Optimal Location of Multi Type Facts Devices for Multiple Contingencies Using Particle Swarm Optimization

Transcription

1 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng Optmal Locaton of Mult Type Facts Devces for Multple Contngences Usng artcle Swarm Optmzaton S. Sua, and N. Kamaraj Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 Abstract In deregulated operatng regme power system securty s an ssue at needs due oughtfulness from researchers n e horzon of unbundlng of generaton and transmsson. Electrc power systems are exposed to varous contngences. Networ contngences often contrbute to overloadng of branches, volaton of voltages and also leadng to problems of securty/stablty. To mantan e securty of e systems, t s desrable to estmate e effect of contngences and pertnent control measurement can be taen on to mprove e system securty. Ths paper presents e applcaton of partcle swarm optmzaton algorm to fnd e optmal locaton of mult type FACTS devces n a power system n order to elmnate or allevate e lne over loads. The optmzatons are performed on e parameters, namely e locaton of e devces, er types, er settngs and nstallaton cost of FACTS devces for sngle and multple contngences. TCSC, SVC and UFC are consdered and modeled for steady state analyss. The selecton of UFC and TCSC sutable locaton uses e crtera on e bass of mproved system securty. The effectveness of e proposed meod s tested for IEEE 6 bus and IEEE 30 bus test systems. Keywords Contngency Severty Index, artcle Swarm Optmzaton, erformance Index, Statc Securty Assessment. I. INTRODUCTION OWER system securty, congeston management, power qualty and power regulatons are major concepts at draw e attenton of power researchers n deregulated surroundngs. Securty assessment s an ssue of utmost grandness under open maret access system to render auentc and procure electrcty to ts customers under all condtons. In a day to day operaton t may be beyond e operator scope to tae preventve control durng emergences. However, e operator can use varous control devces and FACTS devces to restore e system to normal condtons [], [2]. Contngency screenng and ranng s one of e components of on-lne system securty assessment. The target of contngency ranng and screenng s to rapdly and S. Sua s w e Electrcal Engneerng Department,.S.N.A College of Engneerng and Technology,Dndgul,Tamlnadu, Inda (correspondng auor phone No: ; e-mal: suapadmanabhan@lycos.com). N. Kamaraj s w e Electrcal Engneerng Department, Thagarajar College of Engneerng, Madura, Tamlnadu, Inda (e-mal: neee@tce.edu). precsely grade e decsve contngences from a large lst of plausble contngences and ran em accordng to er severty for furer rgorous analyss. Varous I-based meods for contngency screenng and ranng have been reported n lterature [3]-[6]. FACTS devces are sold state converters at have e capablty of control of varous electrcal parameters n transmsson networs. FACTS devces nclude Thyrstor Controlled Serous Compensator (TCSC), Statc Var Compensator (SVC), Unfed ower Flow Controller (UFC) and Statc Compensator (STATCOM) etc. [7] FACTS devces control e power flow n e networ, reduces e flow n e heavly loaded lnes ere by resultng n an ncrease loadablty, mproved securty and stablty of e networ are reported n [8], [9]. Thyrstor Controlled Seres Compensator (TCSC) s one such devce whch offers smoo and flexble control for securty enhancement w much faster response compared to e tradtonal control devces [0]. Unfed ower Flow Controller (UFC) s capable of provdng actve, reactve and voltage magntude control under normal and networ contngences condtons wout volatng e operatng lmts []. opulaton based co-operatve and compettve stochastc search algorms are very popular n e recent years n e research area of computatonal ntellgence. Some well establshed search algorms such as GA [2] and Evolutonary rogrammng [3] are successfully mplemented to solve e complex problems. The SO algorm was ntroduced by Kennedy and Eberhart [4],[5] and furer modfcatons n SO algorm were carred out n [6]. SO s appled for solvng varous