Allocation of capacitor banks in distribution systems using multi-objective function

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1 Vol. 8(27), pp , 18 July, 2013 DOI /SRE ISSN Academc Journals Scentfc Research and Essays Full Length Research aper Allocaton of capactor banks n dstrbuton systems usng mult-objectve functon Noradn Ghadm Department of Electrcal Engneerng, Ardabl Branch, Islamc Azad Unversty, Ardabl, Iran. Accepted 12 July, 2013 Ths paper develops an optmal placement method n order to sze and ste capactor banks n IEEE 33 bus test system. The proposed method n order of optmzaton n ths artcle s Evolutonary programmng and the objectve functon s composed of two parts. Most part of proposed objectve functon consders mprovement of voltage profle and other part s actve power losses of the system n nomnal load of menton system. In order to use Evolutonary programmng algorthm, at frst, placement problem s wrtten as an optmzaton problem whch ncludes the objectve functon and constrants, and then to acheve the most favorte results, Evolutonary programmng (E) method s appled to solve the problem. Hgh performance of the proposed algorthm n menton system s verfed by smulatons n MATLAB software and n order to prove feasblty of proposed method ths optmzaton n three cases one capactor bank, two capactor banks, and three capactor banks- wll be accomplsh. Key words: Capactor lacement, evolutonary programmng, mult-objectve functon, optmzaton. INTRODUCTION Capactors have been wdely employed n radal dstrbuton systems for reactve power compensaton. Reactve power compensaton s necessary n voltage profle correcton and reducton of actve and reactve loss power (Chung-Fu, 2008). Therefore, the capactor banks can have ntrcate effect on the power-flow, voltage profle, stablty and qualty of power supply for customers and electrcty supplers. The benefts greatly depend on how the capactors are nstalled and dspatched n dstrbuton feeders. Ths problem s termed the general capactor placement and schedulng problem. If ths szng and sttng do not have the approprate locaton and value, the profle of voltage, actve and reactve losses may be wll be ncreased (Noradn, 2012). Varous attempts from dfferent perspectves have been made to solve the capactor placement problem. In Noradn (2012) the optmzaton problem s consdered as a nonlnear programmng problem as contnuous varables by treatng the capactor szes and the ste. Fuzzy logc (FL) has shown good results for capactor bank allocaton when combned wth GAs under snusodal operatng condtons n order to loss reducton n Ng et al. (2000) wth consderaton of capactor szes as dscrete varables and applyng dynamc programmng to fnd the optmal soluton (Duran, 1968). In Gallego et al. (2001), the soluton of ths problem was formulated by the gradent method combned wth a clusterng algorthm that may be fast, but does not guarantee fndng the global optmzed soluton. In Huang (2000) an mmune-based optmzaton technque s proposed for radal dstrbuton system n order to reach optmal pont of capactor banks allocaton optmzaton problem. Non-lnear loads effect on the best pont stes of capactor banks n radal system was analyzed (Baghzouz, 1991). Combnaton of Evolutonary rogrammng (E) algorthm wth fuzzy logc n Venkatesh et al. (2006) was proposed n placement of the optmal capactor banks. Cvanlar et al. (1988) conducted the early research on feeder reconfguraton for loss reducton. E-mal: ghadm.noradn@gmal.com. Tel:

2 Ghadm 1283 Baran et al. (1989) modeled the problem of loss reducton and load balancng as an nteger programmng problem. A harmonc power flow method that consders harmonc couplngs caused by the nonlnear loads was used n Masoum et al. (2004). Chang et al. (1990) used the optmzaton technques based on smulated annealng (SA) to search the global optmum soluton to the capactor placement problem. The Genetc Algorthm (GA) s used n (Mendes et al., 2005) to solve the optmzaton problem to select the optmal pont of capactor banks for radal dstrbuton system. In ths paper, Evolutonary programmng (E) whch s capable of fndng global or near global optmum soluton s used for optmal sze and ste of capactor bank n 33- bus of IEEE test system wth te lne present n Kashem et al. (2000). Objectve functons are gathered to form a mult objectve optmzaton problem. The objectve functon s formed by combnng real power losses and voltage profle of the menton system. ROBLEM FORMULATION Ths study dscusses the capactor placement problems of dstrbuton systems. The objectve s to mnmze the system power loss and mprovement of voltage profle, subject to operatng constrants under a certan load pattern. The mathematcal model of the Mult Objectve Functon (MOF) n ths paper n order to acheve the performance calculaton of dstrbuton systems for capactor sze and locaton problem can be expressed as follows: MOF 1VI 2RL (1) where, 1 and 2 are consder n ths paper as 0.7 and 0.3 respectvely. Objectve functons formulaton As can be seen n Equaton (1), objectve functon s combned from two components. One part s Real ower (RL) that s 30% of menton objectve functon and Voltage rofle Improvement (VI) that s combned as 70% of objectve functon. Real power loss formulaton (RL) Buses voltage, lne currents and real power loss n system lnes s calculated from the output results of power-flow whch s used by Newton-Raphson n ths paper. If v s th bus voltage and v j s jth bus voltage that s specfy from power flow results, the lne current between th and jth buses s gven by: I V V j j (2) Zj where, Z j s the mpedance between th and jth buses, the transmsson power between the th and jth buses and vce versa calculated by: S V I j j * j S V I * j j The real actve loss between th and jth buses s defned as:, j loss real( S S ) (5) j j Total loss power n power system s defned by: N Total 1 N j j loss (3) (4), (6) where, N s the number buses of power system and RL s gven by: RL Total nomn al no al where, mn study system. Voltage rofle Improvement (VI) (7) s the real power loss n nomnal condton of One of the components of optmzes locaton and sze of the capactor banks s the mprovement n voltage profle. Ths ndex penalzes the sze-locaton par whch gves hgher voltage devatons from the nomnal value (Vnom). In ths way, the closer the ndex to zero the better the network performance. The VI can be defned as VI n 2 Vnom V Vnom max (8) Constrans formulaton The mult objectve functon (1) s mnmzed subjected to varous operatonal constrants to satsfy the electrcal requrements for dstrbuton network. These constrants are as follow: 1) ower-conservaton Lmts: The algebrac sum of all ncomng and outgong power ncludng lne losses over the whole dstrbuton network should be equal to zero. Gen n 1 D total 0 2) Dstrbuton Lne Capacty Lmts: ower flow through any dstrbuton lne must not exceed the thermal capacty of the lne max Sj S j (9) (10) 3) Voltage Lmts: the voltage lmts depend on the voltage regulaton lmts that should be satsfed.

