An Approach for Optimal Placement of UPFC to Enhance Voltage Stability Margin under Contingencies

Transcription

1 Ffteenth Natonal Power Systems Conference (NPSC), IIT Bombay, December 2008 An Approach for Optmal Placement of UPFC to Enhance Voltage Stablty Margn under Contngences Sreekanth Reddy Donapat and M.K.Verma Abstract Ths paper proposes a senstvty based technque for optmal placement of Unfed Power Flow Controller (UPFC) to enhance voltage stablty margn under contngences. The senstvty of system loadng factor wth respect to the reactve power flowng through lnes computed for the system ntact case and crtcal contngency cases have been used to decde optmal locaton for the placement of UPFC. The proposed senstvty factor has been derved from the reactve power flow balance equaton. The effectveness of the proposed method for the placement of UPFC n voltage stablty margn enhancement has been valdated on a practcal 75-bus Indan system representng Uttar Pradesh State Power Corporaton Network. I. INTRODUCTION N recent years an nstablty usually termed voltage Instablty has been responsble for several maor network collapses world-wde [1]. The actual cases of blackouts characterzed by voltage depressons reported n the lterature ndcate that standard practce procedures such as transformer tap-changng, capactor swtchng, synchronous condenser adustment, and load sheddng may aggravate an already unstable voltage profle [2]. The problem of voltage nstablty whch may sometmes result nto voltage collapse n the system, has become a matter of great concern to the utltes n vew of ts predcton, preventon and necessary correctons to ensure a stable operaton. The advent of Flexble AC Transmsson Systems (FACTS) Controllers [3] has created new opportuntes for ncreasng power system stablty margn ncludng voltage stablty margn. However, due to hgh cost and, for maxmum enhancement n voltage stablty margn, these are to be optmally placed n the system. Out of dfferent types of FACTS controllers, Unfed Power Flow Controller (UPFC) seems to be more effectve n voltage stablty enhancement [4] due to ts ablty to control seres and shunt varables, smultaneously. The selecton of optmal bus based on combnaton of contnuaton power flow and optmal power flow for the placement of UPFC has been suggested n [5]. However, no specfc crteron has been proposed for the Sreekanth Reddy Donapat (emal: shrykanth@gmal.com) s wth Relance Infrastructure Lmted, Noda, Uttar Pradesh, Inda. M.K.Verma (e-mal: mkverma.eee@tbhu.ac.n) s wth the Department of Electrcal Engneerng, Insttute of Technology, Banaras Hndu Unversty,Varanas, Uttar Pradesh, Inda. selecton of optmal lne. The senstvty of loadng factor wth respect to reactve power generaton at buses and reactance of the lnes has been proposed n [4] to decde optmal locaton for the placement of Statc Var Compensator (SVC) and TCSC, respectvely. Two sets of senstvty factors have been utlzed together to optmally place the UPFC. The crteron for placement of UPFC suggested n [4] has gnored phaseshfter acton of UPFC whch may lead to naccurate results. A voltage stablty L ndex of load buses n coordnaton wth mnmum sngular value has been proposed n [6]. The ndex has been computed to dentfy optmal locaton of UPFC for mprovng system securty. A lnear programmng based optmal power flow algorthm for the placement of UPFC has been proposed n [7] to reduce overloads and voltage volatons. However, reducton of loads and voltage volatons may not always be helpful n mprovng voltage stablty margn. Partcle Swarm Optmzaton (PSO) technque has been used [8] to acheve maxmum system loadablty wth mnmum cost of nstallaton. Partcle swarm optmzaton technque has been employed n [9] to maxmze the loadablty of transmsson system usng Unfed Power Flow Controller under lne outages. Optmal placement of UPFC based on evolutonary programmng has been suggested n [10] to enhance maxmum loadablty of the system. The work on UPFC placement has manly concentrated to see ts mpact for the system ntact case and under lne outage