Research Article Multiobjective Economic Load Dispatch Problem Solved by New PSO

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1 Advances n Electrcal Engneerng Volume 2015, Artcle ID , 6 pages Research Artcle Multobjectve Economc Load Dspatch Problem Solved by New PSO Nagendra Sngh 1 and Yogendra Kumar 2 1 Department of Electrcal Engneerng, Mewar Unversty, Chttorgarh, Rajasthan, Inda 2 Department of Electrcal Engneerng, Maulana Azad Natonal Insttute of Technology, Bhopal, Inda Correspondence should be addressed to Nagendra Sngh; nsngh007@redffmal.com Receved 30 September 2014; Accepted 2 February 2015 Academc Edtor: Nkos D. Lagaros Copyrght 2015 N. Sngh and Y. Kumar. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Proposed n ths paper s a new partcle swarm optmzaton technque for the soluton of economc load dspatch as well as envronmental emsson of the thermal power plant wth power balance and generaton lmt constrants. Economc load dspatch s an onlne problem to mnmze the total generatng cost of the thermal power plant and satsfy the equalty and nequalty constrants. Thermal power plants use fossl fuels for the generaton of power; fossl fuel emts many toxc gases whch pollute the envronment. Ths paper not only consders the economc load dspatch problem to reduce the total generaton cost of the thermal power plant but also deals wth envronmental emsson mnmzaton. In ths paper, fuel cost and the envronmental emsson functons are consdered and formulated as a multobjectve economc load dspatch problem. For obtanng the soluton of multobjectve economc load dspatch problem a new PSO called moderate random search PSO was used. MRPSO enhances the ablty of partcles to explore n the search spaces more effectvely and ncreases ther convergence rates. The proposed algorthm s tested for the IEEE 30 bus test systems. The results obtaned by MRPSO algorthm show that t s effectve and effcent. 1. Introducton Electrcal power system s a very large nterconnected system. It plays very mportant role n the economy of the country. For the effcent and relable operaton of such large nterconnected power system, t requred proper analyss and the way to operate such system economcally. Economc load dspatch problem s an mportant optmzaton task n the electrcal power system and study of economc load dspatch helps to operate power systems economcally wth an effcent way and provde power wthout any nterrupton. The economc load dspatch s an onlne process of allocatng generaton among the avalable generatng unts to mnmze thetotalgeneratoncostandsatsfytheequaltyandnequalty constrants. Snce the cvlzaton ncreases day by day the demand of electrcty ncreases n the same rato. For the satsfacton of the load demand large numbers of thermal power plants are nstalled and the capacty of coal burnt also ncreases. Due to burnng large amounts of coal emtted many toxc gases lke carbon doxde (CO x ), sulphur doxde (SO x ), and ntrogen oxdes (NO x )atthermalpowerplants and pollute the envronment. Polluton s very harmful for the envronment as well as lvng creatures. Envronmental polluton ncreases the global warmng and damage of the Ozone layer. So n recent trends t s requred to generate the power wth mnmum cost and mnmze the pollutant envronment emsson. The study of economc load dspatch helps to generate power on mnmum cost and also reduce the envronmental emsson effects. Manyclasscalaswellasmoderntechnqueswereused to solve economc load dspatch problem wth envronmental emsson lsted n the lterature. Dfferent methods have been reported n the lterature for solvng ELD problem as multobjectve problem. Talaq et al. [1] gve a deep summary of economc load dspatch wth envronmental constrants. Lnear programmng technques were proposed by Farag et al. [2] for the soluton of ELD problem ncorporated wth envronmental emsson. They solved ELD problem as multobjectve problem wth constrants. Authors of [3] proposed drect Newton-Raphson method for the soluton of

