Optimal Size and Location of Capacitors Placed on a. Distribution System

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1 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong Optmal Sze and Loaton of Capators laed on a Dstrbuton System CHING-TZONG SU CHENG-YI LIN JI-JEN WONG Department of Eletral Engneerng WuFeng Insttute of Tehnology Mng-Hsung, Chay 62, Tawan Tanan Branh Tawan ower Company En-Su, Tanan 3, Tawan tsu@mal.wf.edu.tw u406@tapower.om.tw u59345@tapower.om.tw Abstrat:-Ths paper proposes a study of reatve power ompensaton for eletr dstrbuton systems to fnd out the optmal apatve ompensaton loaton and quantty. The most ommonly used reatve power soures for ompensaton n dstrbuton systems are apator banks. The ompensaton problem under study s an optmzaton problem. A new method-evolutonary smulated annealng, wth evoluton strateges embedded n the smulaton annealng, s employed to solve a 36-bus dstrbuton system omposed of radal-type and loop-type ruts, to fnd out the optmal apator plaement solutons. Lastly, aordng to the results of smulaton, t valdates the proposed approahes and provdes the way to promote the power-supply qualty of dstrbuton systems. Keywords:-Capatve ompensaton, Radal-type, Loop-type, Evolutonary smulated annealng.,ower loss,. Introduton Bus voltage The radal type system s the most ommonly used one for power dstrbuton[-6], yet when somethng does go wrong n the system, an nstantaneous blakout may our. In order to satsfy the hgh expetatons of the hgh-teh ndustry for a relable power supply system, we pay greater attenton to the use of a loop dstrbuton system. Ths system not only mproves relablty and serve qualty of the power supply, but also entals less power loss than ours wth the radal type. At present, Tawan ower Company has been atvely promotng the use of the loop type dstrbuton system to satsfy the demand of users n general, and those n hgh-teh ndustry, n partular, for relable power supply, and to prevent the ourrene of nstantaneous blakouts aused by mantenane, swthng operaton, and sngle ndents of the dstrbuton system. Ths paper ams to dentfy the best poston settng (fxed or swthed apator) and the apaty of apators n the dstrbuton system by addng the loop type to that of the radal type, to mnmze nvestment ost and prevent power loss. The ultmate goal s to aheve the lowest total ost, mprove voltage drops and relablty of power supply, and smultaneously redue lne loss. Ths study proposes a large-sale dstrbuton system by usng evolutonary smulated annealng whh has been effetvely appled to dspath n var ompensator to examne whether the same effetveness an be aqured. Ths method adopts ompetton proedures n evoluton strategy and mult-path searhng Issue 4, Volume 3, Aprl ISSN:

2 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong sklls of ndvduals to onentrate the lmted omputng resoures on the possble area of best-so-far for mprovng the effetveness of smulated annealng and the determnaton of the best-so-far. 2. Feeder ower Flow Equaton For a balaned three-phase system wth sngle feeder as shown n Fg.. Let and refer to the real power and reatve power of bus, respetvely; V shows the voltage, δ the phase angle; also let R, + and X, + ndate the resstane and reatane for the feeder seton from bus to bus +, respetvely. Some results are aqured from equatons () ~ (6) [,2,]: X R δ,, δ tan = 2 (4) V ( R, + + X, + ) I = I + + IL+ (5) L+ + L+ I L+ = (6) 3 V + In general, the two values of and + X,+ 2 V + R,+ 2 V are far smaller than the transmsson power of feeders, and ; t s reasonable to make the followng assumptons to speed up the omputaton : ) The ntal value of bus voltage s + = + + L + + R, + 2 () V + = + + L + + X, + 2 (2) V V + = V 2 (R,+ + X,+ ) + + (R, + X, ) 2 V + + (3) assumed as pu;.e. V =pu. T 2) The power flow of the feeders s equvalent to: + + L+ + + L+ Above equatons () and (2) are amended to the followng equatons of () and (8): = + + L+ + R, + Issue 4, Volume 3, Aprl ISSN:

3 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong ( + + L+ ) + ( + + L+ ) 2 V = L X ,+ ( + + L+ ) + ( + + L+ ) 2 V () (8) The power of buses s derved from the end of the feeder to the startng bus of the feeder. Bus voltages an be omputed from the startng bus to that of the end of the feeder. 3. Mathematal Model The ompensatng apator n the dstrbuton system s used to provde reatve power, n order to redue power loss of the feeder and mprove the stablty of bus voltage wthn the spefed range. The nstallaton ams to defne the most approprate poston, sze, and type of the ompensatng apator to mnmze power loss and nvestment ost at the same tme. By dong so, the system wll work to mnmze the total ost goal, and the objetve funton s demonstrated n the followng equaton : m F = K loss + K Δ = (9) Where K : Cost fator of real power loss (dollar/kw-year) K : Annual ost of apator per kvar (dollar/kvar-year) loss :Total power loss of the system durng peak load (kw) Δ :Capatane added at bus ; and an ntegral tme of the unt apatane Δ 0 assumed. Equaton (0) shows the ost of power loss [8]: E = C loss FLS = K loss Where :Capator beng equpped to bus o :Unt apator avalable S :ostve nteger (0) m: system bus number Based on the above objetve funton and lmtatons, the problem s modeled as equaton (4): Mnmze: F = K loss Subjet to + 4.Evolutonary Annealng K m = Δ V mn V Vmax m S 0 0 = = > s (4) Smulated.C.Yp and Y.H ao ombned smulated annealng wth another powerful optmum tool, evolutonary strategy algorthm, to solve the famous travelng salesperson problems n 995 and ths new method s referred to as evolutonary smulated annealng [9-2]. Evolutonary smulated annealng ntegrates evolutonary strategy algorthm wth smulated 0 Issue 4, Volume 3, Aprl ISSN:

