MULTI-OBJECTIVE GENERATION DISPATCH USING PARTICLE SWARM OPTIMISATION WITH MULTIPLE FUEL OPTION

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1 Proceedigs of the 6th WSEAS/IASME It. Cof. o Electric Power Systems, High Voltages, Electric Machies, Teerife, Spai, December 16-18, MULTI-OBJECTIVE GENERATION DISPATCH USING PARTICLE SWARM OPTIMISATION WITH MULTIPLE FUEL OPTION ABSTRACT C.RANI 1 M.RAJESH KUMAR 2 K.PAVAN 3 School of Electrical Scieces Vellore Istitute of Techology-Deemed Uiversity, Vellore, Tamil Nadu, Idia ABSTRACT The advacemet i power systems has led to the developmet of geeratio dispatch (GD) that is difficult to solve by classical optimisatio method. The proposed paper work is to evolve simple ad effective method for optimum geeratio dispatch to miimise the fuel cost, evirometal cost ad security requiremet of power etworks. The approach is based o the bi-criterio global optimisatio ad Particle Swarm Optimisatio (PSO) techique. The proposed techique is tested o 3-area itercoected ad logitudial system. The effectiveess of the proposed optimisatio is verified i simulatio studies usig MATLAB software. The PSO based approach has bee exteded to evaluate the tradeoff curve betwee the fuel cost of power productio ad the evirometal cost accordig to the bi-criterio objective fuctio. Idex terms: geeratio dispatch, multi-objective global optimisatio, particle swarm optimisatio, bi-criterio costat. 1 INTRODUCTION Today s power systems are highly complex ad their operatios are upredictable. The primary objective i the plaig ad operatio of power systems is to provide quality supply to cosumers at ecoomical cost. Previous efforts o solvig geeratio dispatch problem have employed the covetioal methods icludes the lambda iteratio ad gradiet method [1], [2]. The icreasig eergy demad ad the decreasig eergy resources have made optimisatio a great ecessity i power system operatio ad plaig. Ecoomic dispatch is the optimisatio scheme of geeratio system to determie the best geeratio schedule to supply a give load with miimum cost, while satisfyig a set of costraits. Because of the icreasig size ad complexity of power system etworks, such as multiple fuel optios, evirometal costraits, more attetio is beig give to develop optimisatio methods that automatically accout for such practical costraits. Also the aual fossil fuel costs are i the order of several billios of dollars ad eve a small improvemet i the ecoomic dispatch fuctio ca lead to sigificat cost savigs. A lot of efforts has also bee devoted to the improvemet of covergece ad the reductio of computatio time. The paper proposes a method for optimisatio approach to determie the GD while satisfyig a set of costraits. The geeratio dispatch solutio is based o PSO ad formatio of a bi-criterio objective fuctio. The approach icludes the evaluatio of trade-off curve betwee fuel cost ad evirometal cost i power dispatch by solvig bi-criterio fuctio at differet values of bi-criterio costat (w) ad its effectiveess is demostrated through a 3-area itercoected logitudial test system i order to fid its security margi. A MATLAB program was developed to implemet the PSO algorithm for solvig the bi-criterio problem. 2. MULTI-OBJECTIVE GENERATION DISPATCH The pollutio of the earth atmosphere caused by the emissios of SO 2, NO x ad CO 2 from thermal geeratig plats is of great cocer to power utilities. Traditioally, electric utilities dispatch geeratio usig miimum fuel cost as the criterio. However the best ecoomic dispatch does ot lead to miimum emissio ad vice- versa. The goal of emissio dispatch is to determie the geeratio schedule, which has the least pollutat emissio cost. The two criteria are cotradictory to each other ad are i tradeoff relatioship. This makes it difficult to hadle this problem by covetioal approaches that optimise a sigle objective fuctio.oe feasible approach to solve this kid of problem usig covetioal optimisatio method is to covert the bi-objective ito a sigle objective fuctio by givig relative weightig values. I this case the emissio dispatch is added as a secod objective to the ecoomic dispatch problem which leads to combied evirometal / ecoomic dispatch. (CEED) 2. 1 MULTI-OBJECTIVE GENERATION DISPATCH FORMULATION The multi-objective thermal dispatch problem is to miimise the umber of objectives like the fuel cost, evirometal cost ad overloadig of trasmissio lies etc subject to its costraits. (a) Ecoomic Objective The objective of the dispatch problem is to miimise the total fuel cost F 1 for ruig geerators.

