A Genetic Algorithm Based Multi Objective Service Restoration in Distribution Systems

Transcription

1 Journal of Computer Scence 7 (3): , 2011 ISSN Scence Publcatons A Genetc Algorthm Based Mult Objectve Servce Restoraton n Dstrbuton Systems Sathsh Kumar Kannaah, Jayabarath Thangavel and D.P. Kothar Power Systems Dvson, School of Electrcal Engneerng, VIT Unversty Vellore. Tamlnadu, , Inda Abstract: Problem statement: A Genetc Algorthm (GA) used here to fnd exact or approxmate solutons to optmzaton and search problems. Genetc algorthms are a partcular class of evolutonary algorthms that use technques nspred by evolutonary bology such as nhertance, mutaton, selecton and crossover. Approach: GA s a method for search and optmzaton based on the process of natural selecton and evoluton. In ths approach, several modfcatons are done for effectve mplementaton of GA to solve the Electrc Power Servce Restoraton Problem. Results: The problem statement ncludes all the objectves and constrants requred for a practcal supply restoraton scheme. GA s used here to obtan the better result compared wth other methods. GA starts wth number of solutons to a problem, encoded as a strng of status of sectonalzng and te swtches. Concluson: The status of the swtch 1 and 0 has been consdered as close and open condton of the swtch. The strng that encodes each strng s chromosome and the set of solutons are termed as populaton. Obtaned results are good and ths technque s recommended here for future study. Key words: Genetc algorthm, Electrc Power Dstrbuton Systems (EPDS), Electrc Desel Generator (EDG), Optmstc Tme (OT), Pessmstc Tme (PT), Maxmum Tme (MT), Standard Devaton (SD), current transformer INTRODUCTION Servce Restoraton Process Usng Crtcal Path Method: The servce restoraton process nvolves several actons based on certan condtons before the start of each restoraton actvty. The man processes n restorng the supply to the radal feeder can be classfed n two types: restoraton of supply under power falure and restoraton of supply after occurrence of fault. The frst process nvolves the start of EDGs and closure of swtches and breakers at the dstrbuton network. The second process requres solaton or dsconnecton of the faulty load and then reconnecton of the feeders wthn the mnmum tme. The crtcal path method (Saraban and Lee, 2010) helps n exact estmaton of restoraton tme at each and every stage of the above mentoned processes or actvtes. At each stage of the restoraton process or restoraton actvty, three estmaton of duraton are consdered namely OT, PT and MT. The OT s taken as the actual operatng tme based on the repeated testng condtons. The PT s taken as less than the optmstc tme to account for addtonal loadng effects and swtchng transents under abnormal condtons. The MT s taken as more than the OT to account for the probablty of falure due to ageng, poor mantenance and defects n manufacturng of the accessores of the power plant. Experence of feld engneers n optmal operaton of power systems shows that these duratons of actvtes follows the beta dstrbuton of probablty. Then the Expected Tme (ET) for an actvty can be approxmately expressed as: ET = (OT +4 * MT + PT)/ 6 σ = (OT - PT)/6 Correspondng Author: K. Sathsh Kumar, School of Electrcal Engneerng, VIT Unversty Vellore, Tamlnadu, , Inda 448 (1a) (1b) where, σ s Standard Devaton (SD) n seconds. If the breaker or relay s a fast electroncally controlled devce and ts operatng tme s n terms of mllseconds, then OT, PT and MT can be treated as almost equal. For these very fast operatng swtches the ET of operaton s gven by: ( ) Total Restoraton Tme TRT n = ET (1c) where, =1,2,3.n.(n s the total no: of actvtes.) TRT1 n operaton of the varous relays n the part of system under fault (Alfred, 2010).

