location of facts

8/3/2019 Location of Facts

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Optimal locationof shunt FACTS devices in longtransmission linesM.H.Haque

Abstract: FACTS devices are now recognised a s a viable solution for controlling transmissionvoltage, power flow, dynamic response, etc. and represent a new era ror transmission systems. It hasbeen proved that the centre 01-midpoint of a transmission line is the optimal location for shuntFACTS devices or reactive power support and the proof is based on the simplified line model. Thevalidity of the above optimal location of shunt FACTS devices is investigated, when the actual modelof the line is considered. It is found that the FACTS device needs to be placed slightly off-centre toget the highest possible benefit. Both the power transfer capability and stability of the system canfurther be improved if the shunt FACTS device is placed at the new optimal point instead of at themidpoint of a line having some resistance. This finding contradicts the previous results found for thesimplified line mo del.

1 IntroductionThe flexible AC transmission system (FACTS ) has receivedmuch attention in the last two decades. It uses high-currentpower electronic devices to con trol the voltage, power flow,stability etc. of a transmission system. Some forms ofFAC TS devices are already available for prototype installa-tion [ l, 21 and others are still under development. FAC TSdevices can be connected to a transmission line in variousways, such as in series, shunt or a combination of seriesand shunt. For example, the static VAr compensator(SVC) and static synchronous coinpensator (STATCOM)are connected in sh unt; static synchronous series compensa-tor (SSSC) and thyristor-controlled series capacitor (TCS C)are connected in series; thyristor controlled phase shiftingtransformer (TCPST) and unified power flow controller(UP FC) are connected in a series and shunt combination.The terms and definitions of various FACTS devices aredescribed in a recent IEEE article [3].The pressure associated with economical and environ-mental constraints has forced the power utilities to meet thefuture demand by fully utilising the existing resource oftransmission facilities without building new lines. FACTSdevices are very effective and capable of increasing thepower transfer capability of a line, if the thermal limit per-mits, while maintaining the same degree of stability [4-71.In fact, Kinibark [8] has proved that the steady-state powertransfer capability of a line can be doubled when a shuntcapacitor is placed at m idpoint to suppo rt the voltage. Thistechnique can double the power transfer capability at amuch lower cost than building a second line of the samecapacity. The main role of the shunt capacitor is to supplyadequate reactive power to support the voltage and it can0 EE , 2000IEE Proceedings online no. 20000412DOL 10.1049/ip-gtd:20000412Paper lint received 24 November 1999 and in icviscd fomi 23 Fcbrimy 2000The author is with the School of Elecliical and Electronic Engineeiing,Nan-yang Tcchnological University, Naiiyang Avenue, Singapore

easily be replaced by a shunt FACTS device that has verysmoo th control of reactive power over a wide range. How-ever, the proof of doubling the pow er transfer capability isbased on the simplified model of the line that neglects theresistance and capacitance. Based on this simplified model,many researchers determined the performance of midpointsiting FAC TS devices [5, 9-11]. How ever, when the actualmodel of the line is considered, th e results may deviate sig-nificantly from those found for the simplified model.This paper investigates the erfects of considering theactual line model on the power transfer capability and sta-bilily when a shunt FAC TS device is connected to the line.The paper consists of the comparison of various resultsfound for the simplified and actual models of the line. Thediscrepancies observed between the results of these twomodels are discussed with app ropriate mathematical justifi-cations. It is found that some of the results obtained orconclusions made for the simplified line model are not validfor the actual line model, especially when the FACTSdevice is placed at the midpoint.

Ps+lQs P R+IQ R--IT.S transmission line's--2 Transmission line model

In this study, it is considered that the transmission lineparameters are uniformly distributed and the line can bemodelled by a two-port, four-terminal network as shown inFig. 1. This represents th e actual model of the line. Therelationship between the sending end (SE) and receivingend (RE ) quantities of the line can be w ritten asv y = AVn + BIR (1)1.5 = cvn +D1n (2)

Th e ABCD constants of a line of length 4, aving a series218


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impedance of zSl/km and shunt admittance of yS/kni aregiven byA = D = cosh(yl)

where y = dz y an d Zc:= d d ythe line can be written as [ I21

r , y = c,Q S = CI sin@ - N ) - C, sin(j3' +6) (5)PR == Ca (:Os([) - 6)- Cs cos(h ' - 0) (6)& I < = Ca sin(p- 6) - C3 s in (P - a ) (7)

wherc C, = AV?IB, C2 = VyVR/B,C, = AVR2/B nd A =It is clear from eqn. 6 that the RE powcr P , reachcs themaxim um value when the angle 6 becomes P. However, theSE powcr Ps of eqn. 4 becomes maximum at S = (x- p).For the simplified model of the line, the resistance andcapacitance are neglected. For such a model, the ABCDconstants of the line becomc