2 Proceedigs of the 6th WSEAS/IASME It. Cof. o Electric Power Systems, High Voltages, Electric Machies, Teerife, Spai, December 16-18, dispatch solutio. F 1 = (a j P j 2 +b j P j + c j ) (1) Step 4: Form trade-off curve betwee fuel cost ad j= 1 evirometal cost. Where a j, b j,c j are fuel cost co-efficiet of uit j Step 5: Determie the security level of the etwork usig the optimum geeratio dispatch solutio. Power balace costrait Total geeratig power has to be equal to the sum of load demad ad the trasmissio loss j= 1 P j -P D -P L = 0 (2) Capacity limit Costrait The power output level of geerator j should be betwee its P j mi ad P j max power output limits P j mi P j P j max for j = 1,2,.. ( b ) Evirometal Objective The objective is to miimise the total emissio cost F 2 due to burig of fuels. I the preset work, oly Nox emissio is take ito accout. 2 F 2 = (d j p j + e j p j + f j ) (3) j = 1 Where d j, e j, f j are co-efficiet of emissio of uit j (c) Security objective The objective is to miimise the level of security of supply to meet the load demad. Total security cosidered to be achieved whe there is o overloadig of lies (or) stability margi is high.the overall security is domiated by the MW trasfer level at the itercoectio betwee the subsystems, ad thus by the MW output of o lie geerator [4]. 3. OVERVIEW OF PARTICLE SWARM OPTIMISATION Keedy ad Eberhart first itroduced PSO i year of 1995 [4]. PSO is motivated from the simulatio of the behaviour of social systems such as fish schoolig ad birds flockig [5]. The PSO algorithm requires less computatioal time ad less memory. The basic assumptio behid the PSO algorithm is, birds fid food by flockig ad ot idividually. This leads to assumptio that iformatio is owed joitly i flockig. Basically PSO was developed for two-dimesio solutio space by Keedy ad Eberhart[4]. The positio of each idividual is represeted by XY axis positio ad its velocity is expressed by Vx i x directio ad Vy i Y directio. Y S k+1 V K V k+1 V gbest S K V pbest X 2.2 BASIS FOR SOLVING PROBLEM Fuel cost ad evirometal cost ca be combied liearly to form sigle objective fuctio as follows. The total cost Ft = w F 1 + ( 1 w) F 2 (4) w =bi-criterio costat ( 0 to 1) w =0 (oly evirometal objective is cosidered) w =1 (oly fuel objective is cosidered) The value of w is betwee 0 ad 1 idicates the relative sigificace betwee the two objectives.by varyig the values of w ad by a appropriate optimisatio process the trade-off betwee the fuel cost ad evirometal cost ca be determied over the rage of values of w. 2.3 FORMATION OF BI-CRITERION OBJECTIVE FUNCTION Step 1: Combie the ecoomic ad evirometal objectives. Step 2: Form the bi-criterio objective fuctio. Step 3: Determie the ear global or global optimum Figure 1. Cocept of Modificatio of Searchig poit of PSO where S K = Curret searchig poit S K+1 V K V K+1 = Modified searchig poit = Curret Velocity = Modified Velocity Vpbest = Velocity based o pbest Vgbest = Velocity based o gbest The curret positio (searchig poit i the solutio space) ca be modified usig the followig equatio ad this is also show fig.1 S K+1 i = S K K+1 i + V i ( 5 ) 3.1 OPTIMIZATION ALGORITHM

3 Proceedigs of the 6th WSEAS/IASME It. Cof. o Electric Power Systems, High Voltages, Electric Machies, Teerife, Spai, December 16-18, Represet the i th particle 2. Pi = [Pi 1, Pi 2, Pi 3, Pi 4..Pi d, Pi] 3. Geerate the velocity V jmax 4. Evaluate Pbest ad the idetify gbest 5. Calculate ew velocities Vij (Iter+1) =w*vij (Iter+1) +c 1 *rad 1 *(pbest i -p ij (iter) )+ c 2 *rad 2 *(gbest i -p ij (iter) ) 6.Update geeratio P ij (iter+1) = P ij (iter) + V ij (iter+1) 3.2 IMPLEMENTATION OF PROPOSED ALGORITHM The proposed method ca be split ito three major processes 1. Iitializatio Process 2. Fitess Evaluatio Process 3. Updatig Process Iitializatio Process Let P be the particle co- ordiate (positio) ad V its speed (velocity) i search space. Cosider i as a particle i the total populatio (swarm).now i th particle positio ca be represeted as Pi = [P i1, P i2,..p in ] i the N dimesioal space. Fitess Evaluatio Process: I this fitess evaluatio process, each particle i the populatio is evaluated usig the fitess fuctio i the first iteratio Fe = (a j P 2 j +b j P j + c j ) for j= 1 to ( 6 ) The best previous positio of i th particle is stored ad represeted as Pbesti = (Pbest i1, Pbesti2, Pbesti3, Pbestij). All the Pbest are evaluated by usig a fitess fuctio. The best particle amog all Pbest is represeted as gbest. Updatig Process I this