Firefly Algorithm based Optimal Reactive Power Flow
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1 ISSN (e): olume, 06 Issue, 0 February 016 Internatonal Journal o Computatonal Engneerng Research (IJCER) Frely Algorthm based Optmal Reactve Power Flow G. K. Moorthy 1, R. K. Santh, S. M. Alamelunachappan 3 1 Research Scholar Department o Electrcal Engneerng Annamala Unversty aml Nadu, INDIA Proessor o Electrcal Engneerng Annamala Unversty aml Nadu INDIA 3 Proessor o Electrcal Engneerng Pondcherry Engneerng College Puducherry, INDIA Abstract he optmal reactve power low (ORPF) helps to eectvely utlze the exstng reactve power sources or mnmzng the networ loss. Frely Algorthm (FA), nspred by socal lashng behavor o reles, s one o the evolutonary computng models or solvng multmodal optmzaton problems. hs paper attempts to obtan global best soluton o ORPF usng FA. he results o IEEE 57 bus system are presented to demonstrate ts perormance. Keywords: optmal reactve power low, rely algorthm FA rely algorthm -th rely -th desgn varable o -th rely Nomenclature G B real and magnary terms o bus admttance matrx correspondng to -th row and - -th column g conductance o the transmsson lne connected between buses - and g ( x, u ) equalty constrant h ( x, u ) nequalty constrant J ( x, u ) obectve uncton lght ntensty o -th rely nc number o shunt reactve power compensators n number o decson varables nob number o obectves ng number o generators nt number o transormers n number o reles n the populaton ORPF optmal reactve power low PFAM proposed FA based method G reactve power generaton at bus- C reactve power necton by -th shunt compensator RPL real power loss r Cartesan dstance between -th and -th reles P tap settngs o -th transormer voltage prole voltage at -th bus lm L t lmt volated voltage magntude at -th load bus Open Access Journal Page 6
2 Frely Algorthm Based Optmal Reactve Power Flow lm G t lmt volated reactve power generaton at -th P bus G voltage magntude at -th generator bus L voltage magntude at -th load bus x vector o dependant varables u vector o control or ndependent varables random movement actor attractveness parameter o attractveness between -th and -th reles absorpton actor and penalty actors structure o -th molecule a set o transmsson lnes a set o load buses a set o generator buses superscrpt mn and lower and upper lmts respectvely I. Introducton he Optmal Reactve Power Flow (ORPF) attempts to mnmze the real power loss (RPL) va the optmal adustment o the power system control varables, whle at the same tme satsyng varous equalty and nequalty constrants. he ORPF problem s a large scale hghly constraned nonconvex and multmodal optmzaton problem [1,]. Several tradtonal optmzaton technques such as gradent method [1,], Newton method [3], lnear programmng [4-7], nteror pont method [8] and non lnear programmng [9] have been appled to solve the ORPF problem. hese methods have severe lmtatons n handlng non-lnear and dscontnuous obectves and constrants. Besdes, these classcal optmzaton technques nvolvng dervatves and gradents may not be able to determne the global optmum. In order to overcome these drawbacs, nature nspred optmzaton methods such as genetc algorthm (GA) [10-1], evolutonary programmng [13], partcle swarm optmzaton (PSO) [14], derental evoluton (DE) [15-17], seeer optmzaton algorthm [18] and bogeography based optmzaton (BBO) [19] have been recently appled n solvng the ORPF problems. Recently, rely optmzaton (FFO) has been suggested or solvng optmzaton problems [0,1]. It s nspred by the lght attenuaton over the dstance and reles mutual attracton rather than the phenomenon o the reles lght lashng. In ths approach, each problem soluton s represented by a rely, whch tres to move to a greater lght source, than ts own. It has been appled to a varety o power system problems [-4] and ound to yeld satsactory results. hs paper attempts to develop FA based method or obtanng the soluton o ORPF. he results on IEEE 57 bus system are presented to demonstrate the eectveness o the developed strategy. II. Frely Algorthm he