Solution of Unit Commitment Problem Using Enhanced Genetic Algorithm

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1 Soluon of Un Commmen roblem Usng Enhaned Gene Algorhm raeek K. Snghal, R. Naresh 2 Deparmen of Eleral Engneerng Naonal Insue of ehnology, Hamrpur Hmahal radesh, Inda snghalkpraeek@gmal.om, 2 rnareshnh@gmal.om Veena Sharma 3, Gouham Kumar N 4 Deparmen of Eleral Engneerng Naonal Insue of ehnology, Hamrpur Hmahal radesh, Inda veenanaresh@gmal.om, 4 gowhamkumar28@gmal.om Absra In hs paper, enhaned gene algorhm (EGA) s used o solve he shor-erm un ommmen problem (UC) and he enhaned lambda eraon (ELI) mehod s used o solve he eonom dspah (ED) sub-problem. Based on EGA, he problem spef operaors have been negraed n he smple GA algorhm and hus, enhaned he qualy of he soluon. erformane of EGA s esed on 2 es sysems omprsng of 4- un and 0-un over he shedulng me horzon of 8 hours and 24 hours respevely. Resuls demonsrae ha he proposed mehod s superor o he oher repored mehods n he leraure. Keywords eonom dspah; gene algorhm; un ommmen I. INRODUCION Un Commmen roblem (UC) s one of he mos mporan opmzaon ask whh has o be performed by power engneers n a daly operaon plannng of power sysems so ha obaned generaon shedule resuls n a grea savngs of dollars for power generaon ompanes espeally n a deregulaed envronmen where eah GENCO runs s own generaor n order o oban more prof. Sne he load demand vares hroughou he day and reahes o a dfferen peak values from one day o anoher and hus, he oal power generaon an be kep onsan []. he man objeve of onvenonal UC s o mnmze he oal generaon os (operang fuel os, sar-up and shudown oss) over he shedulng me horzon of 24-h or 68-h wh -h me nerval subje o he number of sysem (or ouplng) and un (or loal) onsrans. Many opmzaon ehnques have been proposed n he pas o solve he UC and manly lassfed no hree groups. hese groups are lassal (or mahemaal) ehnques, sohas (or heurs) ehnques and hybrd ehnques. he mosly used mahemaal ehnques are prory ls (L) mehod [2], dynam programmng (D) [3], branh-andbound (BB) mehod [4], mxed-neger lnear programmng (MIL) [5] and lagrangan relaxaon (LR) mehod [6]. Ou of whh, L mehod s fas bu produes sub-opmal soluon. D faes dmensonaly problem as he problem sze nreases. MIL requres large memory and suffers from grea ompuaon delay for large sale UC. LR suffers from numeral onvergene and soluon qualy problems. Alhough he soluon produed by mahemaal ehnques s aurae and opmal, bu requres large ompuaon me even for medum szed UC. he sohas ehnques are hghly heurs n naure and manly lassfed as smulaed annealng (SA) [7], evoluonary programmng (E) [8], gene algorhm (GA) [9,0], parle swarm opmzaon (SO) [], dfferenal evoluon (DE) [2], baeral foragng algorhm (BFA) [3], mperals ompeon algorhm (ICA) [4], harmony searh algorhm (HSA) [5] and arfal bee olony algorhm (ABC) [6]. Sne hese ehnques are parameer sensve and hus, requre proper unng n order o oban he near global opmal soluon n leas exeuon me. Improper unng of hese parameers resuls n premaure or slow onvergene whh may lead he soluon o loal opmum. Some hybrds of he mehods have been also proposed n he pas whh ulzes he feaure of one mehod o overome he drawbak of anoher mehod. he manly onss hybrd mehods are GA and LR [7], GA and abu searh (S) [8], arfal neural nework (ANN) and D [9]. he hybrdzaon redues he searh spae for large sale UC and hereby, redues he exeuon me. he GA s a populaon based searh algorhm based on he mehans of naural seleon and genes [9]. GA has been suessfully appled o many non-lnear large sale engneerng opmzaon problems. In hs work, enhaned GA (EGA) s used o dede he ON/OFF saus of he hermal uns n eah hour of he shedulng me horzon and he power generaon values of he ommed uns are deermned by solvng he eonom dspah sub-problem usng enhaned lambda eraon (ELI) mehod adoped from [20]. Moreover, he performane of EGA for UC has been enhaned by negrang he problem spef operaors o he smple GA algorhm. he res of he work s organzed as follows: Seon II presens he un ommmen (UC) problem formulaon, Seon III presens he mappng of EGA for UC, Seon IV provdes he smulaon resuls and her dsussons and fnally Seon V onludes he paper. II. ROBLEM FORMULAION A. Objeve Funon he man objeve of UC s o deermne he opmum ON/OFF shedule so as o mnmze he oal generaon os [ /4/$ IEEE]