A = D = 110" B=z! i9O0 C=O ( 8 )Hcre x s the series reactance of the line in Wkm. In thiscase, the line is represented by only it lumped series reac-tance X = x4, nd both Ps an d P,< ecome maximum at S= 90". Such a simplified model may provide reasonablygood results for a short linc for which the power transfercapability is normally dictated by its thermal limit. When itFACTS device is connected to a long line to increase thepower transfer capability, the use of simplified line modelmay prov ide erroneous results.In this study, a 345kV, single circuit transmission line oflength 450kni is considered. It is assumed that each phaseof the line has a bundle of two conductors of size one mil-lion c-mils each and the conductors are fully transposed.The tower configuration of the line is considered as 3P1[13].The series impedance and shunt a dmittance of the lineare found to be z = (0.02986 + ,j0.2849)SZ/km and y =,j3.989 x 10-6S/km, respectively, at 50Hz. The parametersare obtained by using the software given in [14]. The resultsof the line are presented in p.u. on a IOOMVA, 345kVbase.

B = Z c sinh(y!)C = s inh(y t ) /Zc : ( 3 )

The active and reactive power flows at the SE and RE of- k!) - c2COS( /9 + 6) (4)

ALa , B = BLP, Vi


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because the line is lossless. The nuxiinurn power increasesfrom 9.3p.u. (for lr = 0) to its double value (for k 0.5) asexpected. However, for tlie actual line model, Pg' > P;i'because of tlie loss in the line. The value of P; increases a stlie value of k is increased from zero and reaches tlic high-est value of 2 2.8p.u. at k = 0.45 (but not 0.50). The highestvalue of 9:' for the actual line model IS much higher thanthe corresponding value foulid for the simplified line model(1 X.6p.u. at k = 0.5). For the actual hie model, the slope ofthe Pi ' curve suddenly changes at k = 0.45 and tlic valueof P,? decreases when k > 0.45. A similar pattern can alsobe observed for the Pg curve. It may be meiitioiied herethat the value or Pg is important in determining the powerdelivering capability of the line at the inliiiite bus. However,the value of PLY is equally imp ortant in cletermining thestability of th e generator that depends 011 the power thatcan be delivered at its terminal.

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both the power and angle curves at k = 0.45. This itnex-pected pattern of powcr and angle curves is hrther investi-gated throug h the powcr-angle character istics of the line.3.1 Power-angle characteristics and stabilityThe power-angle character istics of thc system of Fig. 2 arcshown in Figs. 7 and 8 for the simplified and actual inod-CIS of tlie line, respectivcly. The cliaractcristics arc plottedfor various values of k (0-0.5). Note that for k = 0, th eshunt device is located at the SE of the line where the volt-age magnitude is considered to be constant. In this case, theshunt dcvice has no cufect on the line characteristics and theline can be considered as totally uiicompcnsated. Theresults for the simplified liiic model of F ig. 7 ar e very obvi-ous and well presented in [8]. I1 can be noticed in Fig. Xthat tlie maximum powcr PJiincreases a s the value of Ir isincreased. However, an unusual pattern of thc P-6 urvecan be observed for k = 0.5. For k 5 0.4, all P-6 curvesapproach the point y (191.8" at zero power). But fo r /z =0.5, the P-6 curve is shifted towards left after reaching themaxiinuiii power and approaches the point .x (167" at zeropowcr). The above change in the pattern of the P-6 urvesignilicantly affects the stability of tlie system. I t inay beiiieiitioned here that, for a given initial operating power (


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much larger than that for k = 0.4. T h ~ she system ca n beconsidered a s more stable for /C = 0.5 than for /r = 0.4.However, even though the niaxiniuiii power for /C = 0.5 isIiiglier than that for k = 0. 4 in Fig. 8, the system is less sta-ble for lc = 0.5. This happens becausc of the smaller deccl-erating area caused by the shift of th e P-6 ciirvc towardsthe left. Thus, when the stability of the system is comparedbetween these two linc models for IC= 0. 4 aiid 0.5, a con-tradictory result can be found. The reason for shifting theP-6 curve, is further investigated and a search is carried outto find the optiinal location of the shunt FACTS devicethat provides the maximum bcndit in terms ol' the systemstability when the actual liiic model is considcl-cd.3.2 Optimal location of shunt FACTS devicesFig. 9 shows thc P-6 curve of the halr-length ( U 2 ) of theline using the actual line iiiodcl. Both SE an d R E powersare shown in th e Figure. I t can be noticed in Fig. 9 thatwhen the angle 6 increases from zero, both th e SE and REpowers are increased. The R E power first reaches the m i x -imuni valuc (point a) at an angle /-I followed by the niaxi-mum SE power (point /?) a t an angle (n /)). Theseinaximuni power points c i i i i easily be Found from eqns. 4an d 6. Wlicn the angle 6 is further increased, both the R Ean d SE powers decrease and ultimately reach zero values atangles and ay, respectively. The values of 6, an d 6,.canalso be determined from eqns. 6 and 4 , respectively.

