Maintenance Scheduling of Distribution System with Optimal Economy and Reliability

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1 Egeerg, 203, 5, Publshed Ole September 203 ( Mateace Schedulg of Dstrbuto System wth Optmal Ecoomy ad Relablty Syua Hog, Hafeg L, Fegjao Wag School of Electrcal Power, South Cha Uversty of Techology, Guagzhou, Cha Emal: Receved Jue 203 ABSTRACT Wth the cotuous expaso of power dstrbuto grd, the umber of dstrbuto equpmets has become larger ad larger. I order to make sure that all the equpmets ca operate relably, a large amout of mateace tasks should be coducted. Therefore, mateace schedulg of dstrbuto etwork s a mportat cotet, whch has sgfcat fluece o relablty ad ecoomy of dstrbuto etwork operato. Ths paper proposes a ew model for mateace schedulg whch cosders load loss, grd actve power loss ad system rsk as objectve fuctos. O ths bass, Dfferetal Evoluto algorthm s adopted to optmze equpmet mateace tme ad load trasfer path. Fally, the geeral dstrbuto etwork of 33 odes s take for example whch shows the mateace schedulg model s effectveess ad valdty. Keywords: Mateace Schedulg; Mult-Objectve; Dfferetal Evoluto Algorthm; Codto Based Mateace. Itroducto Wth the cotuous developmet of dstrbuto etwork, mateace schedulg of dstrbuto equpmets has become a mportat work of dstrbuto etwork operato dspatchg. Makg scetfc ad reasoable mateace pla s beefcal to ehace the relablty of power dstrbuto system operato. Besdes, t ca mprove the maagemet level ad ecoomc beefts of Power Supply Compay. I actual work, mateace schedulg of dstrbuto etwork s arraged artfcally, accordg to the experece of power departmet, whch s checked by operatg crew to make sure the stablty of power dstrbuto system. However, ths arragemet method oly focuses o the securty of dstrbuto system, whle eglects the ecoomcal effcecy. Istead of artfcal schedulg, mateace schedulg should be a optmzed process based o scetfc ad effectve mathematcal model, whch ca avod the subjectvty ad radomess of mateace. The study of mateace schedulg geerally optmzes the objectve fucto of ecoomc dex by dfferet optmzato algorthms. Referece [] troduces a automatc schedulg method usg heurstc algorthm to obta the optmal swtchg combato, whch cosders load loss ad swtch operato cost as the objectve fuctos. Referece [2] puts forward a mproved Geetc Algorthm (GA) usg feasble degree to reta the good gees o feasble soluto, ad shows that the optmzato procedure has less chace to get to local covergece. O the other had, relablty dex s also a mportat factor of mateace schedulg. Recetly, Power Supply Compay has coducted plot applcato of the Relablty Cetered Mateace (RCM) [4], referece [5], ts optmzato objectve s to lower the value of Expected Eergy Not Suppled (ENNS) ad mprove the power system s relablty. However, for the mateace schedulg problem of dstrbuto system, the relablty ad ecoomy of dstrbuto etwork operato should be both cosdered as the optmzato objectve fuctos. Ths paper makes a comprehesve aalyss of objectve fuctos, cludg load loss, grd actve power loss ad system rsk. The, establsh a mult-objectve mathematcal model wth the three objectve fuctos above. I the followg, the method of usg Dfferetal Evoluto algorthm to optmze the mateace schedulg s proved to be effectve ad feasble by the example. 2. Mateace Schedulg Model 2.. Mult-Objectve Optmzato Model Geeral mateace schedulg optmzato problem wll tegrate several objectve fuctos to sgle oe by the weghtg method as follow: Copyrght 203 ScRes.