cases. However, outage of some of the generators may also cause voltage nstablty n the power system. In ths paper a senstvty based approach has been presented to study mpact of UPFC placement n loadng margn enhancement under crtcal contngences consderng lne as well as generator outage cases. The effectveness of the proposed method of UPFC placement has been establshed on a practcal 75-bus Indan system representng Uttar Pradesh State Power Corporaton Network. II. UPFC MODEL In the present work, UPFC has been represented by steadystate necton model [5],[11]. The UPFC conssts of two swtchng converters operated from a common DC lnk, as shown n fgure-1 [12]. In ths fgure, the seres converter of UPFC (Converter-2) has been assumed to be connected between buses and havng voltages V andv, 541

2 Ffteenth Natonal Power Systems Conference (NPSC), IIT Bombay, December 2008 respectvely. Converter-2 nects an AC voltage V s wth controllable magntude and phase angle n seres wth the transmsson lne. Converter-1 (shunt converter) nects or absorbs an ndependently controllable reactve power to bus-. Ths s represented by the current, I q. It also supples or absorbs the actve power demanded by Converter-2, through the common DC lnk. Ths s represented by the current, I p. In (1), varables r and control magntude and phase angle of nected voltagev s, r max represents maxmum lmt of varable r. In the present work, r max has been taken as 0.2 consderng t as a reasonably hgh value. V V represents complex voltage at bus-. The steady-state necton model of UPFC has been derved from fgure-2 [5] and has been shown n fgure-3. In fgure -3 UPFC has been represented as controllable loads connected at buses and. In [4], shunt converter has been represented as a constant voltage varable reactve power source, whereas seres converter has been consdered as a varable reactance n the lne. Ths model of UPFC gnores phase-shfter acton of seres converter. Steady-state necton model of UPFC overcomes ths lmtaton. Fgure-1: UPFC schematc dagram The UPFC crcut arrangement has been shown n fgure-2. In ths fgure, the seres converter has been represented by an AC voltage source V s n seres wth a reactance X s. The shunt converter has been represented as an ndependently controllable reactve power Q conv1 nected to or absorbed from bus-. In addton, ths converter also supples or absorbs real power to the seres converter through the common DC lnk. P conv1 I and I represent current flowng from bus- to V ' represents bus- and from bus- to bus-, respectvely. complex voltage of a fcttous bus-'. Fgure-2: UPFC crcut arrangement The seres voltage source Vs s controllable n magntude and phase and can be gven by: V s = r V e (1) 0 < r < r max and 0 < < 2 Fgure-3: UPFC necton model III. METHODOLOGY The proposed senstvty based approach for determnaton of the optmal locaton of UPFC s descrbed below: The reactve power balance equaton at bus- can be gven by: QG ( QD K S sn ) Q k n 1 k V b V Y D base sn ( QG = Reactve power generaton at bus QD b = Reactve power demand at bus- at the base case operatng pont Q k = Reactve power flowng from bus- to bus-k = Loadng factor common to all the buses K D = Constant multpler showng the rate of change of load at the th bus S base =Mega Volt Ampere (MVA) base used for scalng to equvalent Mega Volt Ampere Reactve (MVAR) load ncrease. = power factor angle of the ncreased load at th bus V = Complex voltage at bus Y =G + BB = th element of the bus admttance matrx n= Total number of the buses n the system ) (2) 542