4 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong annealng to ounter the drawbaks of random searhng as well as the vulnerablty of beng nfluened by ntal searhng. Evolutonary strategy algorthm omes from the Darwnan noton of survval of the fttest, emphaszng the elements of ompetton and elmnaton among varous groups. Based on natural ompetton, those performng well, expand n number, and those dong poorly derease or are even elmnated. Through evolutonary smulated annealng and ths nspratonal evolutonary strategy, we are able to use lmted omputng resoures on the more lkely best-so-far area to avod random searhes, and the nfluene of ntal value to mprove soluton effetveness. We assume that there s a need to determne the mnmum value of the objetve funton f x, x ) on the developed surfae ( 2 of x horzontal axs and x 2 vertal axs; that s, to evenly dstrbute N on the spae for searh before omputng, and then treat N ponts as the parents of N famles. In ths example, eah of the parents and the offsprng onsttute the ndvdual of ( x, x 2 ), and the value of f ( x, x2 ) refers to the qualty of eah ndvdual used as the elmnaton base. There are two ompetton levels n the evolutonary smulated annealng method. Flow hart of Fg. 2 demonstrates the proess of the applaton of evolutonary smulated annealng to apatve ompensaton n dstrbuton systems. 5. Illustratve Applaton Example Ths applaton system adopts the struture of the dstrbuton system, as shown n Fg. 3 [3,4]. Fg. 3 s omposed of one man feeder wth 8 buses and three branhng lnes (among them, one branhng wre ontans 4 loop system buses) for a total of 36 buses. The load apaty of eah bus s ndated n Table and the nformaton on the resstane and reatane of the feeder s shown n Table 2. Table :The three phase load power of the dstrbuton system Bus no. Real power load (kw) Reatve ower load Bus No. Real power load (kw) Reatve power Load Total Table 2:The mpedane parameters for feeders of From Bus the dstrbuton system To Bus + R, + ( Ω ) X, + ( Ω ) Issue 4, Volume 3, Aprl ISSN:

5 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong The nomnal voltage of the dstrbuton system s kv, and the base power s 5 MVA. Before ompensaton, buses 6 through 8 and 28 through 36, wth a total of 2 buses have voltages volatng the voltage lmtaton range of 0.95 p.u. ~.05 p.u. as shown n Table 3, and the bus voltage profle s shown n Fg. 4. Table 3:Bus voltages before ompensaton Bus Voltage Bus Voltage Degree no (p.u.) no. (p.u.) Degree Table 4 shows the real and reatve power losses of eah feeder seton before ompensaton for the llustratve system. Table 5 shows those apators avalable for addton. Table 4:The real and reatve power losses of every feeder seton before ompensaton From Bus To Bus + Real power loss (kw) Reatve power loss Total We assume the unt apator 0 as 00 kvar. Lmt the apatve ompensaton of eah bus as L,total, where L,total s the Issue 4, Volume 3, Aprl ISSN:

6 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong Table 5:Avalable apators for ompensaton andther assoated annual osts (Dollar /kvar-year) (Dollar /kvar-year) (Dollar/kVAr-year) (Dollar /kvar-year) reatve power loaded on the feeders of the 36-bus system and s assumed as 3000 kvar. Based on the above nformaton, there are up to L, total 30 types( 3000 = = 30 )of unt pres 00 of apator avalable for bus reatve ompensaton. Other parameters for the proposed method are as follows: the annual ost of power loss per kw, (dollar/kw-year); K = 630 = and ts maxmum and mnmum lmtatons of bus voltage are V max =. 05 p.u. and V mn = 0.95 p.u., respetvely. arameters spefed for applyng the smulated annealng Smulated annealng s used to determne the ompensaton of the apator, and the parameters are set as ntal temperature, T 0 = 00, fnal temperature, T f = 25, temperature droppng o-effent, α = 0. 95, and teraton tmes, K (perturbatons) = 000. max arameters spefed for applyng the evolutonary smulated annealng The famly of N parents n evolutonary annealng s set as 0 and 00; ntal temperature, T o = 00, fnal temperature, T f = 25 ; and temperature droppng o-effent, α = Computatonal results The ompensated results from applyng the two methods the smulated annealng and the evolutonary smulated annealng together wth the results before ompensaton are shown n Table 6 and Fg. 5 for onvenent omparson. The omputatonal results reveal that the objetve funton value has been greatly redued by reatve power ompensaton. Moreover, the evolutonary smulated annealng gves a better objetve funton value of,068,090 omparng wth that from the smulated annealng of,080, Conluson revous lterature has shown that the study of reatve power ompensaton n the dstrbuton system mostly fouses on radal struture and ths paper takes another perspetve to address the effetveness ssue based on rut wth loop-type struture. At present, power systems use apators to redue feeder loss, to mprove bus voltage, and to aheve the ultmate goal of safety and qualty of power supply. In addton Issue 4, Volume 3, Aprl ISSN:

