PSO Approach for Dynamic Economic Load Dispatch Problem

Transcription

1 Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 Certfed Organzaton Vol. 3, Issue 4, Aprl 2014 PSO Approach for Dynamc Economc Load Dspatch Problem P.Svaraman 1, S.Manmaran 2, K.Parthban3, D.Gunaprya 4 Dept. of Electrcal & Electroncs Engneerng, M.Kumarasamy College of Engneerng, Karur, Anna Unversty Regonal Offce, Madura, Inda M.Kumarasamy College of Engneerng, Karur, Tamlnadu, Inda M.Kumarasamy College of Engneerng, Karur, Tamlnadu, Inda Abstract- The man objectve of Dynamc Economc Load Dspatch (DELD s to reduce the total fuel cost of the generators n system. In ths paper Partcle Swarm Optmzaton (PSO algorthm s used to solve the Dynamc Economc Load Dspatch (DELD problem. DELD s to lst the generatng unts output as to meet the load demand at mnmum fuel cost whle satsfyng all unts and operatonal constrants. Enhancement n schedulng the unt outputs can show the way to fuel cost savng. Keywords: Dynamc economc load dspatch; partcle swarm optmzaton; ramp rate lmt; numercal methods more convenent for solvng ELD problems artfcal ntellgent technques, Hopfeld neural networ[2] are employed to solve ELD problems for unts wth pecewse quadratc fuel cost functons and prohbted zones constrant. On the other hand, Hopfeld model may suffer from excessve numercal teratons, resultng n large calculatons [3]. In the past decade, a global optmzaton technque nown as genetc algorthms (GA or smulated annealng (SA, whch s a form of probablstc heurstc algorthm, have been used to solve the optmzaton problems. Though the Genetc Algorthm methods have been employed to solve complex optmzaton problems, n recent study has dentfed some defcences n Genetc Algorthm performance. Partcle swarm optmzaton (PSO frst I. INTRODUCTION ntroduced by Kennedy and Eberhart, s one of the modern heurstc algorthms. The PSO algorthm technque can Economc load dspatch (ELD problem s one of the basc produce the hgh-qualty solutons wth tme and stable ssues n power system operaton. In essence of optmzaton convergence characterstc than other stochastc methods. and ts objectve s to reduce the total generaton costs of the Dynamc economc load dspatch s solvng the economc load unts whle satsfyng all the constrants. In conventonal dspatch n every second power varaton. ELD solve the load lambda-teraton method, base pont and partcpaton factors dspatch economcally at fxed power demand that s power s method, lagrangan relaton method and the gradent methods not varyng n every seconds and DELD s solve the load are used to solve the ELD [1]. In these conventonal methods dspatch economcally at varyng power demand n every for soluton of ELD problems have essental assumpton that second. s ncremental cost curves of the unts are monotoncally II. PROBLEM FORMULATION ncreasng pecewse-lnear functons[1]. Unfortunately these assumpton may cause these methods are nfeasble because of The ELD s one of the sub problem of unt commtment. It s ts nonlnear characterstcs n practcal systems [1]. These a nonlnear programmng optmzaton problem. Practcally nonlnear characterstcs of a generator nclude rregular the scheduled combnaton of unts at each specfc perod of prohbted zones and cost functons whch are non smooth or operaton are lsted, the ELD plannng must carry out the convex and large-scale generatng system these conventonal optmal generaton dspatch among the all operatng unts to method results n longer soluton tme [1]. A dynamc satsfy the system load demand, spnnng reserve capacty, programmng (DP method for solvng the ELD problem wth and practcal operaton constrants of generators that nclude valve-pont effect may cause the dmensons of the ELD the ramp rate lmt and the prohbted operatng zone. problem to become enormously large, therefore t requrng large computatonal efforts[2]. In order to formulate the Copyrght to IJIRSET

