APPLICATION OF BINARY VERSION GSA FOR SHUNT CAPACITOR PLACEMENT IN RADIAL DISTRIBUTION SYSTEM

Transcription

1 IJRET: Internatonal Journal of Research n Engneerng and Technology eissn: pissn: APPLICATION OF BINARY ERSION GSA FOR SHUNT CAPACITOR PLACEMENT IN RADIAL DISTRIBUTION SYSTEM Nasm Al Khan, S. Ghosh, Sandeep S. R 3, SalmMondal 4 Assstant Professor, Alah Unversty Professor, NIT Durgapur; 3 Assstant Professor, SJBIT, Bangalore 4 PG Student,Alah Unversty Abstract Ths paper presents a bnary gravtatonal search algorthm () s appled to solve the problem of optmal allotment of Shunt capactors n radal dstrbuton systems. In ths work, total lne loss (TLL) and the total voltage devatons (TD) are to be mnmzed separately by ncorporatng optmal placement of shunt capactors wth constrants whch nclude lmts on voltage, szes of nstalled capactors. Ths s appled on the balanced IEEE -Bus dstrbuton network and the results are compared wth conventonal bnary partcle swarm optmzaton () *** INTRODUCTION It has been seen that as much as 3% of total power generated s wasted n the form of losses at the dstrbuton level []. Granger and Lee [] developed a nonlnear programmng based method n whch capactor locaton and capacty were expressed as contnuous varables. Baran and Wu [3] dstngushed capactor placement problem separately nto a master problem and a slave problem. The master problem was used to determne the locaton of the capactors whle the slave problem was used to determne the type and sze of the capactors. Chen et al. [4] consdered the mutual couplng effect of conductors to nstall capactors n unbalanced dstrbuton systems. Duran et al. [5] consdered the capactor szes as dscrete varables and employed dynamc programmng to solve the problem. Schmll [6] developed well-known two-thrd rule for the placement of one capactor assumng a unform load and a unform dstrbuton feeder. Granger et al. [7] formulated the capactor placement and voltage regulator problem and proposed decoupled soluton methodology for general dstrbuton system. Placement and szng of shunt capactors by usng loss senstvty factors and plant growth smulaton algorthm were done n Raoet al [8]. The loss senstvty factor was used to predct whch bus has the largest loss reducton when a capactor was placed. S. G. Saranyaet al. [9] employed fuzzy expert system (FES) method for determnng sutable canddate nodes n dstrbuton systems for capactor nstallaton. Recently, Rashedet al. [0] proposed a new optmzaton algorthm called Gravtatonal Search Algorthm (GSA), whch has been demonstrated to be very nterestng to fnd solutons of unmodal and multmodal functons. GSA s based on the law of attracton of masses supported by the Newtonan gravty, whch says that a partcle n the unverse attracts every other one wth a force that s drectly proportonal to the product of ther masses and nversely proportonal to the square of the dstance between them. The orgnal verson of GSA was desgned for search spaces of real valued vectors. However, many optmzaton problems are set n bnary dscrete space, such as feature selecton and data mnng [] dmensonalty reducton [- 6], unt commtment [7], and cell formaton [8], n whch t s natural to encode solutons as bnary vectors. In addton, problems defned n the real space, may be consdered n the bnary space, too. The soluton s to dsplay real dgts wth some bts n the bnary mode. The bnary search space s consdered as a hypercube n whch an agent may move to nearer and farther corners of the hypercube by flppng varous numbers of the bts. In the lteratures, very few papers use the optmzaton of voltage profle as objectve functons. In ths work, a bnary verson of GSA () [9] s utlzed to decde the optmal locatons of shunt capactors to obtan an overall better voltage profle for a radal dstrbuton system. In the, the outcome of these forces s converted nto a probablty value for each element of the bnary vector, whch gudes whether that elements wll take on the value 0 or. The objectve functon s to mnmze total lne loss (TLL) and maxmze the lowest voltage level of the system.e., nothng but mnmze total voltage devaton (TD) to reach a better voltage profle. The locatons of capactors are formulated by bnary varables as decson varables n the constrants.. POWER FLOW SOLUTION IN RADIAL DISTRIBUTION SYSTEM The load flow soluton s carred by the followng set of recursve equatons () and () derved from the sngle lne dagram as shown n Fg.. olume: 05 Specal Issue: 08 NCATEE-06 May-06,

