Implementation and Validation of Different Reconfiguration Strategies Between HSA and PSO for Loss Reduction

Transcription

1 Implementaton and Valdaton of Dfferent Reconfguraton Strateges Between HSA and PSO for Loss Reducton Jamal Darusalam Gu 1, Ontoseno Penangsang 2, Rony Seto Wbowo 3 Master Student, Department of Electrcal Engneerng, Insttut Teknolog Sepuluh Nopember, Surabaya, Indonesa 1 Professor, Department of Electrcal Engneerng, Insttut Teknolog Sepuluh Nopember, Surabaya, Indonesa 2 Assocate Professor, Department of Electrcal Engneerng, Insttut Teknolog Sepuluh Nopember, Surabaya, Indonesa 3 Abstract: In electrc dstrbuton system, the problem of fndng the optmal confguraton of radal network may be classfed as the Travellng Salesman Problem. When a medum voltage system (20 kv) has a number of connected feeders whose crcut breakers (CBs) can be opened or closed, the combnatoral number of possble system confguratons created by swtchng CBs become very large. In order to determne the mnmum loss confguraton of medum voltage system, a new computaton algorthm s proposed. Harmony Search Algorthm (HSA) s proposed to solve the network reconfguraton problem to get optmal swtchng combnaton n the network. The HSA s a recently developed algorthm whch s conceptualzed usng the muscal process of searchng for a perfect state of harmony. It uses a stochastc random search nstead of a gradent search whch elmnates the need for dervatve nformaton. Smulatons are carred out on 33- bus radal network of IEEE test system to valdate the proposed algorthm. The results are compared wth PSO (Partcle Swarm Optmzaton) as a popular approaches avalable n the lterature. It s observed that the proposed method performed well compared to the PSO n terms of the qualty of solutons. Keywords: TSP, HSA, optmal swtchng, loss reducton, electrc dstrbuton system, stochastc, PSO I. INTRODUCTION Power loss reducton s one of the man targets n a power company amed for ncreasng proft margn. One of the practcal soluton n electrc dstrbuton system s reconfgurng the old structure of the feeders to a new one wthout exceed some electrcal constrants. Power system operators have to determne the optmal system structure from the great number of possble system structures. For nstance, the total number of possble system structure s the n th power of 2, f the total number of the connected lne or cables s n[1]. So, a system wth 32-connected cables wll results the total number of confguraton canddates about 2 32 (=4,294,967,296). Practcally, they determne t usng ther experence and engneerng knowledge. However t s not easy to verfy objectvely whether the system structure whch they choose s optmal or not. The dstrbuton network reconfguraton problem may be classfed as the Travellng Salesman Problem. Morton and Mareels [2] stated that the problem can be recast nto a graph-theoretc frame-work, where the problem s to fnd a spannng tree n a graph wth weghted nodes and branches, such that an objectve functon of the weghts, obtaned by reference to Ohm s and Krchoff s Laws, s mnmzed. In fact, the network reconfguraton n electrc dstrbuton systems belongs to a complex combnatoral optmzaton problem where reconfguraton s realsed by changng the status of sectonalzng and te swtches [3]. Several approaches to solve the problem based on heurstcs and metaheurstcs have been made. Heurstc methods nclude Swtch Exchange Method by Cvanlar et al. [4], Sequental Swtch Openng Method by Shrmo-hammad and Hong [5] and a Nonlnear Constructve Approach by McDermott et al. [6]. On the other hand, metaheurstc approaches have been developed snce 1990 nclude Smulated Annealng by Chang and Jean-Jumeau [7], Ant Colony Search Algorthm by Chang [8], Genetc Algorthms (GA) by Nara et al. [9], and the last but the most popular artfcal ntellgent approach, Partcle Swarm Optmzaton (PSO). For example, [10]-[12] have appled PSO and ts varan to a Dstrbuton Network Reconfguraton (DNR) problem. Copyrght to IJIREEICE 32