2 2 Advances n Electrcal Engneerng the multobjectve ELD problem n Goal programmng approach was proposed by Nanda et al. [4] forthesoluton of ELD problem wth emsson constrants. Yokoyama et al. [5] presented multobjectve economc power generaton dspatch based on probablty securty crtera. Multobjectve ELD problem wth securty constrant proposed by Chang et al. [6] was solved by usng bcrteron global optmzaton technques. Granell et al. [7] presented emsson constraned dynamc ELD. New stochastc search technque was proposed by Das and Patvardhan [8] forthemultobjectveeconomc load dspatch problem. Some authors have proposed modern heurstc technques such as fuzzy logc optmzaton technque [9] proposed for soluton of multobjectve generaton schedule. Genetc algorthm technques were proposed by Xu et al. [10] to solve constraned multobjectve ELD problem. Partcle swarm optmzaton technques were proposed [11, 12] for obtanng multple objectves. Evolutonary programmng technque was suggested by Suganya et al. [13] for multobjectve economc/emsson load dspatch problem. Advanced MOEPSO-based multobjectve envronmental, economc load dspatchng was gven by Mor and Okawa [14]. Abdo [15] proposedmultobjectve evolutonary algorthms for the electrc power dspatch problem. Dutta and Snha [12] suggested PSO technque for the soluton of envronmental economc dspatch problem wth voltage stablty constrant. Kennedy and Eberhart [16] for the frst tme n 1995 ntroduced partcle swarm optmzaton (PSO) technque. It s a populaton-based evolutonary technque, nspred by the socal behavour of a flock of brds searchng for food. The PSO algorthm smulates socal behavour among the partcles flyng n a multdmensonal search space. In comparson wth other evolutonary optmzaton technques the PSO has a superor search performance wth faster and more stable convergence rates. PSO s a very popular optmzaton technque between the researchers and many of the researchers used t for the soluton of multobjectve economc load dspatch problem, but PSO has a drawback that t lacks global search ablty n the last stage of teratons. So PSO s unable to gve the global optmal soluton for the multobjectve economc load dspatch problem. Ths problem of PSO may be overcome by usng proposed MRPSO, because the MRPSO enhances the ablty of partcles to explore the soluton spaces more effectvely and ncreases ther convergence rates. The proposed algorthm s tested on the IEEE 30 bus test systems. The results obtaned by MRPSO algorthm show that t s practcally effcent. The multobjectve problem consdered n ths paper s solved by PSO and MRPSO wth generaton lmt and power balance constrants. Ths study nvolves the soluton of two objectves; the frst of these s to mnmze the total generaton cost of generatng unts and second aspect s to mnmze the envronmental emsson of thermal power plant. Effectveness and effcency of the proposed PSO technque were tested for the data of IEEE 30 bus network. Results obtaned by PSO and MRPSO technques were compared wth other optmzaton technques lsted n the lterature and t s found that MRPSO gves superor results compared to other technques. 2. Mathematcal Model of Objectve Functon and Constrants In ths paper two objectve functons were consdered. Frst objectve s to mnmze the total generaton cost of generatngpowerplantandthesecondobjectvestomnmzethe envronmental emsson of the generatng plants Objectve I Economc Generaton Cost Functon. Generaton quadratc fuel cost characterstc of generatng power plant s formulated as follows: F T = Mn f (FC), f (FC) = N =1 a P 2 +b P +c, where F T s the total fuel cost, f(fc) s the fuel cost functon, a, b,andc are the cost coeffcents of the th generator, P s the generated power of th power plants, and N s the number of generators Objectve II Emsson Objectve Functon. In ths paper envronmental emsson was evaluated wth consderaton of NO x gas. A typcal NO x emsson at thermal power plants [12] canbe formulated as shown n (2). Consder the followng: E T = Mn N =1 (1) f(e (P )), (2) E (P )=(α +β P +γ P 2 )+ξ sn (λ P ). (3) Now both objectves may be combned n a sngle objectve as gven n (4), (5), and(6). The generaton cost of each generator was evaluated at ts maxmum output: F (P max )=(a P 2 max +b P max +c ). (4) NO x emsson of each generator at ts maxmum output was evaluated: E (P max )=(α +β P max +γ P 2 max )+ξ sn (λ P max ). (5) By (4) and (5) get F (P max ) E (P max ) =k. (6) So the fnal objectve ncorporated total generaton cost and envronmental emsson generaton whch s gven as F fnal object =F T + k (E T ), (7) where E T s the total emsson, F T s the total generaton cost, f(e (P )) s the emsson functon, and α, β, γ, ξ,andλ are the emsson coeffcents of the th generators.