25 r._ 20-: !.c+-EQWLTUmW(I)

increasc in 6 , . Note that (S2 caiinot increase because of theconstraint P,, = PLs2nd P,, cannot suddenly junip frompoint c to cJ (in Fig. 9). In ract, decreases when 6, > PIto satisfy the sanic power cons traint. Thus a t higher angles,section I operates in the iiiistable region wliilc section 2operates in the stable region. It can also be noticed inFig. 9 that the power at the midpoint ( P R l an d PLs2)reduces to zero when 6, = 6, an d (8 i : ". Thus at higheranglcs or for unstable operation, the midpoint powerreaches the zero value when th e total angle (6, + 6J isabout 6, = 168.2") which is very close to th e corrcspond-ing valuc (1 67") found a t point s in Fig. 8 for k = 0.5.Note that when the power at the midpoint is zero, bothsides of th e linc feed some power to cover the loss in thelinc and that causes the above discrepancy of 1.2".For lower values of k , the maximum RE power of sec-tion 1 increases while tlic maxiiiiuni SE power of section 2dccreases. Thus the point I / in Fig. 9 moves upwards andpoint h goes downwards. when the point L/ is higher thanpoint / I , section 2 (but not section 1) operates in the unsta-ble region if the system operation crosscs the maximumpossible power point during th e transient period. In thiscase, zero power a t bus 117 occurs when 6, ~ i : an d a2= a,,.Thus the overall P-6 curve approaches th e angle 6, + d2 =d,, = 191.9"(but not to 6., = 168.2") its can also be seen inFig. 8 fo r /c 5 0.4. Thus, when P;;; > { section 2 oper-ates i n the iinstablc region at higher anglcs and the P-6curve approaches a,,. However, when Pi;; < P';, scctioii 1operates in the uiistablc region and tlie P-6 curveapproaches 6,. The transition of shifting the P- 6 curvetakes place when the condition PiI; = Cq,' is satisfied and italways occurs for lr < 0.5 when the loss of the line is con-sidered.

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Consider that the shunt FACTS device is now placed atthe midpoint of the line (lc = 0.5) of Fig. 2. For such iicase, Fig. 9 also represents the power-angle characteristicsof both the line sections I an d 2 (half-length). It may againbe mentioned here that the FACTS device does not absorb01-deliver any active power. Thus thc R E power of section1 must be equal to the SE power of scction 2. Considerthat section I delivers the maximum power at its receivingend (bus nz ) . This situation can be represented by the pointwhere the angle 6 , = PI (= 84.1"). The correspondingoperating point of section 2 can be represented by the pointc (at the same power level) and th e angle a t t h a t point is(= 58.4"). Thus tlie total transmission angle a t the niaxi-niiini power point is 8" = 6, + (= 142.5'). Note t h a teven though section 2 is capable of tl-ansferriiig morepower through its SE (up to point /I), section 1 is unable todeliver that power at its RE. Thus, the maximum powertransfer capability of the system is limited by the maximuinRE power of section 1. When thc transmission angle is fur-ther increased (6 > 8" = 142.5") durin g the transient period,the power transfer through the line decreases because of the1LE Proi,. Gnirr. T I~ I I I I ,V I I .i.stdi., Vol. 147, N~ J .,/ r i l l , 2000

Fig. IO shows the variation of the maximuin RE powerof section 1 (P,':; ) and the niaxiniuin SE power of section 2(lT;") against th e valuc of k . I t can be seen iii Fig. 10 thatthc inaxiinuiii power curves cross at k = 0.447 and thecrossing point is the transition point. T ~ L I So get the high-est benefit in terms of the power transfer capability and sta-bility, the shun t FAC TS device must be placed at k = 0.447which is slightly off-centre. Note that Figs. 5 and 6 weieplotted for an incremental value of k of 0.01, aiid thus thetl'ansition was found at lc = 0.45. The optimal location ofthe shunt FACTS device depends on the line resistance orloss aiid hence the IZIX ratio of the linc. Fig. I 1 shows thevariation of the optimal off-ccntre location of the shuntFAC TS device against th e R / X ratio of the line for variousvalues of V,,,. It can be obscrved in Fig. 1 1 that the optimal

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off-centre location increases linearly as the value of RIXratio of the line is increased. The slope of the line is about0.5% fo r Vn,= l .0p.u.6,86._>

