Optimal Placement of Sectionalizing Switches in Radial Distribution Systems by a Genetic Algorithm

Transcription

1 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 Optma Pacement of Sectonazng Swtches n Rada Dstrbuton Systems by a Genetc Agorthm K. Kneam and S. Srsumrannuku Abstract Proper nstaaton of sectonazng swtches n a dstrbuton system can mprove system reabty. Subectve pacement of sectonazng swtches coud ead to undernvestment whch, athough ess reabe, can produce unacceptabe oad pont faures or to overnvestment whch, athough more reabe, s uneconomc. Therefore, pacement of sectonazng swtches shoud be udcousy determned to provde the baance between the utty s cost and the customers outage cost. Ths probem fas nto a cass of combnatora optmzaton whch can be effcenty soved by a genetc agorthm. The genetc agorthm s used to search for the number of swtches and ther ocatons. Reabty cost/worth anayss s then performed to cacuate the customer s outage cost. The methodoogy s ustrated by a subdstrbuton network of Provnca Eectrcty Authorty (PEA) of Thaand, whch conssts of 2 prmary feeders and 26 oad ponts. Keywords Dstrbuton system reabty, Genetc agorthm, Sectonazng swtches, Servce restoraton.. INTRODUCTION Reabty n a dstrbuton system, whch transfers eectrca energy from transmsson systems to end-user customers, can be mproved by the nstaaton of sectonazng swtches. A sectonazng swtch s a devce that soates a fauted part from the system so that the heathy part can st be eectrcay supped and the nterrupton duraton s mnmzed. Swtch pacement pays an mportant roe n automated dstrbuton network, where the sectonazng swtches can be remotey actvated. Uttes normay empoy past experence, customer data, and other consderaton for the approprate number of swtches and ther ocatons. Subectve pacement of sectonazng swtches woud, however, ead to undernvestment and therefore ow reabty for the customers. On the other hand, athough hgh reabty, t woud ead to uneconomc owng to the utty s ncreased nvestment for the nstaaton costs of the swtches, whch are qute sgnfcant as ndcated by []. Therefore, the evauaton of the costs assocated wth dfferent pacements and the correspondng reabty worth assocated wth the dfferences shoud be udcousy determned. The souton to the probem presented n ths paper s based on a genetc agorthm and reabty cost/worth anayss. Genetc agorthms are stochastc optmzaton technques that have a arge number of appcatons, ncudng power system areas, for exampe optma reconfguraton dstrbuton networks, optma capactor K. Kneam (correspondng author) s wth Facuty of Technca Educaton, Kng Mongkut s Unversty of Technoogy North Bangkok (KMUTNB), Bangkok, Thaand. Phone ext.333; Fax: ; E-ma: kanokwa@kmutnb.ac.th. S. Srsumrannuku s wth Facuty of Engneerng, Kng Mongkut s Unversty of Technoogy North Bangkok (KMUTNB), Bangkok, Thaand. E-ma: spss@kmutnb.ac.th. pacement n dstrbuton system and optma power fow. Wth the genetc agorthm and reabty cost/worth anayss, the optma pacement of sectonazng devces can be obtaned provdng the owest tota cost that s the sum of nvestment cost, mantenance cost and customer outage cost. The methodoogy s ustrated by a subdstrbuton network of Provnca Eectrcty Authorty (PEA), whch conssts of 2 prmary feeders and 26 oad ponts. 