2 Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 Certfed Organzaton Vol. 3, Issue 4, Aprl 2014 Objectve functon The core objectve of economc load dspatch (ELD s to reduce the operatng costs or the generaton costs of the power system whle satsfyng the varous constrants n the system. The DELD problem s formulated to fnd the optmal fuel cost of the generators whle fulfllng the all load demands and also fulfllng the varous equalty and nequalty constrants. The objectve functon s to mnmze the total generatng cost (total cost of the system subjected to the varous constrants of the system. Ft = Σ F(P (1 N=Total number of generators, Ft=Total fuel cost, P=Real power output of th generator. The cost of every generator represented by a sngle quadratc cost functon defned below F (P = a P 2 + b P + c (2 a,b,c are fuel cost functons. Ths quadratc equaton changes f we consder the valve pont effects. A snusodal functon s added to the exstng equaton (2 and the equaton becomes F (P = a P 2 + b P +c + e sn(f (P,mn P (3 e and f are cost functons correspondng to valve pont loadng. The nequalty constrant P,mn P P, (4 The generaton power of each generator should place between the mnmum and mum lmts. The equalty constrant N Σ P =PD+P Loss (5 =1 PD = total system demand. P Loss = total transmsson lne loss. Ths s called generator constrants. Ths s also called power balance equaton. The transmsson loss can be calculated by the B-coeffcents method or power flows analyss. B-coeffcents used n the power system are P =P T B T (6 P = Power output of the unt. III. LEAST PTH NORM ALGORITHM The partcle swarm optmzaton s a populaton based stochastc optmzaton technque ntroduced by James Kennedy and Russel Eberhart n the year of PSO based on the concept of swarms and ther ntellgence as well as ther movement. PSO comprses of a collecton of creatures (partcles performng the same acton n a search space. The swarms are mostly the groups that serve the same purpose le food huntng. The PSO s motvated from the relatve behavour of the creatures that lve and move n groups le swarm of brds and school of fshes etc. The above fgure.1 shows a swarm of brds. Ths concept s used n PSO algorthm. Here the brds are analogous to the partcles. In PSO there s large multdmensonal search space wth partcles wthn t. These partcles are move freely n the search space loong for the optmal (best possble soluton. Each partcle has a partcular velocty and poston. The partcles and velocty are denotng by vectors V and X. V= [v1, v2, v3... ] X= [x1, x2, x3...] Every partcle represents a potental soluton to the problem and they are responsble to search the solutons wthn the search space. All partcles contan a partcular ftness value whch s evaluated by the ftness functon. The velocty and partcle poston s updated by ther rules. The poston of the partcles s updated wth the flyng experence of the partcle and ts neghbours. The best values s acheved by the partcles are stored n the memory as Pbest or personal best and the best among all the partcles s called as Gbest or Copyrght to IJIRSET

3 Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 Certfed Organzaton Vol. 3, Issue 4, Aprl 2014 global best. By usng the concept of Pbest and Gbest the velocty of each partcle s updated 1 V V c1r1 ( Pbest X c2r2 ( Gbest X (7 = Inerta weght, c 1, c 2 = Acceleraton coeffcents, r 1, r 2 = Random number between 0 and 1, X = Poston of ndvdual, Pbest = Good poston of ndvdual. Gbest = Good poston of the group. In the equaton (7 the nerta weght s ntroduced to enable the swarm to fly n the larger search space. The rght value of should be selected so as to provde balance between the local and the global exploratons. Ths reduces the teratons to fnd the optmal soluton. 1 X = current partcle poston at teraton +1, X = partcle poston at teraton, 1 V = partcle velocty at teraton +1. In general, the nerta weght can be set accordng to the followng equaton. mn Iter (9 Iter, mn = mum and mnmum weghts, Iter = mum teraton number, Iter = current teraton number. A. PSO Algorthm The step by step procedure of proposed PSO method whch s used to solve DELD problem are as gven below Step 1: Read the nput data such as fuel cost coeffcent and the varous constrants le as generator constrants and transmsson lne loss coeffcents etc. Step 2: Intalze the populaton of the partcles n random manner. Also set the teraton counter. Step 3: Evaluate the ftness for each partcles. Step 4: Now compare the ftness wth Pbest and the value of ftness s mproved then set ths value as Pbest. Step 5: Identfy the best ftness value whch s Gbest. The best value among the Pbest of all partcles s Gbest. Step 6: Update the velocty of each partcles. Fgure 1: Poston and velocty. Poston updated by the X X V (8 1 1 The velocty update rule defned by 1 V V c1r 1 ( Pbest X c2r2 ( Gbest X Copyrght to IJIRSET