2 (C ) over he shedulng me horzon of 24-h wh -h me nerval by sasfyng varous sysem and un onsrans. Mahemaally he problem o be mnmzed [2] s where SU N [ ( ), ( )] = = C = F + SU U U () 2 F( ) = a + b + ( ) (2) HS, f, down, off, down +, old, = (3), f, off >, down +, old where F ( ) s he quadra fuel os funon represenng produon os of h un a hour n S/h, a, b and are he fuel os oeffens of h un, s he real power generaon of h un a hour n MW, SU, s he sar-up os of h un a hour n S/h, HS and are he ho and old sar-up oss of h un n $/h respevely, U s he ON/OFF saus of h un a hour ( on, 0 off ), N s he number of hermal uns, s he number of shedulng me nervals n hours,, down s he mnmum-down me of h un n hours, off, s he onnuously-off me of h un ll me n hours, old, s he old sar-up me of hours. = h un n B. Consrans he varous sysem and un onsrans mposed on he sysem are: ) ower balane onsran: he generaed power mus be equal o he load demand as follows N U D = 0 (4) where D s he load demand a hour n MW. 2) Spnnng reserve onsran: Sysem spnnng reserve s expressed as exess power generaon as follows N max U D + R (5) = max where s he maxmum power generaon apay h of un n MW, R s he sysem spnnng reserve a hour n MW. 3) Generaon lm onsran: Eah ommed un mus be whn s spefed generaon lms as follows mn max U U (6) mn where s he mnmum power generaon apay h of un n MW 4) Mnmum up and down me onsran: A un mus be on/off for a mnmum number of hours before ommng and deommng as follows 0, f U f 0 or, oherwse, off, down = 0,, on, up where up, s he mnmum-up me of h hours, on, s he onnuously ON me of h hour (-) n hours. (7) un n un ll III. ENHANCED GENEIC ALGORIHM (EGA) FOR UNI COMMIMEN ROBLEM (UC) In hs seon, he mplemenaon of EGA for UC has been presened. he onrol parameers nvolved n EGA are populaon sze (number of hromosomes), seleon mehansm, rossover and muaon probables and he maxmum number of generaons requred for obanng he opmal soluon. A. Represenaon of Chromosomes for UC In UC, he deson varables are bnary srngs whh show he ON/OFF saus of he hermal uns over he omplee shedulng me horzon. If N s he oal number of hermal uns and s he omplee shedulng me nervals, hen a hromosome n a populaon onss of N bnary bs. Eah b n a hromosome represens a gene havng or 0 bnary values. A hromosome n a populaon self represens an ndvdual soluon for UC. B. opulaon Inalzaon For he omplee s randomly nalzed as follows N hromosomes, eah hromosome 2 d n j [ j j... j... j] ; {,2,..., } ; {,2,..., } X j X = x x x x j N d n (8) where j represens he hromosome n a populaon, d represens he dmenson of a hromosome, n represens he oal number of bnary varables equals o N bnary bs and N s he populaon sze (number of hromosomes). he poson of x d j s generaed usng a unformly dsrbued random number, whh generaes eher 0 or and hey are equally lkely. C. Fness Funon Evaluaon Afer generang he nal populaon, he eonom dspah (ED) has o be performed only on feasble hromosomes so as o eonomally dspah he load demand n eah hour of he shedulng me horzon. he enhaned lambda eraon (ELI) algorhm s used o solve he ED subproblem and hen he produon os an be alulaed usng (2). he fness of eah hromosome s he oal generaon os (C) whh an be alulaed usng (). he hromosome havng leas C has he hghes fness value. D. Generae ral soluons In smple GA, he hree bas operaors vz. seleon, rossover and muaon have been used o updae he soluon