3 NO 1284 Sc. Res. Essays start Generate artcles ower Flow calculatng and Computng Objectve Functon Constrans Checkng and Changng partcle oston End of Iter Yes end Fgure 1. Optmzaton flowchart n E. V mn V V max (11) Ths paper employs Evolutonary rogrammng technque to solve the above optmzaton problem and search for optmal or near optmal set of problem. Typcal ranges of the optmzed parameters are [ ] MVAr for capactor and [ ] for voltage of buses. Evolutonary programmng algorthm In ths optmzaton method lke the other methods the ntal ponts are selected n the stochastc manner as shown n the flowchart of the Fgure 1. As t can be seen from the fgure, after selectng these ponts, for each of them the power flow wll be accomplshed and the objectve functon wll be calculated. Therefore, ths pont are checked n the constrants and any of them whch s not wthn ths vable soluton zone should be elmnated and for the ponts wthn ths area the value of the objectve functon should be determned; and n the next state, partcles are moved wthn ths area and f the omtted partcles are more, new partcles wll be regenerated and ths process s contnued untl the selecton of the optmum pont (So et al., 2000a). artcles changes are done accordng to the Gauss normal dstrbuton. These changes are expressed n Equaton (12). In Equaton (12) x s the th partcle poston n the current state, ' x s the poston of the partcle n the next stage. N (0,1 ) s the

4 Ghadm 1285 te lnes Fgure 2. IEEE 33 bus study system wth te lnes n Kashem et al. (2000) Gauss normal dstrbuton, and s a weghted functon obtaned from Equaton (13). s the movement coeffcent; here t s equal to 1, s the offset value adjusted n zero, and (x) s the value of objectve functon for the partcle n the prevous stage whch s affected by the next movements (So et al., 2000b). x x. N (0,1) (12) ' ( x). (13) In ths optmzaton problem, the number of partcles and the number of teratons are selected 30 and 50, respectvely. Dmenson of the partcles wll vary for each condton. CASE STUDY AND LACEMENT RESULTS In the case study presented n ths part of ths work, we nvestgate how capactor placement affects system power loss reducton and voltage profle enhancement. The placement of only a sngle capactor, two capactors and three capactors are consdered. To demonstrate the utlty of the proposed placement algorthm, a 33-bus test system wth te lnes that are present n Kashem et al. (2000) and shown n Fgure 2 s consdered and the system detals are gven n Table 1. At frst, ths paper assumed that one capactor unt of sze varyng between 25 kvar to 10 MVAr wll be placement n menton network. The results of ths study are shown n Table 2 and Fgure 3. Table 2 shows the power loss of the network wth capactor and wthout capactor. Wth the comparng of power loss n two cases that s obvous the capactor placement can have effect n power loss n the whole menton network. Fgure 2 llustrate buses voltage n two cases. Wth attenton to ths Fgure, the voltage profle wth capactor bank s better than wthout capactor and almost capactor bank can be effected n all buses voltage. In other cases, two capactor banks of sze between 25 kvar to 10 MVAr too are consdered n order to locate the mentoned system. Results of ths case are presented n Table 3 and Fgure 4. In ths fgure the voltage profle of three cases (wthout capactor, one capactor and two capactor banks szng and sttng) are presented. As can be seen, t s obvous that the two capactor placement results n lne power losses and voltage profle s better

5 1286 Sc. Res. Essays Table 1. Lnes, actve and reactve power detals n study system. Branch nom Sen. node Rec. node Actve ower of Rec. node (kw) Reactve ower of Rec. node (kvar) Resstance (ohms) Reactance (ohms) * * * * * Table 2. Results of szng and sttng wth a sngle capactor bank. Number of capactor Capactor sze Capactor ste Network loss (kw) Wthout capactor One capactor kw than one capactor bank and wthout capactor n study system. In the next study, we assume that three capactor banks n order to optmal placement are consdered. The results of ths study are represented n power system. The results of lne power loss that are present n Table 4 depcted n ths case of power loss become less than other cases and n Fgure 5 the voltage profle s shown. The voltage profle n ths case s better than the prevous cases.