2. GENETIC ALGORITHM The genetc agorthm (GA) s a stochastc search technque based on the prncpes of genetcs and natura seecton [2]. The GA operates on popuatons that consst of a number of ndvduas. The nta popuaton s randomy generated. Each ndvdua s then evauated to obtan a measure of ts ftness n terms of the obectve functon to be optmzed. The agorthm aows a popuaton composed of many ndvduas to evove by two basc operators crossover and mutaton. The crossover operator creates new ndvdua by combnng substrngs from the parent ndvduas. The mutaton operator creates a new ndvdua by changng randomy seected bts n ts codng. The genetc agorthm empoyed n ths paper s based on the foowng ten steps [3]. Step : Generate popuaton and popuaton 2 whch satsfy the constrants of a probem. Step 2: Evauate the ftness of each ndvdua n popuaton 2 to fnd the best ftness of popuaton 2. The ftness s cacuated from the obectve functon. Step 3: Create a new popuaton 3 from the crossover operator between popuaton and the best ftness ndvdua of popuaton 2. If t turns out that the ftness of an ndvdua n popuaton 3 s better than the best ftness ndvdua n popuaton 2, then that ndvdua n popuaton 2

2 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) repaces the best ftness ndvdua. Otherwse, the ndvdua repaces ts parent n popuaton wth a probabty of repacement. Step 4: Seect and keep the best ftness from popuaton 2. Step 5: Brng popuaton to the crossover and mutaton process. Step 6: Ths s the same as step 3 except that nstead of usng the best ftness ndvdua n popuaton 2, a randomy seected ndvdua from popuaton 2 s brought to crossover wth some probabty. Step 7: Seect and keep the best ftness from popuaton 2. Step 8: Compare the best ftness ndvdua from step 4 wth that of step 7. Step 9: Update the best ftness ndvdua of popuaton 2 n step 3 wth the one obtaned from step 8. Step 0: Repeat step 3 through step 7 unt the maxmum generaton has been reached. 3. RELIABILITY COST/WORTH IN DISTRIBUTION SYSTEMS A dstrbuton crcut normay uses prmary or man feeders and atera dstrbutons. A prmary feeder orgnates from a substaton and passes through maor oad centers. The atera dstrbutors connect the ndvdua oad ponts to the man feeder wth dstrbuton transformers at ther ends. Many dstrbuton systems used n practce have a snge-crcut man feeder and defned as rada dstrbuton system. Rada dstrbuton systems are wdey used because of ther smpe desgn and generay ow cost. A rada dstrbuton system conssts of seres components (e.g., nes, cabes, transformers) to oad ponts. Ths confguraton requres that a components between a oad pont and the suppy pont operate and therefore poor reabty can be expected because the faure of any snge component causes the oad ponts dsconnected. However, many dstrbuton systems have normay open ponts that can be swtched to meshed systems n the event of a system faure [4]. In addton, oad pont reabty can be mproved by nstang sectonazng swtches that can remove the fauted part from the remanng heathy system. Reabty cost s quantfed n forms of nvestment ncurred by nstaaton of sectonazng swtches, whereas reabty worth s quantfed n forms of customer outage costs served as nput data for cost mpcatons and worth assessments of system pannng and operatona decsons. The customer outage costs are cacuated from reabty ndces of the oad ponts and customer damage functons. The customer damage functon utzed n ths paper s shown n Fgure [5]. The basc dstrbuton system reabty ndces are average faure rate, average outage duraton r, and annua outage duraton U. Wth the three oad pont ndces and oad mode at oad ponts, system average nterrupton frequency ndex (SAIFI), system average nterrupton duraton ndex (SAIDI), expected energy not supped (ENS), and expected outage cost (ECOST) can be cacuated. These four reabty ndces are cacuated from where n n n L r k λ P k SAIFI = SAIDI = ENS = n n = k = n ECOST = = k = n = = k = n k n λ P P () k = n = λ r P P (2) n = = k = L k r λ (3) L k C k ( r ) λ (4) = number of oad steps = number of oad ponts that are soated due to a contngency = number of outage events = tota number of oad ponts = oad at oad pont k for the th step of oad duraton curve at oad pont k = average outage tme of contngency = faure rate of contngency = number of customers connected to a oad pont k C k ( r ) = outage cost ($/kw) of customer cass k due to outage wth an outage duraton of r Fg.. Customer Damage Functon. 4. PROBLEM FORMULATION The obectve functon of the probem of sectonazng swtch pacement s to seect the number of swtches and ther ocatons such that the sum of the nstaaton cost mantenance cost and ECOST s mnmzed subect to 22