3 Advances n Electrcal Engneerng Constrants Power Balance Constrants. The total generated power should be equal to the sum of total load demand and lne loss. It can be formulated as (8). Consder the followng: n =1 P =P D +P L, (8) n n P L = P B j P j, (9) =1 j=1 where P D and P L are the total system demand and lne loss, respectvely, and B j s the lne loss elements Generator Lmts. Generatng output of each generatng unt should le between the maxmum and mnmum lmts as gven n P mn P P max, (10) where P s the output power of th generator and P mn and P max are the mnmum and maxmum generated power of th generator, respectvely. 3. Overvew of PSO Strateges Ths secton represents a revew of partcle swarm optmzaton technques whch wll serve as a performance measured for the PSO wth moderate random search technque (MRPSO) [17] appled n ths paper for solvng of multobjectve ELD problem Partcle Swarm Optmzaton. PSO s a very popular optmzaton technque and s used to solve optmzaton problems. It s a populaton-based optmzaton technque and t s motvated by the behavour of socal systems such as fsh schoolng and brds flockng. Partcle swarm optmzaton was frst ntroduced by Kennedy and Eberhart n the year 1995 [16]. It s a smple and powerful optmzaton tool whch scatters random partcles nto the search space. Randomly ntalzed partcles are called swarms; collect the nformaton from each array of the problem constructed by ther respectve postons. The poston of the partcles s updated by usng the veloctyof partcles. Both poston and velocty are updated n a heurstc manner by usng gudance from partcles by ther own experence and the experence of ts neghbor s partcles. PSO randomly starts wthn the lmts of maxmum and mnmum value of the power of the th generator. The poston and velocty of the th partcle of a d-dmensonal search space can be represented n the followng: P =(P 1,P 2,...,P d ), (11) V =(V 1,V 2,...,V d ). The best prevous poston of a partcle s recorded and s represented as gven n the followng: P best =(P 1,P 2,...,P d ). (12) If the gth partcle s the best among all partcles n the group so far, t s represented as P gbest =g best =(P g1,p g2,...,p gd ). (13) Velocty and poston of the partcle are updated by usng V (K+1) =W V K +c 1 rand 1 (P best S K ) +c 2 rand 2 (g best S K ), S (K+1) =S K +V K+1, (14) where V K s velocty of the partcles at teraton K, W s the nerta wegh, c 1 and c 1 are the acceleraton coeffcents, rand 1 and rand 2 are the random numbers between 0 and 1, S K s the current poston of partcle at teraton K, P best s the best poston of ndvdual th partcle, and g best s the global best poston of the group. The acceleraton coeffcents c 1 and c 2 pull each partcle towards P best and g best postons and W s the nerta weght parameter whch provdes a balance between global and local exploratons. Snce W decreases lnearly from about 0.9 to 0.4 qute often durng a run, the weghng functon can be formulated as gven n the followng: W=W max W max W mn ter, (15) ter max where W max and W mn are the ntal and fnal nerta weght parameter, respectvely, termax s the maxmum number of teratons, and ter s the current teraton poston Moderate Random Search Partcle Swarm Optmzaton (MRPSO). PSO s a very smple and popular optmzaton tool used for solvng the ELD problem but t has some dsadvantages also, such that PSO lacks global search ablty atthelaststageofteratons.sotsunabletogvetheglobal optmalsolutonoftheeldproblem.intheyearof2011[17] Gao and Xu frst ntroduced the PSO wth moderate random search technque called MRPSO. Moderate random search strategy enhances the global search ablty of the partcles. It can overcome the problem of PSO and gves the optmal soluton for the proposed multobjectve ELD problem. In case of PSO, t s requred to update the poston and velocty of the partcle, but after some teraton the velocty of partcles should be zero so that n case of the MRPSO poston of thepartclecanbeupdatedasgvenn(17). Ifthepartcle s poston s updated as gven n (17) partcles velocty does not change and t gves the global soluton of the problem. In MRPSO technque the partcles are randomly generated for a populaton sze wthn the range of 0-1 same as n case of basc PSO and t s located wthn the maxmum and mnmum operatng range of the generators as gven n the followng: P Intal =P mn + rand (P max P mn ), (16) where P Intal s the ntally generated partcles, rand s random value between 0 and 1, and P max and P mn are the maxmum and mnmum value of generated power of generator, respectvely.