optmzaton problems n electrcal engneerng [7], [8]. In s paper, utlzaton of e mult type devces, combnaton of TCSC and UFC durng sngle and double contngences s nvestgated. UFC s modeled as a combnaton of a TCSC n seres w a lne and SVC connected across e correspondng buses between whch e lne s connected. Contngency severty ndex values are calculated for every branch usng [9]. Ths ndex s used to decde on e best locaton for e mult type devces. Once located, e type and optmal settngs of FACTS devces w respect to sngle and multple contngences can be obtaned by optmzaton. The objectves used n s problem are elmnatng or allevatng e lne overloads and mnmzng e nstallaton cost of e mult type FACTS devces. Internatonal Scholarly and Scentfc Research & Innovaton 2(0)

2 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 Computer smulatons are done for IEEE 6 bus, IEEE 30 bus test systems. From e test results t s observed at e number of over loads and nstallaton cost are reduced after placng certan number of FACTS devces. Furer ncrease of FACTS devces, shows no mprovement n reducton of overloadng or cost of nstallaton. II. ROBLEM FORMULATION A. Optmal lacement of FACTS Devces The essental dea of e proposed mult type FACTS devces, UFC and TCSC placement approaches s to determne a branch whch s most senstve for e large lst of sngle and multple contngences. Ths secton wll descrbe e defnton and calculaton of e contngency severty ndex CSI and e optmal placement procedure for e UFC and TCSC. The partcpaton matrx U: Ths s an (m x n) bnary matrx, whose entres are or 0 dependng upon wheer or not e correspondng branch s overloaded, n s e total number of branches of nterest, and m s e total number of sngle and multple contngences. The rato matrx W: Ths s an (m x n) matrx of normalzed excess (overload) branch flows. It s (, j) element, w j s e normalzed excess power flow (w respect to e base case flow) rough branch j durng contngency and s gven by :, j cont j, cont W j = () oj, Base, - ower flow rough branch j durng oj Base Contngency, - Base case power flow rough branch j. The Contngency probablty array : Ths s an (m x ) array of branch outage probabltes. The probablty of branch outage s calculated based on e hstorcal data about e faults occurrng along at partcular branch n a specfed duraton of tme. It wll have e followng form: T = ] (2) mx [ p p2... p m - robablty of occurrence for contngency and s taen as m - The number of contngences Thus e CSI for branch j s defned as e sum of e senstvtes of branch j to all e consdered sngle and multple contngency, and s expressed as CSI j = m = p u j w j (3) u j and w j are elements of matrces U and W respectvely. CSI values are calculated for every branch by usng (3). Branches are en raned accordng to er correspondng CSI values. A branch has hgh value of CSI wll be more senstve for securty system margn. The branch w e largest CSI s consdered as e best locaton for FACTS devce. B. Optmal Settngs of FACTS Devces In s paper UFC s modeled as combnaton of a TCSC n seres w e lne and SVC connected across e correspondng buses between whch e lne s connected. After fxng e locaton, to determne e best possble settngs of FACTS devces for all possble sngle and multple contngences, e optmzaton problem wll have to be solved usng SO technque. The objectve functon for s wor s, obj = mnmze { SOL and IC} m n a c = = = SOL (4), m - Number of sngle contngency consdered n - Number of lnes a - weght factor=. - real power transfer on branch. - mum real power transfer on branch. IC - Installaton cost of FACTS devce SOL - Represents e severty of overloadng Installaton cost ncludes e sum of nstallaton cost of all e devces and t can be calculated usng e cost functon gven by, 2 C TCSC = 0.005S 0.7S ( US$ / KVAR) (5) 2 C UFC = S 0.269S ( US$/ KVAR) (6), S - Operatng range of UFC n MVAR S = Q 2 Q Q MVAR flow rough e branch before placng Q 2 - FACTS devce. MVAR flow rough branch after placng FACTS devce. The objectve functon s solved w e followng constrants:-. Voltage Stablty Constrants VS ncludes voltage stablty constrants n e objectve functon and s gven by, 0 f 0.9 < Vb <. VS = Vb f Vb < 0.9 (7) Vb -. f Vb >. 4 Internatonal Scholarly and Scentfc Research & Innovaton 2(0)

