss

(4)

These additional losses can be attributed to thereactive power supply to get the related value inkW/kVAr (or kWh/kVArh in energy units):

( )( )

( )tQtP

tP lossloss

=

(5)

With the loss curve of Figure 4 this leads to therelated additional losses caused by reactive powersupply as displayed in Figure 5. The graph islimited by the semicircle of the devices maximalapparent power Smax and the maximal active powerPmax. It shows the symmetry of negative and positivereactive power supply. These additional relatedactive power losses for reactive power are thebasis for the following cost calculation.

Figure 5: Losses due to reactive power supply Qwith different active power transfer P

(Smax = 1.1Pmax and step size = 5%Pmax)

Two cases are distinguished for the costassessment:

Active WEC (P > 0):Active power generated by the wind turbine is fedinto the mains grid. In addition reactive power issupplied. The additional losses accompanying thereactive power supply reduce the active powerinjection. Hence, the costs of the additional lossesare the opportunity costs due to reduced activepower supply. Active power production by WECs issite-dependent and can vary considerably.Average costs of active power generation byWECs in Germany can be estimated as 9 c/kWh[13,14] within the range of the feed-in tariffs of 4-

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9 c/kWh for the years 2005-2015 [15].

Inactive WEC (P = 0):According to the measurement database (Table 1)the WEC did not generate active power in 5% ofthe 5 minutes intervals. The inverters losses arethen compensated by the external grid (here:

mains) resulting in costs due to the tariff of activepower purchase. These costs of active powerpurchase vary with regard to voltage level, energysupplier and consumption profile. Here weconsider costs of 9 c/kWh [16].

With the given assumptions the operational costsof reactive power supply by WECs can beclassified in cost ranges as given in Figure 6showing an increase of the costs with increasing

reactive power supply; and a decline of the costs of a certain reactive

power supply with increasing active powersupply.These functional dependencies lead to the generalfinding that the operational costs are the lowest atlow levels of reactive power supply. This goesalongside with the finding in section 3.1: Reactivepower should be preferably delivered by manyWECs instead of few ones.

Figure 6: Ranges of operational cost of reactive

power supply by WECs(Smax = 1.1Pmax and step size = 1%Pmax)

These costs are compared to the benefits ofreactive power supply and costs of alternativesupply technologies in the following section.

4 Cost-Benefit-Analysis

The benefits of reactive power supply by WECscan be assessed by looking at alternative sources

of reactive power which are presently used. IfWECs have lower costs they can economicallysubstitute the conventional technologies. Anotherapproach is the analysis of the network effects by

studying the benefits for network operation.This section provides a comparison withconventional reactive power supply technologies,network purchase, and an analysis of the benefitsof reactive power based ancillary services fornetwork operation.

4.1 Comparison with ConventionalReactive Power Supply Technologies

The following conventional devices for reactivepower supply are looked at:

1. static capacitors and reactors;2. static compensators with power

electronics;3. synchronous condensers; and4. synchronous generators of conventional

power plants.

4.1.1 Static Capacitors and ReactorsA standard network component for reactive powercompensation is a capacitor bank. The analysis ofcosts of capacitor banks results in the kVArhprices displayed in Figure 7. They depend on theused full load hours: few full load hours cause highcosts per kVArh which are reduced rapidly withincreasing full load hours. The cost estimation isbased on the following assumptions: investmentcosts of 15 /kVAr [17], lifetime of 20 years,discount rate of 5%, losses of 1.5 W/kVAr [17] andpower purchase costs of 9 c/kWh [16]. Figure 7

includes two operational cost ranges of reactivepower supply by WECs according to Figure 6. Theadditional investment costs are not yet considered.