2 S. Y. HONG ET AL. 5 m λ f ( x) = st.. g ( x) 0, j =,2.. l () h j z ( x) = 0, h=,2.. m where x s the mateace tme vector, λ s the weght of optmze objectve fucto, l s the total umber of equalty costrats, m s the total umber of equalty costrats. However, weghtg sgle objectve optmzato method has the followg defects: Eough pror kowledge s requred to determe the weght of each objectve fucto. Oly oe Pareto optmal soluto ca be obtaed each optmzato tme, whch s dffcult to judge the relablty ad optmalty of the optmzato results. Each objectve fucto has dfferet dmeso. Cosderg about all these, ths paper adopts mult-objectve optmzato model to optmze several objectve fuctos ad requres that all objectve fuctos meet the codto of settg costrats, whch s show as follow: M F( X) = ( f ( X), f ( X)..., f ( X)) X R 2 st.. g( X) = ( g( X), g2( X),.. g ( m. X, )) 0 {( XgX ( ) 0} R= (2) X = ( x, x.. x ), X R 2 where F(X) s the optmzato target vector, g(x) s the costrat vector, X s the decso varable Optmzato Objectve Fuctos The purpose of arragg mateace schedulg s ot oly to trasfer load as much as possble, but to cosder the ecoomy ad relablty of dstrbuto etwork operato. Therefore, mateace schedulg of dstrbuto s a combatoral optmzato problem of mult-objectve ad mult-costrat, whch s related to the objectve fuctos cludg the followg aspects: ) Load Loss f = M( λ P T) (3) N where λ deotes average electrcty prce, N meas the assemblage of trasfer odes, P s the load loss, T s the mateace cotuous tme. 2) Grd Actve Power Loss I order to avod the outage of dstrbuto etwork caused by equpmet mateace, we should coduct the etwork load trasfer ad besdes, choose the optmal trasfer path to reduce the grd actve power loss, whch k s the target of load trasfer equpmet mateace. f2 = M( Pk ) (4) k M where Pk deotes the grd actve power loss of trasfer path k, M deotes the assemblage of all trasfer paths. 3) System Rsk Geerally, mateace schedulg optmzato model requres oly that trasfer strategy meet the etwork power flow costrat, seldom cosderg the problem of load equalzato. The rsk value of power dstrbuto system s calculated as follow: f M( P R ) 3 = (5) j j= e= where P j deotes the load of ode j, R e s the falure rate of ma equpmets o trasfer path. The rsk assessmet value ca be dvded to three levels as Low Rsk, Medum Rsk ad Hgh Rsk, correspodg to evaluato score 0-0.3, , respectvely. The selecto of power load trasfer paths s closely related to the relablty of trasfer le. If the power load of mateace le s trasferred to aother le of low relablty dstrbuto etwork, the falure rsk of trasfer le wll greatly crease, whch wll mpact the relable operato of dstrbuto etwork. Therefore, we should coduct the calculato of le rsk ad trasfer the power load to a hgh relablty le as far as possble. I ths paper, combg wth Codto Based Mateace (CBM) coducted by Power Supply Compay, the health status of dstrbuto equpmets o trasfer path are evaluated ad the, make a predcto of equpmet falure rate accordg to the health evaluato results. After that, Per-ut value of the le load s calculated based o the max le load. I the followg, system rsk s calculated ad the level of rsk assessmet s set up accordg to results of rsk value Health State ad Falure Rate Health evaluato s a comprehesve evaluato process, whch meas that the electrcal equpmet s health state s evaluated by varous state parameters, accordg to the health state, the hdde defects of equpmet are foud out tme ad Power Supply Compay ca coduct the mateace to make sure that the equpmet s healthy codto [6]. Ths paper adopts Fuzzy Varable Weght Aalyss method to evaluate the health degree of dstrbuto equpmets. The method ca adjust the weghts of equpmets state parameters automatcally accordg to the relatoshp ad qualty of dfferet parameters. The procedure of dstrbuto equpmets health evaluato ca be descrbed as follows: e Copyrght 203 ScRes.

3 6 S. Y. HONG ET AL. m b = W R (6) j j j = [ ] B = b, b2,..., bs (7) s Y= cb (8) f f f = where R j deotes the fuzzy evaluato score ad A j deotes the weght of each evaluato state parameter. B deotes the fuzzy membershp matrx of evaluato result. Formula (8) s the weghted summato formula; c f s the values of dfferet evaluato dexes. I practcal evaluato, whe some state parameters of power equpmets are extremely serous status, we ca adjust the parameters weghts by usg equlbrum coeffcet. The varable weght formula s as follow: a a o o = W( x ) = w x / w x (9) where X deotes the value of each state parameter, W o deotes the fxed weght of each parameter. a s the equlbrum coeffcet whch values betwee 0 ad. After that, refer to the EA geeral formula of rsk ad falure probablty, the fault rate formula of equpmet health state s as follow: CY λ ( Y ) = Ke (0) where K deotes the proportoalty coeffcet ad C deotes the curvature coeffcet, whch are calculated accordg to the statstcs of equpmets health state ad falure probablty the rego. 3. Dfferetal Evoluto Algorthm Dfferetal Evoluto (DE) algorthm s a effectve ad robust method, whch s used to solve the complex fuctos wth the Characterstcs of No-lear, o-dfferretable ad hgh-dmesoal. At preset, DE algorthm has bee wdely used by the experts ad scholars dfferet research feld, whch has become a mportat brach of Evolutoary Algorthm (EA). DE algorthm adopts the searchg strategy of greed, whch meas after operato process of mutato ad t crossover, test dvdual u + ca become the ext geerato oly whe ts ftess s better tha the orgal t dvdual x. Otherwse, x t s regarded as the ext t geerato. I ths process, completely domate ( u + x ) based o the cocept of Pareto theory domat s t used amog the chose operato. I addto, aother feature of DE algorthm s adoptg eltsm strategy to keep the dversty of fal solutos. The reaso s that we ca t guaratee that the Pareto optmal soluto of curret geerato s always the optmal each geerato. Therefore, we use a exteral storage to store the Pareto optmal solutos whch have bee foud startg from the tal populato ad compete the dstace betwee the curret solutos ad the solutos the storage. 4. Example Aalyss Ths paper optmzes a mateace schedule of the geeral 33 odes dstrbuto etwork [], whch uses the preseted method ths paper. The dstrbuto system etwork s show as the Fgure. Based o the method above, the mateace week schedulg of two les o 33 odes etwork s arraged. The parameters of objectve fuctos are set as Table. Usg Dfferetal Evoluto algorthm to optmze the mateace schedulg, the parameters of Dfferetal Evoluto algorthm are set as Table 2. The optmzato results are show as Table 3. I Table 3, we ca see that whe system rsk s cosdered as objectve fucto (Strategy ), the grd actve power loss s more tha but close to that the stuato wthout cosderg (Strategy 2) ad that, all etwork loads ca be trasferred by cotact swtch operato. Fgure. Dstrbuto etwork of 33 odes. Table. Parameters settg of objectve fuctos. Parameters Settg Parameters Settg of Objectve Fuctos Average Prce The Mateace Tme Mateace Items Parameters Value 0.5 RMB/kWh hour Le 2-22 Le 0 - Copyrght 203 ScRes.