2 IJRET: Internatonal Journal of Research n Engneerng and Technology eissn: pissn: Reactve Power Flow wth Shunt Capactor Placement P Q Q Q Q X L,. RP (4) Q WhereRP + s shunt capactor reactve power magntude njected at bus +;μqs Shunt capactor power multpler, set to zero when there s no capactor power source or set to when there s a capactor power source. Fg. : Sngle lne dagram of a Radal dstrbuton system P Q P P PL R,. ().3 Computaton of Bus oltages (,.,. ) ( R P X Q R, X, P Q (5) ). P Q Q Q QL X,. Where P s the real power flow nto the sendng end of branch +connectng bus and bus +; P L+ s real component of load at bus +; R,+ s the resstance of lne secton between buses and +and s the bus voltage magntude at bus. Q s the reactve power flow nto the sendng end of branch +connectng bus and bus +; Q L + s reactve component of load at bus +; X,+ s the reactance of lne secton between buses and+. The problem of capactor allotment wth ther proper capactes s of great mportance. The nstallaton of shunt capactors at non-optmal places can result n an ncrease n system losses, voltage devatons and costs. Therefore, a power system plannng engneer requres an effcent and fast optmzaton method capable of ndcatng the best soluton for a gven dstrbuton network. The selecton of the best places for nstallaton and the preferable szes of the shunt capactor banks n large dstrbuton systems s a complex dscrete optmzaton problem. In order to ncorporate the proposed method recursve equatons () and () are modfed as follows:. Real Power Flow wth Installaton of Shunt Capactor P Q P P P R L,. AP P WhereAP + s shunt capactor actve power magntude njected at bus+; μps shunt capactor power multpler, set to zero when there s no shunt capactor power source or set to when there s actve power source. () (3) 3. PROBLEM FORMULATION The followng sectons descrbe the detals of the proposed problem formulaton. 3. The Objectve Functons The man advantages of Shunt capactors n the dstrbuton system are loss mnmzaton n the feeders and the mprovement n the voltage profle,.e. mantanng the voltages at customer termnals wth reactve power compensaton. The followng functons are computed usng the proposed algorthm: Total Lne Loss (TLL), Total oltage Devaton (TD). 3. Total Lne Loss (TLL) The nstallaton capactor banks should not result n an ncrease n the system losses. The power loss of the lne secton connectng buses and + s computed as: (, ) R, * Where =,, 3..n and s the voltage of th bus n per unt for the system buses; the deal magntude of each bus voltage s unty. olume: 05 Specal Issue: 08 NCATEE-06 May-06, P loss n TLL P loss Q (7) 3.3. Total oltage Devaton (TD), P oltage devaton can also be mnmzed wth ntegraton of Shunt capactors. The total voltage devaton (TD) n the system, whch s to be mnmzed, s expressed as: n TD (6) (8)

3 IJRET: Internatonal Journal of Research n Engneerng and Technology eissn: pissn: Constrants The followng constrants are consdered [0]. ) Total Power Conservaton: The algebrac summaton of all ncomng and outgong powers over the feeders, takng nto consderaton the feeders losses and the powers suppled by Shunt capactors should be equal to the total demand at that bus. ) Dstrbuton Feeder s Thermal Capacty: Power flows n feeders must be wthn ther capactes. ) Dstrbuton Substaton s Capacty: The summaton of total powers delvered to the network by the substaton s transformers must be wthn the substaton s capacty lmt. v) Shunt capactor Operaton Lmts: The Shunt capactor s generated power must be wthn the Shunt capactor s capacty. v) oltage Drop Lmts: The voltage levels at dfferent buses must be wthn predetermned values. 