An Efficient Metaheuristic Algorithm for Optimal Capacitor Allocation in Electric Distribution Networks

Transcription

1 2017 2nd Internatonal Conference on Software, Multmeda and Communcaton Engneerng (SMCE 2017) ISBN: An Effcent Metaheurstc Algorthm for Optmal Capactor Allocaton n Electrc Dstrbuton Networks Bogdan Constantn NEAGU and Gheorghe GRIGORAȘ * Gheorghe Asach Techncal Unversty of Ias, Romana *Correspondng author Keywords: Capactor allocaton, Dstrbuton network, Metaheurstc. Abstract. The capactors are generally used to provde the compensaton of reactve power n the electrc dstrbuton systems. Ths paper nvestgates a partcular approach that hghlghts the nfluences whch the connecton of shunt capactors may have over the solutons for voltage control n the medum voltage dstrbuton networks. The problem of optmal capactor allocaton for mnmzaton of bus voltage devaton ndex was solved by usng the Bat algorthm n order to fnd the near-optmal solutons for the capactor allocaton problem n electrc dstrbuton systems. To demonstrate the feasblty of algorthm, a real dstrbuton network was used and the results were compared wth those obtaned usng genetc algorthm. Introducton The electrc dstrbuton networks operated wth tradtonal methods can have hgh power losses and poor voltage regulaton. The optmzaton problem of voltage n nodes represents an ndspensable task for system operators, both for ensurng operatonal securty and ncreasng the transfer capacty. The basc dutes of a reasonable electrc dstrbuton network (EDN) are allowable voltage profle, the accessblty of power on demand and relablty. Takng nto account some advantages and dsadvantages, the EDN effcency can be developed by choosng one, two or more of the next knowng sngle or hybrd methods [1]: optmal network confguraton, capactors allocaton, voltage regulaton, and dstrbuted generaton mplementaton. The capactors are usually used n order to provde the compensaton of reactve power n EDN. Shunt capactors placement s a strong method used n EDN for power losses reducton, voltage profle mprovement, the maxmzaton power capacty of the dstrbuton elements and the power factor correcton [2]. On the other hand, the capactor allocaton n EDN requres approprate locaton and szng, playng an mportant role n losses mnmzaton acheved by usng optmzaton methods. The capactors are oftentmes used n the EDN for mantan the node voltage n allowable lmts, and also for power loss reducton or lne capacty upgrade. The capactors are effcent n overall current mnmzaton through wtherng the reactve current suppled by the transformer. In lterature, for solve the optmal capactors allocaton problem n dstrbuton networks, a lot of metaheurstc technques were used, such as: modfed cultural algorthm, [1]; ant colony optmzaton algorthm, [3]; shark smell optmzaton algorthm [4]; bee colony optmzaton algorthm, [5]; plant growth smulaton algorthm, [6]; monkey search optmzaton algorthm [7]; partcle swarm optmzaton algorthm, [8]; flower pollnaton algorthm, [9]; mne blast algorthm, [10]; gravtatonal search algorthm, [11]; cuckoo search algorthm, [12]; self-adaptve harmony search algorthm, [13]; bacteral foragng optmzaton algorthm [14], etc. In a comprehensve descrpton of the paper, the capactors allocaton problem ams to determne an effcent combnaton between locaton and sze of these capactors n order to mnmze the ftness functon. Therefore, the analyss s made for an EDN to hghlght the nfluences whch the connecton of capactors could have over the solutons on voltage control. The capactor allocaton problem for mnmze the ndex of bus voltage devaton was solved by fnd the near-optmal solutons for the placng of a gven number of capactors, va Bat Algorthm. 327

