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Visualization and Investigation of Unified Power Flow Controller(UPFC) Non-linearity in Power Flow

Seyed A li Nabavi-Niaki, Member, IEEE, M. R. Iravani , Fellow, IEEE

Abstract- This paper investigates the nonlinearity ofunified power flow controller (W F C ) on the powersystem load flow problem. Since the various W F Cparameters equations are non-linear, a form ofvector presentation in complex pow er plane is usedto visualize the effect of d ifferent control parametersof W F C on line powe r transfer. This visualizationhelps to identify the effectiveness of each controlparameters on power control region.Index Terms-Unified pow er flow contro ller, pow erflow control, UPFC.

I. INTRODUCTIONThe unified pow er flow co ntroller (UPFC), with itsunique combination of shunt and series compensat ion, sa powerful device which can independently control upto three power system parameters [I-21. The mostimportant point for considering the UPFC load flowmod el is to he suitable for incorp oratio n into an existingload flow programs. The first power flow model ofUPFC was introduced by the author in [3] while theUPFC is considered as two ideal voltage sources.Several papers have been published on stead y-state andpower flow analysis based upon this model 14-61.Generally, based on the power flow control strategychosen for the UPFC at the steady-state, two typ es ofpower flow model can he developed as shown in figure 1. In Figure 1(b) the sending-end bus is transformedinto a P Q bus while the receiving-end is transformedinto PV bus. The active and reactive power loads in theP Q bus and the voltage magnitude at the PV bus are setat the values to he controlled by the UPFC. The active

Fig. 1- UPFC p resentations for pow er flowstudy (a) Study system(b) UPFC as PV an d P Q buses(c) UPFC as two P Q busespower injected into PV bus has the same value as theactive power extracted in the P Q bus since the UPFCand the coupling transformers are assumes to belossless. A standard load flow is carried out todetermine the nodal, complex voltages at th e W F Cterminals. After load flow convergence, an additionalset of non -linear equatio ns, relating the various UPFCparameters, is solved by iteration. The sam e concept isshown in Figure I (c) excep t that the receiving-end isalso t ransformed into another PQ bus.In order to fully analyze the effect of every limitationand determine UPFC control setting and at the sametime easy understanding the rule of each control

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parameters, a visualization approach is used in [7] .T h eobjective of this paper is to visualize and investigate thenon-linearity characteristics of a UPFC on pow er flow.

11. STEA DY-S TAT E CHAR ACTE RISTICS OFU P F C

A power transmission system composed of a lineequipped with a UPFC can adequately demonstratebasic characteristics of the UPFC for steady-stateconditions. Figure 3 shows a single-phase equivalentcircuit of such a system. The line is connected betweentwo voltage buses VI .G1 an d V2L6,. The UPFC isrepresented by the steady-state model developed in [3].Series reactance of voltage source V,L6, is included inX,. The UPFC controls power flow of the line throughcontinuous control of V, an d 6,. Depending upon thesystem operating condition, voltage source V,L6Bexchanges real and reactive power with the system.Since a UPFC can neither absorb nor deliver real power( losses are neglected), phase-angle 6E is adjusted tocompensate for real power exchange between VEL6Band the system. The amplitude of V, ca n be used tocontrol the reactive power exchange between VEL6Eand the system. V can he adjusted to compensate forthe reactive power exchange between and thesystem. In general, by means of control ling V the ne treactive power exchange between the LJPFC and thesystem can he regulated.Applying KCL to the system of Figure 3, the systemcurrent components are obtained.

UPFC_i -Figure 3. Single-line diagram oftransmission line and UPFC

Wh ere X, =XIX, +X,X,+X I Y , ,The sending-end and receiving-end powers areexpressed as:SI'VI I ;

(4)The power exchange of the voltage sources VBL8, andV E h E ith the system are:

from (3) to (6) it is obvious that the equation sets ofUPFC are highly non-linear and the effect of everycontrol parameters on power flow is not clear. To set the

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control parameters and find the borders o f limitations oftheses parameters a visualized presentation of theUPFC control parameters is very helpful.111 POWER LOWVECTORDIAGRAMW I T H UPFC

When the UPFC is in service, the com plex power at thesending-end of the system of Figure 3is given by (3).Equation (3) can be decomposed into four componentsas given by (7).SI= sa+s,+s,+S,Where S, to Sd are

(7 )

(8)In (8), 6 is equal to 6, - j2. The voltage angle of the

receiving-end (6,) is chosen as the reference angle.Figure 4 graphically represents SI n t e r m of its fourcomponents.

PI1 .67VI =1LWv, =0.9~9.4-v,=0.15 ~ 1 3 ~XI=X2=0.5 pu

,._...__.......'......I ,0 0 1 0 2 03 0 4 05 0 6 0 7PI (PU)Figure4. Graphical representation of SI nthe complex power plane.

Neglecting W F C losses, during steady-state operationthe UPFC neither absorbs real power from the systemnor injects real power in the system (PE+ PE =0).Physical interpretation of this statement is that thevoltage of the dc link capacitor remains constant at its

pre-specified value V This constraint m ust he satisfiedby the UPFC steady-state equations.The constraint P, +PE=0 implies that:- no real-power is exchanged between theUPFC and the system; thus, the dc link voltageremains constan t,the two voltage sources V , an d V, ar e

mutually dependent (PE+PE=0).Assuming that variable 6, is assigned to regulate the dclink voltage, power flow (both real and reactive) can besimultaneously controlledchanged by variables 6,, V,an d V , of the W FC . Among 6,, V , an d V, The controlparameter of 6, has the most dominant effect on themagnitude of real power flow.To visualize the parameters affecting on the line powerflow, we con sider the two following cases, 1- the effectof W F C parameters on tie l ine power flow and 2-. theeffect of system parameters on tie line power flow

Iv. POWER R O W CHARACTRRlSTICSW I T H UPFC

To visualize the effect of W F C parameters on tie l inepower flow, we rewrite (3) as follows:SI=A +BVEe-j'E +CVge-J'B (9)whereA =S. +S, in (7).

In this form, the tie line power is expressed by UPFCcontrol parameters (V,, 6,, VE an d 6). If systemparameters are kept unchained, A, B an d C remainconstant. Therefore the tie line power flow becomesonly as a function of UPFC control parameters. Now,we can visualize the effect of these control parameterson power flow. Figure 5represents Figure 4in the formof (9).As 6, an d (or) V , are changed to regulate power flow,

also changes to ensure that P, +P E=0. Thus, the tipof vector S, traces a closed path in the complex powerplane of Figure 5. This closed path is the powerdi ag am of the tie l ine when the UPFC is in service. To

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0 01 0 2 03 0 4 05 06 07PI (PU)

Figure 5 . Graphical representation of SI as afunction of UPFC con trol parameters in form of (9).identify the power diagram correspon ding to (9), it canhe decomp osed to real and reactive powers as ( IO ) .

E j = a + c s i n 6 BQi = h+ c c o sS g

where

from ( IO ) , the following expression is deduced2(PR a ) + QR - )=c (11)

Q PU)1.5

1

0.5

0

-0.5 ,0 0. 1 0.2 0.3 0.4 -0.5Figure 6. The tie line Power v ector f&r'p%different values of 6 , .

0.20.1

04.

-0.2Qol0 . 3 0.3 0.35 0.40.1 0.15 0.2 -.45 0.5

Pd p (PU)Figure 8. The tie line complex power region for6 =20" when the UPFC is located at the middleof the line.

If a an d b are assumed as con stant values, then ( I 1) canrepresent a circle in the com plex power plane. However,In general a an d b in ( I 1) can not he assumed as fixedvalues, since it is functions of 6E an d V, which in turnare varied as a result of changing 6, and/or V,. Thus fordifferent values of 6,. there are some different valuesfo r 6E as shown in Figure 6.Therefore ( I 1 ) identifies aclosed path, with constant radius c and centers on arc efas shown i n Figures 7 . Figure 8shows the sending-endcomplex power regions at 6 =20" when the UPFC islocated at the m iddle of the line. Based upon controllingV, an d F E , any complex power associated with a pointwithin the enclosed areas, can he controlled by theUPFC.

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Figure 8clearly demon strates that fo r any value of realpower transfer (e.g. Po). there are two distinct v alues ofreactive power transfer (Q,, an d Qm) or any fixed valueof other parameters. Shaded area in Figure 8 identifiesthe control regions where real power flow is achieved atlower reactive power.

V. EFFECT F VEO N TH E POWER FLOWTerminal voltage at the connection of parallel part ofUPFC ( V , n Figure 3) ca n he regulated by VE.When V ,is larger than V,,, the U PFC injects reactive power intothe system and vice versa. As a result, the amount ofrequired reactive power to be provided by the sending-end will be less. This corresponds to the length of S, inFigure 4.

VI. TH E SYSTEM PARAMETERS EFFECTSO N POWER FLOW

When two systems are inter connected, we can assumetwo kind of connections, either two systems are at thesame level of strength (same Thevenan equivalentimpedance) or one is weaker than the other (differentThevenan equivalent impedance). Figure 10depicts theeffect of the strength (or weakness) of the system oncomplex power regions of the receiving-end. Thesystem strength's (o r weakness') is changed by varyingXI an d Xz of Figure 3.Figure 10shows that for a givenlevel of real power transfer, reactive power demandedfrom the receiving-end depends on the system'sstrength.The system power angle (6) is another system parameterthat can have the significant effect on tie line power

Q PU)Xh 0.81

P (P4-1 0.1 0.2 0.3 0.4 0.5 0.6Figure 10.Effect of system weakness on thetie line power flow.