3 Ffteenth Natonal Power Systems Conference (NPSC), IIT Bombay, December 2008 In [4], senstvty of loadng factor wth respect to reactve power generaton at bus- (/QG ), and senstvty of loadng factor wth respect to reactance X of a lne connected between buses and (/X ), have been derved from reactve power balance equaton (2) as: V 1 2V B QG V V V V QG QG (3) 1 n QG K D S base sn Ysn V V Ycos 1 QG QG 1 V V V cos (4) X K D S basesn 2 X The senstvty factors /QG and /X have been used n [4] to determne prorty buses for the placement of shunt converter and prorty lnes for the placement of seres converter, respectvely. However, the senstvty factor /X has been obtaned by neglectng the senstvty terms relatng change n complex voltages wth respect to lne reactance (.e. Vk k and, k = 1,., n, have been neglected). Ths X X may result n naccurate selecton of prorty lnes. Therefore, a new senstvty, whch relates changes n loadng Q k factor wth respect to change n reactve power flowng from bus- to bus-k has been proposed n ths work. Ths senstvty factor has been obtaned by dfferentatng reactve power balance equaton (2) wth respect to Q k and s gven as: Y Q k 1 [ Z 1 (1 X ) 1] V V V n V Y sn( ) QG QG X (6) 1 k V V Y cos( ) QG QG Y K D S sn (7) base Qk Vk V Z V Vk Yk sn( ) QG QG QG (8) k V V Yk cos( k ) QG QG The senstvty factor can be computed usng (5) for Q k each of the lnes under system ntact case and crtcal contngency cases. Each lne s havng two such senstvty (5) values ( and ). Based on maxmum absolute value Q k Qk of senstvty factors computed for system ntact case and crtcal contngency cases, prorty lnes for the placement of seres converter of UPFC have been determned. Dependng upon magntude of and correspondng to prorty Q k Qk lnes, bus- or bus-k can be consdered as prorty buses for the placement of shunt converter. If s havng hgher absolute value compared to Q k Q k bus- s consdered as the prorty bus for the placement of shunt converter. On the other hand, f s greater n magntude compared to Q k Qk bus-k s consdered as the prorty bus. The loadng margn (the dstance between the base case operatng pont and the nose pont) can be computed after UPFC placement at each of the canddate locatons for the system ntact case and crtcal contngency cases. The combnaton of prorty lne and prorty bus producng maxmum enhancement n loadng margn for maorty of the crtcal contngences has been selected as the optmal ste for UPFC placement. Snce voltage nstablty occurs at the maxmum loadablty pont, the Q k senstvtes have been calculated for each of the lnes at a stressed pont close to the maxmum loadablty pont. The partal dervatves V/QG, /QG, ( = 1,,n) n (6) & (8) can be derved for dfferent buses from the nverse Jacoban matrx of the full Newton Raphson Load Flow (NRLF) n polar Form. An addtonal crteron for optmal placement of the UPFC n ths work has been that UPFC should not be placed at generator buses. The placement of UPFC s a plannng ssue accuracy s mportant and computatonal speed s nsgnfcant. Therefore, crtcal contngences have been dentfed based on post-contngency loadng margns computed usng contnuaton power flow method [13]. In order to obtan loadng margns, real power generatons, real and reactve power demands have been vared as per followng: PG 1 (9) PG b PG = Real power generaton at bus- PG b = Real power generaton at bus- at the base case operatng pont. PD PD b 1 (10) PD = Real power demand at bus- PD b = Real power demand at bus- at the base case operatng pont 543

4 Ffteenth Natonal Power Systems Conference (NPSC), IIT Bombay, December 2008 QD QD b 1 (11) where QD =Reactve power demand at bus- IV. CASE STUDIES The proposed method of placement of UPFC controller has been tested on a practcal 75-bus Indan system representng Uttar Pradesh State Power Corporaton Network. The 75-bus Indan system has 15 generators (at buses 1-15) and 98 transmsson lnes (ncludng 24 transformers). Ths system has been taken from [14] wth loadngs reduced to 90% of orgnal values. The loadng margn for the system ntact case & contngency cases (consderng lne and generator outages) were obtaned usng contnuaton power flow based software package UWPFLOW [15]. Whle runnng repeated load flows real power generatons, real and reactve power demands were ncreased as per equatons (9), (10) & (11), respectvely. The crtcal contngences were obtaned based on post contngency loadng margns. Based on post contngency loadng margns crtcal contngences were ndentfed to be the outages of lnes 29-30, 36-37, 74-73, 23-29, 29-75, 22-25, 55-44, 26-22, 44-15( generator-15) and