4 4 Advances n Electrcal Engneerng The poston of the partcles s updated for the th partcle at the (K + 1)th teraton usng (17). Consder the followng: S K+1 =P d +αλ(m best S K ), (17) m best = N =1 P best N, (18) where N s the populaton sze n the MRPSO. The parameter α used n (17) may be consdered as a constant value between 0.45 and 0.35 ors obtaned by changng α from 0.45 to 0.35 wth the lnear-decreasng method durng teraton. P d s theattractor movng drecton of partcles; t s gven as P d = rand 0 P best + (1 rand 0 ) g best, (19) where rand 0 s a unformly dstrbuted random varable wthn 0-1, P best s the best value of partcle, and g best s the best value of P best values: λ= rand 1 rand 2, (20) rand 3 where rand 1 and rand 2 are two random varables wthn [0, 1] and rand 3 s a random varable wthn [ 1, 1]. 4. Algorthm of MRPSO for Multobjectve Economc Load Dspatch Problem In ths paper PSO wth the moderate random search technque (MRPSO) s used to solve multobjectve ELD problem. The study carres two objectves; the frst objectve s to mnmze the total generaton cost and the second objectve s to reduce the envronmental emsson of the thermal powerplant.thefollowngstepsarebengusedtosolvethe proposed multobjectve problem by usng MRPSO. Step 1. Select the constants. Step 2. Intalze the swarm. Frst of all partcles are randomly generated for a populaton sze n the range 0-1 and located between the maxmum and the mnmum operatng lmts of the generators as gven n (16). Step 3. Intalze velocty and poston for all partcles randomly set to wthn ther mnmum and maxmum lmts. Step 4. Set generaton counter: counter = counter + 1. Step 5. Evaluate the ftness for each partcle accordng to the proposed objectve functon. Step 6. Compare partcles ftness evaluaton wth ts personal best (P best )andglobalbest(g best ). Step 7. Update poston of partcles by usng (17). Step 8. Apply stoppng crtera. Number of teratons s the stoppng crtera taken n ths study. Means when number of teratons wll completed the converson of algorthm stopped. Table 1: Cost coeffcent wth generaton lmts of IEEE 30 bus, 6 generatng unt systems, and load demand = MW. Bus number a b c P mn P max Table 2: Envronmental emsson coeffcents of IEEE 30 bus systems. Bus number α β γ ξ λ Table 3: Lne loss coeffcents of lne loss of IEEE 30 bus systems Problem Formulaton and Results The proposed algorthms are tested for the data of standard IEEE 30 bus, 6 generator systems [12]. The MRPSO has been appled for solvng IEEE 30 bus system for the demand of MW. Data of IEEE 30 bus cost coeffcents are gven n Table 1, and the data of emsson coeffcents are gven n Table 2, respectvely.table 3 showsthevalueoflneloss coeffcents (B-coeffcent). Table 4 shows the results obtaned by PSO [16], WIPSO [18], and MRPSO [17] wthout consderng lne loss. Table 5 shows the result obtaned by dfferent PSO technques consdered by lne loss. Constant used n ths study for solvng multobjectve ELD problem s shown n Table 6. To assess the effectveness and the effcency of the proposed MRPSO algorthm for solvng multobjectve ELD problem n ths paper, a case study of IEEE 30 bus system wth 6 generatng unts and ther loss coeffcents was taken. All data were consdered from [12]. Dfferent PSO technques such as PSO, CPSO, WISPO, and MRPSO were used to solve the multobjectve ELD problem for the gven data n Tables 1, 2,and3. All PSO technques were run on a 1.4 GHz, core-2 solo processor wth 2 GB DDR RAM. Each PSO technque was tested for 100 numbers of teraton and for 20 populaton szes. The robustness of the proposed algorthms s judged n each case of 100 trals.

