Economic Load Dispatch of IEEE-26 Bus System with the use of Ant Colony Optimization Technique

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1 IJSRD - Iteratioal Joural for Scietific Research & Developmet Vol. 2, Issue 03, 204 ISSN (olie): Ecoomic Load Dispatch of IEEE-26 Bus System with the use of At Coloy Optimizatio Techique Pirmahamad Jamalbhai Vasovala Chimay Y. Jai 2 Vasim H. Ghachi 3 Parth Harshad Kumar Bhavsar 4,3, 4 PG Studet 2 Assistat Professor, 2, 3 Electrical Egieerig Departmet, 2, 4 Parul Istitute of Egg & Techology, Vadodara 3 The Maharaja Sayajirao Uiversity of Baroda, Vadodara Abstract--- Optimal System operatio ivolves the Cosideratio of ecoomy of operatio, system security, emissio of certai fossil-fuel plat. The mai aim of this study is to miimize the fuel cost ad to eep the power outputs of the geerator withi prescribed limit with the use of A At coloy Optimizatio Techiques. It is based o the ideas of at foragig by pheromoe commuicatio to mae path. At Coloy Optimizatio techique is a metaheuristic approach for solvig hard combiatorial optimizatio problems which ca be applied for power system optimizatio. The wor reported i this paper is carried out with the objective to mae use of At coloy Optimizatio for solvig the ecoomic load dispatch problem. IEEE-26 Bus 6 geerator system is cosidered to test the Algorithm with cost fuctios. The proposed approach result has bee compared to those which reported i the literature. Keywords: At Coloy Optimizatio, Optimal power flow, meta-heuristic, IEEE Systems, power systems, optimizatio. I. INTRODUCTION Electric power grids are cosidered to be oe of the most complex ma-made systems maily due to their wide geographical coverage, various trasactios amog differet utilities, ad diversity i idividual electric power compaies layouts, size, ad equipmet used. Egieers eed special tools to optimally aalyze, moitor, ad cotrol differet aspects of such sophisticated system. Some of these tools are ecoomic dispatch, uit commitmet, state estimatio, automatic geeratio cotrol, ad optimal power flow. The mai objective of electrical power utility is to esure that electrical eergy requiremet from the cosumer is delivered. However for doig so, the power utility has also to cofirm that the electrical power is geerated with reduced cost. So for ecoomic operatio of the system, the total demad must be equally shared amog the geeratig uits with a objective to miimize the total geeratio cost for the system. Ecoomic Dispatch is a method to fid the electrical power to be geerated by the committed geeratig uits i a power system so that the total geeratio cost of the system is miimized, with satisfyig the load demad simultaeously. To show this problem, optimizatio is a ecessary i solvig the cost miimizatio problems. Power system optimizatio is a importat area i the operatio, plaig ad cotrol of power systems. May advaced heuristic techiques to the solutio of complex power system optimizatio problems have bee proposed, each differig i their procedure of represetatio, implemetatio ad solutio procedure: Ecoomic load dispatch is oe of the basic problems i power system operatio ad plaig. It is defied as the process of givig geeratio levels to the geeratig uits so that the system load is supplied fully ad most ecoomically. It cocered o the reductio of a objective fuctio, usually the total cost of geeratio, while cosiderig both the equality ad iequality costraits. Load variatio depeds upo the output of geerators has to be chaged to meet the balace betwee loads ad geeratio power to mae the system efficiet. There are a lot of covetioal optimizatio techiques which are applied i solvig the ELD problems that are briefly listed i literature referece [8] such as Newtobased techiques, Liear Programmig, No-Liear Programmig, Quadratic Programmig, Iterior poit methods, Parametric method, Sequetial ad