2 Ths paper presents a metaheurstc method based on Harmony Search to solve DNR problem. The proposed method s tested on 33-bus system whch ts complete data can be found n [13]. Smulaton results are obtaned to evaluate ts effectveness and robustness comparng wth the PSO. II. FORMULATION OF THE DISTRIBUTION NETWORK RECONFIGURATION PROBLEM FOR LOSS REDUCTION The reconfguraton problem can be formulated as follows: N R 2 mn F R I...(1) j j j1 Subjected to the followng constrants: 1. The bus voltage magntude V mn V V max ; N b....(2) 2. The current lmt of branches I j I j max ; j N R.....(3) 3. Radal Topology Where, F s the objectve functon to be mnmzed corresponds to the total power loss n the system, R j s the resstance of the branch j and I j s the magntude of the current flowng through the branch j, V s the voltage on bus, V mn and V max are mnmum and maxmum bus voltage lmts respectvely, I j and I jmax are current magntude and maxmum current lmt of branch j respectvely and N b and N R are the total number of buses and branches n the system respectvely. The objectve functon s calculated startng from the soluton of the power flow equatons that can be solved usng the BIBC BCBV method [14]. Ths method has excellent convergence characterstcs and s very robust and proved to be effcent for solvng radal dstrbuton networks. To check the radalty constrants for a gven confguraton, a method based on the bus ncdence matrx  s used [15] n whch a graph may be descrbed n terms of a connecton or ncdence matrx. Partcular nterest s the branch to node ncdence matrx Â, whch has one row for each branch and one column for each node wth a coeffcent a j n row and column j. The value of a j = 0 f branch j s not connected to node, a j = 1 f branch j s drected away from node and a j = 1 f branch j s drected towards node. For a network calculaton, a reference node must be chosen. The column correspondng to the reference node s omtted from  and the resultant matrx s denoted by A. If the number of branches s equal to the number of nodes then, a square branch-to-node matrx s obtaned. The determnant of A s then calculated. If det(a) s equal to 1 or 1, then the system s radal. Else f the det(a) s equal to zero, ths means that ether the system s not radal or group of loads are dsconnected from servce. The HS algorthm s a new metaheurstc populaton search algorthm derved from the natural phenomena of muscan s behavor when they populaton members collectvely play ther muscal nstruments decson varables to come up wth a pleasng harmony global optmal soluton. Ths state s determned by an aesthetc standard ftness functon. When a muscan s mprovsng, he has three possble choces; playng any famous tune exactly from hs memory Memory Consderaton ; playng somethng smlar to the aforementoned tune ptch adjustment ; composng new or random notes from the ptch range Random Selecton. The Man Steps of HS are as follows: A) Intalzaton In ths step, the optmzaton problem, algorthm parameters and harmony memory are defned. The optmzaton problem s specfed as follows: Mnmze F(x) (4) Where, F(x) s an objectve functon, x s the set of each decson varable x, N s the number of decson varables, X s the set of the possble range of values for each decson varable. The HS algorthm parameters are also specfed n ths step. These are the Harmony Memory Sze (HMS); Harmony Memory Consderng rate (HMCR); Ptch Adjustng Rate (PAR) and the maxmum number of mprovsatons (N ). The harmony memory (HM) s a memory locaton where all the soluton vectors (sets of decson varables) are stored. Here, (HMCR) and (PAR) are parameters that are used to mprove the soluton vector, whch are defned n Step 2. The ntal (HM) conssts of a certan number of randomly generated solutons for the optmzaton problem under consderaton wthout volatng the constrants. For a problem of N varables, a (HM) wth the sze of (HMS) can be represented as follows: x x... x x F 1 2 N1 N x x... x x F 1 2 N1 N 2 HM (5) : :... : : : HMS HMS HMS HMS x x... x x F 1 2 N 1 N HMS... Where, (x 1, x 2,, x N ) represents a canddate soluton for the optmzaton problem and F 1 s the value of the ftness functon correspondng to the frst soluton vector. For the network reconfguraton problem, the soluton vector s represented by the set of te-swtches n the radal confguraton of the network [16]. The ntal confguraton of te-swtches for 33-bus test system whch s shown n Fg. 1 can be represented as n (6). Confguraton = [ ] (6) Copyrght to IJIREEICE 33

