Optimal Allocation of FACTS Devices to Enhance Total Transfer Capability Based on World Cup Optimization Algorithm

Transcription

1 World Essays Journal / 5 (): Avalable onlne at www. worldessaysj.com Optmal Allocaton of FACS Devces to Enhance otal ransfer Capablty Based on World Cup Optmzaton Algorthm Farzn mohammad bolbanabad avd taghzadegan kalantar Electrcal Engneerng Department Faculty of Engneerng Azarbajan Shahd Madan Unversty abrz Iran Correspondng Author emal: Farzn.mohammad99@gmal.com Abstract: In ths paper a new optmzaton algorthm called world cup optmzaton s proposed to acheve the optmal allocaton of FACS devces for mzng the total transfer capablty of power transactons between source and snk areas n a power system. World cup optmzaton algorthm n ths study searches for the locaton and the sze of FACS. Mult-objectve OPF wth consderng penalty functon wll be performed to solve and handle dfferent nequalty constrants. For analyzng the performance of the proposed method t has been appled on IEEE 4 bus system. Fnal smulatons show that the world cup optmzaton based method gves good results whch may be used for onlne total transfer capablty calculaton and even the optmzed method could enhance the transfer capablty calculaton value far more than OPF wthout FACS devces. Keywords: otal ransfer Capablty (C); hyrstor Controlled Seres Compensator (CSC); world cup optmzaton algorthm IRODUCIO In the last years by ncreasng the compettve market about the electrc power systems electrc utltes are forced to operate ther facltes at a hgher effcency. Flexble AC ransmsson Systems (FACS) can be utlzed n the exstng power systems to control mprove system dynamcs power flow and ncrease system relablty [. In addton FACS devces can be also employed for mprovng the power system transfer capablty [ 3. otal ransfer Capablty (C) s a sgnfcant ndex n power markets whch s descrbed as the amount of electrc power that can be transferred from one area to another over the nterconnected transmsson network n a relable manner based on pre-contngency and post- contngency condtons [4. For enhancng the open-access of transmsson systems we need to calculate each control area and posted on a publc communcaton system by provdng a market sgnal of the capablty of the transmsson systems to delver electrc energy [5. here are great deals of methods whch have been developed for achevng C. hese methods can be categorzed nto four types ncludng: ) lnear AC (LAC) method [6 whch s based on lnear ncremental power flow approxmaton ) contnuaton power flow (CPF) method [7 and repettve power flow (RPF) method [8 whch utlze common loadng factor to determne C value and the last s optmal power flow (OPF) based method whch can be appled by optmzaton technques lke sequental quadratc programmng (SQP) [8 and transfer based securty constraned optmal power flow (SCOPF) method [9. For achevng an optmal soluton for the presented methods convexty of the cost functon s requred. Although the OPF problem s generally non-convex snce many local mnma are especally n a hghly nonlnear system when FACS devces are ncluded n the system [0. In addton the parameters FACS have addtonal control varables whch cannot be calculated by tradtonal OPF because of makng change n the admttance matrx. herefore tradtonal optmzaton approaches may converge to a local optmal value n order to ts drected search based on local nformaton. World cup optmzaton (WCO) algorthm whch s ntroduced by Razmjooy et al. s a new meta-heurstc algorthm based on the human socal sport compettons to get the cup (best soluton). WCO lke to the other compettve optmzaton algorthms starts wth an ntal populaton (teams) and the competton among them wll be contnued untl one of them reach the best soluton [. hs algorthm can acheve the global optmal pont by movng over hlls and across valleys. Because of ths WCO s more robust than the exstng drect search methods. Snce n ths research WCO algorthm s utlzed for descrbng the optmal allocaton of FACS devces for mzng the C of power transactons

2 World Essays J. Vol. 5 () between source and snk areas. In ths approach WCO seeks for FACS parameters and locatons real power generatons except slack bus n source area real power loads n snk area and generaton bus voltages to acheve the mum C value. Problem Formulaton For achevng the feasble C value of power transactons OPF wth FACS devces s utlzed. he man purpose n ths study s to mze the objectve functon whch s related to the power that can be transferred from a specfc set of generators n a source area to loads n a snk area subject to real and reactve power generaton lmts lne flow lmts voltage lmts and FACS devces operaton lmts. In ths research thyrstor-controlled phase shfter (CPS) thyrstor-controlled seres capactor (CSC) unfed power flow controller (UPFC) and statc var compensator (SVC) are employed. For applyng the steady-state studes mathematcal models of the FACS devces are utlzed. Hence for drect modfyng the reactance of transmsson lnes the CSC s modeled. From the [ njected power model s used to model the UPFC CPS and SVC. he fnal ftness functon s consdered as follows: Max PI Subject to: D _ SK PDI () m ( ) n ( ) () P P P ( ) P ( V ) V V Y ( )cos( ( ) ) 0 G D P PK U Uk UK j j S j S j k k j m ( ) n ( ) (3) Q Q Q ( ) Q ( V ) Q V V Y ( )sn( ( ) ) 0 G D P PK U Uk UK V j j S j S j k k j mn P P P G (4) G G G mn Q Q Q G (5) G G G mn V V V (6) S L S L L (7) 0 S S (8) (9) mn P P P 0 VU VU (0) U () Q Q Q () mn V V V Where PI s the objectve (ftness) functon and descrbes the total load n snk area. PD and QD are the real and reactve loads at bus. PG and QG are the real and reactve power generatons at bus respectvely. P and P are the lower and upper lmts of real power generaton at bus. Q and Q are the lower and mn G G upper lmts of reactve power generaton at bus. PP ( PK ) and QP ( PK ) defne the njected real and reactve powers of CPS at bus. ( ) and Y ( ) are the angle and magntude of the j th element n bus admttance matrx wth CSC ncluded. j S j S PU ( V ) and QU ( V ) descrbe the njected real and reactve powers of UPFC at bus. Q V s the fxed Uk UK Uk UK njected reactve power of SVC at bus. V and Vj are the voltage magntudes at bus and j respectvely. and are the voltage angles of bus and j. S L and mn V and V are the lower and upper lmts of voltage magntude at bus. S L are the th lne or transformer loadng and the th lne or transformer-loadng lmt. S defnes the vector of reactance of CSC. P s the phase shft angle of CPS at bus. V U s mn G G j 4

3 World Essays J. Vol. 5 () the voltage magntude of UPFC at bus. U s the voltage angle of UPFC at bus. s the total number of buses. G s the number of generators. L s the number of branches and D _ SK s the number of load buses n snk area. For provdng the nequalty constrants n the optmzaton process a penalty functon s consdered as below: ( x x ) f x x mn mn h( x ) ( x x ) f x x 0 f x x x mn mn where x has a a penalty functon as h(x ) and x and Snce the fnal objectve functon can be consdered as follows: D _ SK (3) x are the lower and upper bounds of x. Max PI PD h( x ) (4) World Cup Optmzaton algorthm World Cup Optmzaton (WCO) algorthm s a new Meta-heurstc optmzaton algorthm whch s nspred by the compettons among descrbed teams to become the champon. In ths algorthm based on the rank of compettve teams they stand n ther proper seeds [. Indeed rank has sgnfcant mpact on the compettons whch s acheved for each team accordng to ts fals and wns n the past challenges [3. By consderng the parameter rank n frst stronger teams fall nto the frst seed; the other teams by less strength have been fall nto the next seeds herarchcally. In the frst competton frst seed survve from the competton to save and upgrade tself to the hgher level. In the followng all the other teams n seeds challenge wth each other to acheve more scores to mprove ts rank and arse nto the next stage. After the prmary challenge two hgh pont teams n the seeds arse nto the next stage and the rest are omtted. It should be ponted that f the Play-Off s consdered the thrd place of each seed can also compete wth the rest teams wth the same condtons and the hghest score of these teams can be arse nto the hgher level of competton. he challenge wll be contnued untl one of teams acheves the hghest score. WCO algorthm can be summarzed as the followng steps: Step ) Intalze and generate random contnents and ther teams By consderng dmensonal ( ) optmzaton problem wth M contnents contnents wll have an array of var as follows: var Contnent country country country (5) [ var country [ x x x var where x s the th team n the country. he varable s values ( var (6) x x x ) descrbe the floatng pont number. he rank of the contnents can be acheved by consderng the rank ponts x x x ) as follows: var Rank f ( contnent ) f r r ( x x x Ovar ) f r n a contnent ( O M (8) where M s the number of contnents and descrbes the varables dmenson. Intalzng n WCO s the best part of ths algorthm; n ths step contnents consst of dfferent values of random teams by dfferent standard devaton. For mprovng the convergence tme an nterval s selected and gets the random values. Afterwards t s dvded nto parts wthn ther contnents. hs feature makes ths algorthm to have a faster convergence rather than the other algorthms. he generated contnents are matrces of sze pop var ; where and var pop are the number of varables n the problem and the number of teams respectvely. A number of random numbers of teams are also exst for the ntal contnents. Usually n the real FIFA compettons there are 5 contnents wth ther teams. Step ) Evaluatng Ftness Functon (7) 4