n the order of relatve severty. The proposed senstvty factors Q k were calculated for all the lnes usng (5) at a loadng value correspondng to 90% of maxmum loadng value for the system ntact case and for each of the crtcal contngences. The absolute value of these senstvty factors for two most senstve lnes for the ntact case and crtcal contngency cases are shown n Table-I. It s observed from Table-I that lne (towards bus-29) has maxmum value of senstvty factor for outages of lnes 23-29, 55-44, and (generator-15). Lne (towards bus-39) has maxmum value of senstvty factor for the system ntact case and for the outage of lne Lne (towards bus-35) has maxmum value of senstvty factor for the outage of lne Lne (towards bus-54) has maxmum value of senstvty factor for the outage of lnes and Lne (towards bus-43) has maxmum value of senstvty factor for outage of lnes and Hence, lnes (towards bus-29), (towards bus-39), (towards bus-35), (towards bus-54), (towards bus-43) were consdered as prorty locatons for the placement of UPFC. The loadng margn for the ntact system and for the crtcal contngency cases, wth UPFC placed n each of the prorty locatons were calculated usng repeated load flows. For obtanng maxmum loadablty ponts, startng from the base case operatng pont, loads were gradually ncreased n the steps of 0.01, untl load flow dverged (loads were ncreased n the steps of near the pont of dvergence to get more accurate estmate of loadng margns). Whle runnng repeated load flows steady-state necton model of UPFC [5] was consdered and real power generatons, real and reactve power demands were ncreased as per equatons (9), (10) & (11), respectvely. The loadng margns wthout UPFC and wth UPFC placed n prorty locatons for the system ntact case & crtcal contngency cases are shown n Tables II and III. It s observed from Tables II and III that UPFC placement n lne (towards bus-29) causes maxmum enhancement n voltage stablty margn for system ntact case and for most of the severe outage cases. Hence, lne (towards bus-29) was consdered as the optmal locaton for UPFC placement. TABLE I ABSOLUTE VALUE OF FOR TWO MOST SENSITIVE Q k LINES 75 BUS INDIAN SYSTEM Outage Lne Lne (Towards bus) k Q (Towards bus) Q k Intact System (No outage) (39) (43) (35) (39) (54) (43) (Generator -15) (54) (18) (36) (35) (63) (35) (45) The voltage profles of most crtcal bus for ntact case and for the crtcal contngency cases were plotted usng UWPFLOW & MATLAB. Fgure-4 shows the voltage profle of most crtcal bus for the ntact system wth and wthout UPFC controller placed n the system. The voltage profle of the most crtcal bus for the three most severe outage cases (vz. outage of lnes 29-30,36-37,74-73) are shown n fgures 5, 6 and 7, respectvely. It s observed from fgures 4, 5, 6 and 7 that placement of UPFC at the optmal locaton results n sgnfcant enhancement n voltage stablty margns. 544

5 Ffteenth Natonal Power Systems Conference (NPSC), IIT Bombay, December 2008 TABLE II IMPACT OF UPFC ON LOADING MARGIN (75-BUS INDIAN SYSTEM) Loadng Margn TABLE III IMPACT OF UPFC ON LOADING MARGIN (CONTINUED) (75-BUS INDIAN SYSTEM) Loadng Margn Outage Wthout UPFC Controller Wth UPFC n lne towards bus- 29 Wth UPFC n lne towards bus-43 Outage Wthout UPFC Controller Wth UPFC n lne towards bus-39 Wth UPFC n lne towards bus-54 Wth UPFC n lne towards bus-35 Intact System (No Outage) Intact System (No Outage) * (Generator -15) (Generator-15) *Load flow dvergence Fgure 4: Voltage profle of the most crtcal bus for the ntact case for 75 -bus Indan System Fgure 5: Voltage profle of the most crtcal bus under lne outage for 75 -bus Indan System 545