U

1 I1 ov,=o.9

0 2 3 4 6 a 10line R/X ratio, %

Fig.11device uguinst the lUX rrtio qf the lineVrriution of the optimul ojkntre loccition cf U shunt FACTS

It is worth mentioning here that the line capacitance isfound to have a very insignificant effect on all the resultsshown in this paper. However it slightly affects the amoun tof reactive power supplied by the shunt FAC TS device.4 ConclusionsIt is a common practice to consider the centre or midpointof a line as the optimal location of reactive power supportor sh unt FA CTS devices. This is true only when the simpli-fied line model is considered. This paper investigates theeffects of the actual line model on the optimal location ofshunt FACTS devices to get the highest possible benefit.Various results found for both the simplified and actualmodels of a 345kV, 450km line are compared and the dis-crepancies observed are discussed with a ppropriate justifi-cation.It has been found that the shunt FACTS device mayneed to be placed slightly off-centre to get the highest possi-ble benefit when the power flows in a particular direction.The optimal location from the centre point depends on theline resistance, and it increases almost linearly as the RIA

ratio of the line is increased. Both the powcr transfer capa-bility and stability of the system can be further improved ifthe shunt FACTS device is placed at the new optimal loca-tion instead of at the midpoint of a line having nonzeroresistance. However, when thc line carries power in bothdirections, the optimal location of shunt FACTS devicesmay be considered at the midpoint. The results found inthis papcr would be very useful in selecting the best loca-tion for various shunt FACTS devices to gct the highestpossible benefit when the pattern of power flow of the lineis known.5 References1 URBANEK, J., PIWKO, R.J., LARSEN, E.V., DAMSKY, B.L.,FURUMA SU, B.C., MITTLESTADT,W., aiid EDEN, D.J.: Thyr-istor-controlled series compensation prototype installation at the Slatt500 kV substation, ZEEE T,.nm., 1993, PD-X, (3) ,pp. 1460-14692 S CH A U D E R, C., GERNHA RDT, M., STACEY,E.,LEMARK, T . , G Y U G Y I , L., CEA SE, T.W., and EDRIS, A.:Development of a +I00 MVAR static condenser for voltage controlof transmission systems, ZEEE f iuns . , 1995, PD-10, (3) , pp, 1486-1496IEEE TASK FORCE, : Proposed terms and definitions for flexibleAC transmission system (FACTS). IEEE Trrm.7.. 1997, PD-12, (4),

G Y U G Y I , L.: Unified power-flow control concept for flexible ACtransmis sion systems, IE E Proc.-C, 1992, 139, (4), pp . 323 331M O O RE , P., ASHMOLE, P., an d : Flexible AC lraasniissioii sys-tems: Par1 2 - Methods of transmission line compensation. lEfiPower Erg. J. , 1996, 10, (6), pp . 273-2786 RA H M A N , M. , A H M E D , M . , G U T M A N , K ., O K E E F E . KJ.,NELSON, R.J., and BIAN, J.: UPFC application on the AEP sys-tem: planning considerations, IEEE Truns., 1997, PWRS-12, (4), pp.1695-1 7017 GYUGYI, L . , SCHAUDER , C.D. , WILLIAM, S .L . , RIET-MA N, T.R ., TOR GEIZSON , D.R., and EDRIS, A.: The unified

3pp. 1848-18534

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power flow controller: A new approach to powcr transmission con-trol, ZEIX Truns., 1995, PD-IO, (2) ,pp. 1085-1093KIMBARK. E .W.: I-low to improve system stability without riskingsubsynchronous resotmiice, ZEkE Tr&s . , 1977, PAS-96, (5) , p g1608-16199 00 1, B.T ., KAZERANI, M., MARCEAU, R. , WOLANSKI, Z . ,GALIANA, F.D., MCGILLS, D., and JOOS, G.: Mid-point sitingof FACTS devices in transmission lines, I BEE Twm , 1997, PW12,(4), p. 1717-172210 TA N, Y.L.: Analysis or line coinpensalion by shunt-conncctedFACTS controllers: A comparison betwccn SVC and STATCOM,IEEE Power Eng. Rev., 1999, 19, (X), pp . 57-5811 AREE, P., and ACHA, E.: Block diagram model for fiiiidameiitalstudies of a synchronous geiicrator- talic VAR compensator system,/Eh Proc. Gcner. T ~ ~ i s n ? .isfrib., 1999, 146, (5) , pp. 507-514Palo Alto, California, 1982(PWS Publishing Company. 1994, 2nd Edn.)

12 SAADAT , H. : Power system analysis (McGraw-Hill, 1999)13 EPRI : Transink sion line refercncc book: 345kV and above 2nd E dn.,14 GLO VER , J.D. and SA RM A, M.: Power system aiialysis and design

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