4 Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 Certfed Organzaton Vol. 3, Issue 4, Aprl 2014 Also, the partcles fly to a new poston usng the poston update rule X X V 1 1 Step 7: If mum number of teratons reaches then go to step 8, else ncrease the teraton counter and go to step2. Step 8: The partcles that generates the newest best s the soluton. Ths s the optmal soluton (result. The above procedure s llustrated n fgure 2. IV. Fgure: 2 Flowchart. SIMULATION RESULTS In ths wor we have consder a 6 generatng unts. The load demand s to be allotted to these unts whle mnmzng the costs of generaton subjected to the varous constrants. Here the constrants le as transmsson losses and generators lmts are consder. The partcles ntal poston s random and Copyrght to IJIRSET

5 Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 Certfed Organzaton Vol. 3, Issue 4, Aprl 2014 the parameters le as acceleraton constants and nerta weght factors, number of teratons and populaton sze are defned. The populaton sze must be set, that t s not too small or too large. If t s small there wll be nadequate number of partcles so there wll be dffculty n producng the best possble soluton. If the populaton sze s too large then the algorthm wll become slow. Table I Intalzaton Parameters Parameters Value Intal postons Populaton sze 100 No of teratons 300 Random Acceleraton constants: 2.0 c 1,c 2 c Inerta weght:, 0.9,0.3 mn Generaton Unts Table II Data of sx generatng unts Cost coeffcent P mn P a b c G G G G G G S.NO Table III Schedulng of Generatng Unt Demand (MW Table IV Cost comparson Conventonal Method (RS Proposed Method (RS B=1e-5 [ ] Fgure 3: Comparson of proposed method and conventonal method. V CONCULSION Dynamc Economc load dspatch s a mportant tas n the electrcal power system as t s essental to supply the power at the mnmum cost. The total generaton costs are mnmzed by dvdng the load demand nto the several unts at the same tme t s satsfyng the varous constrants. The Copyrght to IJIRSET

6 Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 Certfed Organzaton Vol. 3, Issue 4, Aprl 2014 Load dspatch problem here s solved for the sx generatng unts. The wor s done by mplementng Partcle swarm optmzaton (PSO n the MATLAB envronment. REFERENCES [1] S. Ore and D. W. Corne, A Memetc Algorthm for Dynamc Economc Load Dspatch Optmzaton, Proc IEEE Symposum Seres on Comp. Intellgence (SSCI, Sngapore, Aprl [2] S. Ore and D. W. Corne, Improved Evolutonary Algorthms for Economc Load Dspatch Optmsaton Problems, In Proceedngs of 12th IEEE UK Worshop on Computatonal Intellgence (UKCI, Ednburgh, 5-7 September [3] G. Sreenvasan, C. H. Sababu and S. Svanagaraju, Soluton of Dynamc Economc Load Dspatch Problem wth Valve Pont Loadng Effects and Ramp Rate Lmts usng PSO, Int l Journal of Electrcal and Computer Engneerng, vol. 1, no. 1, September. 2011, pp [4] D. He, G. Dong, F. Wang, and Z. Mao, Optmzaton of Dynamc Economc Dspatch wth Valve-Pont Effect usng Chaotc Sequence based Dfferental Evoluton Algorthms, Journal of Energy Converson and Management, vol. 52, 2011, pp Elsever. [5] A.I. Selvaumar and K. Thanushod, A new partcle swarm optmzaton soluton to Non-convex economc dspatch problems, IEEE Trans.Power Syst,. 22 (February (1 (2007, pp [6] Zwe-Lee Gang, Partcle Swarm Optmzaton to solvng the Economc Dspatch Consderng the Generator Constrants, IEEE Trans. On Power Systems, Vol.18, No.3, pp , August [7] F. N. Lee and A. M. Brepohl, Reserve constraned economc dspatch wth prohbted operatng zones, IEEE Trans. Power Syst., vol. 8, pp , Feb Copyrght to IJIRSET