4. PROPOSED BINARY GRAITATIONAL SEARCH ALGORITHM The conventonal GSA was orgnally desgned to solve problems n contnuous valued space [6]. The search algorthm s based on the metaphor of gravtatonal nteracton between masses n the Newton theory. A j th bt of the th agent (x j ) n a system s represented as a bt 0 or where a combnaton of bts gves the th agent poston. The next agent s velocty (v j )s calculated based on ts current velocty and ts acceleraton as expressed n (9). Then, a new agent s poston (x j ) s updated usng a condton as shown n (). However, the velocty s lmted n nterval [-6, 6] so as to acheve a good convergence rate. v j (t+) = r* v j (t) + a j (t) (9) Sgmod v x d d d e 0,f r sgmod v, otherwse v d (0) () sze and maxmum populaton are set to 60 and 00, respectvely. In the, two postve coeffcents are set to ( c = c =) and nerta weght, (w) monotonously decreases from 0.9 (w max ) to 0.4 (w mn ). In the, the ntal gravty constant, G0 s set to 00 and the best applyng force, (K best ) s monotonously decreased from 00% (K bestmax ) to.5% (K bestmn ). The proposed algorthm has been mplemented on IEEE -bus radal dstrbuton network. IEEE -Bus [] has sngle lne man feeder (Base oltage = K, Base MA = 0. MA) wthout laterals and sublaterals and havng total actve and reactve powers of 435 kw and 8 kar, respectvely. Wthout any njecton of shunt capactors reactve powers, the normal power flow () yelds Total Lne Loss (TLL) and total voltage devaton (TD) as kw and p.u. respectvely. 5. Total Lne Loss (TLL) Mnmzaton Wth no constrants on the total capactes of Shunt capactors, convergence characterstcs of lossmnmzaton and voltageprofle obtaned by dfferent algorthms are depcted n Fg. (a) and (b) respectvely. It s observed from Table 3, voltage profle s mproved as that of, and lowest bus voltage ncreased.0% by whereas n Bnary GSA, t s mproved by.7 %. In TLL mnmzaton, TLL s reduced from kw to.455 kw n case of, where as n t reduces to kw only and TD s mnmzed from p.u. to p.u. and p.u. by and, respectvely wth njecton of optmal placement of Shunt capactors, as ndcated n Table. From Table 4, t s observed three Shunt capactors, each of 5 kar capacty, equvalent to total 75 kar, are optmally placed for TLL mnmzaton n approach but, n, total capactes of shunt capactors s seems to be more. 5. Total oltage Devaton (TD) Mnmzaton Fg. (a) represents voltage profle of IEEE -bus radal dstrbuton system obtaned by optmzaton technques (, ) and normal power flow (). It can be seen that voltage profle s mproved as that of, lowest bus voltage ncreased.3% by whereas n Bnary GSA, t s mproved by.5%, as seen from Table 3. Convergence characterstc of TD mnmzaton s shown n Fg. 3(b). It can be found from Table 5, three Shunt Capactors (at nd, 3 rd and 8 th bus poston), each of 5 kar capacty, are equvalent to total 75 KAR optmally placed n. Some more capacty of Shunt capactors s used n technque for TD mnmzaton. 5. SIMULATION RESULTS AND DISCUSSION To demonstrate the performance of the proposed n solvng the optmal shunt capactor placement problem, the IEEE -bus dstrbuton system s used n ths study. In ths paper, for ths test system, TLL and TD were mnmzed and compared to the conventonal as to llustrate ts performance n solvng the same problem. All the optmzaton parameters are standardzed where populaton olume: 05 Specal Issue: 08 NCATEE-06 May-06, 3

4 T..D n p.u. Bus voltage magntude n p.u. T.L.L n kw. Bus voltage magntude n p.u. IJRET: Internatonal Journal of Research n Engneerng and Technology eissn: pissn: Bus number 0 (a) 6. CONCLUSION Ths paper presented a and a comparatve performance of and n solvng the two separate sngle-objectve optmzaton problem for optmal Shunt capactor placement n IEEE radal dstrbuton test system. The optmzaton technques have been tested on ths dstrbuton test system for determnng the best optmal Shunt capactor placements for TLL and TD mnmzaton. The comparatve results showed that the proposed s the most effectve and precse among the aforementoned optmzaton technques. In concluson, the authors contrbuton n ths work s successful applcaton of a bnary GSA algorthm for smultaneous soluton of optmal number and placements of Shunt capactors n a balanced dstrbuton system Iteraton cycles (b) Fg. : TLL Mnmzaton Characterstcs of IEEE Bus Radal Dstrbuton System; (a) oltage profle obtaned by dfferent algorthms, (b) Convergence characterstcs Bus number (a) (b) Iteraton cycles Fg. 3: TD Mnmzaton Characterstcs of IEEE Bus Radal Dstrbuton System; (a) oltage profle obtaned by dfferent algorthms, (b) Convergence characterstcs. REFERENCES [] Y. H. Song, G. S. Wang, A. T. Johns and P. Y. Wang, Dstrbuton Network Reconfguraton for Loss Reducton usng Fuzzy Controlled Evolutonary Programmng, IEE Proc. Generaton, Transmsson and Dstrbuton, 997, 44(4), pp [] J. J. Granger and S. H. Lee, Optmum Sze and Locaton of Shunt Capactors for Reducton of Losses on Dstrbuton