ucostraied miimizatio techique. However, these methods usually suffer from some disadvatages such as covergece to local solutios istead of global oes if the iitial guess is i the viciity of a local solutio, applicability to a specific ELD problem based o its mathematical ature ad some iheret theoretical assumptios (such as covexity, differetiability, ad cotiuity) which are icosistet with the actual OPF formulatios [8]. Several stochastic search techiques are also listed ad discussed briefly by the researchers of [8] such as geetic algorithms (GA), evolutioary programmig (EP), particle swarm optimizatio (PSO), bacteria foragig (BF) algorithm [8] At coloy optimizatio (ACO)[9] have bee proposed to solve the OPF problem without ay restrictio o the shape of the cost curves. The results reported were promisig ad ecouragig for further research i this directio. The remaiig parts of the paper are orgaized as follows. I the secod sectio, the formulatio of ELD problem is briefly itroduced. The at coloy optimizatio algorithm described i sectio three. The proposed ACO ad its applicatio for the solutio of the ELD problem are preseted i sectio four. Obtaied umerical results from extesive testig of the proposed solutio approach o differet case studies are preseted i sectio five ad compared with the results of several other recetly published methods. Sectio six cocludes the paper. All rights reserved by 23

2 II. ECONOMIC DISPATCH PROBLEM FORMULATION Ecoomic Dispatch problem ca be solved by miimizig the cost of geeratio i the system. The solutio gives the optimal geeratio output of the olie geeratig uits that satisfy the system s power balace equatio uder various system ad operatioal costraits. The Ecoomic Dispatch problem ca be formulated mathematically as follows Objective Fuctio is to miimize the cost ( ) () Which is the sum of operatig cost over all cotrollable power sources, Where Fi(Pgi) is the geeratio cost fuctio for geeratio Pgi at bus i. NG idicate the umber of geeratio icludig the slac bus. The idividual costs of each geeratig uits are cosider beig fuctio, oly, of active power geeratio ad are showed by quadratic curves of secod order. The objective fuctio for the whole power system ca be preseted as the sum of the quadratic cost model at each geerator. The covetioal quadratic fuel cost fuctio of geeratig uits is give by (2) Where Pgi is the geerated active power at bus i. a i, b i ad c i are the uit costs curve for geerator i. Costrait Equatios : Uit Operatio Costraits ca be preseted by: mi max (3) Where mi ad max : Lower ad upper limit of active power geeratio at bus i. 2: Power Balace equatio: ad evolutioary approach where several geeratios of artificial ats i a cooperative way search for good solutios. Iitially artificial ats move radomly alog paths ad deposit chemical substace trails, called pheromoe, o the groud whe they move. Ad ats collect ad store iformatio i pheromoe trails durig their movig. This pheromoe trails motivate them to follow the path with high itesity of pheromoe. With time, the pheromoe trail is reiforced or evaporated by the move of ats. Fially, all ats ca choose the shortest path i their movemet [25]. At coloy optimizatio algorithm As show i Fig. 2, the agets (i.e. ats) are guided by the itesity of pheromoe trails. The path rich i pheromoe becomes the best tour with time. This cocept ispired the ACO algorithm. Iitially, each aget is positioed o a startig ode. Agets move to feasible eighbor odes followig the state trasitio rule. This rule idicates the preferece of ats i choosig their paths that coect the curret ode to the ext ode. Durig the movig process, ats modify the level of pheromoe o the paths they choose by applyig the local updatig rule. If the pheromoe level o the chose paths is lowered, these paths become less attractive to other agets. This property gives agets a higher probability to explore