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AN IMPROVED STATCOMMODEL OR POWER LOW ANALYSISZhiping Yang Chen Shen Mariesa L. Crow Lingli Zhang

Department of Electrical and Com puter Engineering,University of M issouri-Rolla, MO, 65409,US A

Abstract:. The StatCom is traditionally modeled forpower flow analysis as a PV or PQ bus depending onits primary application. The active power is either setto zefo (neglecting the StatCom losses) or calculatediteratively. The StatCom voltage and reactive powercompensation are usually related through themagnetics of the StatCom. This traditional powerflow model of the StatCom neglects the impact of thehigh-frequency effects and the switchingcharacteristics of the power electronics on the activepower losses and the reactive power injection(absorption). In this paper, the authors propose a newStatCom model appropriate for power flow analysisderived directly from the dynamic model of theStatCom The proposed model can therefore accountfor the high-frequency effects and power electroniclosses, and more accurately predict the active andreactive power outputs of the StatCom.

Keywords: StatCom, FACTS, load flow, powersystems

I. INTRODUCTIONThe STATic synchronous COM pensator (StatCom) sa main member of the FACTS family of power electronic-based controllers. It has been studied for many years, and isprobably the most widely used FACTS device in todayspower systems. Many papers have discussed its operatingprinciples, static and dynamic models, control theories andapplications 11-51. Few papers however, address the issueof how to model S tatCom s for load flow calculations. TheStatCom is traditionally modeled for power flow analysis asa PV or PQ us depending on its primary application. Theactive power is either set to zero (neglecting the StatComlosses) or calculated iteratively. The StatCom voltage andreactive power compensation are usually related through themagnetics of the StatCom. This traditional power flow

model of the StatCom neglects the impact of the high-frequency effects and the switching characteristics of thepower electronics on the active power losses and thereactive power injection (absorption).In a load flow calculation, a StatCom is typicallytreated as a shunt reactive power controller assuming thatthe StatCom can adju st its injected reactive power to controlthe voltage magnitude at the StatCom terminal bus. Fig.l

depicts a StatCom and the traditional simp le model used forload flow calculations. Note that specified reactive powerload at bus i , jQ i , s combined with the StatCom reactivepower output ja - and therefore the reactive power variesas varies. This model is essentially a PV bus with theStatComs active power output set to zero [ 6 ] . The primarydifficulty with t h i s model is that inaccuracies occur whenthe device losses (including the losses of the connectiontransformer and StatCom) are neglected.

4+ia-ia

Fig.1 Simple modelof a StatCom in load flow calculationIn order to consider the loss of the connectiontransformer, a modified model is presented (as shown inFig.2). Note that a new PV bus, bus j , is added to representthe StatComs output terminal, while the connectiontransformer is replaced by its leakage reactance andresistance - RT+jXT The losses on the transformer arethen calculated iteratively within the standard load flow.

IYl fixed

e+xLpig.2ModifiedStatCom model in loadflow calculation

Because the losses of the connection transformer of aStatCom have been included, the accuracy of load flowcalculation can be improved by using the modified StatCommodel. However, inaccura cies are still present in this modelpresent due to the power losses caused by the StatComsVoltage Source Inverter (V SI), which are neglected.In this paper, a new StatCom model is proposed that isappropriate for power flow analysis that can account for thehigh-frequency effects and power ele,ctronic losses, andmore accurately predict the active and reactive poweroutputs of the StatCom.

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TI.AN MPROVED STATCOM MODELAn accurate load flow analysis should accuratelyforecast the steady-state losses of a StatCom, including bothtransformer and inverter losses. The losses caused by theVSI include main three parts: the harmonic losses, theswitching losses, and the conduction losses of the powerelectronic elements. Th e percentage of each losscomponent relates to the conduction mode of the StatComsVSI and the steady state operating point.

A. Harmonic lossesGenerally speaking, a StatCom output voltage alwayscontains harmonics, due to the switc hing behav ior of theVSI. These voltage harmonics will generate harmoniccurrents and further cause power losses in the systemnetwork. If the impedance of the lines that connect aStatCom to the power system is neglected, the harmoniclosses are primarily apparent on the connectiontransformer. The effect of these losses in the transformer

can by analyzed by considering an expansion of thetransformer impedance.4, c StatCom

n 1

+4

c+00

Wg.3 Modified StatCom model in the load flow calculationFig.3 shows the circuit of a StatCom connected to apower system by a connection transformer, where V, and

e represent the system RMS voltage and the StatComsRMS output potential respectively, and RT and 4 denotethe resistance and leakage reactance of the connectiontransformer. Assuming that there are not any harmon ics inthe system voltage V,, the StatComs output voltage econsists of fundamental and high-order harmonics, andmay berepresentedas:

where e, is the RMS value of the fundamental harmonic,

e, represents the RMS values of high-order harmonics,and n , , n z , - . . are the harmonic indices. Thus, the firstdiagram of Fig3 can be represented as he sum of the otherharmonic diagrams (whereX, ,X,,,,n l -. e denote thetransformers inductance under different harmonicfrequencies).

The harmonic losses on the connection transformercan be expressed as:P =P +P

(2)e * R=P-+ c-..R +X:e : * R=P-+ 2-R + i X :Usually, the magnitude of a StatC oms output voltagerelates to the StatComs DC side voltage and theconduction mode of h e StatComs VSI. For example, ifthe VSI applies the square wave conduction mode, theoutput voltage magnitude is a function of the DC sidevoltage and the firing angles of the VSI. f the PWM modeis used, the output voltage magnitude is a function of theDC side voltage and the du ty cycle ratio of the PWM. Inthe following parts of this paper all derivations will bebased on PWM assumption. Therefore using PWM, heoutput voltage magnitude of the StatCom can be expressed

e , = f , ( V , . K ) i = n , . n , ; . - (3 )as

where K is the duty cycle ratio. Since, e, is directlyproportional to the DC side voltage V, , equation (3) canbe simplified as

e, = V * * f , ( K ) i =n , ,n2 , . . - (4)Substituting equation (4) into equation (2), the lossescaused by the high order harmonics can be expressed as

where

From equation (6) . it can be seen that the high orderharmonic losses relate to the StatComs operating pointand vary with the duty cycle ratio. Typically, when aStatCom is in steady-state operation, the duty cycle ratiodoes not change or changes in a very limit range. TheStatComs output reactive power is regulated throughfiring angle change. Then Rh CM be treated as a constant.Equation (5 ) also implies that the high order harmoniclosses can be equivalently represented as the active powerlosses caused by a DC side shun t resistor.

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B. Switching and conduction lossesThe switching losses are introduced when the powerelectronic switches of a StatCom are in their turn-on andturn-off transients. Because of the strong non-linearcharacteristics of the switching behavior of powerelectronic switches, it is difficult to precisely model theswitching losses of a StatCom. Th e conduction losses of aStatCom are caused by the voltage drops across theelectronic power switches when they are in the on-state. Inthis section, the switching and conduction losses of aStatCom will be estimated.

Fig.4 show s the collec tor-e mit ter voltage V, andcurrent isof a power electro nic switch (such as an IGBT) ina typical turn-on and turn-off process [7].

V, , i ,

Rg.4 A typical tum-on and tum-off procedureofa power switchAssuming that no losses are incurred when the switchis off, then all the switching and conduction losses areintroduced in the period from t , - 6 . If this period is

divided into five intervals, the losses can be estimatedsegment by segme nt as follows12tl - 1 : wI l =-V, * i , * ( I , - I l )

r, - r , : w, - 4 ~ ~v , ) * i , * ( t , t , )c, - , : w,, =V I *i, * ( r , - I , ) (7)1 - I , : w, =-(V, +V,)* i , *( t , I , )t, - I , : w, 0-v, * i , *(I' - I , )

21212

Suppose t 2- , = 6 - t , and t , - 2= , - t s , hen bycombining the above equations, it is possible to get theswitching and conduction losses of a sw itch in one phaseleg and in one switching cycle:

w i V , * i , *( t , t , ) + V , *i, *(t , Il) (8)If the switching frequency f, of a VSI is constant,

then the average switching and conduction power lossesP,.,~ of the VSI can be app roximately expressedas:P - m * f , . * [ ~ , * ( I , t , ) + v m *(r, - t 1 ) ~ * i , (9)

where m is a coefficient which relates to the VSI'stopology. Further, the following relationships hold:V,, =V,,+k , *io,, (10)

t 3 - q - t r + & , * i , , (1 1)(12)

where V,, represents the constant voltage drop across apower electronic switch in its on-state, and t , , ,,,, , , , ,are constant coefficient . Therefore, equation (9) can berewritten as:

t4 - 2 - omt.=

(13)Equation (13) indicates that the switching andconduction losses of a StatC om relate to the current passingthrough its VSI into the AC side system. When theStatCom is operating at high cur ient levels, the second termon the right of equation (13) dominates the switching andconduction losses of the S tatCom.If the effect of the first term on the right of equation(13) is neglected, then the use of a serie s resistor in the ACside system of a StatCom can approximately represent theStatCom power elec tron ic losses.