6 Ffteenth Natonal Power Systems Conference (NPSC), IIT Bombay, December 2008 Fgure 6: Voltage profle of the most crtcal bus under lne outage for 75 -bus Indan System Fgure 7: Voltage profle of the most crtcal bus under lne outage for 75 -bus Indan System V. CONCLUSION A senstvty based approach has been proposed n ths paper for the optmal placement of UPFC n power system to enhance voltage stablty under contngences. The senstvty of loadng parameter () wth respect to reactve power flowng through lnes has been computed to decde optmal locaton for the placement of UPFC. From the case studes carred out on 75-bus Indan system, a consderable ncrease n loadng margn have been observed after UPFC placement at the optmal locaton. These senstvty factors can be easly computed and are qute smple to adopt. REFERENCES [1] Jame De La Ree, Ylu Lu, Lamne Ml, Arun G. Phadke, and Luz Daslva, Catastrophc falures n power systems: Causes, Analyses, and Countermeasures, Proceedngs of the IEEE, Vol. 93, No. 5, pp , May [2] Clark H.K, New challenge: voltage stablty, IEEE Power Engneerng Revew, pp , Aprl [3] N G. Hngoran, and L. Gyugy, Understandng FACTS: Concepts and Technology of Flexble AC Transmsson Systems, IEEE Press, New- York, [4] M.K.Verma and S.C.Srvastava Enhancement of voltage stablty margn under contngences usng FACTS controllers Proc. of the Internatonal Conference on Power System Operaton n Deregulated Regme, IT-BHU, Varanas (Inda), pp , March 6-7, [5] H.A. Abdelsalam, G.E. M. Aly, M. Abdelkrm and K.M. Shebl, Optmal locaton of the Unfed Power Flow Controller n electrcal power system, Proc. of the Large Engneerng Systems Conference on Power Engneerng LESCOPE-2004, Westn Nova Scotan, pp , July 28-30, [6] D. Thukaram, L. Jenkns and K. Vsakha, Improvement of system securty wth unfed-power flow controller at sutable locatons under network contngences of nterconnected systems, IEE Proc.-Gener. Transm. Dstrb., Vol. 152, No. 5, pp , September [7] Weshao and Vay Vttal, LP based OPF for correctve FACTS control to releve overloads and voltage volatons, IEEE Trans on Power Systems, Vol. 21, No. 4, pp , November [8] M. Saravanan, S. Mary Raa Slochanal, P. Venkatesh, Prnce Stephen Abraham. J Applcaton of PSO technque for optmal locaton of FACTS devces consderng system loadablty and cost of nstallaton, Power Engneerng Conference, Sngapore, Vol- 2, pp , Nov 29- Dec 2, [9] S.T.Jaya Chrsta and P.Venkatesh, Applcaton of Partcle Swarm Optmzaton for optmal placement of Unfed Power Flow Controllers n electrcal Systems wth lne outages, Internatonal Conference on Computatonal Intellgence and Multmeda Applcatons,, Svakas (Inda), Vol. 1, pp , Dec [10] J. Hao, L.B. Sh and Ch. Chen, Optmsng locaton of unfed power flow controllers by means of mproved evolutonary programmng, IEE Proc.-Gener. Transm. Dstrb., Vol. 151, No. 6, pp , November [11] M. Noroozan, L. Angust, M. Ghandhar and G. Andersson, Use of UPFC for optmal power flow control, IEEE Trans. on Power Delvery, Vol. 12, No. 4, pp , October [12] L. Gyugy, C. D. Schauder, S. L. Wllams, T. R. Retman, D. R. Togerson and A. Edrs, The Unfed Power Flow Controller: A new approach to power transmsson control, IEEE Trans. on Power Delvery, Vol. 10, No. 2, pp , Aprl [13] Venkataramana Aarapu and Coln Chrsty, Contnuaton Power Flow: A tool for steady state voltage stablty analyss, IEEE Trans. on Power Systems, Vol. 7, No. 1, pp , February [14] S.N.Sngh and S.C. Srvastava, Correctve acton plannng to acheve optmal power flow soluton, IEE Proceeedngs, Part C, Vol. 142, pp , November [15] Software Package UWPFLOW avalable at Sreekanth Reddy Donapat (b 1984) receved B. Tech. degree n Electrcal Engneerng from Bapatla Engneerng College, Andhra Pradesh, Inda n 2006 and M. Tech. Degree from Insttute of Technology, Banaras Hndu Unversty, Varanas, Inda n Presently he s workng n Relance Infrastructure Lmted, Noda, Inda. Hs research nterests nclude voltage stablty studes and applcaton of FACTS controllers. M. K. Verma (b 1965) receved B. Tech. degree n Electrcal Engneerng from NIT, Rourkela (Inda) n 1989, M. Tech. degree from BIT, Sndr (Inda) n 1994 and Ph.D. degree from Indan Insttute of Technology, Kanpur (Inda) n Presently he s a Reader n Electrcal Engneerng Department at Insttute of Technology, Banaras Hndu Unversty, Varanas, Inda. Hs research nterests nclude voltage stablty studes, applcaton of FACTS controllers, power system dynamcs and operaton and control of modern power systems. 546