2 J. Computer Sc., 7 (3): , 2011 TRT = TRT1 (ET1) + TRT2 (ET2) TRT1 (ET1) TRT2 (ET2) TRT for the restoraton of power supply to dstrbuton network wll be sum total of total restoraton tme of solatng the faulty crcut and the startng of EDG: TRT= TRT1 + TRT2 = sec = sec by: The standard devaton of whole actvty s gven σ t = (Σ σ 2 ) 1/2 (1d) The longest path wll draw more attenton to the substaton operator or the dstrbuton engneer, whch needs more tme to receve the power supply from the dstrbuton substaton and hence t s consdered a crtcal path. Programmng methodologes: The dsturbances n the dstrbuton system are classfed nto two man categores: phase to phase fault, called a short crcut fault and a phase to earth fault called an earth fault. These dsturbances were further classfed as ether temporary or permanent faults. The restoraton tme under faulty condtons need the calculaton of fault current. Here symmetrcal and unsymmetrcal faults consdered. The fault current can be easly calculated (Alfred, 2010) by formng the bus mpedance matrx, consderng the faults wth and wthout mpedance. The fault current at the faulted bus k s gven by: I k =V ko /(Z kk +Z f ) (2a) where, Z f s mpedance of the fault and ts value wll be zero for the bolted faults. Z kk s the k th row and k th column mpedance element of Z bus. V ko s the prefault voltage at the bus K. The sequence network nterconnecton has to be done for unsymmetrcal faults. Based on the total equvalent sequence mpedances the postve, negatve and zero sequence currents and then the fault currents can be calculated. For example, for the commonly occurrng lne to ground fault the postve sequence current s gven by: MATERIALS AND METHODS I a1 =V k0 /(Z akk1 +Z akk2 +Z akk0 ) (2b) Genetc algorthm s mplemented as a computer smulaton n whch a populaton of abstract representatons (called chromosomes) of canddate solutons (called ndvduals) to an optmzaton problem evolves towards better solutons. Tradtonally solutons are represented n bnary as strngs of 0s and 1s, but other encodngs are also possble. The evoluton starts from a populaton of randomly generated ndvduals and happens n generatons. In each generaton, the ftness of every ndvdual n the populaton s evaluated, multple ndvduals are stochastcally selected from the populaton (based on ther ftness) and modfed (recombned and possbly mutated) to form a new populaton. The new populaton s then used n the next teraton of the algorthm. Commonly, the algorthm termnates due to maxmum number of generatons has been produced, or a satsfactory ftness level has been reached for the populaton. If the algorthm has termnated due to maxmum number of generatons, a satsfactory soluton may or may not have been reached. The steps nvolved n GA are Intalzaton, Selecton, Reproducton and Termnaton (Deb Kalyanmoy, 2004). where, Z akk1, Z akk2, Z akk0 are postve, negatve and zero sequence mpedances of the a phase, k th row and k th column element of bus mpedance matrx. Then the fault current n the phase a s gven by: I af = 3I a1 (2c) Operatng tme calculaton of relays: The relay n power system network senses the fault and actuates the crcut breaker to solate faculty crcut from the healther one. These protectve devces are connected va Current Transformer (CT). The current n the secondary wndng of the current transformer s gven by: I s =I f / (CT Rato) PSM= I s / (OLS * PS) (2d) (2e) I f = Fault current PSM = Plug settng multpler OLS = Overload settng for operaton of transformer crcut breaker PS = Plug settng of relay 449