P =m *f, *[( t , V, +Vo * t , ) * i ,+(k, *V , + k , * t , ) * i : ]

C. An imptoved model of a StWComBy shunting a resistor in the DC side of a StatComand putting a resistor in series with the AC line, theapproximate losses of the StatCom can be taken intoaccount.

-4- pd

Inverter

Fig5 Schematic of a StatCom connected to apowersystemFig. 5 shows the proposed improved StatCom model,where R is the combination of the series resistor and theconnection transfo rmer 's resistance. To derive the newmodel, let

v, = f i * y * c o s ( a ) * r )2?rv ,=f i* V,* cOS(a )* t - - ) 3

Ke, =-* V* * W S(a )* I+6 )e o-*v, *coS(a) ' I+S-- ) 2R2 3

K 2.?c2 3e, I -* V,* co s (a )* t+6 +- )

where 6 s the firing angle of the StatCom's VSI,md V,is the RMS value of the system line-to-neutral voltage.Because the losses of the VSI have already beenrepresented by two eq uivalent resistors, the VSI can be

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then assumed to be lossless. This yields the followingpower balance equation:

The state-space equation sof the Stat.Comare:P, =V,i, =P, =e , +e&, +q i C ) (16)

where

In order to validate the accuracy of the proposedmodel, a device level sim ulation and a state-spacesimulation are c a n i d o u t in Matlab. In the device levelsimulation, the full power switches characteristics arespecified. In the state-space simulation, two cases areconsidered. In the first case, the simple model of aStatCom is used in which the losses of the VSI areneglected (by substituting R with Rr , nd letting Rh +0in equation (17)). In the second case, the improved modelof the StatCom expre ssed by equation (17) is used. Fi gdand Fig.7 show the start-up dynamics of a StatComs ACside current and DC side voltage. The device levelsimulation is shown with the solid line, the simple modelwith a dashed line, and the proposed model results with adotted line. The dotted line is coincident with the center oft h e solid line so it isdifficult to differentiate.

Rg.6AC sidecurrent of aStatCom in start process

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From the simulation results, it is apparent that theimproved model can accurately capture the StatComsdynamic behavior, whereas the traditional simple modelproduces some errors. The simulation results demonstratethat the proposed m odel is more accura te in representing aStatCom esponse.

Hg.7 DC i& voltageof a StatComin start process

III. AN IMPROVED TATCOM MODELFOR LOADFLOW ANALYSISBased on the analysis presented in the previoussection on the improved modeling of StatCom losses, animproved StatCom model for load flow calculations ispresented in t h i s section.

A. An improved StatCom modelfor oad f low calculationsTo better reflect the effect of a StatCom on line powerflow, the StatComs power losses should be considered inthe load flow calculation. As discussed in the last section,the switching and conduction losses can be represented byan AC ide series resistor. This resistor can be added to theconnection transformers resistance. A lthough the harmoniclosses of a StatCom can be roughly reflected by a DC sideshunt resistor, in a load flow calculation the shunt resistormust be manipulated so that it can take part in the load flowcalculation.The harm onic losses are given as:p - = z

4Therefore, when PWM mode is appliedbecomes

leading to

1 1 2 4

the voltage

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This implies that the DC side resistor can be moved to theAC side so long as a scaling coefficient is added.The proposed improved load flow StatCom modelgiven in equation (1 8) is shown in Fig.%.

Rg.8 Improved modelofa StatCom in LdrcalculationIn Fig.8, bus j represents the StatComs VSI output

terminal. It is treated as a PV bus j i n the load flowcalculation. Th e injected power of bus is set to zero. TheStatComs reactive power compensation holds bus jvoltage magnitude constant. The resistance R includes theVSI switching and conduction losses and the connectiontransformers resistance. The harmonic losses are embodiedin RL.