3 Where, 33 s the te-swtch from loop 1, 35 s the te-swtch from loop 2, etc. The (HM) s sorted n ascendng order wth respect to the ftness functon such that confguraton wth the least power loss (best confguraton) s at the top and the one wth the hghest power loss (worst confguraton) s at the bottom. B) Improvse a New Harmony A new harmony vector (x 1, x 2,, x N ) s generated based on three man rules: (1) memory consderaton (2) ptch adjustment and (3) random selecton. Generatng a new harmony s called mprovsaton. Each component of the soluton s chosen ether from the harmony memory or by randomness dependng on the value of the (HMCR), whch vares between 0 and 1, and defned as the rate of choosng one value from the hstorcal values stored n the (HM), whle (1-HMCR) s the rate of randomly selectng one value from the possble range of values as follows: f rand( ) < HMCR else x x x, x,..., x 1 2 HMS x x X end...(7) Where, rand( ) s a unformly dstrbuted random number between 0 and 1 and X s the set of the possble range of values for each decson varable. Every varable x obtaned by the memory consderaton s examned to determne whether t should be ptch-adjusted. Ths operaton uses the (PAR) parameter, whch s the rate of ptch adjustment and the value (1-PAR) s the rate of dong nothng as follows: f rand( ) < PAR x else x x rand( )*BW x end...(8) Where, BW s an arbtrary dstance bandwdth for the contnuous desgn varable and rand( ) s unform dstrbuton between -1 and 1. If the problem s dscrete n nature as the network reconfguraton problem, BW s taken as 1. C) Update Harmony Memory If the new harmony vector (x 1, x 2,, x N ) s better than the worst harmony n the HM, judged n terms of the objectve functon value (yelds to a better ftness than that of the worst member n the HM), the new harmony s ncluded n the HM and the exstng worst harmony s excluded from the HM. The HM s rearranged n ascendng order accordng to the ftness functon. Otherwse, the new harmony s dscarded. D) Check Stoppng Crtera If the stoppng crteron (maxmum number of mprovsatons) s satsfed, computaton s termnated and fnally the best one among the soluton vectors stored n the HM s selected, whch s the optmum soluton of the problem. Otherwse, Steps 2 and 3 are repeated. Fg. 1. The base confguraton of 33-bus system III. IMPLEMENTATION OF HSA FOR RECONFIGURATION PROBLEM The system s a 33 bus, kV, radal dstrbuton system as shown n Fg. 1. It conssts of fve te lnes and 32 sectonalzng swtches. The normally open swtches are 33 to 37, and the normally closed swtches are 1 to 32. The lne and load data of the network are obtaned from [13], and the total real and reactve power loads on the system are 3715 kw and 2300 kvar, respectvely. The ntal power loss of ths system s kw. The lowest bus bar voltage s p.u., whch occurs at node 18. The substaton voltage s consdered as 1 p.u. and all te and Copyrght to IJIREEICE 34

4 sectonalzng swtches are consdered as canddate swtches for reconfguraton problem. The algorthm was developed n MATLAB, and the smulatons were done on a computer wth Pentum Centrno Duo, 1.8 GHz, 1GB RAM. The parameters of HSA used n the smulaton of the network are shown n Table 1. The optmal confguraton obtaned by the proposed algorthm s 7, 35, 13, 28, 36, whch has a real power loss of kw. Ths amounts to a reducton of 40.28% n total power loss. The mnmum node voltage of the system s mproved to p.u. (node 33) after reconfguraton. The node Voltages at each bus are shown n Table 2. The voltage profles of the system before and after reconfguraton are shown n Fg. 2. The mnmum voltage n the system after reconfguraton s mproved by 34.4%. The real power flows n each branch before and after reconfguraton are shown n Fg. 3. From Fg. 3, t s observed that the power flow n each branch s reduced after reconfguraton. Ths shows that feeders are releved from the overloadng and makes t possble to load the feeders further. The power loss n each branch before and after reconfguraton s shown n Fg. 4. It s observed that the losses n almost every branch s reduced, except at 8, 9, 20, 21, 24, 25, 26, 33 and 34, where the losses are ncreased because of shftng of loads onto these feeders. To verfy the performance of the proposed algorthm, ths case was repeatedly solved 200 tmes. The best and the worst