FFO, a nature-nspred optmzaton algorthm, s based on the socal lashng behavor o reles and smlar to other optmzaton algorthms employng swarm ntellgence such as partcle swarm optmzaton. FFO ntally produces a swarm o reles located randomly n the problem space. he poston o each rely n the problem space represents a potental soluton o the optmzaton problem. he tness uncton taes the poston o a rely as nput and produces a sngle numercal output value denotng how good the potental soluton s. he brghtness o each rely depends on the tness value o that rely. Each rely s attracted by the brghtness o other reles and tres to move towards them. he velocty or the pull o a rely towards another rely depends on the attractveness. he attractveness depends on the relatve dstance between the reles and s a uncton o the brghtness o the reles as well. A brghter rely ar away may not be as attractve as a less brght rely that s closer. In each teratve step, FFO computes the brghtness and the relatve attractveness o each rely. Dependng on these values, the postons o the reles are updated. Ater sucent amount o teratons, all reles converge to the best possble poston n the search space. Each -th rely s denoted by a vector as [0,1] 1 nd,, (1) he search space s lmted by the ollowng nequalty Open Access Journal Page 7
3 Frely Algorthm Based Optmal Reactve Power Flow ( mn ) ( ) : 1,,, nd () Intally, the postons o the reles are generated rom a unorm dstrbuton usng the ollowng equaton ( ) ( mn rand ( mn ) ) (3) Here, rand s a random number between 0 and 1, taen rom a unorm dstrbuton. Eq. (3) generates random values rom a unorm dstrbuton wthn the prescrbed range dened by Eq. (). he ntal dstrbuton does not sgncantly aect the perormance o the algorthm. Each tme the algorthm s executed, the optmzaton process starts wth a derent set o ntal ponts. However, n each case, the algorthm searches or the optmum soluton. In case o multple possble sets o solutons, the algorthm may converge on derent solutons each tme. But each o those solutons wll be vald as they all wll satsy the requrements. he lght ntensty o the -th rely, s gven by Ftness ) (4) ( he attractveness between the -th and -th rely, s gven by Where r exp r (5) o r s Cartesan dstance between -th and -th rely nd 1 s a constant taen to be 1. o s another constant whose value s related to the dynamc range o the soluton space. he poston o rely s updated n each teratve step. I the lght ntensty o -th rely s larger than the ntensty o the -th rely, then the -th rely moves towards the -th rely and ts moton at t -th teraton s denoted by the ollowng equaton: ( t 1) ( t 1) rand 0.5 ( t ) ( t 1) (7) s a random movement actor, whose value depends on the dynamc range o the soluton space. At each teratve step, the ntensty and the attractveness o each rely s calculated. he ntensty o each rely s compared wth all other reles and the postons o the reles are updated usng Eq. (7). Ater a sucent number o teratons, all the reles converge to the same poston n the search space and the global optmum s acheved. III. Problem Formulaton he ORPF problem s ormulated as an optmzaton problem wth several equalty and nequalty constrants as Mnmze J ( x, u ) RPL g cos Subect to g ( x, u ) 0 (9) h ( x, u ) 0 (10) Where x s the vector o dependant varables consstng o load bus voltage magntudes, reactve power generaton at generator buses and real power generaton at slac bus. u s the vector o control or ndependent varables comprsng o generator bus voltage magntudes, transormer tap settngs and output o reactve shunt compensators. RPL can be calculated rom the load low soluton. he equalty constrants g ( x, u ) are the sets o non-lnear power low equatons that govern the power system P G P D nb 1` ( G cos B sn ) 0 (11) (6) (8) G D nb 1` ( G sn he equalty constrants h ( x, u ) settngs and voltage magntudes. B cos ) 0 (1) represent the operatng lmts on reactve power generatons, transormer tap Open Access Journal Page 8