3 J. Computer Sc., 7 (3): , 2011 Table 1: Multplcaton factor of crcut breakers Multplcaton factor Type of crcut breaker cycle or slow breaker cycle breaker cycle breaker cycle breaker The tme correspondng to the operatng current or PSM has been evaluated from the tme current characterstcs of the relay. The momentary rated r.m.s current of the crcut breaker I gven by: I mom = MF * (E/X d ll ) (2f) ll X d = Subtransent reactance of the generator E = Rated phase operatng voltage of the generator MF = Multplcaton factor The MF for dfferent types of crcut breaker (Manjunath and Mohan, 2007; Mohan and Manjunath, 2004) s gven n Table 1. In ths analyss the breaker s assumed to be a fve cycle one. Approach for solvng EPSR usng GA: In the past, consderable efforts have been devoted to the subject of servce restoraton n EPDS. The approaches are based on the applcaton of varous optmzaton methods to determne the optmal restoraton plan of the EPDS. The shortcomng of these methods s that, the nature of the problem s so complex and due to the burdenng of performance varants and due to practcal dffcultes, the desred optmal soluton cannot be obtaned n the mnmum possble tme. The ncreased computatonal tme wth large sze dstrbuton systems lmts the effcent use of these approaches n servce restoraton procedures of DAS. The theory behnd GA s taken from (Mah and Izabatene, 2011). Intal populaton generaton: An n feeder EPDS remans radal f at least n P 2 number of branches are kept n OFF status. To ensure ths the faulted bus number s searched n bus data and correspondng branches where the faulted bus s found s swtched OFF. Now randomly n 1 number of branches s swtched OFF. Where n 1 = n P 2 -no. of branches swtched off due to fault. Rest of the branches s kept ON to restore maxmum possble number of loads n the EPDS (Kothar, 2004). Reproducton or selecton operator: (1) Identfy good solutons n a populaton, (2) Make multple copes of good solutons, (3) Elmnate bad solutons from the populaton so that multple copes of good solutons can be placed n the populaton. There exsts a number of ways to acheve the above tasks, but the method appled here s the tournament selecton operator. In the tournament selecton, tournaments are played between two solutons and the better soluton s chosen and placed n the matng pool. Two other solutons are pcked agan and another slot n the matng pool s flled wth the better soluton f carred out systematcally, each soluton can be made to partcpate n exactly two tournaments. The best soluton n a populaton wll wn both tmes there by makng two copes of t n the new populaton usng a smlar arguments, the worst soluton wll lose n both tournaments and wll be elmnated from the populaton. Crossover operator: A crossover operator s appled next to the strngs of the matng pool. Here two chromosomes are taken together and a random probablty s generated f ts less than the specfed probablty of cross over then only the cross over operaton wll take place. Now a number s generated between zero and sze of the chromosome strng. The bt strngs of two selected chromosomes are swapped from the random number generated to the last bt of the chromosome. Hence the cross over operator recombnes together good substrngs from two good strngs to hopefully form a better substrng. Checkng of constrants: Now all the chromosomes are arranged n ascendng order accordng to ther ftness functon value computed after mutaton. Startng from the frst chromosome havng the mnmum value of ftness functon s tested for constrants checkng. The frst chromosome whch satsfes all the constrants s chosen as the soluton. If none of the chromosomes satsfes all the constrants then the whole process s repeated for one more generaton. The soluton to the mult-objectve servce restoraton optmzaton problem should meet the followng requrements: The Power Loss n the reconfgured PDN should be as less as possble Radal Structure of the PDN should be retaned The swtch operatons should be as less as possble n order to mnmze the nterrupton of power supply The Power supply should be restored to as much load as possble n the mnmum tme and the load 450

4 sheddng should be accordng to the hghest prorty order consderaton of the loads The Restoraton tme should be mnmal The mult-objectve functon for solvng the Electrc Power Servce Restoraton Problem s formulated as follows: Mnmze F =w 1 f 1 +w 2 f 2 +w 3 f 3 +w 4 f 4 +w 5 f 5 where, w 1 = w 2 = w 3 = w 4 = w 5 =0.2 Subject to the followng constrants: J. Computer Sc., 7 (3): , 2011 (2g) Constrant on bus voltages: V k mn V k V k max Constrant on Real Power Transmsson Loss: P LL P LLmax Constrant on Radal structure of the PDN: PDN must be Radal f = LostP /TP,f = P /PP, 1 Load Load 2 LL Load nbch j= 1 2 (SW j SWB j) f3 = SWmax f4 = ( Vmn V k )/V max,f Vk < V mn, = ( Vk V max )/V max,f Vk < V max, k = 1,2,...n bus, f 5 = 1 (SMLP/ nload nload + 1) / 2) V k = Voltage at the k th bus LOSTP LOAD = Loss of Real Power Demand due to change of network confguraton n each teraton TP LOAD = Total Real Power Demand of the pre fault PDN PP LOAD = Present total real power demand on each teraton P LL = Total Real Power Transmsson Loss n each teraton P LLmax = Maxmum allowable PLL nbch = Total number of branches SW OP = Number of swtchng operatons SW j = Status of the swtch j after the reconfguraton SWB j = Status of the swtch j before the reconfguraton SW max = Sum of total number of sectonalzng and te swtches N bus = Total number of buses SMLP = Sum of Prorty order of the loads n the post fault PDN 451 n load w = Total number of connected loads n the post fault power dstrbuton network = Postve weghts for the th objectve of the objectve functon F : RESULTS AND DISCUSSION n w = 1 Algorthm of the new hybrd mult-objectve quck servce restoraton technque for EPDS: Step 1: Read the Bus Data, LPRO s, Real and Reactve Power Demand, Shunt Capactor Bank Ratngs Fg Read the Lne Data, the number of feeders and the bus number at whch substaton/source s connected and Read the convergence tolerance (Moon et al., 1999) Step 2: Obtan the Connectvty of the pre-fault PDN usng New Network Connectvty Method. Form the Matrx of nodes beyond a partcular node nbe. Step 3: Perform the Load Flow Analyss Usng Forward Substtuton Method. Data for Load Flow Analyss s gven n the Table 2. Step 4: Compute the lne flows and also the branch currents n varous sectons of the feeders. Step 5: Check whether any fault s occurred? If there s any occurrence of fault, go to the next Step, otherwse go to Step 27. Step 6: Check whether the fault s symmetrcal or unsymmetrcal. If the fault s symmetrcal, form the Z bus of the dstrbuton network usng Harrson et al. (2008). If the fault s unsymmetrcal, form the postve, negatve and zero sequence mpedance matrces of the post fault PDN usng Harrson et al., 2008 Step 7: Set the generaton count, Gen = 1. Step 8: Obtan the Network Connectvty of the post fault PDN usng the above algorthm of ths study. Form the Matrx of nodes beyond a partcular node n be. Step 9: Select the populaton sze based on the number of branches n the EPDS. Choose the length of the chromosome as same as that of total number of buses n the PDN. Step 10: Consder the loads n the order of ther hghest prorty usng preemptve method. Step 11: Perform the load flow analyss usng forward substtuton method and then, calculate the post fault voltages of the PDN. Step 12: Compute real and reactve power lne flows, real and reactve power losses n the PDN. Step 13: Compute all the objectves of the objectve functon f 1, f 2, f 3, f 4 and f 5. Step 14: Compute the objectve functon F for each Chromosome.