values among the best solutons as well as the average value and standard devaton (STD) for the best solutons of these 200 runs are lsted n Table 3. A smaller standard devaton mples that most of the best solutons are close to the average. The best solutons for these 200 runs are compared wth the best objectve functon values obtaned by the PSO. The PSO got premature convergence so that ther standard devaton s larger than that of the HSA method. The convergence rate of the proposed HSA algorthm compared wth that of the PSO method for 33-bus system s depcted n Fg. 5. It can be seen that although the PSO has a relatvely fast convergence compared to the proposed method but the PSO usually beng trapped n to the local optmum durng teratons. Before Reconfguraton After Reconfguraton Bus Voltage Bus Voltage Bus Voltage Bus Voltage Fg. 2. Voltage profle of 33-bus radal system TABLE I PARAMETERS OF THE HSA HMS 10 HMCR 0.85 PAR 0.3 Number of teratons 250 TABLE II NODE VOLTAGES OF 33-BUS SYSTEM (P.U.) Fg. 3. Power flow n 33-bus system before and after reconfguraton Copyrght to IJIREEICE 35

5 TABLE IV RESULTS BASED ON DIFFERENT PARAMETERS SETTING OF HSA FOR 33- BUS SYSTEM Fg. 4. Losses n 33-bus system before and after reconfguraton Scenaro Parameter Settng Power Loss HMCR PAR HMS (kw) TABLE III COMPARISON RESULTS BETWEEN HSA VERSUS PSO Intal Fnal Confguraton Item Confguraton Method HSA Proposed PSO Te Swtches 33,35,34, 37,36 07,35,12, 28,36 07,35,13, 28,36 Best Loss Worst (kw) Average STD (For 200 Runs) Average Loss Reducton (%) Loss Reducton (Best value n %) Mnmum Voltage (p.u.) CPU Tme (sec.) Fg. 5. Convergence characterstcs of 33-bus system Smulatons are carred out for 250 teratons and optmum soluton s obtaned after 150 teratons. The average CPU tme taken by the processor to carry out the smulatons for 250 teratons s 2.7 second, whch s less than the PSO. To determne the mpacts of dfferent parameters of the HS algorthm on the soluton qualty and convergence behavor, an emprcal study s performed. To show the effects of sngle parameter changes, 12 dfferent cases are tested as shown n Table 4. Each case s tested over 200 runs n three scenaros, and maxmum number of teratons s fxed to 250 for all runs. In scenaro 1, 2, and 3, HMCR, PAR, and HMS are vared, respectvely, and other two parameters are kept constant. The total power loss for 33-bus dstrbuton by varyng the parameters are summarzed n Table 4. The HMCR determnes the rate of choosng one value from the hstorcal values stored n the HM. The larger the HMCR, the less exploraton s acheved; the algorthm further reles on stored values n HM, and ths potentally leads to the algorthm gettng stuck n a local optmum. On the other hand, choosng the HMCR too small decreases the algorthm effcency, and the HS algorthm behaves lke a pure random search, wth less assstance from the hstorcal memory. As shown n Table 4, large and small HMCR values lead to a decrease n the soluton qualty. Large and small HMS values decrease the effcency of the harmony memory as seen n Table 4. For most problems, a HMS between N and 2N s reasonable. It s observed that the algorthm has small senstvty to PAR values. IV. CONCLUSION In ths paper, a recently developed metaheurstc HSA s successfully appled to optmze radal dstrbuton systems wth objectve of reducng power losses. Smulatons are carred on 33 buses and results are compared Copyrght to IJIREEICE 36

6 wth a popular method avalable n the lterature called [8] Chang CF, Reconfguraton and Capactor Placement for Loss Reducton of Dstrbuton Systems by Ant Colony Search Algorthm, IEEE Partcle Swarm Optmzaton (PSO). Results show that the Transacton on Power System, 2008; 23(4), pp proposed algorthm can converge to optmum soluton [9] Nara K, Shose A, Ktagawa M, and Ishhara T, Implementaton of Genetc quckly wth better accuracy compared to the PSO. Algorthm for Dstrbuton Systems Loss Mnmum Re-confguraton, Computatonal results of 33-bus system showed that IEEE Transacton on Power System, 1992; 7(3), pp [10] Xu L, Lu L, and Lu J, Modfed Partcle Swarm Optmzaton for proposed HSA method s better than PSO. It can be observed Reconfguraton of Dstrbuton Network, Automaton of Electrc Power that 36.53% of average loss reducton s acheved by