3 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 system constrants. The system constrants are votage and ne current mts. The obectve functon s mathematcay expressed by (5). The frst two costs of (5) depend on the number of sectonazng swtches whereas the ast cost s cacuated from (4). + ECOST ns ns Instaaton cost + n= n= Mnmze Mantenace cost (5) subect to where ns V I mn max max V mn max I I V V max = number of sectonazng swtches = votage at th node = current of feeder secton V = mnmun votage at th node V = maxmun votage at th node I = rated current of feeder secton 5. DISTRIBUTION POWER IN RADIAL SYSTEM Load fow souton n a radcay operated dstrbuton network can be effcenty soved by the formaton of a constant spare upper trange matrx to determne the bus votages. Ths method requres nta votages, system confguraton, and a branch-to-node matrx. The votages at a nodes are cacuated by teratve process wthout matrx nverson. Ths method s effcent n terms of speed, convergence and computer storage requrement. The agorthm s descrbed as foows [7]. Step : Consder the network topoogy descrpton, network data, and oad data. Step 2: Form matrx [ C ] from branch-to-node of the branch currents from topoogy descrpton of the gven system. Step 3: Assume votages at a nodes are equa to the source node or ntaze a nodes wth prevousy cacuate votage Step 4: where Determne the oad current at a nodes by P - Q V J = + + YV + I =, 2,..., nb * L V Z nb = number of node (ncudng source node) n = nb - b = number of branches V o = source node votage J = oad current at th node V = votage at th node P, Q = rea and reactve oads at th node, respectvey Z = oad at th node modeed by a constant mpedance Y = oad at th node modeed by a constant admttance I L = oad at th node modeed by a constant current [ b ] = vector of branch currents of order ( b ) [ v b ] = vector of branch votage of order ( b ) [ J L ] = vector of oad current at a nodes of order ( n ) [ C ] = branch-to-node matrx of order ( b n) [ z ] = prmtve mpedance matrx of order ( b b) Step 5: Determne the branch currents of a branches by [ ] = [ C][ J ] b L Step 6: Determne the branch votages of a branches [ v ] [ ][ ] by b = z b Step 7: Determne a the new node votages from V = V 0 b = C v, =, 2,, n Step 8: Check for convergence based on node votage dfferences between consecutve teratons and repeat step 4 to step 7 unt the souton converges to a prespecfed toerance of per unt. 6. SOLUTION ALGORITHM The foowng steps present the souton agorthm for the optma pacement of sectonazng swtches n rada dstrbuton systems based on the genetc agorthm and reabty cost/worth anayss. Step : Input ength of feeder n each secton, oad eve per oad pont, faure rate, repar tme, swtch tme, repacement tme, transfer tme, outage cost to customer due to suppy outage, swtch ocatons and faure probabty of fuses. Step 2: Input popuaton sze and maxmum generaton. Step 3: Generate popuatons and 2 as descrbed n step of Secton 2. Each ndvdua n the popuatons s represented by a strng of bnary numbers. Bnary vaues of 0 and ndcate swtch nstaaton and unnstaaton, respectvey. Step 4: For each ndvdua, consder a contngency at oad pont k (e.g., outage of a ne or a transformer) n the network for a oad step. Determne a the affected customers ( ) due to the contngency and the nterrupton duraton r. The vaue of r s repar tme, repacement tme or swtchng tme. Repar tme and repacement tme are used for the customers who are subected to ong nterruptons. 23