0.00

0.05

0.10

0.15

0 2000 4000 6000 8000

Full Load Hours [h/a]

Cos

tso

fQ[c/kVArh

]

WEC:

< 0.03 c/kVArh

WEC:

0.03 - 0.10 c/kVArh

Capacitor Banks

Figure 7: Cost of capacitors (in c/kVArh) over theused full load hours (in h/a) in comparison to the

cost ranges of WECs

The comparison in Figure 7 shows that reactivepower supply by WECs in the low cost range of< 0.03 c/kVArh (approx. |Q| < 15%Pmax) ischeaper than capacitors in general. Consideringthe middle cost range of 0.03 0.10 c/kVArh(approx. 15%Pmax < |Q| < 50%Pmax) WECs arecheaper than capacitors if only used for few 1000full load hours per year. Taken these insightstogether it can be stated that reactive power supply

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by WECs can be beneficiary compared to reactivepower supply by capacitor banks at the samenetwork node (without additional network losses)and without taking into account additionalinvestment costs assuming that no 100%availability is necessary.This conclusion is also valid for static reactors

which tend to be some tens of percent moreexpensive than capacitors. If reactors as well ascapacitors have to be installed at one node WECshaving the full range are even more attractive.

As discussed in section 3.1 it is necessary toconsider the additional investment costs if 100%availability of Q is required. A comparison withTable 2 and Figure 3 shows that guaranteeing 10-20% of the reactive power capacity already resultsin investment costs in the order of those ofcapacitors. However, if reactors have to beinstalled as well up to 40% of Qmax can be

guaranteed. Including investment costs it becomesmore difficult for WECs to be competitive.However, with higher inverter efficiencies anddecreasing inverter costs this situation mightimprove in the future.

The comparison with static capacitors and reactorsmight be not reasonable in all cases. An importantfeature of reactive power supply by WECs is theirpossibility to follow smoothly the demand. This isan important advantage compared to capacitorbanks which switch discretely resulting insuboptimal compensation and transient voltage

disturbances. In many cases a comparison tostatic compensators with power electronics ofsimilar functionalities should be preferred.

4.1.2 Static Compensators with PowerElectronicsDifferent types of static compensators with powerelectronics are available. Static VARCompensators (SVCs) are capacitors and/orreactors connected by thyristors (grid-commuting).Static Compensators (STATCOMs) are powerelectronics-based (self-commuting) with gate turn-off thyristors (GTOs) or insulated gate bipolar

transistors (IGBTs) comparable to those ofinverter-coupled WECs. Kueck et al. [18] estimatethe investment costs in the range of 40-100US$/kVAr which is assumed to be in the range of30-75 /kVAr. This cost range corresponds tocosts for oversizing the inverter of a WEC in orderto have up to 100% of the reactive power capacitysecured available (cf. Table 2 and Figure 3).The energy losses depending on the efficiency ofSTATCOMs and grid-side inverters of WECs aresimilar due to similar power electronic designs.Figure 8 shows that STATCOMs tend to havehigher operational costs because all losses would

be attributed to Q (blue line) while only theadditional losses are attributed to Q in case ofWECs (red area) because P is transferred as well.If designed properly WECs can be competitive in

supplying Q in comparison to conventional powerelectronic based compensators.

Figure 8: Operational cost (in c/kVArh) of Qsupply by inverters which only supply Q (blue) and

WECs which supply Q in addition to P (red)(Smax = 1Pmax and step size = 2%Pmax)

4.1.3 Synchronous CondensersSynchronous condensers are synchronousgenerators without prime mover. They are devicesdedicated for reactive power supply. Because ofthis dedication all costs are attributed to reactivepower supply. Figure 8 can also be referencedwith regard to operational costs. In contrast, theinvestment costs are approx. one order ofmagnitude lower than those of inverters of WECs[18]. Nevertheless, at low Q capacities (seeFigure 3) WECs can be competitive at the samenetwork node, also because of low efficiencies ofsynchronous condensers.

4.1.4 Synchronous Generators of ConventionalPower PlantsConventionally also central power plants are usedfor reactive power supply in the transmissionnetwork. The efficiency of their synchronousgenerators can be assumed to be similar to theefficiency of the grid-side inverter of WECs. Oneimportant difference is that they generally sell theirpower generation on the power exchange with

average prices, for instance, of 2.9 (2004), 4.6(2005) and 5.1 c/kWh (2006) on the EuropeanEnergy Exchange (EEX). They are with 4.2c/kWh (average 2004-2006) considerably lowerthan the feed-in tariff prices in Germany of 9c/kWh (see section 3.2). A second difference toWECs is that conventional power plants normallyoperate at rated power and not with variable Pwhich tends to lead to lower losses (see Figure 6).Even more significant is the situation for theinvestment costs of inverters compared tosynchronous generators which can be about oneorder of magnitude higher at MW sizes.