Feeders, IEEE Trans. on Power Apparatus and Systems, 98, vol. 00, no. 3, pp [3] M. Baran and F. Wu, Optmal capactor placement on radal dstrbuton system, IEEE Trans. on Power Delvery, 989, 4(), pp [4] C. S. Chen, C. T. Hsu and Y. Yan, Optmal dstrbuton feeder capactor placement consderng mutual couplng effect of conductors, IEEE Trans. on Power Delvery, 995, 0(), pp [5] H. Duran, Optmum Number Sze of Shunt Capactors n Radal Dstrbuton Feeders: A Dynamc Programmng Approach, IEEE Trans. on Power Apparatus and Systems, 968, 87, pp [6] J.. Schmll, Optmum Sze and Locaton of Shunt Capactors on Dstrbuton Feeders, IEEE Trans. on Power Apparatus and Systems, 965, 84, pp [7] J. J. Granger and S. Cvanlar, olt/var control on Dstrbuton systems wth lateral branches usng shunt capactors as oltage regulators Part I, II and III, IEEE Trans. on Power Apparatus and systems, 985, vol.04, no., pp [8] A. Swarnkar, N. Gupta and K. R Naz, Optmal Placement of Fxed and Swtched Shunt Capactors for Large- Scale Dstrbuton Systems usng Genetc Algorthms, Innovatve Smart Grd Technologes Conference, 00, pp.- 8. [9] S. G. Saranya, E. Muthukumaran, S. M. Kannan and S. Kalyan, Optmal Capactor Placement n Radal Dstrbuton Feeders Usng Fuzzy-Dfferental Evoluton, Proceedngs of the Natonal Conference on Innovatons n Emergng Technology, 0, pp [0] C. S. Chen, C. T. Hsu and Y. Yan, Optmal dstrbuton feeder capactor placement consderng olume: 05 Specal Issue: 08 NCATEE-06 May-06, 4

5 IJRET: Internatonal Journal of Research n Engneerng and Technology eissn: pissn: mutual couplng effect of conductors, IEEE Trans. on Power Delvery, 995, 0(), pp [] K. G. Srnvasa and K. R. enugopal, A self-adaptve mgraton model genetc algorthm for data mnng applcatons, InfSc, 007, 77(0), pp [] P. Avshek and J. Mat, Development of a hybrd methodology for dmensonalty reducton n Mahalanobs Taguch system usng Mahalanobs dstance and bnary partcle swarm optmzaton, Expert System Applcatons, 00, 37(), pp [3] M. Beretaa and T. Burczynsk, Comparng bnary and real-valued codng n hybrd mmune algorthm for feature selecton and classfcaton of ECG sgnals, Engneerng Applcatons of Artfcal Intellgence, 007, 0, pp [4] X. Wang and J. Yang, Feature selecton based on rough sets and partcle swarm optmzaton, Pattern Recognton Letter, 007, 8, pp [5] L. H. Chuang and H. W. Chang, Improved bnary PSO for feature selecton usng gene expresson data, Computatonal Bologcal Chemstry, 008, 3(), pp [6] X. P. Zeng and Y. M. L, A dynamc chan-lke agent genetc algorthm for global numercal optmzaton and feature selecton, Neuro-computng, 009, 7, pp [7] X. Yuan and A. Ne, An mproved bnary partcle swarm optmzaton for unt commtment problem, Expert Systems Applcaton, 009, 36(4), pp [8] T. H. Wu and C. C. Chang, A smulated annealng algorthm for manufacturng cell formaton problems, Expert Systems Applcaton, 008, 34(3), pp [9] E. Rashed, H. Nezamabad-pour and S. Saryazd, : bnary gravtatonal search algorthm, Natural Computng, 00, vol. 9, pp [0] R. Annaluru, S. Das and A. Pahwa, Mult-level ant colony algorthm for optmal placement of capactors n dstrbuton systems, Congress on Evolutonary Computaton, 004, ol., pp [] D. Das, H. S. Nag and D. P. Kothar, Novel Method for Solvng Radal Dstrbuton Networks, IEE Proc. C, 994, ol. 4, (4), pp Test System IEEE - Bus Table : Comparatve Study Of TLL Mnmzaton Ieee -Bus % Improvement n over % Improvement n over EEE -Bus Table : Comparatve Study Of TD Mnmzaton Ieee -Bus % Improvement n % Improvement n (p.u.) (p.u.) over (p.u.) BCAB over IEEE -Bus Table 3: Comparatve Study Of Lowest Bus oltage Improvement n Tll and TvdMnmzaton Ieee -Bus TLL Mnmzaton TD Mnmzaton % Improvement BGS % Improvement % Improvement BGS (p.u. (p.u.) n over A n over (p.u.) n over A ) (p.u.) (p.u.) Table 4: Optmal Locatons Of Shunt capactors for TLL Mnmzaton Ieee -Bus Shunt Optmal locatons of shunt Shunt Capactors Capactors capactors (kar) (kar) IEEE -Bus 00 [,4,5,7], each capactor of 5kAR % Improvement n over Optmal locatons of shunt capactors 75 [,3,5], each capactor of 5kAR Table 5: Optmal Locatons Of Shunt capactors for Tvd Mnmzaton Ieee -Bus Shunt Optmal locatons of shunt Shunt Capactors Capactors capactors (kar) (kar) IEEE -Bus 00 [,4,5,7], each capactor of 5kAR Optmal locatons of shunt capactors 75 [,3,5], each capactor of 5kAR olume: 05 Specal Issue: 08 NCATEE-06 May-06, 5