3 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 Vb - Voltage at bus b 2. FACTS Devces Constrants The FACTS devce lmt s gven by, 0.5 X L < X TCSC < 0. 5 X L 200 MVAR QSVC 200 MVAR (8) X L - orgnal lne reactance n per unt X TCSC - reactance added to e lne UFC s placed n per unt Qsvc - reactve power njected at SVC placed bus n MVAR 3. ower Balance Constrants Whle solvng e optmzaton problem, power balance equatons are taen as equalty constrants. The power balance equatons are gven by, G = + D L (9) G Total power generaton D Total power demand L Losses n e transmsson networ = E E G cos( θ θ ) + B sn( θ θ )](0) [ Q = E E G sn( θ θ ) + B cos( θ θ )] () [ Real power njected at bus. Q Reactve power njected at bus. θ, θ The phase angles at buses and respectvely. E, E Voltage magntudes at bus and respectvely. G, B Elements of Y bus matrx. III. OVERVIEW OF SO AND ITS IMLEMENTATION FOR OTIMAL LOCATION OF FACTS DEVICES SO s ntalzed w a group of random partcles and e searches for optma by updatng generatons. In every teraton each partcle s updated by followng two best values. The frst one s e best soluton (ftness value) t has acheved so far. Ths value s called best. Anoer best value at s traced by e partcle swarm optmzer s e best value obtaned so far by any partcle n e populaton. Ths best value s e global best called Gbest. After fndng e best values e partcles update ts velocty and poston w e followng equaton: + ( S ) + C * rand *( G S ) V = W (2) * V + C * rand * best = S + V S (3) W W W mn = W ter * ter (4) V = Velocty of agent at teraton + V = Velocty of agent at ( + ) teraton W = The nerta weght C = = Weghtng Factor (0 to 4) C 2 S = Current poston of agent at teraton + S = Current poston ofagent at (+ ) teraton ter = Maxmum teraton number ter = Current teraton number = of agent best best best G = of e group G best W = Intal value of nerta weght = 0.9 W = Fnal value of nerta weght = 0.2 mn The velocty of e partcle s modfed by usng (2) and e poston s modfed by usng (3). The nerta weght factor s modfed accordng to (4) to enable quc convergence. Calculaton of ftness functon: Ftness functon = SOL + ( λ VS ) + ( λ2 IC ) (5) λ enalty factor λ - Scalng factor 2 Algorm: Step. The bus data, lne data, and number of FACTS devces are gven as nputs Step 2. The ntal populaton of ndvduals s created n normalzed form so as to satsfy e FACTS devce s constrants gven by (8) Step 3. Step 4. best For each ndvdual n e populaton, e ftness functon s evaluated by usng (5) n denormalzed form after smulatng all possble sngle and multple contngences by usng AC Load flow The velocty s updated by usng (2) and new populaton s created by usng (3) Internatonal Scholarly and Scentfc Research & Innovaton 2(0)

4 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng Step 5. Step 6. If mum teraton number s reached, en go to next step else go to step 3 rnt e best ndvdual s settngs. TABLE II OVER LOADING OF BRANCHES- BEFORE AND AFTER LACING MULTI TYE FACTS DEVICES IV. RESULTS AND DISCUSSION The solutons for optmal locaton of FACTS devces to mnmze e nstallaton cost of FACTS devces and overloads for IEEE 6 bus, IEEE 30 bus test systems were obtaned and dscussed n s secton. The smulaton studes were carred out on Intel entum IV rocessor computer w 3GHZ, 256MB RAM, 40GB Hard drve usng MATLAB 7.0 verson. Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 A. IEEE 6-Bus, Eleven Branch System The bus data and lne data of e sx bus test system are taen from [20]. Ths system s analyzed foe bo sngle and double contngences.. Sngle Contngency The locaton of FACTS devces depend upon e CSI values whch are calculated for branches by consderng all sngle contngences. Then e branches are raned accordng to er values of CSI whch are gven n Table I. 2. Double Contngency Consderng two branches outaged at a tme for branches, 55 double contngency combnatons are avalable. Consderng all e double contngency combnatons, e branches are raned based on er CSI values are gven n Table I. TABLE I RANKING OF BRANCHES FOR IEEE 6-BUS SYSTEM Table I shows at, branch number -2, 3-6 s chosen as e best locaton to place e frst avalable mult type FACTS devces for sngle and double contngences. Dependng on e avalable budget, e placement of oer FACTS devces can proceed branch 2-6, 2-3 wll be e second choce, branch -4, -2 are e rd choce and so on. Once e locaton s determned, er type, er optmal settngs and cost of nstallaton can be obtaned by solvng e optmzaton problem usng SO. The Table II shows e overloadng of branches when dfferent numbers of FACTS devces are nstalled. Table II shows at e severty ndex (SOL) and e number of overloads are reduced from 23 to 5 when four FACTS devces are placed for sngle contngences and 88 to 75 when ree FACTS devces are placed for double contngences. Furer ncrease of devces, shows no mprovement n reducton of severty, overloadng and cost of nstallaton, raer ey start ncreasng. Hence n s case, four and ree number of FACTS devces s consderable for optmal system securty for sngle and double contngences. The optmal settngs, lne number and e type of devce are obtaned by solvng optmzaton algorms usng SO s gven n Table III. TABLE III OTIMAL SETTINGS MULTI TYE FACTS DEVICES Internatonal Scholarly and Scentfc Research & Innovaton 2(0)

5 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng ) No. of populaton = 30 ) Max Generaton = 50 ) C =C 2 = 2 Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 Fg. Ftness convergence curve for IEEE 6Bus system-sngle contngency Fg. 2 Ftness convergence curve for IEEE 6Bus system-double contngency Fg. and Fg. 2 represent e ftness convergence curve for IEEE 6 bus system for sngle and double contngences. Number of populaton taen n X axs and Ftness functon taen n Y axs. The smulaton carred out w multple runs to get e optmal results of mult-type FACTS devces. SO parameters used n s wor are: B. IEEE 30-Bus, Forty one Branch Systems The IEEE 30 bus system conssts of 4 branches. Lne data, bus data are taen from [2]. Ths system s also analyzed for bo sngle and double contngences.. Sngle Contngency There are 4 possble contngences, leavng 3 branches(25-26,9-,2-3) connected to solated buses only 38 sngle contngences are consdered. The CSI ndex s calculated for all e 4 lnes consderng 38 contngences and e branches are raned and t s gven n Table IV. 2. Double Contngency Consderng two branches are outaged at a tme, for 4 branches, 820 double contngency combnatons are avalable. Leavng e branches connected to solated buses, e remanng double contngency combnatons are consdered n s wor. These contngences are raned based on CSI values whch are gven n Table IV. TABLE IV RANKING OF BRANCHES FOR IEEE 30-BUS SYSTEM After rang of e branches e SO algorm s used to fnd out e locaton of e devces, er types, and settngs to allevate e lne overloads and to mprove e system securty margn whch are gven n Table V and VI. Internatonal Scholarly and Scentfc Research & Innovaton 2(0)

6 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng TABLE V OVER LOADING OF BRANCHES - BEFORE AND AFTER LACING MULTI TYE FACTS DEVICES Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 TABLE VI OTIMAL SETTINGS OF MULTI TYE FACTS DEVICES Fg. 3 and Fg. 4 represent e ftness convergence curve for IEEE 30 bus system for sngle and double contngences. Number of populaton taen n X axs and Ftness functon taen n Y axs. SO parameters used n s wor are: ) No. of populaton = 25 ) Max Generaton = 00 ) C =C 2 = 2 Fg. 3 Ftness convergence curve for IEEE 30Bus system-sngle contngency Internatonal Scholarly and Scentfc Research & Innovaton 2(0)