4 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 Swtchng tme s used for those to whom the servce s restored through aternate suppy. Step 5: Cacuate the current n each feeder secton and the votage at each oad pont usng the dstrbuton oad fow agorthm presented n Secton 5, takng nto account oad transfer f an aternatve suppy s avaabe. Step 6: Obtan the oad pont nterrupton cost C ( r ) wth the customer damage functon shown n Fgure. Step 7: Cacuate the contrbuton of the contngency to system ECOST usng Lk C k = k ( r ) λ. Step 8: If k =, go to step 9. Otherwse, repeat step 5 to step 7 for a next oad step. Step 9: If = n (a the contngences on the prmary and the atera sectons at a oads have been consdered), go to step 0. Otherwse, repeat step 5 for next contngency. Step 0: If = n, go to step. Otherwse, repeat step 5 for next oad eve. Step : Cacuate the obectve functon from the summaton of the nvestment cost, mantenance cost, ECOST and a penaty term. The penaty term s used f the popuaton beng consdered voates the constrants of ne current and bus votage mts. Step 2: Do step 4 to step unt every ndvdua n popuatons and 2 are consdered. Step 3: Perform step 3 to step 0 n Secton CASE STUDY The test system n ths case study conssts of two feeders of PEA desgnated as KWA0 (stand for Kongkwang0) and KWA06 (stand for Kongkwang06) [8]. These two feeders have 2 feeders and 26 oad ponts shown n Fgure 2 and connected wth resdenta customers, sma users, medum users, arge users, speca users and government. Fuses are nstaed at the tee-pont n each atera. The network data s provded n appendx. Three phase pad mounted sectonazng swtches are consdered for the test system. The nvestment cost of a pad mounted sectonazng swtch s taken as 200,000 Baht. The annua mantenance cost s 2% of the annua nvestment cost. The fe perod of the swtch s consdered to be 20 years and the nterest rate as 8%. Fve cases are nvestgated. Case : Sectonazng swtches are nstaed aong the man feeders at the postons numbered n Fgure 2. The fuses at the atera dstrbutors are assumed to be 00% reabe. Case 2: Ths s the same as case except that no sectonazng swtches are nstaed at the ocatons numbered n Fgure 2. Case 3: Ths s the same as case except that the number and ocatons of sectonazng swtches k are determned by the genetc agorthm wth 00 generatons and 70 popuatons. Case 4: The same as case 3 except that the fuses are 90% reabe. Case 5: Ths s the same as case 3 except that a seven step oad duraton curve shown n Fgure 3 nstead of the average oad s apped to each oad pont wth a oad ncrement of 0%. The correspondng step probabtes are 0.032, 0.4, 0.65, , 0.247, , [5]. KWA LP LP2 KWA LP3 LP8 LP LP9 LP 0 LP LP Probabty LP 6 LP 9 LP LP LP5 LP6 LP7 LP 2 48 LP 8 LP LP2 LP3 LP4 LP5 LP LP 3 LP 4 Fg. 2. Feeder KWA0 and KWA Crcut Breaker Normay Open Swtch %Max oad Fg. 3. Seven Step Load Duraton Curve. 24

5 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 Tabe. Resuts of Fve Cases Case SAIFI SAIDI ENS ECOST Tota Cost No. of Swtches Locatons ,554.40,696,498 3,005, , ,940,85 2,940, ,526.77,759,36,925,580 8,4,2,6,2,49,50, ,632.06,764,575,930,794 8,4,2,6,2,49,50, , ,303,629 2,469,848 9,4,2,6,2,3,49,50, ,543.02,625,078,79,297 8,4,2,5,2,49,50, ,85.7 2,60,063 2,472,774 8,4 (automated),2,6,2,49,50,5 Unts: SAIFI nterruptons/customer.year SAIDI hour/customer.year Tota Cost Baht/year ENS kwh/year Expected Outage Cost Baht/year The smuaton resuts for the fve cases are shown n Tabe. In case, the system requres 63 sectonazng (63 postons) wth a tota cost of 3,005,474 Baht. Wthout any sectonazng swtches n case 2, the tota cost s 2,940, 85 Baht. We can see that the tota costs of the two cases are not much dfferent. The nvestment cost s hgher n case but ower n case 2. The expected outage cost s ower n case but hgher n case 2. These two cases represent two extremes from the utty s and customers pont of vew; to