6 Ghadm Capactor Sze (KVAr) Bus Number Fgure 3. Voltage profle of study system wth a sngle capactor bank and wthout capactor. Table 3. Results of szng and sttng wth two capactor banks-sngle capactor and wthout capactor. Number of capactor Capactor sze Capactor ste Network loss (kw) Wthout capactor One capactor Two capactor Capactor Sze (KVAr) Bus Number Fgure 4. Voltage profle of study system wth two capactor banks - sngle capactor bank and wthout capactor. Concluson In ths paper, a dfferent approach based on Evolutonary rogrammng n order of Mult-objectve optmzaton analyss, ncludng one, two and three capactor banks, for sze-ste plannng of dstrbuted generaton n dstrbuton system was presented. In solvng ths problem, at frst the problem was wrtten n the form of the optmzaton problem whch ts objectve functon was defned and wrtten n tme doman and then the problem has been solved usng E. The proposed optmzaton algorthm was appled to the 33-bus test system wth te lnes.

7 1288 Sc. Res. Essays Table 4. Results of szng and sttng wth three capactor banks-two capactor banks-sngle capactor and wthout capactor. Number of capactor Capactor sze Capactor ste Network loss (kw) Wthout capactor One capactor Two capactor Three capactor Capactor Sze (KVAr) Bus Number Fgure 5. Voltage profle of study system wth three capactor banks- two capactor banks - sngle capactor bank and wthout capactor. The results clarfed the effcency of ths algorthm for mprovement of voltage profle and reducton of power losses n study system. REFERENCES Baghzouz Y (1991). Effects of nonlnear loads on optmal capactor placement n radal feeders. IEEE Trans. ower Delv. 6(1): Baran ME, Wu FF (1989). Network reconfguraton n dstrbuton systems for loss reducton and load balancng. IEEE Trans. ower Delv. 4(2): Chang HD, Wang JC, Cockng O, Shn HD (1990). Optmal capactors placements n dstrbuton systems. art I: A new formulaton of the overall problem. IEEE Trans. ower Delv. 5(2): Chung-Fu C (2008). Reconfguraton and Capactor lacement for Reducton of Dstrbuton Systems by Ant Colony Search Algorthm. IEEE Trans. ower Syst. 23(4): Cvanlar S, Granger JJ, Yn H, Lee SSH (1988). Dstrbuton feeder reconfguraton for loss reducton. IEEE Trans. ower Delv. 3(3): Duran H (1968). Optmum number, locaton, and sze of shunt capactors n radal dstrbuton feeder: A dynamc programmng approach. IEEE Trans. ower Appl. Syst. 87(9): Gallego RA, Montcell AJ, Romero R (2001). Optmal capactor placement n radal dstrbuton networks. IEEE Trans. ower Syst. 16(4): Ng HN, Salama MMA, Chkhan AY, Salama MMA, Chkhan AY (2000). Classfcaton of capactor allocaton technques. IEEE Trans. ower Delv. 15(1): Huang SJ (2000). An mmune-based optmzaton method to capactor placement n a radal dstrbuton system. IEEE Trans. ower Delv. 15(2): Kashem MA, Ganapathy V, Jasmon GB, Buhar MI (2000). A Novel Method for Mnmzaton n Dstrbuton Networks. Internatonal Conference on Electrc Utlty Deregulaton and Restructurng and ower Technologes 2000, London, 4-7 Aprl 2000, pp Masoum MAS, Ladjevard M, Jafaran A, Fuchs EF (2004). Optmal placement, replacement and szng of capactor banks n dstorted dstrbuton networks by genetc algorthms. IEEE Trans. ower Delv. 19(4): Mendes A, Franca M, Lyra C, ssarra C, Cavellucc C (2005). Capactor placement n large-szed radal dstrbuton networks. roc. Inst. Elect. Eng. Gen. Transm. Dstrb. 152(4): Noradn G (2012). Optmal lacement of Capactor Banks n order to Improvement of Voltage rofle and Reducton based on SO. Res. J. Appl. Sc. Eng. Technol. 4(8): Noradn G (2012). Genetcally tunng of lead-lag controller n order to control of fuel cell voltage. 7(43): So CW, L KK (2000a). Overcurrent relay coordnaton by evolutonary programmng. Electr. ower Syst. Res. 53: So CW, L KK (2000b). Tme coordnaton method for power system protecton by evolutonary algorthm. IEEE Trans. Ind. Appl. pp Venkatesh B, Ranjan R (2006). Fuzzy E algorthm and dynamc data structure for optmal capactor allocaton n radal dstrbuton systems. roc. Inst. Elect. Eng. Gen. Transm. Dstrb. 153(1):80-88.