Taken these differences together shows that costsfor reactive power by conventional power plantsare generally lower than those of WECs. However,the dispersed installation of WECs increases the

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competitiveness because a distributed supply nearthe consumer loads reduces the network lossescompared to more centralized supply ofconventional generators.

4.1.5 Additional AspectsAdditional aspects need to be considered, e.g.:

Harmonics:IGTB-based inverters are capable tocompensate harmonics while synchronousgenerators have no influence and SVCs evengenerate harmonics [4].

Short-circuit behaviour and overloadcapability:Synchronous generators add with their inertiato system stability and they have an inherenttransient overload rating which does not existwith the other technologies.

Q dependency on bus voltage V: Independent: synchronous generator

Q ~ (1/V): inverter Q ~ (1/V): SVC, capacitors, reactorsIn case of voltage dips the behaviour ofsynchronous generators but also inverters isbeneficiary.

These and further aspects should be included incomprehensive comparisons (see also [19]) ofalternative reactive power sources.

4.2 Comparison with Network Purchase

A comparison with reactive power supply costs ortariffs of network operators allows taking allpresent sources of reactive power together.An analysis of [20] shows that German distributionnetwork operators charge on average1.1 c2005/kVArh (0.0 - 2.7 c/kVArh) if the powerfactor is lower than 0.9 (in average). In the highvoltage network the average charge is 1 c/kVArh(0.0 1.5 c/kVArh) and in the extreme highvoltage one network operator has a charge of0.3 c/kVArh. However, this charge is more apenalty than the real costs which should be loweraccording to section 4.1.

National Grid in the United Kingdom spendsapprox. 0.2 c/kVArh on the reactive power marketof the transmission network [21].The three transmission network organizationsPJM, NYISO ad ISO-NE in the United Statesprovide an annual payment in the range of 1005-5907 US$/MVAr [18] assumed to be 0.75-4.4/kVAra. This payment would compensate anoversizing of more than 40% of WECs according toTable 2. In addition, the three US networkorganizations also provide a compensation for lostprofits on real energy sales (opportunity costs).ERCOT, for instance, pays not for capacity but for

the utilization 2.65 US$/MVARh at power factorssmaller than 0.95 [18].

In Spain a royal decree [3] defines three load

situations (peak, plateau, and off-peak). Ifgenerating units provide the correct power factorsthey receive an incentive if they counteract theyhave to pay a penalty. This incentive is attractivefor operators of WECs in Spain. But it cannot becontrasted reasonably here because the incentiveis paid per kWh.

If the converter is designed appropriately reactivepower supply by WECs can be economicallyattractive looking at the actual prices of networkpurchase or incentives for network delivery.However, many countries have not yet establishedany market design. It is recommended to improvereactive power market designs based on real costsof this ancillary service (see also [22]).

4.3 Comparison with Benefits forNetwork Operation

Reactive power is necessary for an optimizednetwork operation. It is used mainly for threeancillary services:

1. voltage control,2. reduction of grid losses, and3. reduction of congestions.

The value of these services is analyzed in thefollowing sub-sections individually. It is difficult toanalyze all three of them combined in generalbecause reactive power control might haveopposed effects on these ancillary servicesdepending on the systems state. However, the

network operator can take into account all theseeffects within the optimization of the networksoperation.

4.3.1 Voltage ControlVoltage control is a basic need for networkoperation because the voltage has to stay withincertain limits throughout the whole network (cf.EN50160). Capacitive reactive power increasesthe voltage level while inductive reactive powerdecreases the voltage level. However, the voltageneeds to stay within certain limits demanding fordistributed reactive power compensation. Differentreaction times are used to optimize the voltage inthe network: primary, secondary and tertiaryvoltage control during normal operation, as well asgrid design in the installation phase (especially ofdistribution networks), and transient voltage controlduring faults.WECs can be integrated in primary, secondary andtertiary voltage control during normal networkoperation. Here they have to be compared tostandard network components providing thisservice: tap-changing transformers andconventional reactive power sources. Thecompetitiveness of WECs in comparison toconventional reactive power suppliers is analysedin section 4.1. Depending on the convertersdesign, its location as well as the network

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operators needs WECs can be attractive suppliersof reactive power.Another benefit can arise at the installation phase.The grid design might have caused a restriction oflarger WECs due to voltage limits [1,2]. Suchconnection conditions might be complied by usingreactive power control of the respective WECs.

The network can be utilized more effectively withthis functionality.Transient voltage control happens in milliseconds.This is a service already required from WECs. Dueto very fast reaction times and their spatialdistribution throughout the network the voltage issupported effectively during faults (cf. fault-ride-through requirements e.g. in [2,23]). The generalbenefit is difficult to assess but is expected to bebigger than the costs of providing reactive powerfor few seconds if the security of supply can beincreased.

4.3.2 Reduction of Grid LossesThe transfer of reactive power causes active powerlosses in the network. Reactive powercompensation reduces these active power losses.In addition, more network capacity can be used foractive power transfer. This additional benefit is notincluded in the following considerations.Different load power factors cos() and differentaverage network losses dPL (in %) are looked atwith constant active power flow P. A quadraticcorrelation (at constant voltage: ~I) is assumedbetween losses PL and the apparent power flow S:

( )222

QPdPSdPP LLL +== (6)

with

( ).01

cos

12

>

=

PQ (7)

The reduction of active power losses by reactivepower compensation Q relative to Q [kW/kVAr] isthen defined by:

( )[ ]

( )1

cos

12

222

=

=+

=

PdP

QdPQ

PQPdPP

L

LL

L

(8)

With costs for the compensation of active powerlosses of 5 c/kWh [24] the benefit of the lossreduction is given in Table 3.A comparison with the costs in Figure 6 shows thatit can be economically attractive to use WECs forreactive power compensation in network situationswith high network losses and low load power

factors (high reactive power flow).

Average Network Losses dPLcos() 1% 2% 3% 4%

0.95 0.016 0.033 0.049 0.0660.9 0.024 0.048 0.073 0.0970.85 0.031 0.062 0.093 0.124

Table 3: Savings in c/kVArh due to reduction

of active power losses due to reactive powercompensation with different load power factorscos(), average network losses dPL, and with

costs for active power losses of 5 c/kWh

4.3.3 Reduction of CongestionsBy active compensation of reactive power it ispossible to reduce the reactive power flows in thenetwork. Particularly at peak load situations thiscan reduce the loading of the network helping toavoid congestions. In addition, also network lossesare reduced but not considered in the economicassessment in this subsection.

Figure 9 displays the relative reduction of theloading of a considered network element (e.g. lineor transformer) by reactive power compensation.The network element is assumed to operate at100% rated capacity Sg considering different loadpower factors cos() with active power flows P andreactive power flows Q. The reactive power flow iscompensated by WECs with 50% of their ratedcapacity. Their installed capacity Pw is assumed tobe 5%, 20% and 50% of the network capacity Sg.The reduction of apparent power S (in %meaning [kVA/kVAr]) relative to reactive powercompensation with the reactive power supply Qwby the WECs can be calculated by:

( )

( )( ) ( )( )

w

wggg

w

wg

Q

QSSS

Q

QQPSS

22

22

sincos +=

+=

(9)

Figure 9 shows that the loading can be reduced by15% (cos()=0.98), 30% (cos()=0.94) or 45%(cos()=0.87) of the WECs reactive power supply

at a penetration level of 20%. This reduction issignificant. With the range ofS = 15-45% andnetwork costs of 30-60 /kVAa [20,25] the benefitcan be calculated as 4.5-27 /kVAra which is byfar greater than the investment costs in Table 2.The operational costs can be neglected becausesome hours of reactive power compensation, say10-30 h/a for solving the congestions, result in only1-3 c/kVAra with 0.1 c/kVArh according toFigure 6.The calculated benefit is by far higher than thecosts of reactive power compensation by WECs.However, most networks operate below 100%

capacity. In such state the described congestionmanagement does not have any benefit. However,in the future with a more optimised networkoperation and design, the reactive power

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compensation capability of distributed generationcan be applied effectively for using the networkinfrastructure more effectively at higher loadinglevels. The peak load normally occurs on winterevenings in Europe [26] or under emergencynetwork situations.