4 S. Y. HONG ET AL. 7 Table 2. Parameters settg of algorthm. Parameters Settg Parameters Settg of Algorthm Parameter of Crossover Parameter of Mutato Populato Sze Maxmum Geerato CR m CR max F 0 Parameters Value Table 3. Results of optmzato. Results of Optmzato Objectve Fucto Mateace Tme Cotact Swtch Operato Load Loss Grd Power Loss System Rsk Cosderg LINE RISK (Strategy ) Wed 8:00 Wed 4:00 Close S 2 Close S 3 S 4 Ope S 5 Close S 2 Close S 3 S 4 Ope S Wthout Cosderg LINE RISK (Strategy 2) Wed 8:00 Mo 8: However, as the table show, the system rsk (Medum Rsk) of the secod strategy s much hgher tha the system rsk (Low Rsk) of strategy because the trasfer le - 8 s the state of hgh system rsk. The falure rate of trasfer le wll greatly crease ad lead to the hgher system rsk f the power load s trasferred to le. Therefore, accordg the optmzato results, le rsk degree ought to be take to accout the load trasfer path selecto of mateace schedulg. 5. Coclusos Ths paper establshes a mult-objectve optmzato model of dstrbuto equpmets mateace schedulg, cosderg the fuctos of load loss, grd actve power loss ad le rsk. Through the aalyss of dstrbuto etwork system of 33 odes, coclusos are draw as follows: ) Combg wth the Codto Based Mateace ad rsk assessmet of dstrbuto etwork equpmets, ths paper puts forward to cosder system rsk as optmzato objectve fucto, by evaluatg equpmets health state, forecastg equpmet falure rate ad system rsk, order to avod the dsadvatage of overload operato. 2) Based o the theory of Pareto domato, a multobjectve optmzato mathematcal model s establshed accordg to the practcal stuato of mateace schedulg. The dversty valdato ca keep the dversty of the Pareto optmal solutos, whch s a effectve method of solvg mult-objectve problem ad makg mateace pla. 3) The optmzato results of mateace schedulg provde a feasble mateace schedulg ad trasfer path, whch greatly mprove the relablty ad ecoomy of power system s operato ad have theoretcal ad practcal sgfcace. 6. Ackowledgemets Ths work s supported by Hgh-tech Idustralzato Key Project Guagdog Provce (No. 200A ). REFERENCES [] X. Y. Mo, Research of Optmal Load Trasfer Path for Dstrbuto Network Mateace, Master Thess, North Cha Electrc Power Uversty, Cha, [2] X. C. Huag, Research o Mateace Schedulg Problem of Dstrbuto Network, Ph.D. Thess, North Cha Electrc Power Uversty, Cha, [3] T. Sawa, T. Furukawa, M. Nomoto, T. Nagasawa, T. Sasak, K. Deo ad T. Maekawa, Automatc Schedulg Method Usg Tabu Search for Mateace Outage Tasks of Trasmsso ad Substato System wth Network Costrats, IEEE Power Egeerg Socety 999 Wter Meetg, Vol. 2, 999, pp [4] J. X. Huag, Y. P. Ba ad W. S. Ca, Equpmet Mateace Decso-makg Research Based Improved RCM Aalyss, Qualty, Relablty, Rsk, Mateace, ad Safety Egeerg (ICQR2MSE) Iteratoal Coferece, 202, pp [5] D. F. Zhao, X. F. Dua ad L. Zhag, Mateace Schedulg of Power Trasmsso Equpmet Cosderg Equpmet Codto ad System Rsk, Joural of X a Jaotog Uversty, Vol. 46, No. 3, 202, pp [6] J. J. Hua, G. Wag ad H. F. L, Rsk Assessmet of XLPE Power Cables Based o Fuzzy Comprehesve Evaluato Method, Power ad Eergy Egeerg Coferece (APPEEC), 200, pp. -4. [7] P. Dua, Evaluato the Impacts of System Load Demads ad Load Rates o System Relablty Perfor- Copyrght 203 ScRes.

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