be precse, the customers are served wth a very good eectrc suppy n case whereas case 2 woud be favored by the utty. Nevertheess, there exsts the optmum baance between the two cases. Such a baance can be found n case 3, where 8 sectonazng swtches at ocatons, 4, 2, 6, 2, 49, 50, 5 (see Fg. 4.) are requred wth a tota cost of,925,580 Baht. Note that the frst three cases have the same SAIFI because sectonazng swtches have nothng to do wth system faure frequency but they do affect SAIDI and ENS. If the fuses n the atera are consdered 90 % reabe as n case 4, ts SAIFI, SAIDI, ENS, ECOST and tota cost are ncreased, compared wth those of case 3. The number and ocatons of sectonazng swtches reman, however, unchanged. If the seven step oad mode are apped to each oad pont for case 5, 9 sectonazng swtches n tota shoud be nstaed, namey one addtona swtch s needed at ocaton IMPACT OF AUTOMATED DEVICES It s seen from the case study that suppy restoraton becomes cruca for reabty mprovement. In the other words, the sooner the restoraton tme, the better the system reabty. Fast restoraton can be acheved by automated devces, whch can be remotey actvated (mnute or ess) after a faut has occurred. The mpact of automated devces w be demonstrated by two more cases, case 6 and case 7, that are an extenson from case 3 of the case study n secton 7. Case 6 s the same as case 3 except that the normay open swtch, by whch the oad can be transferred from KWA0 to KWA06 and vce versa, has a swtchng tme of mnute (0.067 hour). The smuaton resut s shown n Tabe. The dfference between the resuts of the two cases s that the swtch at ocaton 6 n case 3 s moved to ocaton 5 n case 6. Athough the optma patterns of sectonazng swtches for both cases are smar, the tota cost of case 6 s sgnfcanty reduced, many because of a decrease n the ECOST. In the case study, sectonazng swtches consdered so far are manuay operated. In fact, system reabty can be further mproved by automated sectonazng swtches. Most dstrbuton systems ether have ony manuay operated devces (no automated devces) or are partay automated wth a combnaton of manua and automated devces. A system wth parta automaton can be two-stage upstream and downstream restoratons as shown n Fgs. 4 and 5, respectvey [9]. In Fg. 4, the breaker w cear the faut. The automated swtch s opened aowng secton A to be qucky restored and the manua sectonazng swtch w ater be opened to restore the customers on secton B. In case of downstream restoraton n Fg. 5, after the faut s ceared, the automated swtch n the downstream path mmedatey pror to secton A w be opened, aowng secton A to be supped from a normay open pont (n.o.). Secton B remans wthout power unt the frst manua sectonazng swtch s opened and the normay open pont n the downstream path (n.o.2) s cosed. If automated sectonazng swtches become a canddate n case 3 of the case study wth a swtchng tme of mnute and an nvestment cost of 400,000 Baht (.e., twce the cost of the manuay operated swtch), no sectonazng swtch s requred. However, f we suppose that the oad at LP were ncreased from MW to 4 MW, 8 sectonazng swtches woud be requred as ndcated n case 7 of Tabe. It can be observed from the resuts that the system shoud repace the swtch of manua type n case 3 at ocaton 4 wth that of automaton type n case 7. Ths repacement s reasonabe because the oad at LP s so hgh enough that fast servce restoraton can hep t reduce the customer nterrupton cost. Therefore, t s worth nvestng the automated sectonazng swtch. Note from the resuts of cases 3 to 7 that many of the swtches are nstaed at common ocatons. To be 25