4 World Essays J. Vol. 5 () After the prelmnary competton among teams the next stage s to acheve the score ponts. hese ponts are not so clear; because there s may be a contnent wth some teams whch ncludes the most pont (optmum ftness) whle the others have weak ponts n the contnents. o solve ths problem s to compute the mean value and the standard devaton of the contnents as follows: n n n n ( ) where n s the number of members n descrbes the mean value of the contnent and s shows the standard devaton of the contnent. Step 3) Rankng stage In ths step teams are ranked by the followng approach: [ [ [ 5 otal 5 n n 5n [ n n n Where n s the number of teams for the contnents and descrbes the transpose operator. Durng ths process two optmal values for the contnents have been selected and perched to the other vector ( next compettons and the optmal values of Rank [ 5 5 have been selected as the frst cup's champon: otal (3) champon mn([ where mn( otal ) n n n ) s the mnmum value of the solutons. champon Rank (9) (0) () () ) for the Step 4) Apply the next stage of challenge among teams In ths part the next competton wll be performed by teams; new contnents and teams ncludng them wll be regenerated accordng to the prevous champonshp compettons and ther rankng. Here the algorthm does dfferently from the real FIFA competton. o do ths a vector wth two parts can be consdered: Pop where total [ s a random nteger n a defnte nterval Pop( ) descrbes the new generated teams of the sze ( M ) and s a vector as follows: L U U ac( Ub Lb) (7) (8) L ac( Ub Lb) where ac s a coeffcent between L b and U b as low and hgh bounds for the problem respectvely. Step 5) Applyng Exploraton and Explotaton and descrbe the exploraton and the explotaton operators. descrbes the process of possesson of the formerly search space and descrbes the process of generatng new random ntegers n the search space. he sze of and are separated by Cross Pont (CP) as follows: total (4) (5) (6) 43

5 World Essays J. Vol. 5 () Pop(: CP M ) Pop( CP : M ) Upgraded contnents n ths step are dvded nto m teams of n contnents as follows: [ Pop(: k) Pop [ new new new [ Pop( k : l) [ Pop( l : r) new [ Pop( r : s) Step 6) If the crteron s reached end the algorthm; otherwse repeat the algorthm. (9) (30) he Study System and Results In ths study IEEE 30 bus system has been utlzed to demonstrate sutablty of the proposed algorthm. Bus and lne data can be found n [4. he smulaton studes were carred out on Core -7 6 GB of RAM.6 GHZ system n MALAB 03 a platform. hree areas by two generators are ncluded n the system. he lmt of voltage and angle for UPFC are n the ntervals [0 0.(n per unt) and [-π π (n radan). he resstance of CSC s n the nterval [0 0.0 n per unt phase shfter angle lmtaton of CPS s n the nterval [0 0. n radan and the reactve power njecton lmt for SVC s n the nterval [0. MVAR. Dagram of the IEEE 30-bus system s shown n the Fg. (). Fgure. Sngle lne dagram of standard IEEE 30 Bus system able. C results from the IEEE 30-BUS system for the proposed method ransfer Wthout Facts Wth Facts From o C (MW) Lmt Condton C (MW) Lmt Condton 03.5 P G 4.98 Lne P G 68.3 Lne P G P G Lne P G Lne Lne Lne Lne -5 By usng the proposed optmzed method wthout FACS devces the load of area ncreases to 03.5 MW. he real power loads of area n bus number sequence are [ MW. he generaton upper lmts at bus form the lmtng condton. 44