4 Frely Algorthm Based Optmal Reactve Power Flow mn G mn C mn mn G mn L G G (13) C C (14) (15) G G (16) L L (17) I. Proposed Method he proposed FA based method (PFAM) nvolves representaton o problem varables and the ormaton o approprate uncton. Representaton o Control arables: In FA, a soluton s represented by a rely- Open Access Journal Page 9. In the PFAM, each rely s dened to denote the control varables o voltage magntude at generator buses, transormer tap postons and reactve power o shunt compensators n vector orm as 1 nd, [,,,,,,,,,,, ] (18), G 1 G Gng 1 nt C 1 C Formaton o uncton: he proposed method searches or optmal soluton by mnmzng a uncton, whch s ormulated rom the obectve uncton and the penalty terms representng the lmt volaton o the dependant varables such as reactve power generaton at P buses and voltage magntude at load buses. he uncton s bult as lm t lm t J ( x, u ) Where lm t L lm t G mn L L L mn G G G (19) L L L else G G else L mn L L mn G G G Soluton Process: An ntal populaton o reles s obtaned by generatng random values wthn ther respectve lmts. he s calculated by consderng the values o each rely and the movements o all reles are perormed wth a vew o mzng the tll the number o teratons reaches a speced mum number o teratons. he pseudo code o the PFAM s as ollows. Read the ORPF Data Choose the parameters, n, Iter,, and o. Generate the ntal swarm o reles Set the teraton counter t 0 whle (termnaton requrements are not met) do or 1 : n Obtan the control parameters rom -th rely. Perorm load low. Evaluate RPL and then compute or 1 : n usng Eqs. 8 and 19 respectvely Obtan the control parameters rom -th rely. Perorm load low. Evaluate RPL and then compute Compute r usng Eq. (6) Evaluate usng Eq. (5) G Cnc usng Eqs. 8 and 19 respectvely (0) (1)
5 Frely Algorthm Based Optmal Reactve Power Flow end-( ) Move -th rely towards -th rely through Eq. (7) end-() end-( ) Ran the reles and nd the current best. end-(whle) Choose the best rely possessng the largest n the populaton as the optmal soluton Stop. Smulatons he PFAM s tested on IEEE 57 bus test system, whose data have been taen rom Re. [5]. he system possesses seven generators at buses 1,, 3, 6, 8, 9 and 1 and teen tap changng transormers. he controllable shunt reactve power sources wth a capacty o 0.1, 0.06 and per unts are connected at buses 18, 5 and 53 respectvely. he total system actve and reactve power demand are per unt and per unt on 100 MA base. he lower and upper voltages or all buses are taen as 0.95 and 1.1 respectvely. NR technque [6] s used to carry out the load low durng the optmzaton process. he optmal soluton obtaned by the PFAM s presented along wth base-case soluton n able 1. It s very clear rom the table that the PFAM s able to reduce the loss to the lowest value o MW, whch leads to 13.7% loss savngs wth respect to base case. he voltage magntudes o all load buses o the PFAM are graphcally compared wth that o the base-case voltages n Fg.1. It clearly ndcates that the PFAM oer better voltage prole and they le between the lower and upper lmts. able 1 Results o the PFAM Controlarables Base Case PFAM G G G G G G 9 G C C Open Access Journal Page 30
6 Frely Algorthm Based Optmal Reactve Power Flow C RPL Fg. 1 Plot o voltage prole I. Concluson Indeed the FFO s a powerul populaton based method or solvng complex optmzaton problems. ORPF s a complex optmzaton problem determnes the values or system control varables that mnmze the RPL, whle at the same tme satsyng varous equalty and nequalty constrants. he FA s appled to solve ORPF problem. he PFAM attempts to ecently search the soluton space, and nd the global best soluton. he results o IEEE 57 bus test system proect the ablty o the PFAM n obtanng the global best soluton. Besdes the PFAM oers a better P that les n between the lower and upper lmts. he PFAM or solvng ORPF wll go a long way n servng as a constructve tool n load dspatch centre. Acnowledgement he authors grateully acnowledge the authortes o Annamala Unversty and Pondcherry Engneerng College or the acltes oered to carry out ths wor. Reerences [1]. O.Alsac,and B. Scott. (1974). Optmal load low wth steady state securty, IEEE ransactons on power Apparatus and systems. PAS: []. Lee K Y,Par Y M, Ortz J L. (1985). A unted approach to optmal real and reactve power dspatch, IEEE ransactons on power Apparatus and systems. PAS-104: [3]. A.Montcell, M..F Perera and S. Granvlle. (1987). Securty constraned optmal power low wth post contngency correctve reschedulng, IEEE ransactons on Power Systems, (1): [4]. N Deeb and S.M.Shahdehpur. (1990). Lnear reactve power optmzaton n a large power networ usng the decomposton approach, IEEE ransactons on power systems,5(): [5]. Hobson. (1980). Networ constraned reactve power control usng lnear programmng, IEEE ransactons on power apparatus and systems. PAS -99 (3): [6]. K.Y. Lee, Y.M. Par, and J.L.Ortz. (1984). Fuel-cost mnmzaton or both real and reactve power dspatches, IEE Proceedngs C. 131(3): [7]. M.K. Mangol, and K.Y. Lee. (1993). Optmal real and reactve power control usng lnear programmng, Electrcal Power System Research. 6(1): [8]. J.A. Momoh, S.X. Guo, E.C. Ogbuobr and R. Adapa. (1994). he quadratc nteror pont method solvng power system optmzaton problems, IEEE ransactons on Power Systems, 9(3): [9]. Y.C.Wu, A.S. Debs and R.E.Marsten. (1994). A Drect nonlnear predctor-corrector prmal-dual nteror pont algorthm or optmal power lows, IEEE ransactons on power systems. 9(): [10].. H. Wu, Y. J. Cao and J. Y. Wen. (1998). Optmal reactve power dspatch usng an adaptve genetc algorthm, Int. J. Elect. Power Energy Syst., 0(8): [11]. S.Durara, P.S.Kannan and D.devara. (005). Applcaton o genetc algorthm to optmal reactve power dspatch ncludng voltage stablty constrant, Journal o Energy and Envronment, 4: [1]. W. Yan, F. Lu, C.Y. Chung, K.P. Wong. (006). A hybrd genetc algorthm nteror pont method or optmal reactve power low, IEEE ransactons on power. Systems, 1(3): [13]. L.L. La and J.. Ma. (1997). Applcaton o evolutonary programmng to reactve power plannng-comparson wth nonlnear programmng approach, IEEE ransactons on power systems. 1(1): [14]. K. Mahadevan and P.S. Kannan. (010). Comprehensve learnng Partcle Swarm Optmzaton or Reactve Power Dspatch, Int. J. Appled Sot Computng. 10(): Open Access Journal Page 31
7 Frely Algorthm Based Optmal Reactve Power Flow [15]. K. asaa and P. Kanta Rao. (008). Derental evoluton based optmal reactve power dspatch or voltage stablty enhancement, Journal o heoretcal and Appled Inormaton echnology, 4(4): [16]. Y. Chung, C.H. Lang, K.P. Wong and X.Z. Duan. (010). Hybrd algorthm or derental evoluton and evolutonary programmng or optmal reactve power low, IE Proc. Gen., rans. & Dst. 4(1): [17]. A.A. Abou El Ela, M.A. Abdo and S.R.Spea. (011). Derental evoluton algorthm or optmal reactve power dspatch, Electrc Power System research, 81: [18]. B.Da, W. Chen. (009). Seeer Optmzaton Algorthm or Optmal Reactve Power Dspatch, IEEE ransactons Power Systems. 4(3): [19]. Bhattacharya and K.P. Chattopadhyay. (010). Soluton o optmal reactve power low usng bogeography-based optmzaton, Int. Journal o Electrcal and Electroncs Engneerng. 4(8): [0]. Yang. X. S. (008). Nature-Inspred Meta-Heurstc Algorthms, Lunver Press, Becngton, UK. [1]. Yang. X.S. (009). Frely algorthms or multmodal optmzaton, n Proceedngs o the Stochastc Algorthms: Foundatons and Applcatons (SAGA 09), ol. 579 o Lecture Notes n Computng Scences, pp , Sprnger, Sapporo, Japan. []. Kuldeep Kumar Swarnar. (01). Economc load dspatch problem wth reduce power loss usng rely algorthm, Journal o Advanced Computer Scence and echnology, 1(): [3]. Sulaman. M.H, Mustaa. M.W, Zaara. Z.N, Alman. O and Abdul Rahm. S.R. (01). Frely Algorthm echnque or Solvng Economc Dspatch Problem, IEEE Internatonal Power Engneerng and Optmzaton Conerence (PEOCO01), Melaa, Malaysa: 6-7 June 01. [4]. Chandrasearan. K and Ssha P Smon. (01). uned Fuzzy Adapted Frely Lambda Algorthm or Solvng Unt Commtment Problem, J. Electrcal Systems,8(): [5]. est Systems Archve, Avalable at December 01). [6]. W.F. nney and C.E. Hart. (1967). Power low soluton by Newton s method, IEEE ransacton on Power Apparatus And Systems PAS-86(11): Open Access Journal Page 3
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