2

1.5

1

0.5

0

-0.5 0 0.2 0. 4 0.6 0.8 1 1.2

Figure 11 . The tie line power vectors forsystem power angles 6=15" an d 6 =75".

transfer when the UPFC is in service. Figure 11 showsthe tie line power vectors for system power angles 6 =15' an d 6 =75'. This figure conducts that the voltageamplitude of the parallel,voltage (VE)can be used forthe real power control for the large value of 6 b ychanging the magnitude of S,. However the tie linereactive power can he control by V , for the small powerangle condition. Figure 12 also depicts the complexpower region that can he controlled by changing aBfrom 0 to 360" for two different values of power angle(6).

Figure 12. Sending-end complex powerfo r 6 =25'and 6 =45".A vector of Sd fo r6 =130" is also shown.

VII. UPFC PARAMETERSONSTRAITThe volt-ampere rating of the series transformer ofUPFC is defined by the maxim um injected voltage V,

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and the maximum line current. V is determinedbased upon the operational requirement(s) of the UPFC.The maximum line current is determined by the powersystem. The volt-ampere (VA) rating of the seriesconverter, shunt converter, and the excitationtransformer are the same as that of the seriestransformer. The voltage rating of the system-side of theshunt transformer is th e same as the system ratedvoltage. Having specified the VA rating and voltagerating for the shunt transformer, the maximum shuntcurrent (I,) can he determined. This current is anonlinear function of V,. 6,, V, an d 6B. igure 13showsthe variation of 1, as a function of 6 , and V E for thesystem of Figure 1. From this figure and Figure 12with the consideration of UPFC parameters constraints,the real power and reactive power set points of Figure 1to run the power flow program can be determjned. Forexam ple, based on the parallel converter rating, 1,- isset and then from Figure 13 the permitted operatingvalues of V, and 6, are given. By setting these valuesth e P ~ o ~ . , ~ , , ~ ~nd Ql~pe ro , l n gn Figure 12are set.

8

Fig. 13 Variation of 1, as a function of V , an d 6,

VIII. CONCLUTIONSThis paper investigates the ability of UPFC oncontrolling tie line power flow. Since the UPFC has fourcontrol parameters, to identify the effect of eachparameter on power flow, a form of vector presentationin complex power plane is used. This form helps tovisualize the effect of different control parameters ofUPFC on tie line power transfer. The amplitude (V,)and phase angle of series injected voltage (6,) have themost effect on real power transfer if the power anglebetween two systems is small. For the large powerangle, in addition to 6, and VB , he voltage amplitude ofthe parallel voltage ( V , )can he used for the real powercontrol. However the tie line reactive power can hecontrol by V, for the small power angle. The phaseangle of parallel voltage is set to regulate the dc linkcapacitor voltage.

IX. REFERENCES[ I ] L. Gyugyi, A Unified Power Flow Control conceptfor Flexible AC Transmission Systems, IEEProceedings-C, Vol. 139, No 4, July 1992.[Z] S.A. Nahavi-Niaki, M.R. Iravani, Investigation ofStatic Phase-shifter Behavior under Steady-StateConditions, ICEE-94, pp . 126-134.[3 ] S.A. Nabavi-Niaki, M.R. Iravani, Steady-State andDynamic Models of Unified Power Flow Controller(UPFC) for Pow er System Studies, IEEE Transactionson Power Sys tem, vol. 1 1 , No. 4, pp . 1937-1943,November 1996.[4 ] C R. Fuerte-Esquivei, E. Aeha, Unified PowerFlow Controller A Critical Comparison of Newton-Raphson UPFC Algorithms in Power Flow Studies,IEE Proceedings, Generation. Transmission &Distribution. vol. 144, no. 5, September 1997, pp. 437-444.[5 ] W. L. Fang and H. W. Ngan, Control setting ofunified power flow controllers through a robust loadflow calculation, IEE Procegdings, Gene-ation,Transmission &Dist-ibution, vol. 146, no. 4 , July 1999,pp . 365-369.[6 ] Jun-Yong Liu et al., Strategies for Handeling UPFCConstraint in Steady-State Power Flow and VoltageControl, IEEE Transactions on Power Systems, Vol.15, No. 2, May 2000, pp.566-571[7 ] SA . Nabavi-Niaki, Visualization of UPFC C ontrolParameters Effects on the Tie-Line Power Flow, Proceedingo LESCOPE 2002,Halifax, Nova Scotia, Canada, May2002, pp103-107S A . Nabavi-Niaki (M92) is assistant professor of electricalengineering department at University of Mazandaran. Hereceived his B.Sc. and M.Sc. degrees both in ElectricalEngineerins from Amirkabir University of Technology(Tehran Polyfechnique) in 1987 and 1990 respectively. Heobtained the Ph.D. degree in Electrical Engineering fromUniversity of Toronto (1996). His current research interestsinclude analysis, operation and control of power system andFACTS applications.M. Reza Ir av an i received the B.Sc. degree i n electricalengineering in 1976 from Tehran PolytechniqueUniversity and started his career as a consultingengineer. He received the M.Sc. and Ph.D. degrees alsoin electrical engineering from the University ofManitoba, Canada in 1981 an d 1985, respectively.Presently, he is a professor at the U niversity of Toronto.His research interests include power lectronics andpower system dynamics and control.

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