7 World Academy of Scence, Engneerng and Technology Internatonal Journal of Electrcal and Computer Engneerng Internatonal Scence Index, Electrcal and Computer Engneerng waset.org/ublcaton/5754 Fg. 4 Ftness convergence curve for IEEE 30Bus system-double contngency V. CONCLUSION Ths paper presents a procedure to place mult type FACTS devces along e system branches based on e contngency severty ndex (CSI) values to allevate system overloads and to mprove e system securty margn durng sngle and double contngences. TCSC and UFC, e combnaton of TCSC and SVC were consdered n s wor. Smulatons were performed on IEEE 6 and 30 bus systems. The locaton of mult type FACTS devces, e type of devce to be placed, and er settngs were taen as e optmzaton parameters for bo sngle and double contngences. In bo sngle and double contngences, t s observed at e system securty margn cannot be mproved furer after placng certan optmal number of mult type FACTS devces. These settngs can be effectvely used on-lne to enhance e system securty margn wout nvestng n addtonal transmsson resources. IEEE 6 bus, IEEE 30 bus test systems are used to evaluate e performance of s approaches. Numercal results confrm e effectveness of e proposed procedures. REFERENCES [] aserba, N.Mller, E.Laesen and R.wo, A Thyrstor controlled seres compensaton model for power system stablty analyss," IEEE Trans.on ower-delvery, vol. 0, pp , 995. [2] Stephane Gerbex, Rachd Cheraou, and Alan J.Germond,"Optmal locaton of mult type FACTS devces n a power system by means of genetc algorms,," IEEE Trans. on ower Systems, vol.6, pp ,August 200. [3] G. C. Ejebe and B. F. Wollenberg, "Automatc contngency selecton," IEEE Transs. on AS, Vol. AS-98, pp.97-09, 979. [4] T. A. Molnas and B. F. Wallenberg, "An advanced contngency selecton algorm," IEEE Trans. On AS, Vol. AS-00, pp , Feb. 98. [5] G. Lauby, T. A. Molnnas, N. D. Reppen, Contngency selecton of branch outages causng voltage problems," IEEE Trans. on AS, vol. AS-02, pp , Dec [6] Y. Chen and A. Bose, Drect ranng for voltage contngency electon, IEEE Trans. on ower Systems, vol.4, pp , Oct [7] N. G. Hngoran and L. Gyugy, Understandng FACTS Concepts and Technology of Flexble AC Transmsson Systems, scataway: IEEE ress, 999. [8] S. Krshna, K. R. adyar, Dscrete control of unfed power flow controller for stablty mprovement, Electr.ower Systems. Research, vol.75, pp78-89, [9] Ahad Kazem, Mahmoud Val Sohrforouzan, ower system dampng usng fuzzy controlled facts devces, Electr. ower and Energy Systems. vol.28, pp , [0] Garng Huang and Tong Zhu, TCSC as a transent voltage stablzng controller, IEEE conference proceedng, pp , 200. [] K. Vsaha, D. Thuaram. Lawrencee Jenns, Applcaton of UFC for system securty mprovement under normal and networ contngences, Electr. ower Systems. Research, vol.70, pp46-55, [2] S. Gerbex, R.Cheraou, and A.J.Germond, "Optmal locaton of multtype FACTS devces by means of genetc algorms, IEEE Trans. on ower-systems, vol. 6, pp , 200. [3]. Venatesh, R.Gnanadass, N..adhy,"Comparson and applcaton of evolutonary programmng technques to combned economc emsson dspatch w lne flow constraned," IEEE Trans. on ower Systems, vol.8, pp , [4] J. Kennedy, R. Eberhart, "artcle swarm optmzaton n, roceedngs of e IEEE Internatonal Conference on Neural Networs, pp [5] Y. Sh, R. C. Eberhart, "Emprcal study of partcle swarm optmzaton n, roceedngs of e Internatonal Congress on Evolutonary Computaton, vol.3, pp. 0-06, 999. [6] Ratnaweera, S.K.Halgamuge, H.C.Watson"Self-organzng herarchcal partcle swarm optmzer w tme varyng acceleraton coeffcents," IEEE Trans.onEvol.Comput, vol 8, pp , June [7] H. Yoshda, K.Kawata, Y.Fuuyama, S.Taayama and Y.Naansh, "A partcle swarm optmzaton for reactve power and voltage control consderng voltage securty assessment,"ieee Trans.on ower Systems, vol.5, pp , [8] M. Saravanan, S.Mary Raja Slochanal,.Venatesh, J.rnce Stephen Abraham, Applcaton of partcle swarms optmzaton technque for optmal locaton of FACTS devces consderng cost of nstallaton and system loadablty,"electr. ower Systems. Research, vol.77, pp , [9] Yunqang Lu, Al Abur, Statc securty enhancement va optmal utlzaton of Thyrstor-Controlled Seres Capactors, IEEE Trans. ower System., vol.7, pp , May [20] Allen J.Wood, Bruce F.Wollenberg, ower Generaton Operaton and Control, Wley publcaton, [2] M. A. a, Computer Technques n ower System Analyss. New Delh, Tata McGraw-Hll, 979. Internatonal Scholarly and Scentfc Research & Innovaton 2(0)