A Review of Particle Swarm Optimization (PSO) Algorithms for Optimal Distributed Generation Placement

Transcription

1 Internatonal Journal of Energy and Power Engneerng 05; 4(4): 3-39 Publshed onlne August 4, 05 ( do: 0.648/j.jepe ISSN: X (Prnt); ISSN: X (Onlne) A Revew of Partcle Swarm Optmzaton (PSO) Algorthms for Optmal Dstrbuted Generaton Placement Musa H., Ibrahm S. B. Department of Electrcal Engneerng, Bayero Unversty, Kano, Ngera Emal address: harunamusa@yahoo.co.uk (Musa H.), hmusa.ele@buk.edu.ng (Musa H.), sabkbr@yahoo.com (Ibrahm S. B.) To cte ths artcle: Musa H., Ibrahm S. B.. A Revew of Partcle Swarm Optmzaton (PSO) Algorthms for Optmal Dstrbuted Generaton Placement. Internatonal Journal of Energy and Power Engneerng. Vol. 4, No. 4, 05, pp do: 0.648/j.jepe Abstract: Partcle Swarm Optmzaton (PSO) has became one of the most popular optmzaton methods n the doman of Swarm Intellgence. Many PSO algorthms have been proposed for dstrbuted generatons (DGs) deployed nto grds for qualty power delvery and relablty to consumers. These can only be acheved by placng the DG unts at optmal locatons. Ths made DG plannng problem soluton to be of two steps namely, fndng the optmal placement bus n the dstrbuton system as well as optmal szng of the DG. Ths paper revews some of the PSO and hybrds of PSO Algorthms formulated for DG placement beng one of the meta-heurstc optmzaton methods that fts stochastc optmzaton problems. The revew has shown that PSO Algorthms are very effcent n handlng the DG placement and szng problems. Keywords: Dstrbuted Generaton, Power Losses, Optmzaton, Placement, Szng, Objectve Functon, Power flow, Dstrbuton Networks, Mult-objectve. Introducton Dstrbuted generaton placement and szng s an mportant ssue whch requres specal attenton of both planners and system operators. DG nstallaton at nonoptmal places can lead to ncrease n system losses whch mply ncrease n costs and hence havng a negatve mpact opposte to the desred. The selecton of the locaton and sze n large and complex system s a combnatoral optmzaton problem []. Researchers have employed varous methods n addressng the placement problems. It has been observed that among all the methods revewed so far analytcal method s found to be the most accurate and more practcal technque for placement. However, obtanng a truly optmal soluton has presented a challenge as some computatonal methods do not yeld global soluton as many local solutons exsts. Due to ths problem, determnstc algorthms such as Dynamc programmng, NLP, LP, QP and SQP are consdered to be the elegant optons []. However, meta heusutc algorthms such as GA, PSO, EP, Tabu search (TS), smulated annealng (SA) seems to have shared the same domnance as determnstc methods [3]. Ths s due to the fact that meta heurstc are dervatve free problems unlke the determnstc methods and can be solved wthout need for convexcty. Apart from that the meta heurstc algorthms are ndependent of ntal soluton and can avod local optma [4]. The technques are robust and can provde near optmal soluton for large and complex systems. The only drawback s the hgh computatonal efforts requred for good soluton. On the other hand, meta heurstc methods have ther own drawbacks, such as use of tral and error process durng parameter tunnng and lack of guarantee of global soluton attanment atmes. Ths s one of the reasons that made researchers to drect a lot of effort towards elmnatng such problems by combnng more than one algorthms to form a hydrd algorthm. The hybrd algorthms currently utlsed are; such as LP QP, EP SQP GA SA and PSO SQP [5] e.t.c. These efforts have yelded results wth a lot of enhancement over the ndvdual algorthms when utlzed alone. Partcle swarm optmzaton (PSO) algorthm s a populaton based optmzaton method that has ganed much popularty among researchers snce after ts ntroducton. The algorthm mmcs brds behavor durng flght n space. Each of the brd n the aggregaton of the brds called