HSA Systems, 2006; 30, pp comparng wth 35.3% by the PSO as shown n Table [11] 3. Xaolng J, Janguo Z, and Yng S, Dstrbuton network reconfguraton From Table 4, the results based on some dfferent for load balancng usng bnary partcle swarm optmzaton, Intl. Conf. on Power System Technology, November parameters settng for the HSA method show that the [12] Cu-Ru W and Yun-E Z, Dstrbuton Network Reconfguraton Based on proposed method s effectve n loss reducton for varous Modfed Partcle Swarm Optmzaton Algorthm, Intl. Conf. on Machne parameters settng demonstratng a certan extent adaptve Learnng and Cybernetcs, Aug performance for the proposed method. The convergence rate [13] M.E. Baran and F. Wu, Network reconfguraton n dstrbuton system for loss reducton and load balancng, IEEE Transacton on Power Delvery, curve confrms that the HSA method can more effcently 1989; 4(2), pp search the optmal or near-optmal soluton for network [14] Jen-Hao T, A Drect Approach for Dstrbuton System Load Flow reconfguraton problems wthout beng trapped n to the Solutons, IEEE Transacton on Power Delvery, 2003; 18(3), pp local optmum. Moreover, t can be observed from results [15] of P. Wrght, On mnmum spannng trees and determnants, Mathematcs Magazne, 2000; Vol.73, pp bus that the proposed method s the best n the soluton as [16] RS Rao, SVL Narasmham, MR Raju, and AS Rao, Optmal Network well as the CPU tme. Reconfguraton of Large-Scale Dstrbuton System Usng Harmony Search Ths method s useful for analyzng exstng Algorthm, IEEE Transacton on Power Systems, 2011; 26(3), pp systems, helps n plannng a future system, onlne dstrbuton automaton system, and s especally sutable for a large-scale practcal system. A real Indonesan power BIOGRAPHY company (PT. PLN) dstrbuton system wll be used n the future study to verfy the usefulness of the proposed Jamal Darusalam Gu, receved hs S.T. algorthms. The dstrbuted generators (DGs) mpacts on from Unverstas Sam Ratulang, Manado, reconfguraton problem also wll be nvestgated when those Indonesa n Snce 2011, he has been connected to the grd. studyng n Electrcal Engneerng, Insttut Teknolog Sepuluh Nopember (ITS), ACKNOWLEDGMENT Surabaya, Indonesa as a master student. He The authors gratefully acknowledge the s currently as prospectve lecturer wth the Unverstas contrbutons of M. Sya n and Y. Tonce to the program Neger Gorontalo (UNG). Hs research nterests nclude development. Frst author also acknowledge the fnancal power system analyss, dstrbuton automaton, artfcal support from Indonesan Government through Beasswa ntellgent and renewable energy. Unggulan DIKTI. REFERENCES [1] Hayash Y, Matsuk J, Determnaton of Optmal System Confguraton n Japanese Secondary Power System, IEEE Transacton on Power System, 2003; 18(1), pp [2] Morton AB, and Mareels IMY, An Effcent Brute-Force Soluton to the Network Reconfguraton Problem, IEEE Transacton on Power Delvery, 2000; 15(3), pp [3] Ah Kng RTF, Radha B, and Rughooputh HCS, A Real-Parameter Genetc Algorthm for Optmal Network Reconfguraton, Proceedng IEEE ICIT, Marbor, Slovena. 2003; pp [4] Cvanlar S, Granger JJ, Yn H, and Lee SSH, Dstrbuton Feeder Reconfguraton for Loss Reducton, IEEE Transacton on Power Delvery, 1998; 3(3), pp [5] Shrmohammad D, and Hong HW, Reconfguraton of Electrc Dstrbuton for Resstve Lne Loss Reducton, IEEE Transacton on Power Delvery, 1989; 4(2), pp [6] Mc Dermott TE, Drezga L, and Broadwater RP, A Heurstc Nonlner Constructve Method for Dstrbuton System Reconfguraton, IEEETransacton on Power Systems, 1989; 14(2), pp [7] Chang HD, and Jean-Jumeau R, Optmal Network Reconfguraton n Dstrbuton Systems: Part 1: A new formulaton and a soluton methodology, IEEE Transacton on Power Delvery, 1990; 2(4), pp Ontoseno Penangsang, receved hs Ir. from Insttut Teknolog Sepuluh Nopember, M.Sc. and Ph.D. from Unversty of Wsconsn, USA. He s a Professor of Electrcal Engneerng at Insttut Teknolog Sepuluh Nopember (ITS), Surabaya, Indonesa.] Rony Seto Wbowo, receved hs S.T. from Insttut Teknolog Sepuluh Nopember (ITS), M.T. from Insttut Teknolog Bandung (ITB), and Dr.Eng. from Unversty of Hroshma, Japan. He s an Assocate Professor of Electrcal Engneerng at Insttut Teknolog Sepuluh Nopember (ITS), Surabaya, Indonesa. Copyrght to IJIREEICE 37