6 World Essays J. Vol. 5 () Usng the proposed optmzed method make the C value from the transacton from area to area s ncreased to 4.98 MW durng mult-type of FACS devces are ncorporated n the system. Here SVC s nstalled at bus number 7 and CPS UPFC and CSC are nstalled at lne number 3 and 39 respectvely. From [4 the parameters of FACS devces are consdered: S = 0.00 pu. α P = rad V U = pu. α U = -.88 rad and Q V = 0.93 MVAR. COCLUSIO In ths paper a new optmzaton algorthm s used to fnd optmal locaton and settng of CSC for mzng C. he paper llustrates step by step procedure for applyng the World Cup Optmzaton algorthm to solve the problem of optmal placement. Matlab program s performed on IEEE 30 bus system. Expermental results show that optmally placed CSC by WCO could sgnfcantly ncrease C under normal and contngency condtons. REFERECES M.. Khan and A. S. Sddqu "Congeston management n deregulated power system usng FACS devce" Internatonal Journal of System Assurance Engneerng and Management vol. 8 pp M. Sahrae-Ardakan and S. A. Blumsack "ransfer capablty mprovement through market-based operaton of seres FACS devces" IEEE ransactons on Power Systems vol. 3 pp A. Krshna and M. Sndhu "Applcaton of Statc Synchronous Seres Compensator (SSSC) to enhance power transfer capablty n IEEE standard transmsson system" n Internatonal Conference on Soft Computng System ICSCS 06 pp C.. Force "ransmsson transfer capablty" orth Amercan Relablty Councl Prnceton ew Jersey 995. F. E. R. Commsson "Open access same-tme nformaton system and standards of conduct" Order vol G. C. Ejebe J. G. Waght M. Sanots-eto and W. F. nney "Fast calculaton of lnear avalable transfer capablty" IEEE ransactons on Power Systems vol. 5 pp G. C. Ejebe J. ong J. Waght J. Frame. Wang and W. nney "Avalable transfer capablty calculatons" IEEE ransactons on Power systems vol. 3 pp M. H. Gravener and C. wankpa "Avalable transfer capablty and frst order senstvty" IEEE ransactons on Power Systems vol. 4 pp Y. Ou and C. Sngh "Assessment of avalable transfer capablty and margns" IEEE ransactons on Power Systems vol. 7 pp P. L J. Q J. Wang H. We. Ba and F. Qu "An SQP method combned wth gradent samplng for small-sgnal stablty constraned OPF" IEEE ransactons on Power Systems vol. 3 pp Razmjooy M. Khallpour and M. Ramezan "A ew Meta-Heurstc Optmzaton Algorthm Inspred by FIFA World Cup Compettons: heory and Its Applcaton n PID Desgnng for AVR System" J. Control Autom. ES. pp P. Bhasaputra and W. Ongsakul "Optmal power flow wth mult-type of FACS devces by hybrd S/SA approach" n Industral echnology 00. IEEE ICI'0. 00 IEEE Internatonal Conference on 00 pp M. R.. Razmjooy "Model Order Reducton based on meta-heurstc optmzaton methods" presented at the 06 st Internatonal Conference on ew Research Achevements n Electrcal and Computer Engneerng Iran 06. W. Ongsakul and P. Jrapong "Optmal allocaton of FACS devces to enhance total transfer capablty usng evolutonary programmng" n Crcuts and Systems 005. ISCAS 005. IEEE Internatonal Symposum on 005 pp