6 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 precse, a sectonazng swtch s nstaed at or near a man feeder. Ths s ogca because the swtch can cover severa sectons of the feeder and ateras downstream to the swtch, and therefore t can soate any fauts that may occur on those sectons. Frst automated sectonazng pont Upstream Swtch Secton A Secton B Faut Frst manua sectonazng pont Fg. 4. Two-Stage Upstream Restoraton. Secton B Faut Frst manua sectonazng pont n.o. Frst automated sectonazng pont [2] Wnston, W. and Veataramanan, M.A Introducton to Mathematca Programmng. Caforna: Thomson. [3] Zbgnew, M Genetc Agorthm + Data Structhms = Evouton Programs. New York: Sprnger. [4] Bnton, R Reabty Evauaton of Power Systems. London Engand: Ptman. [5] Energy Pocy and Pannng Offce, Mnstry of Energy, 200. Thaand. [6] Aravndhababu, P., Ganapathy, S. and Nayar, K.R A Nove Technque for the Anayss of Rada Dstrbuton Systems. Eectrca Power & Energy System, 23: [7] Provnca Eectrcty Authorty Thaand. [8] Goe, L. and Bnton, R. 99. Procedure for Evauatng Interrupted Energy Assessment Rates n an Overa Eectrc Power System. IEEE Trans. Power Systems, 6(4): [9] Brown, R.E. and Hanson, A.P Impact of Two-Stage Servce Restoraton on Dstrbuton Reabty, IEEE Trans. Power Systems, 6(4): n.o.2 Secton A KWA 06 KWA 0 Fg. 5. Two-Stage Downstream Restoraton. 9. CONCLUSION The optma pacement of sectonazng swtches n a rada dstrbuton system has been presented. The obectve functon s to mnmze the sum of nvestment cost, mantenance cost and customer outage cost, subect to ne current and bus votage mts. The frst two costs depend drecty upon the number of nstaed sectonazng swtches that are determned from agorthm. The ast cost s obtaned from reabty cost and worth anayss. A dstrbuton oad fow agorthm s deveoped based on a constant sparse upper trange matrx to cacuate ne current and oad-pont votages used to penaze popuatons that voate the constrants of ne current and bus votage mts n the optmzaton probem. A case study on a dstrbuton network of the PEA system reveas that methodoogy provdes an optmum decson between economc and reabty consderaton. The mpact of fast servce restoraton from the automated normay open swtch and the automated sectonazng swtch s aso nvestgated. REFERENCES [] Bnton, R. and Jonnavthua, S Optma Swtchng Devce Pacement n Rada Dstrbuton Systems. IEEE Trans. Power Systems, (3): LP LP LP3 LP8 LP LP9 LP 0 LP LP LP 6 LP 9 LP LP LP5 LP6 LP7 LP 2 48 LP 8 LP LP2 LP3 LP4 LP5 LP LP 3 LP 4 Crcut Breaker Normay Open Swtch Sectonazng Swtch Fg. 6. Optma Pacement of Sectonazng Swtches n Test System. 26

7 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 APPENDIX Tabe A. Customer Data of Feeder KWA0 Load Pont Number of Customer Type Demand (MW) Average LP Large Busness LP LP2 Large Busness LP2 LP3 Medum Busness LP3 LP4 Medum Busness LP4 LP5 Medum Busness LP5 LP6 Medum Busness LP6 Tabe A2. Customer Data of Feeder KWA0 Load Pont Number of Customer Type Demand (MW) Average Maxmum LP Large Busness LP LP2 05 Resdence LP2 LP3 3 Resdence LP3 LP4 Medum Busness LP4 LP5 3 Resdence LP5 LP6 3 Resdence LP6 LP7 2 Resdence LP7 LP8 Government LP8 LP9 2 Resdence LP9 LP0 Sma Busness LP0 LP Medum Busness LP LP2 3 Resdence LP2 LP3 84 Resdence LP3 LP4 Medum Busness LP4 LP5 Medum Busness LP5 LP6 Government LP6 LP7 Government LP7 LP8 Government LP8 LP9 2 Resdence LP9 LP20 Government LP20 Tabe A3. Reabty Data of Feeder KWA0 and KWA06 Component r s where = faure rate Transformers r = repar tme (hour) Lnes s = swtchng tme (hour) 27

8 K. Kneam and S. Srsumrannuku / GMSARN Internatona Journa 2 (2008) 2-28 KWA 06 KWA LP LP2 LP LP 9 6 LP4 LP5 LP6 LP LP3 LP5 LP5 LP6 LP7 LP8 4 LP LP9 LP 0 LP LP 3 LP 4 LP LP 6 LP 7 LP 8 LP 9 Crcut Breaker Normay Open Swtch 28 LP 20 Fg. A. Feeder KWA0 and KWA06. Tabe A4. Type and Length of Feeder KWA0 Secton Length (km) Type.0760 SAC SAC SAC SAC SAC SAC SAC SAC SAC 85 Tabe A5. Type and Length of Feeder KWA06 Secton Length (km) Type SAC SAC SAC SAC SAC ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR 50 28