2 Internatonal Journal of Energy and Power Engneerng 05; 4(4): swarm s represented as a partcle. These partcles that form the swarm searches for food based on ther own experence and that of the other partcles wthn the same swarm. The PSO have been studed by many researchers and several newer versons have been developed for applcatons n dfferent real-world problems and are found to be robust and fast n solvng nonlnear non-dfferentable mult-modal problems. Many survey papers wth applcatons have been presented n lterature revews regardng these studes but t s stll n ts nfancy stage requrng a lot of research work. Authors n [6] presented a method for optmal stng and szng of multple dstrbuted generators (DGs) usng PSO based approach. Smlar multple DGs placement was also presented n [7] wth PSO as an optmzaton tool for varable power load wth non-unty power factor. In another development an mproved PSO algorthm was also proposed for optmal placement wth an n bult mechansm for better search that s capable of escapng local optma n [8]. As part of mprovement on ntal PSO algorthm, the concept of hybrdzed PSO was ntroduced by authors n [9] n whch Genetc Algorthm (GA) was combned wth PSO. The GA s made to search for the DG ste whle the PSO optmzes the DG szes whch resulted n drastc reducton n system losses and mprovement n voltage profle. In ths paper an ntroducton of PSO concepts and ts algorthm s presented and survey of exstng work follows based on objectves, methods and contrbutons of the work towards fndng of optmal solutons to placement and szng problems.. DG Placement and Szng The DG placement optmzaton problem has not been assessed thoroughly as done n many optmzaton problems. The revew n ths paper dffers from prevous revews n the sense that all work done s gong to be categorzed based on optmzaton algorthms employed. Fgure.0 shows the publshed research work done on placement and szng based on IEEE Explore Dgtal lbrary data base. The analyss shows sgnfcant mprovement n papers publshed. Fg..0. Dstrbutonof papers publshed on DG placement and szng The gradual ncrease n publshed papers s a clear ndcaton of growng nterest of researchers wllng to fnd soluton to DG placement problems. Many researchers have used varous methods to tackle the placement and szng problems. Methods of optmal placements and szng of the DGs wthn networks always depend on the objectves and soluton technques employed. There are three basc models for DG optmzaton problems that are currently n use whch are: ) Objectve functon model ) Constrants model ) Optmzaton algorthms model Objectve functons are optmzed subject to operatng constrants by usng dfferent technques. The objectve functon can be sngle or multple for the purpose of achevng maxmum benefts of the DG wthout volatng the equalty and nequalty constrants of the entre power system. The most popular objectve s the mnmzaton of power losses [0]. Among other objectves consdered by many researchers ncludes mnmzaton of real and reactve power loss, maxmzaton of DG capacty, maxmzaton of proft and socal welfare to menton a few [-4]. Other objectves handled by many authors are the techncal ssues; envronmental ssues and voltage lmt [5-6]. The constrants are state varable lmts that are placed on operatng condtons. Constrants are bascally categorzed nto equalty and nequalty whch must be satsfed by the objectve functons ether sngle or mult-objectves. The common constrants generally n DG placement ncludes but not lmted to the followng; lne thermal lmt, short crcut rato lmt, voltage step lmt, phase angle lmt, power generaton lmt, DG power generaton lmt, number of DG lmt, power flow equalty constrant, voltage profle lmts, short crcut level lmt, total lne loss lmt, substaton transformer capacty lmt, tap poston lmt, and power factor lmt [, 4, 7-3].