5 Advances n Electrcal Engneerng 5 Table 4: Converson results of IEEE 30 bus systems for the load of MW wthout lne loss. Unt power output PSO CPSO WIPSO MRPSO P1 (MW) P2 (MW) P5 (MW) P8 (MW) P11 (MW) P13 (MW) Total power output Fuel cost ($/h) Envronmental emsson (Ton/h) Total cost ($/h) Tme (sec) Table 5: Converson results of IEEE 30 bus systems for the load of MW wth lne loss. Unt power output PSO CPSO WIPSO MRPSO P1 (MW) P2 (MW) P5 (MW) P8 (MW) P11 (MW) P13 (MW) Loss (MW) Total power output Fuel cost ($/h) Envronmental emsson (Ton/h) Total cost ($/h) Tme (sec) Table 6: Constant used to solve the proposed problem usng MRPSO. S. number Constants Value of constant 1 C 1 =C Α W max W mn 0.4 Optmum results obtaned by dfferent PSO technques are mentoned n Tables 4 and 5. It s observed that for more than 100 trals the values obtaned by dfferent technques were repeated and hence consder best results obtaned n 100 trals. The optmal result obtaned by MRPSO for the load of MW wthout lne loss s shown n Table 4: fuel cost of $ /h, envronmental emsson cost of Kg/h, and total cost ncludng envronmental emsson of $ /h. The best result obtaned by usng MRPSO wth consderng the lne loss s shown n Table 5, gettng a fuel cost of $ /h, envronmental emsson cost of Kg/h, total cost ncludng envronmental emsson of $ /h, and lne loss of MW. Results obtaned by MRPSO are less than other optmzaton technques n both of the cases, that s, wthout lne loss and wth lne loss. The convergence tme taken by MRPSO s also less as compared to other PSO technques. 6. Concluson Analyssoftheeconomcloaddspatchhasawderangeof scope nowadays. Satsfyng the load demand n mnmum fuel cost s a great challenge for the power system. The optmal results obtaned by the dfferent PSO technques are shown n Tables 4 and 5. Results obtaned by dfferent PSO technques are shown n Tables 4 and 5. The fuel cost of the IEEE 30 bus system obtaned by MRPSO s $ /h and envronmental emsson s Ton/h, and total cost (fuel cost + envronmental emsson) s $ /h wthout consderng lne loss. Fuel cost s $ /h, envronmental emsson s Ton/h, and total cost s $ /hwthconsderatonoflne loss. It shows that the results of MRPSO algorthm are better than other PSO technques and t takes mnmum convergence tme. So MRPSO s the better approach when compared to other PSO technques mentoned n ths paper. Results obtaned by MRPSO show that t s an effectve and effcent method for obtanng the result of optmzaton problem.

6 6 Advances n Electrcal Engneerng Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. References [1] J. H. Talaq, F. El-Hawary, and M. E. El-Hawary, A summary of envronmental/economc dspatch algorthms, IEEE Transactons on Power Systems,vol.9,no.3,pp ,1994. [2] A. Farag, S. Al-Bayat, and T. C. Cheng, Economc load dspatch multobjectve optmzaton procedures usng lnear programmng technques, IEEE Transactons on Power Systems, vol.10,no.2,pp ,1995. [3] S.-D. Chen and J.-F. Chen, A drect Newton-Raphson economc emsson dspatch, Internatonal Electrcal Power & Energy System,vol.25,no.5,pp ,2003. [4]J.Nanda,D.P.Kothar,andK.S.Lngamurthy, Economcemsson load dspatch through goal programmng technque, IEEE Transactons on Energy Converson,vol.3,no.1,pp.26 32, [5] R. Yokoyama, S. H. Bae, T. Morta, and H. Sasak, Multobjectve generaton dspatch based on probablty securty crtera, IEEE Transactons on Power Systems, vol.3,no.1,pp , [6]C.S.Chang,K.P.Wong,andB.Fan, Securty-constraned multobjectve generaton dspatch usng bcrteron global optmsaton, IEE Proceedngs: Generaton, Transmsson and Dstrbuton,vol.142,no.4,pp ,1995. [7] G. P. Granell, M. Montagna, G. L. Pasn, and P. Marannno, Emsson constraned dynamc dspatch, Electrc Power Systems Research,vol.24,no.1,pp.55 64,1992. [8] C. B. Das and C. Patvardhan, New mult-objectve stochastc search technque for economc load dspatch, IEE Proceedngs- Generaton, Transmsson and Dstrbuton, vol.145,no.6,pp , [9] D. Srnvasan, C. S. Chang, and A. C. Lew, Multobjectve generaton schedulng usng fuzzy optmal search technque, IEE Proceedngs Generaton, Transmsson and Dstrbuton,vol. 141, no. 3, pp , [10] J.X.Xu,C.S.Chang,andX.W.Wang, Constranedmultobjectve global optmsaton of longtudnal nterconnected power system by genetc algorthm, IEE Proceedngs Generaton, Transmsson and Dstrbuton,vol.143,no.5,pp ,1996. [11] C. A. Coello Coello, G. T. Puldo, and M. S. Lechuga, Handlng multple objectves wth partcle swarm optmzaton, IEEE Transactons on Evolutonary Computaton, vol.8,no.3,pp , [12] P. Dutta and A. K. Snha, Envronmental economc dspatch constranedbyvoltagestabltyusngpso, nproceedngs of the IEEE Internatonal Conference on Industral Technology (ICIT 06), pp , December [13] G. Suganya, K. Balamurugan, and V. Dharmalngam, Mult-objectve evolutonary programmng technque for economc/emsson load dspatch, n Proceedngs of the 1st Internatonal Conference on Advances n Engneerng, Scence and Management (ICAESM 12), pp , Taml Nadu, Inda, March [14] H. Mor and K. Okawa, Advanced MOEPSO-based multobjectve envronmental economc load dspatchng, n Proceedngs of the IEEE Power and Energy Socety General Meetng, pp. 1 7, IEEE, Mnneapols, Mnn, USA, July [15] M. A. Abdo, Multobjectve evolutonary algorthms for electrc power dspatch problem, IEEE Transactons on Evolutonary Computaton,vol.10,no.3,pp ,2006. [16] J. Kennedy and R. C. Eberhart, Partcle swarm optmzaton, n Proceedngs of the IEEE Internatonal Conference on Neural Networks,vol.4,pp ,December1995. [17] H. Gao and W. Xu, A new partcle swarm algorthm and ts globally convergent modfcatons, IEEE Transactons on Systems, Man, and Cybernetcs, Part B: Cybernetcs, vol.41,no. 5,pp ,2011. [18]P.T.Vu,D.L.Le,N.D.Vo,andJ.Tlusty, Anovelweghtmproved partcle swarm optmzaton algorthm for optmal power flow and economc load dspatch problems, n Proceedngs of the IEEE PES Transmsson and Dstrbuton Conference and Exposton,pp.1 7,Aprl2010.

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