An ant colony optimization solution to the integrated generation and transmission maintenance scheduling problem

Transcription

1 JOURNAL OF OTOELECTRONICS AND ADVANCED MATERIALS Vol. 0, No. 5, May 008, An an colony omzaon soluon o he negraed generaon and ransmsson manenance schedulng roblem. S. GEORGILAKIS *,. G. VERNADOS a, C. KARYTSAS b Dearmen of roducon Engneerng & Managemen, Techncal Unversy of Cree, GR-700, Chana, Greece a Technologcal Educaonal Insue of raeus, Dearmen of Elecrcal Engneerng, 50 erou Rall and Thvon sr., GR-44, Ahens, Greece b Cenre for Renewable Energy Sources, 9 h Km Marahon Avenue, GR-9009, Ahens, Greece The negraed manenance schedulng consders ransmsson lne manenance schedulng n generaon manenance schedulng. The ncluson of newor consrans ncreases he comlexy of he above schedulng roblem. An colony omzaon (ACO) s a meaheursc n whch a colony of arfcal ans cooerae n fndng good soluons o dffcul omzaon roblems. Ths aer rooses an an colony omzaon-based aroach o he unfed manenance schedulng roblem of ower generaon and ransmsson sysems. Resuls from he alcaon of he roosed mehod on he IEEE 0 bus sysem demonsrae he feasbly and raccaly of hs aroach. (Receved March, 008; acceed May 5, 008) Keywords: ower Sysems, Generaon manenance schedulng, Transmsson manenance schedulng, An colony omzaon. Inroducon Generaon manenance schedulng no only reduces he overall energy cos bu also ncreases he ower sysem relably by reducng forced ouage raes. The generaon manenance schedulng deermnes he omal sarng me for each generang un revenve manenance ouage n a weely erod for one year n advance, whle sasfyng he sysem consrans and mananng sysem relably. The generaon manenance schedulng s a large-scale, comlex omzaon roblem. Soluon mehods for he generaon manenance schedulng roblem nclude neger rogrammng [], dynamc rogrammng [], smulaed annealng [], fuzzy se heory [4], abu search [5], and genec algorhms [6]. Mos generaon manenance schedulng mehods reresen only he generaon sysem and do no ae no accoun he ransmsson newor consrans effecs on generaon manenance. However, excludng lanned ouages of ransmsson lnes for revenve manenance mgh roduce omsc resuls for he generaon manenance schedulng. On he oher hand, due o hermal caacy of he ransmsson lnes, a serous overloadng roblem could ae lace f ceran lnes and/or generaors were removed from he sysem for manenance smulaneously. In hs case, he omal resulng manenance schedule may no be suable for he sysem a all mes. To avod hs roblem, he negraed generaon and ransmsson manenance schedulng roblem should be solved. Ths maes he negraed manenance schedulng (IMS) roblem more comlex han he ure generaon manenance schedulng roblem. The Benders decomoson [7-0] and he evoluonary rogrammng mehod [] have been aled for he soluon of he IMS roblem. An colony omzaon (ACO) s a naure-nsred mehod for he soluon of hard combnaoral omzaon roblems []. ACO has been successfully aled for he soluon of a number of dffcul omzaon roblems n ower sysems ncludng un commmen [-4], lannng of dsrbuon crcus [5], consraned load flow [6], and dsrbuon sysems renforcemen lannng [7]. Ths aer rooses a new mehod based on an colony omzaon for he soluon of he negraed generaon and ransmsson manenance schedulng roblem. The aer s organzed n sx secons. Secon formulaes he negraed generaon and ransmsson manenance schedulng roblem. Secon resens he basc conces of an colony omzaon. Secon 4 descrbes he roosed ACO soluon mehodology o he IMS roblem. Secon 5 resens he alcaon and resuls of usng he roosed echnque o solve he IMS roblem of he IEEE 0 bus sysem. Secon 6 concludes he aer.. IMS roblem formulaon. Objecve funcon The objecve of he negraed manenance schedulng roblem s o mnmze he overall roducon and manenance cos over he oeraonal lannng erod, subjec o un manenance and oerang consrans.