3 34 Musa H. and Ibrahm S. B.: A Revew of Partcle Swarm Optmzaton (PSO) Algorthms for Optmal Dstrbuted Generaton Placement Many researchers proposed dfferent methods such as analytc as well as determnstc and heurstc methods to solve placements problems. Out of these methods metaheurstc s the only method that has proven ther effectveness n solvng optmzaton problems wth apprecable feasble search space [4]. They can also be modfed easly to become a hybrd of more than one algorthm to cope wth dfferent elements commonly used n most studes. 3. The Concept of PSO Algorthm The search process s smlar to the socal behavour of flyng brds when searchng for food. The ndvdual brd called partcles or swarm fles n the optmzaton problem hyperspace to search for optmal food locaton. The poston and velocty of the partcles s always changng and adjusted accordng to the cooperatve communcaton among the partcles and each ndvdual s own experence smultaneously. Therefore the partcle changes poston by balancng ts socal and ndvdual experence. Each partcle s assgned a velocty V as well as poston vector x For a swarm of m-partcle n hyperspace, the poston and velocty vectors are [4]; =, =,, () =, () where s the partcle ndex, V s the swarm velocty and n s the optmzaton problem dmenson. The partcle s new poston s; where = + s partcle new poston at teraton k + s partcle old poston at teraton k s partcle new velocty at teraton k + Equaton (3) s the updated poston equaton. The updated velocty vector for partcle s = +!" where k V ( ) w # $+ %!" s the prevous velocty of partcle (3) # $ (4) s the nerta weght c, c are the ndvdual and socal acceleraton postve constants. r, r are the random values n the range [0, ], sampled from a unform dstrbuton P s the personal poston assocated wth partcle own experence g s the global poston assocated wth the whole neghborhood experence 3.. Updated Velocty The updated velocty as gven by equaton (4) has three major components consstng of the followng;. The frst component s related to partcle s mmedate prevous velocty, and t conssts of two varables. The varables are partcle last velocty ( k ) V and nerta weght w.. The second component s the cogntve component, whch shows the ndvdual s own experence. 3. The last term s the thrd components that represent the ntellgent exchange of nformaton between partcle and the swarm. In the absence of the second and thrd terms of the velocty formula the partcle wll contnue to fly n the same drecton wth a speed proportonal to ts nerta weght untl t hts one of the soluton space boundares. Therefore soluton can never be obtaned unless the soluton les n the same path of the prevous velocty n such a case. The change n drecton towards the soluton s achevable wth the help of second and thrd term of the equaton. Those three components of the velocty update are responsble for the optmzaton process. Versons of PSO algorthms have been proposed snce after Kennedy and Eberhart whch are the local PSO and the global PSO. The two models dffer n the socal component of the velocty update formula. In the case of the local PSO the swarm s dvded nto several neghborhoods and the g of partcle s ts neghborhood s global value. Whereas the global model consders the swarm as one entty, and therefore the PSO partcle s g s the value for the whole swarm. Generally, the global model s more popular verson snce t needs less work to acheve result. 3.. Prevous Velocty Components The component s gven by the product of prevous ( k ) velocty of partcle V and the nerta weght w. Ths term connects the partcle n the exstng teraton wth mmedate past teraton whch serves as the partcle s memory. It s mportant as t prevented the partcle from sudden change n ts drecton, and also allows the partcle s own knowledge of ts prevous flght nformaton to nfluence ts newer course. The frst verson of PSO has no nerta weght as was assumed to be unty. It was n subsequent versons that nerta weght was ntroduced n order to control the contrbuton of the partcle s prevous velocty n the current velocty decson makng and ths lead to a sgnfcant mprovement n the PSO algorthm [5]. The mplcaton of makng ts value too large s the broadenng of the exploraton msson of the partcle, and f the value s small the exploraton wll be localzed. Several dynamc nerta weghts were proposed n lteratures. The formulatons of the lteratures have expressed nerta weght as follows;

4 Internatonal Journal of Energy and Power Engneerng 05; 4(4): = + (5) = ( & ) +' (, ) &* & $ (6) = +(&) *+ ', & ) ( & *) & + ', & ) (7) Where w (k) s the nerta weght value at teraton k n k s maxmum number of teratons w (n k) s the nerta weght value at the last teraton n k Some authors n [6] have proposed usng 0.9 and 0.4 as the ntal and fnal weght values respectvely. Another factor ntroduced that s smlar to nerta weght functon s the constrcton factor (λ) whch s used for the balancng of the search mechansm between global and local exploraton. Use of ths factor mproves convergence and the partcles velocty s therefore constrcted by a factor λ as expressed n the followng equaton; =λ- +!" where and λ = # $+ %!" # $. (8) /* * *3 / (9) = + 4 Hence, the constrcton factor s a factor of ndvdual and socal acceleraton postve constants C and C respectvely. Ths factor s normally consdered as a specal case of nerta weght PSO algorthm because of the constrants mposed above. The factor λ controls the partcle s velocty vector, whles the nerta weght w controls the contrbuton of the partcle s prevous velocty towards calculatng the new one velocty. Use of constrcton factor elmnates velocty clampng and can safe guards the algorthm aganst exploson [7]. n the update of velocty for future teraton. Ths component of velocty update equaton dversfes searchng process at the same tme helps n avodng possble stagnaton Socal Component Ths represents the socal behavor of the PSO partcles. The g term n ths component s referred to as the poston acheved among all the swarm partcles. Whenever the soluton among the whole populaton of the swarm s acheved, all the partcles are nformed. The g ftness value s the optmal among all the partcles durng the current PSO teraton as; %!" = ;<9'# ),9'# ),,9(# = )> () k where f ( S ) s partcle ftness value at teratonk, and m s the swarm sze Cogntve and Socal Parameters These parameters C and C are cogntve and socal parameters respectvely. They are factors that scaled the P and g n the updated velocty equaton. The trust of the partcle n tself s measured by C, whle C reflects the confdence t has on ts neghbours. If C s 0, the partcle s own experence s elmnated durng search process for a new soluton, whle f C s 0 the search s localzed and exchange of nformaton between the partcles s elmnate. The hghest value recommended for the two n most lteratures s. r and r are two random numbers n the range of [0, ] that are sampled from a unform dstrbuton. The stochastc exploraton nature of PSO s due to these random numbers. A typcal llustraton for velocty and poston update for a sngle PSO partcle durng teraton s shown n Fg..0 durng teraton Cogntve Component The cogntve component of the velocty update equaton uses P whch s referred to as the partcle s personal poston that t has vsted so far snce the begnnng of the PSO teratve process. Each partcle n the swarm tres to evaluate ts own performance by comparng ts own ftness n the current PSO teraton wth that evaluated n the proceedng one. The!"6 gven that ts!"6 s the personal poston so far, s defned as;!"6 = 7 8!" 6 # 9 9'# ) 9!"6 $ 7: (0) 9 9'# ) 9!"6 $ Based on equaton (5) each partcle s suppose to remember ts optmal personal poston acheved for use Fg..0. Velocty and poston updates for a sngle partcle durng teraton k 3.6. Pretty Features of PSO The advantages assocated wth PSO are many just lke other optmzaton algorthm. The man advantages are clearly dstnct when compared to determnstc methods that

5 36 Musa H. and Ibrahm S. B.: A Revew of Partcle Swarm Optmzaton (PSO) Algorthms for Optmal Dstrbuted Generaton Placement are gradent based technques and have no flexblty of dealng wth objectve functons that are not contnuous or dfferentable naturally. The search process for PSO does not nvolve use of dervatve functon; nstead t uses the ftness functon value as a gude for fndng optmal soluton n problem space. Ths concept of ftness functon employed n PSO helps n elmnatng the approxmatons and assumptons usually adapted on objectve functons and constrants as n conventonal optmzaton methods. For ths reason PSO s consdered as a stochastc optmzaton method and found to be very effcent n handlng problems that ther objectve functons are tme varyng or stochastc n nature. Above all the solutons from PSO are not dependant on the ntal solutons unlke the determnstc method. 4. Studes on PSO Algorthms for DG Placements and Szng Ths secton deals wth all the studes done on PSO and hybrdzed PSO Algorthms for DG placements and szng. All the lterature surveyed are summarzed n table 4. Table 4.. Some Publshed Works on PSO Algorthms S/NO. Ref. Objectves Optmzaton method Contrbutons. Haruna M. [8]. El-Zonkoly [7] 3 Nabav, S.M.H[9] 4 Amanfar, O. [30] Mnmzaton of power losses and voltage stablty ndex (VSI) Mult-objectve for short crcut level and other techncal parameters Reduce network congeston and mnmze locatonal margnal prce (LMP) Mnmzaton of nvestment cost of DGs and power losses 5 Das, B.H [3] Mnmzaton of power losses PSO PSO PSO A PSO algorthm ntegrated n harmonc power flow algorthm PSO n Nonlnear Optmal Power Flow (OPF) 6 Gomez-Gonzadez [3] Mnmzaton of cost PSO n Optmal power flow 7 Wong, L.Y. [33] Mnmzaton of power losses 8 Nguyen Cong Hen [34] Maxmzes reactve power flow PSO Pso n Newton Raphson power flow Optmal DG Placement model for better search and mproved (VSI) Determnaton of voltage collapse pont for varable load congeston management and socal welfare n placement/szng Investment cost justfes DG placement for ncrease n power transfer capablty Reducton n search space and mprovement convergence ODGP model usng dscrete PSO and OPF Effectve solutons and mproved voltage profle Enhancement of loadablty of the prmary dstrbuton feeder The PSO algorthms allow the system planner to fnd not only a sngle optmum pont, but a famly of near-optmum plannng alternatves. Ths feature of PSO has become very useful n DG allocaton because dstrbuton network operators usually have lttle or no control on the DG ntegraton and dfferent plannng alternatves can be necessary to face uncertantes and mnmze rsks. Numerous publcatons and wde spread mplementaton of PSO algorthms has been conducted, a lot of barrers to proper mplementaton of these researchers by network operators s stll lackng. Although the algorthm has many advantages over other meta-heurstc methods, the man challenge assocated PSO s that of lack of sold mathematcal background lke many heurstc methods. It s soluton method s problem dependent and for every soluton parameters have to be tuned and adjusted for better soluton. The conventonal PSO ntroduced by Kennedy and Eberhart n 995 and even those that had under gone modfcatons, are stll dependent on a number of parameters that are externally set or arbtrary selected by the user [4]. Ths settng or selecton by the user s a very delcate operaton nvolvng a lot of trals and errors before a reasonable tunng can be acheved especally n practcal problems that requre defnng of nerta weght at each teraton step. Apart from that the usual ntal assumpton that nerta term s elmnated at an early stage of the optmzaton process, can cause the algorthm to be trapped at some local mnmum. As a soluton to ths problem some authors have proposed some procedures of re-seedng the search by generatng new partcles at dstnct places of the search space [35]. Other shortcomng of PSO s the random operaton nvolved that a partcle s ntalzed randomly and ts locaton n the search space s updated durng each teraton n the PSO algorthm. The problem s that when the partcle ntalzaton s not well done the ssue of local mnmum trappng can also arse or convergence can be prolonged as sharng of nformaton between partcles s not properly coordnated. These challenges made researchers to drect a lot of effort towards elmnatng such problems by combnng more than one algorthms to form a hybrd algorthms. The efforts have yelded results wth a lot of enhancement over the ndvdual algorthms when utlzed alone as ndcated n table 4..

6 Internatonal Journal of Energy and Power Engneerng 05; 4(4): Table 4.. Some Publshed Works on Hybrd PSO Algorthms S/No. Ref Objectve Method Contrbuton Morad [9] Mult-objectve wth weghts Hybrd (GA &PSO). Sedghzadeh, M [36] 3. Musa, H. [37] Mnmzaton of power losses and voltage profle mprovement Mult-objectve for power loss reducton and voltage stablty ndex mprovement Hybrd (PSO and Clonal Selecton ) Hybrd (PSO & Evolutonary Programmng) 4. Afzalan, M [38] Mnmzaton of power losses Hybrd ( PSO & HBMO) 5. Zar, I [39] 6 Soroud, A. [40] 7 Wen S. T.