3 of UC hroughou he generaons whereas n EGA hree more operaors are proposed whh are desrbed as below: ) Seleon: he paren hromosomes are seleed based on her fness values usng Roulee wheel seleon mehansm. he hromosomes are seleed based on he probably proporonal o he paren genoype relave fness whn he populaon. hen, he new offsprng genoypes are produed by means of wo oher gene operaors namely rossover and muaon. 2) Crossover: he seleed paren hromosomes from he urren populaon form a mang pool o produe he new offsprngs. he rossover operaon s a random proess of reombnaon of paren hromosomes and her b values are exhanged a he rossover ses based on he rossover probably ( p ) o produe offsprngs. hese offsprngs have he feaure of wo paren genoypes and hus, may have beer fness. Afer performng he rossover operaon, a new poulaon of offsprngs have been formed. 3) Muaon: Muaon nrodues new gene maeral no he gene a some low rae. Wh a small muaon probably ( p m ), randomly hosen bs of he offsprng genoypes hange from 0 o and ve versa and hus, nrodue he dversy n he soluon searh spae. 4) Swap Wndow Operaor: hs operaor s appled o every genoype of he populaon wh a probably of 0.2. he wo uns, a me wndow of wdh w (hours) and a random wndow poson beween,2,, shedulng nervals are arbrary seleed from a genoype. he bs of he wo seleed uns nluded n he wndow are exhanged and hus, a new offsprng s formed. If a new offsprng s beer han he urren one hen he new one s seleed else he old one s resored. hs operaor as lke a sophsaed muaon operaor. 5) Wndow muaon operaor: hs operaor s also appled o all he genoypes of he populaon wh a probably of 0.2. In hs operaor, only one un s randomly seleed wh me wndow of wdh w (hours) and a random wndow poson beween,2,, shedulng nervals. hen, all he bs of ha un le whn he me wndow are flpped from o 0 and ve-versa. hs operaor a as a mul-pon muaon operaor. 6) Swap muaon operaor: hs operaor s appled only o he so-far found global bes hromosome whn he urren populaon. he wo uns are randomly seleed and her bs are exhanged for a spef hour.e. her ON/OFF saus s exhanged. If a beer soluon s obaned hen he soluon s kep oherwse s resored o s old soluon. hs operaor resembles he sohas hll lmbng mehod. he above menoned hree advaned muaon operaors worked smulaneously o generae he offsprngs based on he wo arge probables 0 p p 2. If a unformly dsrbued random number rand(0,) p hen, a swap wndow operaor s o be performed else f rand(0,) p 2 hen, a swap muaon operaor s o be performed else f p < rand(0,) < p2 hen, a wndow muaon operaor s o be performed. hs wll balane he exploraon and exploaon proess and hus, produe he near global opmal soluon. E. Reparng Infeasble Soluons When he soluon s randomly nalzed and whenever he modfaon n he soluon s made hroughou he searh proess, he nfeasble soluons have o be repared n order o mprove he soluon qualy a faser rae. he onsrans n (5) and (7) have been repared based on he sraeges adoped from []. F. Ele Sraegy In order o avod he loosng of bes soluons hroughou he searh proess, an ele sraegy has been adoped from [3]. In hs sraegy, he paren and offsprng hromosomes are frs ombned ogeher and sored aordng o her fness values. hen, he frs 50 % of he bes soluons of he ombned populaon are seleed as he populaon for he nex generaon. G. roedural Seps for UC usng EGA he sep by sep proedure o solve he UC usng EGA s as follows: Sep : Inalze EGA parameers lke N, p, p m, p and p 2 and maxmum generaons ( g max ) as ermnaon rera. Sep 2: Randomly generae he N hromosomes by sasfyng all he onsrans from (4) o (7) wh he sruure shown n (8). Sep 3: erform ED on feasble hromosomes n order o deermne he power generaon values over he omplee shedulng me horzon and hen alulae he produon os of eah un n eah hour usng (2). Sep 4: Evaluae he fness funon as n (). Sep 5: Sele he paren hromosomes from he urren populaon usng Roulee wheel seleon mehansm. Sep 6: erform -pon rossover operaon on he seleed paren hromosomes o generae he offsprngs. Sep 7: erform advaned muaon operaors explaned n prevous seon o modfy he offsprngs. Sep 8: Repar nfeasble soluons and hen perform ED on he feasble offsprngs o alulae he oal produon os and hen evaluae he fness values of hese offsprngs. Sep 9: Apply ele mehansm o preserve he bes soluons found so far.