B. LoadfIow calcukl ion examplesA simple two-area power system shown in Fig.9 isused to illustrate the new StatCom model. The systemconsists of two similar areas. Each area consists of two

coupled units, each having a rating of 9OOMVA and 20kV.The transmission system nominal voltage is 230kV. Theper unit system power and voltage bases are chosen as:9OOMVA and 2OkVn3OkV respectively. A StatCom isconnected to bus 8. The compensated reactive power ofthe StatCom maintains the voltage magnitude of bus 8 at1.Opu. All the other information about the sample systemcan be found in reference [ 9 ] .-2

ad - &-Flg.9A simple two-area system

Both the improved model (shown in Fig.8) and themodel shown in Fig.2 are used in load flow calculation.The results are compared to demonstrate the impact of theStatComs ower losses to the accuracy of the load flowcalculation.The values of shunt and series resistors aredetermined in the follow ing way:

I . Neglect the StatComs iosses;

2. Calculate the StatComs output reactive power whichis needed to maintain bus 8s voltage magnitude at1 Mu;3. Assume the effectiveness of the StatCom is 90%.Switching and conduction losses occupy half of thetotal losses and the harmonic losses share the otherhalf.4. According to the StatC oms output reactive power andits effectiveness determ ine the parameters of the shuntand series resistors

Table 1 gives the maximal errors in the load flowcalculations when diffe rent StatCom models are used.Table 1. Maximalerrors in loadflow calculation mesultsq l

enrors 0.02% 1.2% 3.6%Table 2 shows the maximal errors in the load flow

calculation when the entire loading of the power systemincreases by 50% and the generators increase their outputcorrespondingly to fulfill the energy demand.Table 2.Maximalerrors in LF alculation resultstn i n n on tranrmission

eccoIs 0.08% 0.75 1.2% 13.2%

From the above comparison, it can be noted that thebus voltage magnitudes do not change much regardless ofwhether the StatComs losses are considered or not. TheStatComs losses will have a noticeable impact theaccuracy of the phase angles and active power ontransmission lines. But the most significant impact of theStatComs losses is on the accuracy of the reactive powerflow n the transmission lines, especially when the powersystem is heavily loaded.

IV.CONCLUSIONAlthough the power losses of a StatCom are smallcompared to its capacity rate, the losses play a significantrole in the StatComs mathematical model and the accuracyof the corresponding simulation or calculation results. This

paper analyzes the power losses of a StatCom that arecaused by the switching behaviors of the StatComs VSIand, according to the analysis results, present an improvedmodel of the StatCom that take into account the powerlosses. The model is validated by device level simulation.Consideration of the StatComs losses during load flowcalculations is also addressed. The effects of the StatComslosses on the load flow calculation accuracy are also

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demonstrated by several examples.

V.ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of theNational Science Foundation under grants EEC-9527345and ECS-9257208 and Sandia National Lab oratories undercontract BD-0071-D

VI.ACKNOWLEDGEMENTS[11 Edwards, C. W. et al., Advanced static var generatoremploying GTO thyristors, IEEE, ES W.M. Paper[21 Petitclair,P. t al., Averaged modeling and nonlinearcontrol of an ASVC (Advanced STATIC Varcompensator), IEEE PESC96, pp753 -758 Baveno,Italy, une 24-27,1996.[31 Ni, Y. et al., StatCom power frequency model withVSC charging dynamics and its application in thepower system stability analys is, Proceeding of the 4*

NO. 38WM109-1,1988.

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intemational conference on advan ces in power systemcontrol, operation and management, APSCOM-97,pp119-124 Hong Kong, China, Novem ber, 1997.[41 Gyugyi, L., et al., Advanced static var compensatorusing gate-turn-off thyristors for utility applications,CIGRE paper 23-203,1990.[51 Schauder, C. et al., Development of a +100MVArstatic condenser for voltage control of transmission

systems, IEEE Trans.On Power Delivery, Vol. 10,No.3, 1995.[SI Gotham, D. t al., Power flow control and powerflow studies for systems with FAC TS devices, IEEETrans. On Power Systems. Vol.13, No.1, Feb 1998.[71 Mohan, N. et al., Pow er electron ics: converters,applications, and design, John Wiley & Sons , NewYork, 1995.[81 Schauder, C. et al., Vector analysis and control ofadvanced static VAR compensators,IEE oceeding-C, Vo1.140, No.4, July 1993.[91 Kundur, P, Power system stability and control,McGraw-Hill Inc., 199 4, pp: 813-816.

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