differet paths ad fid a improved solutio. Oce all agets have reached the fial ode ad have idetified the best path which has the optimal value of the objective fuctio, they update the pheromoe level o the best path by applyig a global pheromoe updatig rule. This is iteded to allocate a higher level of pheromoe o the best path. The rules to fid the best path are detailed as below [3]: State Trasitio Rule. This rule guides the agets search toward eighbor odes stochastically. The -th aget at time t positioed o ode r move to the ext ode u alog the shorter path with higher itesity of pheromoe τ ru (t). (4) Where P D is the demad ad P L is trasmissio loss. The trasmissio loss calculated by the B-coefficiets method. B-coefficiets applied i the power system by: MW (5) Where Pgi ad Pgj are geeratio at i th ad j th bus respectively. B is the Loss coefficiet which is costat uder certai assumed coditio, NG o of geerator bus. III. ANT COLONY OPTIMIZATION ALGORITHM Framewor for at coloy system Etomologists have studied the ability of ats to fid the shortest path betwee their est ad a food source. From these studies, At Coloy Optimizatio (ACO) has bee developed by Dorigo et al. [] ad successfully employed to solve various optimizatio problems.aco is a metaheuristic Fig. : A example of fidig the shortest path This is achieved by a state trasitio rule (6) that utilizes both the iverse of the legth of the path η ru (t) ad the amout of pheromoe τ ru (t). S= { All rights reserved by 24

3 τ ru (t): The pheromoe trail at time t. η ru (t) = / TrsC(t) : the iverse of the trasitio cost. TrsC(t) with r-s beig the path from ode r at the curret stage to ode s at the ext stage. α,β: parameters represetig the relative importace q: a radom umber uiformly distributed i [0,]. q0: a pre-specified parameter (0 q0 ). allowed (t ) : the set of feasible odes curretly ot assiged by the at at time t. S: a idex of ode selected from (t) allowed accordig to the probability distributio give by (7). For every geerator the area of its power limits is divided i discrete values. The divisio ca be doe i various ways. I this we ca divide all fragmets i equal umber of subfragmets. So far, every geerator we have doe did ot have a cotiuous fragmet of power but discrete defiite set depedig o the separatio that has tae place. { (7) J ( r): set of odes that remai to be visited by at positioed o ode (to mae the solutio feasible). Local Updatig Rule. A at chages the pheromoe level o the moved path (local updatig) by applyig the local updatig rule (8). This rule has the effect of lowerig the pheromoe level o the search paths. τ(r,s) ( ρ) τ(r,s)+ ρ. τ 0 (8) ρ:evaporatio coefficiet (0<ρ<). τ 0 : iitial pheromoe level, τ 0 =/J where J is a rough approximatio of the optimum value of the cost fuctio. Global Updatig Rule. The global pheromoe updatig is performed oly after all ats have completed their movig. The global pheromoe updatig rule (9) is iteded to provide a greater amout of pheromoe to shorter path. τ(r,s) ( α).τ(r,s)+ α.δτ(r,s) (9) = { α: pheromoe decay coefficiet(0<α<) J * : the best value of the objective fuctio (0) The capability of fidig the optimal path ca be ehaced through this rule i the search process. The pseudo code of Covetioal ACO algorithm ca be described as [3]: Iitialize pheromoe trails Repeat util system covergece coditios satisfied Geerate agets ( ); Move accordig to the trasitio Rules ( ); Update Pheromoe ( ); Ed IV. ACO APPLIED TO ECONOMICAL LOAD DISPATCH Descriptio of algorithm Fig. 2: Movemet of a at betwee machies ad power levels The algorithm wors lie this: each oe at starts from the first geerator ad selects a power level the, it goes to the ext ad chooses aother power level for that geerator ad this is repeated util it reaches the last geerator (Fig.2). At the ed of this the total cost is calculated i séace to decide whether the solutio is satisfactory