0%

10%

20%

30%

40%

50%

60%

0.99 0.97 0.95 0.93 0.91 0.89 0.87 0.85

cos(phi)

Re

lative

Re

duc

tiono

fLoa

ding

by

Reac

tive

Power

Supp

ly

Pw = 5%Sg

Pw = 20%Sg

Pw = 50%Sg

Figure 9: Relative reduction of network loading dueto reactive power compensation by WECsconsidering different WEC penetration levels Pw/Sg

and different load power factors cos()

5 Economic Impact

The cost-benefit analysis shows that the benefitis in most cases greater than the costs of reactivepower supply by WECs. Although seeing costs inthe order of some 0.01 c/kVArh might result in astatement like: negligible. It is correct that

reactive power supply has relatively seen no majorcost influence on the profitability of WECs.However, in absolute terms we are discussingabout costs which should be taken into account.The following two examples should give an ideaabout the relevance.We consider a 1 MW WEC with average reactivepower supply costs of 0.1 c/kVArh, securedreactive power capacity of 0.5 MVAr, and full loadhours of 1000 h/a (for reactive power supply). Theoperational costs of reactive power supply of thissingle WEC are then 500 /a. In addition, anoversizing to secured 0.5 MVAr results in

additional investment costs of 2.9-5.7 /kVAra or1,450-2,850 /a. The total costs due to reactivepower supply are then 1,950-3,350 /a. This is aminor cost factor (approx. 1%) for a 1 MW WECwith active power generation revenues of 225,000/a (full load hours for active power supply of 2,500h/a and 9 c/kWh). But if we are looking at 50 GWof WEC installed in Europe (beginning of 2007) weare talking about annual reactive power supplycosts of 97.5-167.5 Mio .From the network perspective we can have a lookat the total reactive power demand in the electricitynetwork which has been estimated in [17] to be

1759 TVArh annually for the EU-25 in 2002.Further estimations in [17] result in 1069 TVArh tobe compensated and a corresponding networkloss reduction of 48 TWh. With costs of network

losses in the order of 5 c/kWh [24] we get to avalue of approx. 240 Mio of loss reduction. Thiscalculation does not take into account the value ofthe increased network capacity and furtherbenefits for network operation (e.g. voltagecontrol).The overall benefits and costs of reactive power

supply are often considered as minor cost factorsin the total electricity supply turnover.Nevertheless, it is very important from aneconomic perspective because it allows operatingthe network more stable and secure, e.g. bykeeping the voltage limits, solving congestions,supporting stability in case of faults and flexibleislanded operation (Microgrid concept [27]). Asstated in [22]: inadequate reactive power leadingto voltage collapse has been a causal factor inmajor power outages worldwide.

6 CONCLUSIONS

This paper describes the capabilities andavailabilities of reactive power supply by WECsshowing an interesting potential. This potential isstudied concerning its economic usability with anapproach of allocating costs of additional losses aswell as cost due to oversizing to reactive powersupply and assessing the benefits for networkoperation.The cost-benefit-analysis shows that reactivepower supply by WECs can be cheaper thanreactive power supply by conventional devices.

Reactive power supply by WECs for voltagecontrol can be an economic attractive supplement.It can also be economically attractive for reducingnetwork losses and congestions as well asproviding better security of supply in case of faults.One advantageous characteristic of reactive powersupply by WECs is its distribution in the networkand its location which is often next to loads. Thisdispersion of reactive power sources can reducethe overall network losses considerably.The paper presents an economic potential of usingreactive power supplied by WECs. This potentialshould be used to optimize the quality, economy

and security of network operation. Further on,regulatory issues have to be analysed to designappropriate market frameworks based on realcosts of reactive power and giving reasonableincentives to operators of WECs for providing abenefit for network operators. These frameworksshould lead to a win-win-situation: for the operatorsof WECs as well as for network operators.

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ACKNOWLEDGEMENTThis work was supported by the EuropeanCommission in the framework of the FENIX project(SES6 518272, see http://www.fenix-project.org)as well as by the German Federal Ministry for theEnvironment, Nature Conservation and NuclearSafety in the framework of the national project

Multifunktionale Photovoltaik-Stromrichter Optimierung von Industrienetzen und ffentlichenNetzen (FKZ 0329943, see http://www.multi-pv.de). Only the author is responsible for thecontent of this publication.

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