2 An an colony omzaon soluon o he negraed generaon and ransmsson manenance schedulng roblem 47 The objecve funcon o be mnmzed s he sum of a) he un roducon cos, b) he un manenance cos, and c) he ransmsson lne manenance cos, as exressed by equaon (): mn c ( y ) + C y + C T () where c s he roducon cos of un a me (he roducon cos of each un s consdered a quadrac funcon of he un ouu ), y s he manenance saus of un a me (he manenance saus s one, f he un s on manenance and zero oherwse), C s he manenance cos of un a me, C s he manenance cos of ransmsson lne a me, and T s he manenance saus of ransmsson lne a me (he manenance saus s one, f he ransmsson lne s on manenance and zero oherwse). Ths omzaon s consraned by a) manenance schedulng consrans, and b) ower sysem consrans.. Manenance schedulng consrans The negraed manenance schedulng roblem has o sasfy he here below manenance schedulng consrans () o (7). The IMS roblem has o fulfll he generaon manenance wndow consran: for x x + d y = () 0 oherwse where x s he sarng me of manenance for generang un, and d s he duraon of manenance for generang un. The generaon crew consran assgns one generang un o one crew a a me: y = nc () where nc s he number of avalable crews for generaor manenance. The number of ouages for he same generang un s lmed o one durng he manenance horzon: y = (4) The ransmsson lne manenance wndow consran s he followng: for x + x d T = (5) 0 oherwse x s he sarng me of manenance for where ransmsson lne, and d s he duraon of manenance for ransmsson lne. The ransmsson lne manenance crew consran s he followng: T = T (6) where T nc s he number of avalable crews for ransmsson lne manenance. The number of ouages for each ransmsson lne s lmed o one durng he manenance horzon: nc. ower sysem consrans T = (7) The IMS roblem has also o sasfy he ower sysem consrans (8) o (0). The roducon of each generang un mus be beween s lower and uer lms: where me, and mn, (8) s he ouu ower from generang un a mn and s he mnmum and mum ouu ower from un, resecvely. The on lne uns mus mee he sysem demand: ( y ) = D (9) where D s he demand a me. Fnally, he IMS roblem has o sasfy he newor consran (0) so as o manan he flow on each ransmsson lne below s mum lm: F F (0) where F s he flow on ransmsson lne and F s he mum allowable flow on ransmsson lne.. An colony omzaon An colony omzaon s a naure-nsred mehod for he soluon of hard combnaoral omzaon roblems []. The nsrng source of ACO s he foragng behavor of real ans. When searchng for food, ans nally exlore he area surroundng her nes n a random manner. As soon as an an fnds a food source, evaluaes and carres some food bac o he nes. Durng he reurn r, he an deoss a heromone ral on he ground. The heromone deosed, he amoun of whch may deend on he quany and qualy of he food, gudes

3 48. S. Georglas,. G. Vernados, C. Karysas oher ans o he food source. Indrec communcaon among ans va heromone rals enables hem o fnd shores ahs beween her nes and food sources. Afer nalzaon of arameers and heromone rals, he ACO meaheursc algorhm eraes over hree hases: a each eraon, he ans consruc a number of soluons; he heromone s udaed, and fnally daemon acons can by oonally used. In he followng, hese hree hases are exlaned n more deal.. Consrucon of soluons Arfcal ans consruc soluons from sequences of soluon comonens aen from a fne se of n avalable soluon comonens Q = { q }. A soluon consrucon sars wh an emy aral soluon s. Then, a each consrucon se, he aral soluon s s exended by addng a feasble soluon comonen from he se N( s ) Q, whch s defned as he se of comonens ha can be added o he curren aral soluon s whou volang any of he roblem consrans. The rocess of consruced soluons can be regarded as a ah on he consrucon grah G Q = ( VE, ). The se of soluon comonens Q may be assocaed eher wh he se V of verces of he grah G Q, or wh he se E of s edges. The choce of a soluon comonen from N ( s ) s done robablscally a each consrucon se, e.g.: ( q s α β τ n( q ) ) = α τ n( q q ( s ) l l N l ) β, q N( s ) () where τ s he heromone value assocaed wh comonen q, n( ) s a weghng funcon ha assgns a each consrucon se a heursc value, called heursc nformaon, o each feasble soluon q N( s ), and α, β are osve arameers, whose values deermne he relaon beween heromone nformaon and heursc nformaon.. heromone udae The am of heromone udae s o ncrease he heromone values assocaed wh good soluons and decrease hose ha are assocaed wh bad ones. Usually, hs s acheved by ncreasng he heromone levels assocaed wh chosen good soluon s ch by a ceran value Δτ, and by decreasng all he heromone values hrough heromone evaoraon: τ ( ρ) τ + ρ Δτ ( ρ) τ f τ s ch oherwse () where ρ (0,] s he evaoraon rae. heromone evaoraon s needed o avod oo rad convergence of he ACO algorhm. I mlemens a useful form of forgeng, favorng he exloraon of new areas n he search sace.. Daemon acons Daemon acons can be oonally used o mlemen cenralzed acons ha canno be erformed by sngle ans. Examles nclude he alcaon of local search o he consruced soluons, or he collecon of global nformaon ha can be used o decde wheher s useful or no o deos addonal heromone o bas he search rocess from a non-local ersecve. 4. roosed ACO soluon o IMS roblem Due o he comlexy of he IMS roblem and because of he ably of ACO o solve dffcul omzaon roblems, hs aer rooses he ACO mehod for he soluon of he IMS roblem. I s consdered ha he schedulng horzon for he IMS roblem s one year (.e., 5 wees), whle he me se s one wee. 4. Inal soluons As shown n Secon, he ACO meaheursc requres he generaon of nal soluons. roer care has o be aen n he nal random generaon of he canddae soluons due o he followng IMS roblem consrans:. Each generaor should be aen off for manenance n consecuve wees accordng o s duraon for manenance d. Smlarly, each ransmsson lne should be aen off for manenance n consecuve wees accordng o s duraon for manenance d.. In each wee, he number of generaors ha can be mananed s lmed o nc due o resources and crew consrans. Smlarly, n each wee, he number of ransmsson lnes ha can be mananed s lmed o T nc due o resources and crew consrans. Afer much consderaon, he canddae soluon sace has he wo-dmensonal marx form of Fg.. The rows of he marx reresen he sages,.e., he number of wees n he schedulng horzon (5 wees n our case) whle he columns reresen he s,.e., he ndex of he generaors and ransmsson lnes ha are o be aen off for manenance.

4 An an colony omzaon soluon o he negraed generaon and ransmsson manenance schedulng roblem 49 Sage Sage Sage Sage Fg.. The mul-sage search sace Soluon mehodology The roosed ACO soluon for he IMS roblem s comosed of he followng ses:. ACO arameers are se and nal soluons are generaed usng he ses descrbed n Secon 4... Whle he ermnaon creron s no me, he ACO meaheursc eraes over he followng wo hases: a. A each eraon, a number of soluons are consruced by he arfcal ans. For each soluon, calculae he on and he off wees for each generang un and ransmsson lne. For each feasble soluon, solve he economc dsach roblem o oban he omal ouu of each generang un. Nex, solve he DC ower flow roblem o calculae he omal ower flow of each ransmsson lne. Fnally, calculae he overall roducon and manenance cos of each feasble soluon. b. The heromone s udaed.. As soon as he ermnaon creron s me, he soluon roosed by ACO s he one wh he mnmum overall roducon and manenance cos, whch smulaneously sasfes all he manenance schedulng and ower sysem consrans. 