or ot. Mathematical Model (A) Trasitio rule: lets a at be i geerator i ad it must choose a power level j for it, accordig to the probability distributio, called a radom-proportioal rule: p( t) l il J i l if j є (0) J Where i : is the list of the power levels that correspods to geerator i : is the visibility. I the classical problem TSP this is defied as the iverse of the distace betwee two cities, d α ad β: are parameters that cotrol the relative importace of pheromoe itesity versus visibility So, it could be also used here the iverse of the cost for the particular power level: F ( P ) i (t) J i () (B) Pheromoe Update Rule: is the pheromoe quatity that is foud i edge that coects every geerator with power level. Pheromoe updated by the rule: ( ) (2) Where ρ is the coefficiet represetig pheromoe persistece (0 ρ < ), ad, is a fuctio of the solutios foud at iteratio t, ad it is algorithm specific. All rights reserved by 25

, is a fuctio of the solutios foud at iteratio t, give by: : umber of ats : (3) is the quatity per uit of legth of pheromoe additio laid o edge (i,j) by the th at at the ed of iteratio t, is give by:

4 , is a fuctio of the solutios foud at iteratio t, give by: : umber of ats : (3) is the quatity per uit of legth of pheromoe additio laid o edge (i,j) by the th at at the ed of iteratio t, is give by: Q L, if ( i, j) T (4) 0, if ( i, j) T T (t) Where is the tour doe by at at iteratio t L (t), is its legth ad Q is a costat parameter, used for defiig to be of high quality solutios with low cost. The Algorithm for solutio Step : Defie (discrete) power for every geerator. For every geerator ad for every power level we calculate the visibility Fi ( P ). Defie the pheromoe, givig it a large value, i all edges that coect every geerator with the power level respectively. Defie the total umber of ats ad the umber of iteratios. Step 2: For every at ad for every geerator select a power level based o radom-proportioal trasitio rule as accordig to equatio (0). Step 3: Calculate the cost for all ats based o the divisio of power levels which is the based o objective fuctios ad a i,b i ad c i are the uit costs curve ad save the best. Step 4: Reew pheromoe usig pheromoe update rule accordig to specified at algorithm ad the equatio (2, 3 ad 4). Step 5: Repeat the procedure from step 2 util a specific umber of iteratios are completed or all the ats precedig the same path. V. SIMULATION RESULT AND DISCUSSION Test system: IEEE 26-bus system [6] Fig. 3: Sigle Lie Diagram of IEEE-26 Bus system Test System The Proposed algorithm is tested o the stadard IEEE 26 bus test system. This system is havig 26 buses ad 6 geerators. Total demad is 263 MW. Fig 3 shows the Lie Diagram of IEEE-26 bus system. Four parameters of the coloy of ats α β, ρ ad q0 is extesively idepedet of the problem of optimizatio to solve, developed algorithm is tested o the etwor IEEE 26 buses while usig the 0 better combiatios of the three parameters β, ρ ad q0 ad that give the best results for commercial traveler problem for the case of 30 cities [9]. Geerator No Cost Coefficiet MW Limit a b c Mi Max Table : Cost Coefficiets ad Geerator Limits[6] B = MW Table 2.The trasmissio loss co efficiet matrix are give as Results for Test system Various combiatios of four parameters α β, ρ ad q0 ad that give the best results for commercial traveler problem for the case of 30 cities. The ecoomical value of the cost is $/h correspods a (α=8,β=2,ρ= 0.8,q0=) with losses of powers 2.35MW. The obtaied miimum cost results are compared with those results which are there i literature. Proposed Methods ACO SA[7] GA[6] PSO[5] Method Pg(MW) Pg2(MW) Pg3(MW) Pg4(MW) Pg5(MW) Pg26(MW) Pgi(MW) LossP L (MW) Error cost($/hr) Table. 3: Compariso i Miimum cost ad Losses VI. CONCLUSION I this paper, a At Coloy Optimizatio approach to the Ecoomical Load Dispatch problem is itroduced ad tested. As a study case, the IEEE 26 Bus system with three geeratig uits has bee selected with smooth cost fuctios, the simulatio results show that for medium-scale system a at coloy optimizatio method ca give a better All rights reserved by 26