2 The proposed approach admt a lot of operatng restrctons: the maxmum allowed lmts for current; the voltages level n the accepted operatng lmts; the reactve power added by the capactors need to not flow towards the supply source, and the maxmum compensaton s lmted to the total reactve power demand. Proposed Algorthm Metaheurstc algorthms use a compromse between local search and randomzaton that permt a sold strategy to advance from the local to global search. The Bat Algorthm was proposed n [15]. Accordngly, t can be used when the nput parameters of the examned problem can be arranged n a strng of characters. The proposed algorthm s based on the echolocaton comportment of mcro bats. The bats can emt a precsely loud and short sound pulse, and the reflected echo from the surroundng s receved by ther greater aurcle. The approxmated rules are the followng: ) the bats know the dfference between prey and barrers and use echolocaton for dstance percepton. ) the bats randomly fly takng nto account the velocty v at a locaton x and a fxed frequency f mn, havng wavelength λ and loudness A 0 to nspect for prey. Automatcally, the bats can adjust the wavelength or frequency of both emtted pulses and pulse emsson rate (r) that depend on the target proxmty. r can have values between [0,1], where 0 are no pulses and 1 the maxmum pulse emsson rate. ) Loudness can vary from a large postve A 0 to a mnmum constant value, noted as A mn. An ntal populaton of bats s randomly generated [15]. After ntal ftness adoptng for the populaton for the gven ftness functon, the values are updated only used the loudness, locaton and pulse rate. The rules for updatng the frequency f, the veloctes v and locatons x, of bats are computed usng the followng relatons: f f mn f max f mn t t1 t v v x x * f (1) t t1 t x x v where χ s a random vector wth values between 0 and 1. Also, x* represents the global best soluton n the current teraton, and f mn and f max represent the mnmum and maxmum frequency. When the soluton s generated among the current best solutons, a new soluton s generated for each bat through local search usng random stroll, wth: x t n xo A (2) where x n s the new soluton, x o s old soluton, and δ ε [-1, 1] represent a random value. Through the teratve process, both loudness (A ) and rate of pulse emsson (r ) are accordngly updated. Furthermore, f the bat closes on ts prey, the loudness decreases and rate of pulse emsson ncreases, and the equatons for convergence are: t1 t t1 t A A and r r t 1 exp (3) Because α (coolng factor) and γ are constants, for each 0 < α < 1 and γ > 0, f t tends to, then: t 0 A 0 and r r (4) t Thus, the general pseudocode of the proposed Bat algorthm used for capactor allocaton s descrbed n Fgure

3 Fgure 1. The pseudocode of bat algorthm for capactor allocaton. Problem Formulaton The capactor allocaton problem approached n ths paper ams to determne a combnaton for the capactors locaton and sze n an EDN so that the goal functon (voltage devaton) s mnmzed. Consderng a maxmum avalable number of capactors, the Bat Algorthm solves two aspects: Fndng the optmal buses for capactors placement. Fndng the requred compensaton level. The ftness functon consders the mnmzaton of bus voltage devatons wth regard to ther nomnal values: mn du abs( U bus U n, bus ) (5) bus1 wth to the followng operatng constrants: Branch current flows must not exceed the maxmum allowed lmts: I I, branch 1 NB (6) branch max, branch.. Bus voltages must not exceed the allowed range: U U U, bus 1 (7) mn, bus bus max, bus.. The maxmum compensaton s lmted to the total reactve power demand: QC, bus Nc, bus Qd, bus Nl, bus, bus 1.. (8) The capactor power must not flow towards the supply source, n any operatng state: Q q N, mn 0 where the number of buses n the system, NB the number of branches n the system, U bus - the actual value of the bus voltage, U n,bus the nomnal bus voltage, I branch the actual value of the branch current, I max,branch the maxmum branch current lmt, U mn,bus the mnmum bus voltage lmt, U max,bus the maxmum bus voltage lmt, q 0 the reactve power of a capactor, Q c,bus reactve power at bus, Q d,bus the reactve power demand of load at bus, N l the number of load buses, N C, bus (9) 329