[4] Mnmzes loss and mproves system relablty. Mult-objectve for techncal constrant dssatsfacton, costs and envronmental emssons Mult-objectve ndex-based approach for total real power losses, voltage profle, MVA ntake by the grd, number of DG and greenhouse gases emsson 8 Haruna Musa[4] power loss reducton (PLR) value Hybrd (Dscrete PSO & GA) Hybrd (Bnary PSO-based & Fuzzy) Hybrd (PSO & Gravtatonal Search Algorthm ) Hybrd (PSO & Ranked Evolutonary programmng) Optmal DG Plannng for placement usng GA and szng usng PSO Better qualty of solutons and less number of teratons Well-dstrbuted Pareto optmal nondomnated solutons of DG szes obtaned Voltage profle mprovement and branch current reducton Increase n the dversty optmzaton varables n DPSO not to be trapped n a local mnmum Better tmng of nvestment for both dstrbuted generaton (DG) unts and network components obtaned Algorthm can provde effcent and robust soluton to mxed nteger nonlnear optmzaton problem A smple and effectve algorthm for power loss reducton and voltage profle mprovement 5. Conclusons Although there have been numerous publcatons n the area of the stng and szng of DG, t s evdent that, wdespread mplementaton of the PSO optmzatons has not been much. Development of the DG ntegraton strateges and PSO optmzaton methods requres proper dstrbuton system plannng especally wth the prolferaton of electrc vehcle n exstng dstrbuton networks. Further challenges that are yet to be tackled for better optmzaton are the modellng of the dstrbuton networks wth all the necessary detals needed by network operators. Acknowledgements The authors acknowledged wth grattude the fnancal support offered by Bayero Unversty Kano Ngera and the provson of sutable research facltes. References [] Borges, C., Falcao, D., Optmal DG allocaton for relablty, losses, and voltage mprovement, Internatonal Journal of Electrcal power & Energy systems, vol. 8 pp [] T. Grffn, K. Tomsovc, D. Secrest, A. Law, Placement of dsperse generaton systems for reduced losses, Proceedngs of the 33 rd Annual Hawa Internatonal Conference on system Scence, IEEE, pp , Jan [3] M. Gandomkar, M. Vaklan, and M. Ehsan, A genetc-based tabu search algorthm for optmal DG allocaton n dstrbuton networks, Elect. Power Compon. Syst., vol. 33, no., pp ,Aug. 005 [4] Haruna Musa A Revew of Dstrbuted Generaton Resource Types and ther Mathematcal Models for Power Flow Analyss Internatonal Journal of Scence, Technology and Socety Do: 0.648/j.jsts , 05; 3(4): 04- [5] G. P. Harrson, A. Pccolo, P. Sano, and A. R. Wallace, Hybrd GA and OPF evaluaton of network capacty for dstrbuted generaton connectons, Elect. Power Syst. Res., vol. 78, no. 3, pp , Mar. 008 [6] Jan Naveen, Sngh SN, Srvastava SC. Partcle swarm optmzaton based method for optmal stng and szng of multple dstrbuted generators. In Proc 6th natonal power systems conference, 5 7th December, 00. p [7] A. M. El-Zonkoly, Optmal placement of mult-dstrbuted generaton unts ncludng dfferent load models usng partcle swarm optmsaton, IET Gener., Transm., Dstrb., vol. 5, no. 7, pp , Jul. 0. [8] W. Prommee and W. Ongsakul, Optmal multple dstrbuted generaton placement n mcrogrd system by mproved rentalzed socal structures partcle swarm optmzaton, Euro. Trans. Electr. Power, vol., no., pp , Jan. 0. [9] M. H. Morad and M. Abedn, A combnaton of genetc algorthm and partcle swarm optmzaton for optmal DG locaton and szng n dstrbuton systems, Int. J. Electr. Power Energy Syst., vol. 34, no., pp , Jan. 0. [0] D. Q. Hung and N. Mthulananthan, and R.C. Bansal An analytcal expresson for DG allocaton n prmary dstrbuton networks, IEEE Trans. Energy Convers., vol. 5, no. 3, pp , Sept. 00. [] Rau N. S. and Wan Y.-H., Optmum locaton of resources n dstrbuted plannng. IEEE Trans. Power Syst., vol. 9, pp

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8 Internatonal Journal of Energy and Power Engneerng 05; 4(4): [40] A.Soroud, M.Afrasab; "Bnary PSO-Based Dynamc Mult- Objectve Model for Dstrbuted Generaton Plannng under Uncertanty", IET Renewable Power Generaton, 0, Vol.6, No., pp [4] Wen Shan Tan, Hassan, M.Y., Rahman, H.A., Abdullah, M.P., Hussn, F., Mult-dstrbuted generaton plannng usng hybrd partcle swarm optmsaton- gravtatonal search algorthm ncludng voltage rse ssue Generaton, Transmsson & Dstrbuton, IET Volume: 7, Issue: 9, DOI0.049/et-gtd , 03, Page(s): [4] Haruna Musa, Sanus San Adamu Optmal Allocaton and Szng of Dstrbuted Generaton for Power Loss Reducton usng Modfed PSO for Radal Dstrbuton Systems Journal of Energy Technologes and Polcy Volume: 3 Issue: 3, 03 Pages -8.