5 results. The developed algorithm is able to miimize the geeratio cost while meetig the demad requiremet. Obtaied results are also compared with established algorithms lie SA, GA, PSO etc. which are reported i literature compariso shows that developed techique is efficiet compared to others. Further developmet i techique may help to solve dispatch problems with prohibitig operatig zoes as well as evirometal costraits ad uit commitmet problems. REFERENCES [] Marco Dorig ad ThomesStutzle(2005): At Coloy Optimizatio,Pretice-Hall of Idia Privet Limited,New Delhi-0 00, [2] D.P.Kothari ad J.S.Dhillo(202): power system optimizatio,2 d Ed.PHI Learig privet Limited, New Delhi-0 00, 202. [3] Jizhog Zhu(2009): Optimizatio of power system operatio A joh wiley& sos, ic. Publicatio-2009,Chap:5, Page: [4] J. Carpetier(962): Cotributio a. l etude du dispatchig ecoomique Bull. Soc. FracaiseElect., Vol. 3, pp , Aug [5] R.Gadass, Dr.P veetesh, T G Palaivelu, K.Maivaa, Evolutioary programmig solutio of Ecoomic Load Dispatch with combied cycle cogeeratio Effect IE(I) Jurel-EL, vol 85,sep 2004;pp [6] Pablo E. Oñate Yumbla, Jua M. Ramirez ad Carlos Coello Optimal Power Flow Subject to Security Costraits Solved With a Particle Swarm Optimizer IEEE Trasactios o power systems, vol. 23, o., pp.33-40,february 2008 [7] K. Ravi Kumar, S. Aad, M. Sydulu(202): A Novel Multi aget based PSO approaches for security Costraied Optimal Power Flows usig smooth ad o-smooth cost fuctios Iteratioal Joural of Computer Applicatios ( ) Volume 4 No.3, March 202. [8] G. Basar ad M. R. Moha, Security costraied ecoomic load dispatch usig particle swarm optimizatio embedded with evolutioary programmig techiques suitable for utility system Iteratioal Joural of Distributed Eergy Resources,Volume 4 Number 3 (2008) Pages 99 24,Mauscript received: 26. July 2007 [9] BoumedièeAllaoua ad AbdellahLaoufi Collective Itelligece for Optimal Power Flow Solutio Usig At Coloy Optimizatio Leoardo Electroic Joural of Practices ad Techologies ISSN Issue 3, July-December 2008 p [0] K. Mahadeva, P. S. Kaa ad S. Kaa(2005): Particle Swarm Optimizatio for Ecoomic Dispatch of Geeratig Uits with Valve-Poit Loadig,Joural of Eergy & Eviromet 4 (2005) [] L. L. Lai,, T. Y. Nieh, D. Vujatovic, Y. N. Ma, Y. P. Lu, Y. W. Yag, H. Brau(2005): Particle Swarm Optimizatio for Ecoomic Dispatch of uits with Nosmooth Iput-output Characteristic Fuctios ISAP /05/ [2] S.Hemamalii ad Sishaj P Simo(2008): Ecoomic load dispatch with valve-poit effect usig artificial bee coloy algorithm XXXII atioal systems coferece, NSC 2008, December 7-9, [3] Se-Hwa Jag, Jae HyugRoh, Woo Kim, Tezi Sherpa, Ji-Ho Kim ad Jog-Bae Par(20): A Novel Biary At Coloy Optimizatio: Applicatio to the Uit Commitmet Problem of Power Systems Joural of Electrical Egieerig & Techology Vol. 6, No. 2, pp. 74~8, 20 DOI: /JEET [4] Tare Boutir ad Lida Slimai (2005): Optimal Power Flow of the Algeria Electrical Networ usig a At Coloy Optimizatio Method. Leoardo Joural of Scieces ISSN Issue 7, July- December 2005 p [5] Z. L. Gaig, Particle swarm optimizatio to solvig the ecoomic dispatch cosiderig the geerator costraits, IEEE Tras. Power Systems, vol. 8, o. 3, pp , [6] S. Pothiya, I. Nagamroo, ad W. Kogprawecho, Applicatio of multiple tabu search algorithm to solve dyamic ecoomic dispatch cosiderig geerator costraits, Joural of Eergy Coversio ad maagemet, Elsevier,vol. 49, pp , [7] C. Roa-Sepulveda, J. Pavez-Lazo, A solutio to the optimal power flow usig simulated aealig, Electrical Power & EergySystems (Elsevier), vol. 25,, pp.47-57, All rights reserved by 27

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