4 Sep 0: If maxmum number of generaons ( g max ) are no reahed hen go o sep 5, oherwse sop he proedure and prn he opmal generaon shedule. IV. SIMULAION RESULS o demonsrae he feasbly and effeveness of he proposed EGA mehod for UC, EGA s appled o wo es sysems omprsng of 4-un and 0-uns over he shedulng me nervals of 8-hour and 24-hour respevely. he spnnng reserve s onsdered as 0 % of he oal load demand n eah hour of he shedulng me horzon and hus, redued he probably of load nerrupons [7]. he smulaon s performed on Inel ore2duo, 2.20 GHz proessor C and wren n MALAB 7.9. A. es Sysem hs es sysem omprses of 4 hermal uns over he shedulng me horzon of 8 hours wh -h me nerval. he os haraerss and load demand are adoped from [] and menoned n ables I and II respevely. For hs sysem, he populaon sze was kep 0 and he maxmum generaon oun was kep 00. he rossover and muaon probables were kep 0.7 and 0.05 respevely. he range of wo arge probables are [0,]. he bes UC shedule along wh he dspah values, produon os ( os ), sar-up os ( SU ) and oal generaon os (C) are lsed n able III. From able III, an be dedued ha he obaned UC shedule has sasfed all he problem onsrans and hus, produes he qualy soluon. Also, he oal onlne apay of generaors n eah hour of he shedulng me horzon s more han he load plus spnnng reserve requremens. he same problem was also solved wh GA and ompared wh EGA and he resuls are presened n able IV whh also presens he omparson of obaned resuls wh ha of LR. Sne, s a small sysem omprsng of 4 hermal uns, bes os was also aheved by GA bu a margnal dfferene was found n CU me. ABLE I. UNI CHARACERISI FOR 4-UNI SYSEM [] Un Un 2 Un 3 Un 4 max (MW) mn (MW) a b ($/MWh) ($/MW 2 h) INS (h) up, (h) down, (h) HS ($) ($) old, (h) ABLE II. LOAD AERN FOR 4-UNI SYSEM [] Hour (h) Load (MW) ABLE III. OIMAL GENERAION SCHEDULE FOR 4-UNI SYSEM Dspah Values (MW) os ($) U U2 U3 U4 SU ($) C ($) oal generaon os n 8-h ($) 77, ,628.9 ABLE IV. COMARISON IN ERMS OF COS ($) AND CU IME (S) Mehod Cos ($) CU me (S) LR [6] 76, GA 77, EGA 77, B. es Sysem 2 hs es sysem omprses of 0 hermal uns over he shedulng me horzon of 24 hours wh -h me nerval. he os haraerss and load demand are adoped from [4] and presened n ables V and VI respevely. In order o fne une he EGA parameers, he smulaon was repeaed for 0 random rals. In eah ral, he populaon sze was kep 30 o show he effe of small populaon sze and he maxmum number of generaons was kep 00, n order o redue he ompuaonal effors. ABLE V. UNI CHARACERISI FOR 0-UNI SYSEM [4] Un Un 2 Un 3 Un 4 Un 5 max (MW) mn (MW) a b ($/MWh) ($/MW 2 h) INS (h) up, (h) down, (h) HS ($) ($) old, (h) Un 6 Un 7 Un 8 Un 9 Un 0 max (MW) mn (MW) a b ($/MWh) ($/MW 2 h) INS (h) up, (h) 3 3 down, (h) 3 3 HS ($) ($) old, (h)

5 ABLE VI. LOAD AERN FOR 0-UNI SYSEM [4] Hour (h) Load (MW) Hour (h) Load (MW) Hour (h) Load (MW) he range for rossover probably was kep 0.4 o 0.9 (per genoype) and he range for muaon probably was kep o (per b). When pre-maure onvergene was observed, he rossover probably was lowered by 0. whle muaon probably (per b) s nreased by When exessve dversy ours, he rossover probably s nreased by 0. whle muaon probably s lowered by he wo arge probables range from 0 o. ABLE VII. OIMAL GENERAION SCHEDULE FOR 0-UNI SYSEM Generang Un ABLE VIII. os SU BES COS SOLUION FOR 0-UNI SYSEM C os SU C oal generaon os n 24-h ($) 559, ,938 a. All demals are rounded off o he neares negers. he smulaon was agan repeaed 20 mes on he bes found parameers menoned above. he bes generaon shedule obaned n a se of 20 ndependen runs s presened n able VII whereas able VIII shows he os soluon omprsng of produon os ( os ), sar-up os ( SU ) and oal generaon os (C) obaned on he bes generaon shedule menoned n able VII. From able VII, an be nferred ha he obaned UC shedule has sasfed all he problem onsrans mposed on he sysem and hus, produes he qualy soluon. Fg. shows he onvergene graph for smple GA and EGA for UC and s revealed ha he qualy of he soluon has been enhaned by negrang he problem spef operaors n smple GA. Fg. 2 shows he urves for oal onlne apay of uns, load and spnnng reserves and s nferred ha he suffen amoun of generaon s avalable n eah hour whh an sasfy he load plus reserve requremens. oal generaon os ($) 5.95 x GA EGA Generaons Fg.. Convergene haraerss of EGA and GA for 0-un sysem. ower (M W ) demand + spnnng reserve maxmum apay of sheduled uns demand me (hours) Fg. 2. Onlne apay, load and spnnng reserve urves for 0-un sysem. able IX shows he omparson of EGA soluon wh he oher lassal and sohas mehods repored n he leraure lke enhaned prory ls (EL), lagrangan relaxaon (LR), smulaed annealng (SA), evoluonary programmng (E), mproved bnary parle swarm opmzaon (IBSO), dfferenal evoluon (DE), baeral foragng algorhm (BFA), mperals ompeon algorhm (ICA), harmony searh algorhm (HSA), bnary/real arfal bee olony algorhm (BRABC), hybrd of LR and GA (LRGA). From

6 able IX, s revealed ha EGA produes qualy soluon n erms of oal generaon os ompared o mos of he mehods. Alhough he BRABC mehod produes approxmaely he same bes os soluon, bu ompuaonally slow ompared o he proposed EGA mehod. Moreover, he CU me aken by EL, LR and SA are less han ha of EGA, bu produe sub-opmal os soluons ompared o he proposed EGA mehod. ABLE IX. ERFORMANCE COMARISON OF ROOSED EGA WIH HE OHER MEHODS FOR 0-UNI SYSEM Mehod Bes Cos Mean Cos Wors Cos me ($) ($) ($) (s) EL [2] 563, LR [6] 565, SA [7] 565, , , E [8] 564,55 565, ,23 00 IBSO [] 563, ,55 565,32 27 DE [2] 563, BFA [3] 564, ICA [4] 563, , HSA [5] 565, BRABC [6] 563, , , LRGA [7] 564, GA 564, , , EGA 563, , , V. CONCLUSIONS In hs paper, enhaned gene algorhm (EGA) s suessfully mplemened o solve he un ommmen problem (UC) for 4-un and 0-un es sysems over he shedulng me horzon of 8 hours and 24 hours respevely and enhaned lambda eraon (ELI) mehod s used o solve he eonom dspah (ED) sub-problem. In order o enhane he exploraon and exploaon proess of he searh spae, he problem spef operaors are negraed wh he smple GA and hereby, redued he hane of searh o be rapped a loal opmum soluon. Moreover, he onsran reparng sraeges keep he searh spae feasble and hus, aelerae he onvergene proess. he obaned resuls demonsrae he robusness of he proposed EGA algorhm for UC. REFERENCES [] A.J. Wood, and B.F. Wollenberg, ower Generaon, Operaon and Conrol, 2 nd ed. Inda: Wley, 2007, pp [2]. Senjyu, K. Shmabukuro, K. Uezao, and. Funabash, A fas ehnque for un ommmen problem by exended prory ls, IEEE rans. ower Sys., vol. 8, no. 2, pp , May [3].K. Snghal and R.N. Sharma, Dynam programmng approah for solvng power generang un ommmen problem, n ro. IEEE In. Conf. Compuer and Communaon ehnology, Sep. 20, pp DOI: 0.09/ICCC [4] C.L. Chen, and S.C. Wang, Branh-and-bound shedulng for hermal generang uns, IEEE rans. Energy Convers., vol. 8, no. 2, pp , Jun [5] M. Carron, and J.M. Arroyo, A ompuaonally effen mxedneger lnear formulaon for he hermal un ommmen problem, IEEE rans. ower Sys., vol. 2, no. 3, pp , Aug [6].K. Snghal, Generaon shedulng mehodology for hermal uns usng lagrangan relaxaon, n ro. 2nd IEEE In. Conf. Curren rends n ehnology, pp. -6, De 20. [7] N. Smopoulos, S.D. Kavaza, and C.D. Vournas, Un ommmen by an enhaned smulaed annealng algorhm, IEEE rans. ower Sys., vol. 2, no., pp , Feb [8] K.A. Juse, H. Ka, E. anaka, and J. Hasegawa, An evoluonary programmng soluon o he un ommmen problem, IEEE rans. ower Sys., vol. 4, no. 4, pp , Nov [9] D. Daa, Un ommmen problem wh ramp rae onsran usng a bnary-real-oded gene algorhm, Appl. Sof Compu., vol. 3, pp , 203. [0] K. Deb, A. raap, S. Agarwal, and. Meyarvan, A fas and els mulobjeve gene algorhm: NSGA-II, IEEE rans. Evolu. Compu., vol. 6, no. 2, pp , Apr [] X. Yuan, H. Ne, A. Su, L. Wang, and Y. Yuan, An mproved bnary parle swarm opmzaon for un ommmen problem, Exp. Sys. Appl., vol. 36, pp , [2] D. Daa, and S. Dua, A bnary-real-oded dfferenal evoluon for un ommmen problem, In. J. Eler ower Energy Sys., vol. 42, pp , 202. [3] M. Eslaman, S.H. Hossenan, and B. Vahd, Baeral foragng-based soluon o he un-ommmen problem, IEEE rans. ower Sys., vol. 24, no. 3, pp , Aug [4] M.M. Hadj, and B. Vahd, A soluon o he un ommmen problem usng mperals ompeon algorhm, IEEE rans. ower Sys., vol. 27, no., pp. 7-24, Feb [5] Y. ourjamal, and S.N. Ravadanegh, HSA based soluon o he UC problem, In. J. Eler ower Energy Sys., vol. 46, pp , 203. [6] K. Chandrasekaran, S. Hemamaln, S.. Smon, and N.. adhy, hermal un ommmen usng bnary/real oded arfal bee olony algorhm, Eler. ower Sys. Res., vol. 84, pp. 09-9, 202. [7] C.. Cheng, C.W. Lu, and C.C. Lu, Un ommmen by lagrangan relaxaon and gene algorhms, IEEE rans. ower Sys., vol. 5, no. 2, pp , May [8] A.H. Manawy, Y.L.A. Magd, and S.Z. Selm, A new gene-based abu searh algorhm for un ommmen problem, Eler. ower Sys. Res., vol. 49, pp. 7-78, 999. [9] C. Wang, and S. M. Shahdehpour, Effes of ramp-rae lms on un ommmen and eonom dspah, IEEE rans. ower Sys., vol. 8, no. 3, pp , Aug [20].K. Snghal, R. Naresh, V. Sharma, and K.N. Gouham, Enhaned lambda eraon algorhm for he soluon of large sale eonom dspah problem, n ro. IEEE In. Conf. Reen Advanes and Innovaons n Engneerng, May 204, pp. -6. DOI: 0.09/ICRAIE