5 J. Computer Sc., 7 (3): , 2011 Table 2: 16 Bus 3 feeder lne data Branch no: From To Lne length LPRO End bus load End bus Load Qsh n MVAR Bus Bus n km MW MVAR Step 15: Evaluate the ftness of the ndvdual Step 29: Stop. chromosomes n the populaton under consderaton. Step 16: Rank the ftness functon values n the ascendng order. Step 17: Perform selecton of the ndvduals n the populaton. Step 18: Perform the crossover between the chromosomes. Step 19: Perform Mutaton of ndvduals n the populaton. The steps of GA are referred from Madan and Madan, Step 20: Form the new set of objectve functons based on the new populaton. Step 21: Check whether the constrants are met or whether the number generatons reached maxmum generaton lmt or not. If yes go to Step 24, otherwse go to next Step. Fg. 1: bus 3 feeder sample network Step 22: Convert the new objectve functon value to bnary equvalent and then perform the logcal OR operaton of ths bnary equvalent wth to the old chromosomes. Step 23: Update the generaton count Gen = Gen + 1 and then go to Step 8. Step 24: Perform the load flow analyss for the new reconfgured post fault PDN. Compute the lne losses, power suppled from the substaton and also calculate the real and reactve power lne losses. Step 25: Estmate operatng tme of the all the assocated relays/breakers n the post fault PDN. Step 26: Compute the total restoraton tme. Step 27: Prnt the results. Step 28: If any further fault analyss s to be carred out for operatonal plannng of EPDS go to Step 1, otherwse go to next Step. Fg. 2 Result for network connectvty matrx 452

6 J. Computer Sc., 7 (3): , 2011 REFERENCES Fg. 3 Result for post fault connectvty matrx CONCLUSION Here t has been assumed that a lne to ground fault takes place at the bus 13 wth a fault mpedance of 0.l p.u. Due to the occurrence of fault, the relay/breaker connected between buses 3 and 13 s operated and hence bus 13 gets solated from the power supply. Due to operaton of the breaker the power supply also gets dsconnected to the loads whch are connected to the buses 15 and 16. Hence the loads connected to the buses 15 and 16 are n dark state. In order to restore the power supply to the loads whch are connected to the buses 15 and 16, the dstrbuton network has to be reconfgured. The search of optmal confguraton of PDN has been done usng GA. For the 16-Bus EPDS, the GA parameters are selected as follows: Length of the Chromosome = 16 Populaton sze = 16 Probablty of crossover = 0.7 Probablty of mutaton = 0.7/16 = The optmal confguraton of post-fault PDN has been obtaned usng the GA. The statuses of the swtches n optmal confguraton of the PDN are gven as follows: SWSTAT= [ ] Alfred, R., Summarzng relatonal data usng sem-supervsed genetc algorthm-based clusterng technques. J. Comput. Sc., 6: DOI: /jcssp Harrson, G.P., A. Pccolo, P. Sano and A.R. Wallace, Hybrd GA and OPF evaluaton of network capacty for dstrbuted generaton connectons, Elec. Power Syst. Res., 78: DOI: /j.epsr Kalyanmoy, D., Optmzaton for Engneerng Desgn: Algorthms and Examples. 1st Edn., Prentce-Hall of Inda, New Delh, ISBN-10: X, pp: 396. Kothar, D., Power System Optmzaton. 1st Edn., Prentce-Hall of Inda Pvt.Ltd, New Delh, ISBN-10: , pp: 572. Madan, M. and S. Madan, Convalesce optmzaton for nput allocaton problem usng hybrd genetc algorthm. J. Comput. Sc., 6: DOI: /jcssp Mah, H. and H.F. Izabatene, Segmentaton of satellte magery usng RBF neural network and genetc algorthm. Asan J. Appled Sc., 4: DOI: /ajaps Manjunath, K. and M.R. Mohan, A new hybrd mult-objectve quck servce restoraton technque for electrc power dstrbuton systems. Elect. Power Energy Syst., 29: Mohan, M.R. and K. Manjunath, An mproved technque for the estmaton of servce restoraton tme n power dstrbuton systems. Int. J. Power Energy Syst., 2004: Moon, Y.H., S.H. Km, B.N. Ha and J.H. Lee, Fast and relable dstrbuton system load flow algorthm based on the Y BUS formulaton. Proceedngs of the IEEE Power Engneerng Socety Summer Meetng, July 18-22, Edmonton, Alta., Canada, pp: DOI: /PESS Saraban, M. and L.V. Lee, A modfed partally mapped multcrossover genetc algorthm for twodmensonal bn packng problem. J. Math. Stat., 6: DOI: /jmssp ACKNOWLEDGEMENT The researchers are extremely grateful to the management of VIT Unversty, Vellore for provdng the excellent support and encouragement n promotng ths research study. 453