4 total number of capactors placed at bus. In the proposed algorthm, voltages were consdered n klovolts (kv), and currents n amperes (A). Snce the standard Bat algorthm maxmzes ts ftness functon, 1/dU was used. Case Study The proposed approach for optmal capactor allocaton s tested on a real EDN wth 20 substatons of 20/0.4 kv whch supples urban resdental consumers, gven n Fgure 2. The substatons have dstrbuton transformers, wth 400 or 630 kva. In partcularly cases, an EDN operate at medum (MV) or low voltage (LV) and the reactve power compensaton optmzaton s done usng shunt capactors on the LV sde (0.4 kv) of transformers. The Bat Algorthm s used to fnd the optmal capactor allocaton n order to mnmze the bus voltage devatons. The capactor allocaton problem was appled usng a fxed upper lmt of 100 capactors wth 10 kvar. The Bat algorthm was run wth 100 tres for two consdered load cases (mnmum and peak) from a wnter workng day. Populaton szes were set at 40 bats, generated randomly at each run, usng 100 generatons. The parameters of Bat algorthm are the followng: A, α, γ and r 0.9; f mn 0; f max 1.2. Fgure 2. The test dstrbuton network. For the real operatng confguraton and load data wthout compensaton, the voltages range are between to p.u., and the ftness functon s 3.56 at mnmum load, and between to p.u. of a ftness functon by 1.81 at peak load. The obtaned results for each combnaton of populaton sze, number of generatons and both bat and genetc algorthm parameters value s gven n Table 1. Each cell value represents the maxmum ftness functon obtaned n the 100 tres attempted wth a specfc combnaton of parameters. Table 1. Descrpton of bat algorthm parameters. Bat Algorthm Genetc Algorthm Algorthm and Mnmu Peak Mnmum Peak state m load load load load Ftness functon The bus voltage devaton du (n V) and power losses dp (n kw) for uncompensated and compensated wth the Bat and Genetc Algorthm for all real dstrbuton network busses are ndcated n Table 2 for both operatng states. 330

5 Table 2. The bus voltage devaton and power losses for mnmum and peak load wth the two algorthms. Uncompensated state Bat Algorthm Genetc Algorthm Algorthm and du dp du dp du dp state [V] [kw] [V] [kw] [V] [kw] Mmmum load Peak load Conclusons The paper proposes an approach for optmal capactor allocaton problem n real dstrbuton systems usng an effcent metaheurstc algorthm. To confrm the Bat algorthm performances, a real dstrbuton network was tested, and the optmzaton of shunt capactor placement for bus voltage devaton ndex mnmzaton was solved. The man advantage of Bat algorthm s that t does not requre spendng more effort n tunng the control parameters, as n case of Genetc algorthm, or other Evolutonary algorthms. The smulated results obtaned usng the Bat algorthm are compared wth genetc algorthm, and the results show that the performance of the proposed method s found to be better than the other exstng methods. The proposed method can be easly appled to any large-scale partcle radal dstrbuton system. References [1] V. Haldar, N. Chakraborty, Power loss mnmzaton by optmal capactor placement n radal dstrbuton system usng modfed cultural algorthm, Inter Trans Electr Energy Syst, 25 (1), 54-71, [2] B. C. Neagu, G. Georgescu, The Optmzaton of Reactve Power Sources Placement n Publc Repartton and Dstrbuton Systems for Power Qualty Improvement. In Int. Conf. on Optm. Of Electr. a. Electron. Equp., OPTIM 2012, , [3] C. F. Chang, Reconfguraton and capactor placement for loss reducton of dstrbuton systems by ant colony search algorthm. IEEE Trans. on Power Syst., 16 (4), , [4] N. Gnanasekarana, S. Chandramohanb, P. Sathsh Kumarc, A. Mohamed Imran, Optmal placement of capactors n radal dstrbuton system usng shark smell optmzaton algorthm, An Shams Eng. J., no. 7, , [5] A. Baghpour, S. Fallahan, Mult-objectve placement of capactor banks n dstrbuton system usng bee colony optmzaton algorthm, J. of Adv. n Comp. Res., 6 (2), , [6] R.S. Rao, S. Narasmham, M. Ramalngaraju, Optmal capactor placement n radal dstrbuton systems usng plant growth smulaton algorthm, Int. J. Electr. Power Energy Syst., 33, , [7] F. G. Duque, L. W. Olvera, E. J. Olvera, A. L. M. Marcato, I. C., Jr. Slva, Allocaton of capactor banks n dstrbuton systems through a modfed monkey search optmzaton technque. Int. J. of Electr. Power & Energy Syst., 73, , [8] H.S. Ramadana, A.F. Bendaryc, S. Nagyd, Partcle swarm optmzaton algorthm for capactor allocaton problem n dstrbuton systems wth wnd turbne generators, Int. J. of Elect. Power and Energy Syst., no. 84, , Istanbul, [9] A.Y. Abd-Elazz, E.S. Al, S.M. Abd-Elazm, Flower pollnaton algorthm and loss senstvty factors for optmal szng and placement of capactors n radal dstrbuton systems. Int. J. Electr. Power Energy Syst., 78, , [10] S. M. A. Elazm, E. S. Al, Optmal locatons and szng of capactors n radal dstrbuton systems usng mne blast algorthm, Electr. Eng., 1-9,

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