7 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong to system loss, eonom fators suh as the nstallaton ost of the apator, are also taken nto onsderaton and would be benefal to future studes of the dstrbuton system. The omparson results n Table 6 ndate that the evolutonary smulated annealng works better than the smulated annealng n searhng for the optmum value, and both methods have sgnfantly redued the power loss and mproved the system voltage profle.. Referene [] M. E. Baran and F. F. Wu, Optmal szng of apators plaed on a radal dstrbuton system, IEEE Trans. on ower Delvery, vo. 4, no., pp.35-43, January 998. [2] J. V. Shmll, Optmal sze and loaton of shunt apators on dstrbuton feeder, IEEE Trans. on ower Apparatus and Systems, vo. AS-84, no.9, pp , September 965. [3] Y.T. Hsao, C H. Chen, and C.C. Chen, Optmal apator plaement n dstrbuton systems usng a ombnaton fuzzy-ga method, Internatonal Journal of Eletral ower & Energy Systems, vol. 26, ssue, pp ,2004. [4].V. rasad, S. Svanagaraju, and N. Sreenvasulu, A fuzzy-genet algorthm for optmal apator plaement n radal dstrbuton systems, ARN Journal of Engneerng and Appled Senes, vol. 2, no.3, pp , 200. [5] J. Nkoukar and M. Gandomkar, Genet algorthm for apator plaement n radal dstrbuton systems based on a network-topology load flow, WSEAS Transatons on Systems, ssue 0, vol. 3, pp , [6] D. Issaba, A.L. Bettol, J. Coelho, and M.V.. Alantara, Optmal apator plaement n radal dstrbuton systems by renforement learnng approah, WSEAS Transatons on ower Systems, ssue 8, vol., pp , [] G. B. Jasmon and L. H. C. C. Lee, Stablty of load-flow tehnques for dstrbuton system voltage stablty analyss, IEE roeedng-, vo.38, no.6, pp , November 99. [8] J.J. Granger and S.H. Lee, Optmum sze and loaton of shunt apators for reduton of losses on dstrbuton feeders, IEEE Trans. on ower Apparatus and Systems, vol. AS-00, no.3, pp. 05-8, 98. [9].. C. Yp and Y. H. ao, Combnatonal optmzaton wth use of guded evolutonary smulated annealng, IEEE Trans. on Neural Networks, vol. 6, no. 2, pp , Mar [0].. C. Yp and Y. H. ao, A guded evolutonary omputaton tehnque as funton optmzer, IEEE Conferene on Evolutonary Computaton, vol. 2, pp , 994. [] R. A. Rutenbar, Smulated annealng algorthms: an overvew, IEEE Cruts and Deves Magazne, vol. 5, no., pp.9-26, Jan [2] A. Sadegheh, Global optmzaton usng evolutonary algorthms, smulated annealng and Tabu searh, WSEAS Transatons on Informaton Sene and Applatons, ssue 6, vol., pp , [3] M. E. Baran and F. F. Wu, Network reonfguraton n dstrbuton systerms for loss reduton and load balanng, IEEE Trans. on ower Delvery, vo.4, no.2, pp.40-40, Aprl 989. [4] G. B. Jasmon and L. H. C. C. Lee, Stablty of load-flow tehnques for dstrbuton system voltage stablty analyss, IEE roeedng-, vo.38, no.6, pp , November 99. Issue 4, Volume 3, Aprl ISSN:

8 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong Bus no. Table 6:Computaton results obtaned by applyng the smulated annealng and the evolutonary smulated annealng Voltage before ompensaton (p.u.) Smulated annealng number of perturbatons=000 Compensated Voltage after apator ompensaton (p.u.) Evolutonary smulated annealng N = 00 parents Compensated Voltage after apator ompensaton (p.u.) Total real power loss (kw) Objetve funton value (Dollar/year),689,030,080,540,068,090 Issue 4, Volume 3, Aprl ISSN:

9 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong Fg. 2 Flow hart of applaton of evolutonary smulated annealng algorthm to apator VAr ompensaton. Issue 4, Volume 3, Aprl ISSN:

10 Chng-Tzong Su, Cheng-Y Ln, J-Jen Wong Fg. 3 A 36-bus dstrbuton system V(pu) Bus Fg. 4 Bus voltage profle before ompensaton. Fg. 5 Bus voltage magntude (p.u.) before and after ompensaton. Issue 4, Volume 3, Aprl ISSN: