UNIT COMMITMENT SOLUTION USING GENETIC ALGORITHM BASED ON PRIORITY LIST APPROACH

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1 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: UNIT COMMITMENT SOLUTION USING GENETIC ALGORITHM BASED ON PRIORITY LIST APPROACH SARJIYA, 2 ARIEF BUDI MULYAWAN, 3 ANDI SUDIARSO Department of Electrcal Engneerng and Informaton Technology, Unverstas Gadjah Mada, Yogyakarta, Indonesa 2 Department of Electrcal Engneerng and Informaton Technology, Unverstas Gadjah Mada, Yogyakarta, Indonesa 3 Department of Mechancal and Industral Engneerng, Unverstas Gadjah Mada, Yogyakarta, Indonesa E-mal: sarjya@ugm.ac.d, 2 aref.abm@gmal.com, 3 a.sudarso@ugm.ac.d ABSTRACT Ths paper presents the completon of unt commtment (UC) problem usng genetc algorthm based on prorty lst (GABPL) approach. The UC problem s dvded nto two sub problems. The problem of unt schedulng s solved by usng GABPL method. The lambda teraton method s used for solvng the economc load dspatch problem. The proposed method s tested on 0-unts-system case study as well as ts duplcaton. The prorty lst whch s used n ths paper can make genetc algorthm to converge faster and better. The results of the proposed method are compared to other methods referred n ths paper. Keywords: Unt Commtment, Economc Dspatch, Genetc Algorthm, Prorty Lst, Lambda Iteraton. INTRODUCTION The consumpton rate of electrcal energy whose value vares over tme wll create systematc problems n generaton system. Ths problem nvolves whch generatng unts have to be turned on or off and how much power that has to be generated by each generatng unts to fulfll dfferent load demands n each perod. In electrcal power system, t s classfed as optmzaton problem, one of the promnent problem that has to be done. Ths knd of problem s well known as unt commtment (UC). UC s a generaton schedulng problem wth the objectve s to obtan mnmum cost wthout volatng lmts that are already set n a perod of tme []. The tme perod for UC can be chosen as 24 hours, seven days, etc. In ths problem, the cost whch should be mnmzed conssts of fuel cost, start-up cost, and shut-down cost that come from the generatng unts. In solvng the UC problem, there s sub problem that also has to be solved. Ths sub problem s called economc load dspatch (ELD). The ELD dstrbutes loads whch are asked from each onlne generatng unt economcally by ensurng that every onlne generatng unt s used mnmally at below capacty lmt to fulfll load demands. In ts development, many optmzaton methods have been developed to solve the UC problem. The prevous work on UC problem and ts soluton technques have been revewed by [2]. At frst, the optmzaton methods are n the form of conventonal teraton methods, lke Lagrange relaxaton (LR), nteger programmng, dynamc programmng [2], prorty lst (PL) [2], [3], etc.. These methods are often trapped n local optma f UC modelng s gettng complex. Because of ts weakness, other optmzaton methods are begun to be ntroduced,.e. artfcal ntellgence methods (AI) that s based on metaheurstc lke fuzzy methods [2], genetc algorthm (GA) [2], [4], antcolony optmzaton (ACO) [5], partcle swarm optmzaton (PSO) [6], shuffled frog leapng algorthm (SFLA) [7], etc.. These methods use mult-searchng pont to look for optmal soluton so that the produced output can approach optmal global pont. The process of fndng a method that can produce a better soluton s contnued to be sought by researchers. Many researchers combne some methods to solve ths UC problem.e. prorty lst based evolutonary algorthm (PL EA) [8], extended PL (EPL) [9], and hybrd genetc algorthm (HGA) [0]. These methods use PL as ntal populaton from metaheurstc method and can produce a better soluton than before. From the prevous works, t can be concluded that most researchers use GA wth addtonal operator to solve the UC problem. GA method s 394

2 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: used because t s easy to be mplemented and has good convergence level. Another advantage of GA s ts character uses mult-searchng-no-sngle-pont to look for soluton from generated populaton, so that GA can gve many soluton optons []. However, GA method sometmes can also be trapped n local optma soluton because there are too many possble solutons to be tred [7]. In order to overcome ths weakness, researcher use mproved PL method [2] as one of the ntal populaton from GA. The GA method used n ths paper also apply some addtonal operators [3] to produce optmal soluton and there are new addtonal operators presented n ths paper to acheve a better soluton. Parameters from GA are also optmzed by usng desgn of experment (DOE) [2]. 2. PROBLEM FORMULATION 2. Notatons The notatons used n ths paper are, N total generatng unts, t tme, generatng unt T total perod of tme, TOC total operatng cost of generatng unts, U t the on/off status of the -th unt at t-th hour, f unt s up U t =, f unt s down U t =0, F t (P t ) fuel cost functon of -th unt, wth generaton output, P t, at the t-hour, S t start-up cost of -th unt at t-th hour, a, b, c fuel cost coeffcent of -th unt, P t the generaton output of the -th unt at t-th hour, HSC hot start-up cost of -th unt, CSC cold start-up cost of -th unt, MDT mnmum down tme of -th unt, MUT mnmum up tme of -th unt, Toff total tme of -th unt durng down, Ton total tme of -th unt durng up, Tcold cold start-up tme of -th unt, load t load demand at t-th hour, SR t spnnng reserve at t-th hour, Pmax maxmum generated output power of - th unt, Pmn mnmum generated output power of - th unt, UR up ramp of -th unt, DR down ramp of -th unt, M prorty ndex of average producton cost, x multpler factor of -th unt, λ ncremental cost value of all unts. 2.2 Objectve Functon The objectve functon of UC problem can be formulated as () [3]. Mn TOC = T N ( Ut Ft ( Pt ) + Ut. St ) t= =. () There are two cost functons nvolved n (). The frst one s fuel cost whch s the cost ncurred per generated MW that generated by generatng unts and can be formulated as (2). t 2 ( Pt ) = apt + b Pt c F + (2) The second one s start-up cost from the generatng unts that can be formulated as (3). S t HSC, = CSC, f MDT < T f T down, off, > MDT MDT + T cold, + T co (3) 2.3 Constrants In mnmzng the objectve functon, these constrants must be satsfed Power balance constrant In ths constrant, the total power generated by generatng unts must be equal to the total load demanded by consumers. The mathematcal equaton can be seen n (4). N ( Ut. Pt ) = load t, t T. = (4) Spnnng reserve constrant The total capacty of the commtted generatng unts must be bgger than or equal to the load and the specfed spnnng reserve. The formulaton can be seen n (5). N ( Ut. Pmax ) ( loadt + SRt ), t T. = (5) Power generatng lmt The actve powers that can be generated by the generatng unts have mnmum and maxmum values defned as (6). P mn P P max, P R. (6) t 395

3 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: Mnmum up/down tme Before turnng on or off the generator, the mnmum down tme (MDT) or mnmum up tme (MUT) from that generator must be fulflled. The mathematcal formulaton of these constrants can be seen n (7) and (8). T on (, t) MUT ( ) f U (, t + ) should be turned off, f U (, t T off (, t) MDT ( ) + ) should be turned on. (7) (8) Ramp up/down constrants One of the characterstc of the thermal generatng unt s the generated power can t be changed drastcally at a short tme nterval because the ncreasng or decreasng of thermal energy must be done gradually. Mathematcally, these constrants can be formulated as (9) and (0). P, t P, t UR, f generaton ncreases P, t P, t DR, f generaton decreases (9) (0) Intal status The on/off tme of the generatng unts at ntal status must be consdered too. 3. PROPOSED METHOD EXPLANATION GA s frstly founded by John Holland and developed by hs student, Davd Goldberg. Ths GA method utlzes the natural selecton process. In ths process, each ndvdual wll have some gene changes contnuously to adapt to ts envronment through the process known as the selecton process. In ths process, there are several processes to get the new populaton.e. parents search usng roulette wheel, cross over, and mutaton. In solvng the UC problem, ths problem s dvded nto two parts. The frst part s the generaton schedulng problem or ths UC problem tself. The second part s the ELD problem. The detals of how to solve these problems can be seen n the next secton. 3. Genetc Algorthm Based on Prorty Lst Approach for Solvng the Generaton Schedulng Problem For solvng ths UC problem, frstly, the PL method based on the average producton cost (APC) [4] s used. The formulaton to calculate ths prorty ndex can be seen n (). Unt wth the prorty ndex value M lower than the others wll become the frst prorty to be turned on. In solvng ths UC problem, f there s only a MDT constrant volaton, the hold on status method wll be used to fulfll ths constrant [3], [2]. Ths hold on status works by turnng on the generatng unt n prevous hours untl the MDT s satsfed. where, M x F ( P ) = () P x. P max P mn + 2 P max = (2) After the generatng schedulng result from the PL method s obtaned, ths result wll be used as one of ntal populaton from GA. Then, GA wth bnary coded wll be used to solve ths UC problem. The bnary coded used n ths method are 0 and value whch ndcate the status of generatng unt (0 f the unt s down and f the unt s up). The matrx used for solvng ths UC problem s three-dmensonal matrx wth rows represent the schedulng tme, columns represent the number of generatng unts, and the last arrays represent the populaton sze so that f n populatons are used, then the last arrays wll amount to n. The detal can be seen n Fg.. To get the best ndvdual through the selecton process, besdes the result from the PL, the ntal populaton must be formed beforehand. Ths ntal populaton s formed randomly. After the formaton process s done, there wll be a repared schedulng to fulfll the mnmum up/down tme constrants so that the formed ntal populaton s a vable soluton. The repared schedulng steps are as follows, - If at t-hour the generatng unt s down but at (t-)-hour t s up, then the up tme wll be checked frst. If the up tme s over than or equal to the mnmum up tme of the correspondng unt, then the unt can be shutdown. However, f the mnmum up tme s not fulflled yet, then the unt wll stll be up n the t-hour. - If at t-hour the generatng unt s up but at (t- )-hour t s down, then the down tme wll be checked frst. If the down tme s over than or equal to the mnmum down tme of the 396

4 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: correspondng unt, then the unt can be started up. However, f the mnmum down tme s not fulflled yet, then the unt wll stll be down n the t-hour. st chromosome 2nd chromosome Hour T Hour T Gen#... Gen#... Gen# Gen# Gen# Gen# Gen#N Gen#N cross over ponts parents offsprngs 3rd chromosome... N-th chromosome Hour T Hour T Gen#... Gen#... Gen#2... Gen# Gen# Gen# Gen#N Gen#N Fg.. Representaton of The Populaton n GA Wth ths repared schedulng, the ntal populaton whch satsfes the mnmum up/down tme constrants wll be obtaned. The next process s called the chromosomes evaluaton. In ths process, the constrants are checked. Frst, the spnnng reserve constrant wll be checked at each hour usng the schedule from the ntal populaton. If there s a volated spnnng reserve n an hour, then the penalty count wll be added to the penalty functon. Second, the mnmum up/down tme must be satsfed so that the ndvdual can enter the ELD problem. If those constrants can t be satsfed, the ndvdual wll be gven a penalty count. After the ELD problem s solved, each ndvdual wll enter the ftness functon calculaton process. The penalty count wll be multpled by penalty factor and the penalty functon s expressed as n (3). Ths penalty functon, start-up cost, and fuel cost whch are obtaned from the ELD problem wll be summed to obtan the ftness value from each ndvdual nsde ths populaton. The formulaton can be seen n (4). penalty functon= penalty factor penalty count. (3) After calculaton of the ftness functon s done, the next s the selecton process. In ths process, there are several sub-parts of the process. The frst one s the eltsm process. In ths process, the best ndvdual wll be duplcated so that t won t enter the next selecton process whch has the possblty to damage t. Ths best ndvdual wll be kept to be used n the next generaton. Fg. 2 The Illustraton of Crossover Process. Ftness = startup cost + fuel cos t + penalty functon (4) The next process s the reproducton process. In ths process, there are three sub-processes.e. parents search, cross over, mutaton, and addtonal operator. The detals of how to mplement these operators nto GA can be seen n the next secton. 3.. Parents search The parents search n GA use the roulette wheel method. Indvdual whose ftness value bgger than the others wll have a bgger chance to be selected Cross over The cross over process s shown n Fg. 2. In ths sub-process, the genes on both ndvdual parents wll be exchanged based on the cross over pont. Ths sub-process wll be run f the randomzed number s less than or equal to the cross over probablty Mutaton In ths sub-process, the gene wll be mutated f the randomzed number s less than or equal to the mutaton probablty. If the gene s, then after ths sub-process, t wll be changed nto 0 and vce versa. Ths mutaton process can be llustrated n Fg mutated Fg. 3 The Illustraton of Mutaton Process. 397

5 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: hours unts T : : wndow : n OR hours unts T 2 3 : : wndow : n Fg. 4 Ilustraton of Wndow-mutaton for Best Chromosome Operator 3..4 Addtonal operator Besdes these three sub-processes, there are addtonal operators appled to the ndvduals.e. swap-wndow, wndow-mutaton, and the swapmutaton as well as the swap-wndow-hll-clmb for the best chromosome [3]. These addtonal operators are used to produce a more optmal soluton. Besde of these operators, there are two addtonal operators that run only for the best chromosome n every generaton. These operators are ntroduced so that the optmal soluton can be found. These operators, both for the best chromosome, are wndow-mutaton and mutaton-hour. The detals of how to mplement these operators nto GA can be seen n the next sub-secton. 2 Unts 2 3 n Hours : T mutated bt per unts rand=0 rand= chosen perod of tme Fg. 5 Ilustraton of Mutaton-hour for Best Chromosome Operator Wndow-mutaton for best chromosome The wndow-mutaton operator s appled to the best chromosome wth the probablty of one. It generates a random value of 0 or wth equal probablty. Then, t selects one unt at random and a tme wndow of wdth w equal to MDT (f random value s 0) or MUT (f random value s ) of the correspondng unt. After that, ths operator s run from the st hour to the (T+-w) th hour to mutate the bts n that wndow to 0s f w equal to MDT or s f w equal to MUT. If ths task produces a better soluton, ths soluton wll be kept. Otherwse, t wll be restored to the soluton before ths task s performed. The llustraton can be seen n Fg Mutaton-hour for best chromosome Ths operator s also appled to the best chromosome wth the probablty of 0.7. It selects one of a perod tme randomly. After that, ths operator s run from the st unt untl the N th unt to mutate one bt of each unt. If ths task produces a better soluton, ths soluton wll be kept. Otherwse, t wll be restored to the soluton before ths task s performed. The llustraton can be seen n Fg. 5. After ths process s done, a new populaton wth dfferent chromosomes s formed. It wll re-enter the ftness functon process, the selecton process, and so on untl the maxmum generaton s reached. The best ndvdual at the last generaton wll become the soluton of ths UC problem. 3.2 Lambda Iteraton for Solvng ELD Problem In ths ELD problem, the objectve functon s to mnmze the fuel cost whch s represented by quadratc functon. The penalty functon s added to the objectve functon by summng t wth the fuel cost. Ths new functon, after added by the penalty terms, s called the Lagrange functon. The mnmum condton wll be obtaned by (5) []. ( P ) df dp P = λ, = to n. b (5) = λ. (6) 2a λ s the ncremental cost value of all unts. From (5), the formulaton can be modfed nto (6) to get the value of the generated power from each unt. If there are generatng unts at ther lmts, ths drect soluton can t work well so that the lambda teraton method s used to solve ths ELD problem. In lambda teraton, λ s searched usng teraton. The method starts wth two values of lambda, below and above the optmal value, then t wll terate untl the absolute dfference of two lambdas s less than the convergence tolerance. To nclude the nequalty constrant.e. the generatng lmts n 398

6 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: lambda teraton, the formulaton n (7) are used n each teraton []. P ( λ) = P P ( λ) = P max, mn,,, for P ( λ) > P for P ( λ) < P max, mn,. (7) The flowchart to solve these problems can be seen n Fg. 6. After the generated power results from the ELD problem are obtaned, the fuel cost can be calculated and wll be used n the calculaton of the ftness functon process. Solved UC wth PL based on APC Input generaton schedulng from PL result nto st populaton n GA Chromosomes evaluaton Penalty=0? Yes Solvng ELD problem usng lambda teraton Calculaton of ftness functon Selecton process:. Parents search 2. Cross over 3. Mutaton 4. Addtonal operators No Generaton>max generaton? Randomly ntalze populaton Populaton reparng No Penalty= penalty+ Method Total start-up cost Total fuel cost Total operatonal cost PSO [5] ,53 DE [6] , ,042.6 HPSOGA [7] ,960 ICGA [4] ,404 MA [8] ,827 LR [3] ,825 GA [3] ,825 DPSO [7] , ,804 SPL [9] ,950 LRGA [20] ,800 TSRP [2] ,55 MRCGA [22] ,244 DP combned wth PL [23] ,049 ACO [5] ,049 UCCGA [24] ,977 PL EA [8] , ,977 MPL [3] , ,977 HPSO [25] ,942 SFLA [7] , ,937.7 GABPL , ,937.7 In ths case, the spnnng reserve s specfed as 0% from load [7]. The data s taken from [0] and can be seen n Table II and Table III. The GA parameters used n ths case are optmzed usng DOE method [2]. The optmal values of these parameters are obtaned for populaton sze of 30 wth maxmum generaton of 200, crossover probablty 0.7, and mutaton probablty 0.2. Wth these parameters, the best obtaned total cost s $563, Ths result s then compared to the total cost results from other methods n the reference papers shown n Table I. Frst, the GABPL result can be compared wth the PL result on 0 unts test system. The PL result on 0 unts test system can be seen from Table IV and the GABPL best result can be seen n Fnsh Fg. 6 Flowchart of The Proposed Method. 4. SIMULATION RESULTS Ths proposed method s mplemented n Matlab program and tested on 0-unts-system case study and ts duplcaton. 4. Case : 0 Unts System Yes Table I: Comparson of GABPL Method among Other Methods on 0 Unts System Table V. The total cost obtaned by ths PL result s $563,977. Wth ths result, the GABPL method can decrease the total cost as much as $40 to become $563, Unt 5 at 23 th hour wth 25 MW generated power s turned off and unt 6 s turned on. Because the mnmum generated power n unt 6 s 20 MW, 5 MW less than unt 5 s, t can be generated by unt 2 so that the total generated power from unt 2, prevously 420 MW, become 425 MW. From Table I, t can be seen that the obtaned total cost of the proposed method s lower than the 399

7 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: other methods lke dfferental evoluton (DE), nteger coded GA (ICGA), TS random perturbaton (TSRP), memetc algorthm (MA), DP combned wth PL, dynamc PSO (DPSO), hybrd PSO (HPSO), hybrd PSO and GA (HPSOGA), unt characterstc classfcaton GA (UCCGA), stochastc PL (SPL), LRGA, LR, GA, PL EA, and methodologcal PL (MPL). Ths proposed method produces the most mnmal total cost along wth the SFLA [7]. Ths proposed method can get better soluton because of better ntal populaton. The mproved PL as one of ntal populaton can make GA to converge better compare to usual GA method. The proposed method has as much as,887.3$ reducng cost compare to usual GA method [3] n 0 unt system. 4.2 Case 2: The Duplcatons of 0 Unts System In ths case, the generator and loads data are duplcated from the prevous case study nto 20, 40, 60, 80, and 00 unts systems. The spnnng reserve used n these test systems s specfed as 0% from the load too. The maxmum generatons used n these systems are 300, 300, 500, 500, and 500 respectvely. Because of the stochastc nature of metaheurstc method, ths proposed method s run 0 tmes n every case study. The average total costs obtaned n each case study as well as ts comparson to other methods can be seen n Table VI. The average cost of proposed method on 20, 40, 60, 80, and 00 unt test systems are $563,94; $,24,293; $2,246,375; $3,366,34; $4,488,750; $5,607,773 respectvely. The obtaned total cost on 20 unt test system s not twce more expensve than total cost on 0 unt test system, because there s other way to obtan lower total cost. It can be done by maxmzng the power generated from cheaper generaton unt or turnng on cheaper generaton unt so that lower total cost can be obtaned. From Table VI, t can be seen that, on 20 and 40 unts systems, the total costs obtaned by GABPL method s stll hgher than SFLA but lower than the other systems (60, 80, and 00 unts system). Compared to PL EA method, the total costs obtaned by GABPL method are lower on 0, 20, and 00 unts systems. Overall, the applcaton of the proposed method to large test system also gves better average total cost compared to other methods. 5. CONCLUSION The UC problem s an mportant problem that has to be solved n electrcal power system, especally n system generaton. It conssts of two sub problems, namely generaton schedulng problem and economc dspatch problem. Wth optmzng the generaton schedulng and economc dspatch problem, t can save great amount of cost. So, when optmzaton can decrease small amount of cost, t wll be great advantage. Because of the nadequacy of conventonal methods n solvng large UC problem, metaheurstc methods are beng studed. Researcher also developed hybrd method whch combnes several methods to get a better soluton. GABPL method wth addtonal operator to solve the UC problem s presented n ths paper. Ths s the hybrd method whch s ncorporatng mproved PL as one of ntal populaton n GA. Ths approach can make GA obtan a better mnmum value wth faster convergence. Comparson of the results to other methods n 0 unts test system ndcates that the proposed method gves better soluton than the other methods. In obtanng average total cost for large system, the proposed method can generate better average total cost than the other methods. It can be concluded that ths proposed method s good n fndng soluton of the UC problem. In ths paper, GABPL method s only tested to common UC problem. There s no emsson constrant, relablty constrant, or other constrant that can be ncluded n the UC problem to make the UC modelng more realstc. In future work, we can nclude these constrants to UC problem to see the performance of ths method. REFERENCES: [] A. J. Wood and B. F. Wollenberg, Power Generaton, Operaton, and Control, 2nd ed., vol. 37. New York: John Wley & Sons, Inc, 996, p [2] N. P. Padhy, Unt commtment-a bblographcal survey, IEEE Trans. Power Syst., vol. 9, no. 2, pp , May [3] Y. Tngfang and T. O. Tng, Methodologcal Prorty Lst for Unt Commtment Problem, 2008 Int. Conf. Comput. Sc. Softw. Eng., no. 2, pp , [4] I. Damouss, A soluton to the untcommtment problem usng nteger-coded genetc algorthm, IEEE Trans. Power Syst., vol. 9, no. 2, pp , [5] T. Sum-m and W. Ongsakul, Ant colony search algorthm for unt commtment, n IEEE Internatonal Conference on Industral Technology, 2003, 2003, vol., pp [6] Z.-L. Gang, Dscrete partcle swarm optmzaton algorthm for unt commtment, 400

8 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: n IEEE Power Engneerng Socety General Meetng 2003, 2003, vol., pp [7] J. Ebrahm, Unt commtment problem soluton usng shuffled frog leapng algorthm, IEEE Trans. Power Syst., vol. 26, no. 2, pp , 20. [8] D. Srnvasan and J. Chazelas, A prorty lstbased evolutonary algorthm to solve large scale unt commtment problem, n 2004 Internatonal Conference on Power System Technology, PowerCon 2004., 2004, vol. 2, pp [9] T. Senjyu, K. Shmabukuro, K. Uezato, and T. Funabash, A fast technque for unt commtment problem by extended prorty lst, IEEE Trans. Power Syst., vol. 8, pp , [0] W. Chang and X. Luo, A soluton to the unt commtment usng hybrd genetc algorthm, n TENCON IEEE Regon 0 Conference, 2008, pp. 6. [] G. Sheblé, T. Mafeld, and K. Brttg, Unt commtment by genetc algorthm wth penalty methods and a comparson of Lagrangan search and genetc algorthm economc dspatch example, Int. J. Electr. Power Energy Syst., vol. 8, no. 6, pp , 996. [2] Sarjya, A. B. Mulyawan, A. Setawan, and A. Sudarso, Thermal unt commtment soluton usng genetc algorthm combned wth the prncple of tabu search and prorty lst method, n 203 Internatonal Conference on Informaton Technology and Electrcal Engneerng (ICITEE), 203, pp [3] S. Kazarls, A. Bakrtzs, and V. Petrds, A genetc algorthm soluton to the unt commtment problem, IEEE Trans. Power Syst., vol., no. February, pp , 996. [4] V. N. Deu and W. Ongsakul, Ramp rate constraned unt commtment by mproved prorty lst and augmented Lagrange Hopfeld network, Electr. Power Syst. Res., vol. 78, no. 3, pp , Mar [5] B. Zhao, C. X. Guo, B. R. Ba, and Y. J. Cao, An mproved partcle swarm optmzaton algorthm for unt commtment, Int. J. Electr. Power Energy Syst., vol. 28, pp , [6] M. Govardhan and R. Roy, An applcaton of Dfferental Evoluton technque on unt commtment problem usng Prorty Lst approach, n 202 IEEE Internatonal Conference on Power and Energy (PECon), 202, no. December, pp [7] S. M. H. Hossen, H. Sahkal, and Y. Ghalandaran, Thermal Unt Commtment Usng Hybrd Bnary Partcle Swarm Optmzaton and Genetc Algorthm, n 202 Asa-Pacfc Power and Energy Engneerng Conference, 202, no. 2, pp. 5. [8] J. Valenzuela and A. E. Smth, A seeded memetc algorthm for large unt commtment problems, J. Heurstcs, vol. 8, pp , [9] T. Senjyu, T. Myag, A. Y. Saber, N. Urasak, and T. Funabash, Emergng soluton of large-scale unt commtment problem by Stochastc Prorty Lst, Electr. Power Syst. Res., vol. 76, pp , [20] C. Cheng, C. Lu, and C. Lu, Unt commtment by Lagrangan relaxaton and genetc algorthms, IEEE Trans. Power Syst., vol. 5, pp , [2] T. A. A. Vctore and A. E. Jeyakumar, Unt commtment by a tabu-search-based hybrdoptmsaton technque, IEE Proceedngs - Generaton, Transmsson and Dstrbuton, vol. 52. p. 563, [22] L. Sun, Y. Zhang, and C. Jang, A matrx real-coded genetc algorthm to the unt commtment problem, Electr. Power Syst. Res., vol. 76, pp , [23] W. Ongsakul and N. Petcharaks, Unt Commtment by Enhanced Adaptve Lagrangan Relaxaton, IEEE Trans. Power Syst., vol. 9, pp , [24] T. Senjyu, H. Yamashro, K. Uezato, and T. Funabash, A unt commtment problem by usng genetc algorthm based on unt characterstc classfcaton, 2002 IEEE Power Eng. Soc. Wnter Meet. Conf. Proc. (Cat. No.02CH37309), vol., [25] T. O. Tng, M. V. C. Rao, and C. K. Loo, A novel approach for unt commtment problem va an effectve hybrd partcle swarm optmzaton, IEEE Trans. Power Syst., vol. 2, pp. 4 48,

9 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: Unt P mn (MW) P max (MW) Table II: Generator Data of 0-Unt System Fuel Cost Coeffcents a ($/MW 2 ) b ($/MW) c MUT (h) MDT (h) Int cond. (h) Hot SUC Cold SUC Table III: 24-Hour Load Data of 0-Unt System Τ Cold Hour Load (MW) Hour Load (MW) Table IV: Soluton of UC Problem wth Prorty Lst Method on 0 Unts System Hour P P2 P3 P4 P5 P6 P7 P8 P9 P0 Load (MW) Fuel Cost Start-Up Cost Total Operatonal Cost , , , , , , , , , , ,387.04,00 23, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,427.4 TOTAL 559,887 4, ,

10 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: Table V: Soluton of UC Problem wth Proposed Method on 0 Unts System Hour P P2 P3 P4 P5 P6 P7 P8 P9 P0 Total Load Fuel Cost Start-Up Cost Operatonal (MW) Cost , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,427.4 TOTAL 559,847, ,937.7 Table VI: Comparson of GABPL Method among Other Methods on 0 Unts System and the Duplcatons Total Operatonal Cost Number of unts GABPL PL EA SFLA ICGA SPL EPL [9] GA [3] LR [3] EP [8] BF [7] (average) [8] [7] [4] [9]