5. Resuls and dscusson The roosed echnque s exensvely esed on he IEEE 0 bus sysem [8] of Fg. ha has generang uns and 4 ransmsson lnes. The manenance oeraonal lannng horzon s 5 wees. I s consdered ha all he generang uns are o be mananed once durng he schedulng horzon. I s also consdered ha all he ransmsson lnes are o be mananed once durng he lannng horzon. Fg.. Sngle lne dagram of he IEEE 0-bus sysem. Table comares he resuls of he roosed ACO aroach wh he resuls obaned by Benders decomoson [7]. As can be seen from Table, he ACO mehod rovdes an negraed generaon and ransmsson manenance schedulng wh an overall cos of $ , whch s $ cheaer han he schedule obaned by Benders decomoson. Ths 0.46% cos reducon valdaes he effcency and raccaly of he ACO soluon for he negraed generaon and ransmsson manenance schedulng. Table. Comarson of soluon rovded by Benders decomoson and ACO. Cos Benders roosed decomoson ACO roducon ($) Generaon manenance ($) Transmsson manenance ($) Toal cos ($) Table. Comarson of soluon rovded by ACO wh and whou consderng he ransmsson lne manenance. Cos Wh Whou ransmsson ransmsson roducon cos ($) Generaon manenance cos ($) roducon + generaon manenance cos ($) Transmsson lne manenance cos ($) Toal cos ($)

5 50. S. Georglas,. G. Vernados, C. Karysas Table resens a comarson of he soluon rovded by ACO wh and whou consderng he ransmsson lne manenance. Due o he gh hermal caacy lms of he ransmsson lnes, removng some lnes for manenance causes a larger number of ransmsson lnes o volae her lms. Some of he ransmsson lne volaons canno be removed by smly redsachng he generaors. In such cases, he manenance schedule has o be shfed whn he feasble regon away from he omal soluon, whch changes he manenance and roducon coss. As Table shows, when consderng he ransmsson lne manenance, he generaon manenance cos s $ 9 85 hgher (.e., 4.9% hgher) n comarson wh generaon manenance cos when no consderng he ransmsson lne manenance. Ths resul ndcaes ha consderng he ransmsson lnes manenance has a noceable effec on he generaon manenance cos. Ths 4.9% cos ncrease n he generaon manenance cos s he rce for ensurng ha he obaned manenance schedule manans sysem secury. As can be seen from Table, he sum of he roducon and generaon manenance cos s ncreased by $ for he case of consderng he ransmsson lne manenance n comarson wh he case of no consderng he ransmsson lne manenance. Fnally, Table shows ha he oal cos for he case of consderng he ransmsson lne manenance s $ hgher n comarson wh he oal cos for he case of no consderng he ransmsson lne manenance and hs cos dfference s manly arbued o he ransmsson lne manenance cos. 6. Conclusons The negraed generaon and ransmsson manenance schedulng s a comlex combnaoral omzaon roblem. An colony omzaon s a naurensred mehod for he soluon of hard combnaoral omzaon roblems. In hs aer, an an colony omzaon mehod s roosed for he soluon of he negraed generaon and ransmsson manenance schedulng roblem. Tes resuls on he IEEE 0 bus sysem ndcae he effcency of he roosed aroach and s ably o solve he negraed manenance schedulng roblem. References [] J. F. Doazzo, H. M. Merrll, IEEE Transacons on ower Aaraus and Sysems, 94, (975). [] J. G. Wagh, F. Albuyeh, A. Bose, IEEE Transacons on ower Aaraus and Sysems 00, 6-0 (98). [] T. Saoh, K. Nara, IEEE Transacons on ower Sysems 6, (99). [4] C. J. Huang, C.E. Ln, C.L. Huang, Elecrc ower Sysems Research 4, -8 (99). [5] I. El-Amn, S. Duffuaa, M. Abbas, Elecrc ower Sysems Research 54, 9-99 (000). [6] Y. Wang, E. Handschn, Elecrcal ower and Energy Sysems, 4-48 (000). [7] M. Shahdehour, M. Marwal, Manenance schedulng n resrucured ower sysems. Kluwer, Norwell, MA, 000. [8] M. K. C. Marwal, S. M. Shahdehour, Elecrc ower Sysems Research 47, 0- (998). [9] M. K. C. Marwal, S. M. Shahdehour, IEEE Transacons on ower Sysems (), (998). [0] M. K. C. Marwal, S. M. Shahdehour, IEEE Transacons on ower Sysems 4(), (999). [] M.Y. El-Sharh, A.A. El-Keb, Elecrc ower Sysems Research, 65, 5-40 (00). [] M. Dorgo, T. Süzle, An colony omzaon. MIT ress, Cambrdge, MA, 004. [] I. K. Yu, Y. H. Song, Elecrcal ower and Energy Sysems., (00). [4] S. J. Huang, IEEE Transacons on Energy Converson 6(), 96-0 (00). [5] J. F. Gómez e. al., IEEE Transacons on ower Sysems 9(), (004). [6] J. G. Vlachoganns, N. D. Hazargyrou, K. Y. Lee, IEEE Transacons on ower Sysems 0(), 4-49 (005). [7] S. Favuzza, G. Grad, M. G. Iolo, E.R. Sanseverno, IEEE Transacons on ower Sysems (), (007). [8] M. Alomoush, Auconable fxed ransmsson rghs for congeson managemen. h.d. dsseraon, Illnos Insue of Technology, May 000. * Corresondng auhor: georg@dem.uc.gr