updatig process, modify the each idividual velocity V of the each particle P i accordig to the equatio show below: V (Iter+1) ij = w* V (Iter+1) ij +c 1* rad 1* (pbest ij -p (iter) ij ) + c 2* rad 2* (gbest i -p (iter) ij ) ( 7 ) i = 1,2,3, I ad d = 1,2,3,. where is the umber of uits. The use of liearly decreasig iertia weight factor w has provided improved performace i all the applicatio. Its value is decreased liearly from about 0.9 to 0.4 durig a ru. Suitable selectio of the iertia weight provides a balace betwee global ad local exploratio ad exploitatio, ad result i less iteratio o average to fid a sufficietly optimal solutio. Its value is set as w = w max - ( wmax w mi ) * iter ( 8) iter max Where iter idicates curret iteratio, iter max idicates maximum o of iteratios. However, after update the velocity, the idividual velocity may violate its Velocity maximum, miimum costraits. This violatio is corrected as follows V id (Iter+1) < V id max, the V id (Iter+1) = V d mi After this velocity updatig process of all the idividual i each particle, modify the positio (geerator output level) of each idividual i the particle P i accordig to the followig equatio p (iter+1) ij = p (iter) (iter+1) ij + V ij ( 9 ) At the ed of updatig process, if the evaluatio value of each idividual is better tha the previous pbest, the curret evaluatio value is set to be as pbest, if the best Pbest is better tha gbest, that value is set to be gbest. 4. CASE STUDY AND RESULTS 4.1 CASE STUDY FOR CEED I this case study, a test system has bee cosidered ad solved by the proposed PSO method. The test system has six geeratig uits with maximum demad of 700MW.The results obtaied by this method are compared with Geetic Algorithm method (GA) [2] show i Table 1.The covergece characteristics show i fig 2. Method Fuel costf 1 Emissio costf 2 Total cost F t Lie loss (MW) PSO GA Table 1.Comparisio of results for CEED at w=0.5 Figure 2. Covergece characteristics for CEED 4.2 CASE STUDY FOR MULTIPLE FUEL SYSTEM: If V id (Iter+1) > V id max, the V id (Iter+1) = V d max

4 Proceedigs of the 6th WSEAS/IASME It. Cof. o Electric Power Systems, High Voltages, Electric Machies, Teerife, Spai, December 16-18, I this case study, a 6 geeratig system with maximum of three differet types of fuel are solved by the proposed PSO method. The six uits are combied to meet the demad. The piecewise quadratic heat rate fuctios of the geerators are give i the order of G1 to G6 [7] At a break poit the heat rate fuctio for fuel is switched to a fuctio of aother type of fuel. I the multiple fuel problems the solutio obtaied by the proposed PSO method is compared with the result of EP ad GA [7] i Table 2. It is observed that PSO method ca lead to better solutio tha other two methods. Parameters Method compared PSO EP GA P1MW P2MW P3MW P4MW P5MW P6MW Loss MW Total cost Geeratios to coverge Table 2 Compariso of result for multiple fuel system The cost ad security margi for various values of w is tabulated i Table 3. Sl.No w Fuel cost Fe Emissio cost Fp Security Margi (sm) Table 3.Cost ad security margi Trade-off curve is evaluated betwee fuel cost ad emissio cost for various values of w show i Fig 3. Figure 3 Trade-off curves This shows that the PSO method ca lead to better solutio tha ay other method. Istead of defiig the best compromise betwee the ecoomic ad evirometal aspects of the problem is first formed i the form of a tradeoff curve based o this compromise, the aspect of security is ivestigated so that a overall compromise ca be obtaied ad from this the most appropriate geeratio dispatch solutio ca be determied. 5. CONCLUSION A approach for the determiatio of the most appropriate dispatch solutio, which best meets the ecoomic, evirometal ad security objectives i power system operatio has bee proposed. The implemetatio of the approach is based o the formatio of a bi-criterio objective ad a global optimisatio techique. The PSO method has bee utilized i the preset work. The solutio that gives the best compromise amog the three objectives is chose as the most appropriate geeratio dispatch solutio. The trade-off curve evaluated is useful i providig alterate dispatch solutio for egieers i daily operatio. ACKNOWLEDGMENT We sicerely thak the maagemet of Vellore Istitute of Techology for give us a opportuity to work towards our paper. REFERENCES [1] Bakirtzis, V.petridis ad S.kazarlis geetic algorithm solutio to the ecoomic dispatch problem proc.ist.elect.egg-ge.,tras.,dist.,vol141 o.4,pp july 1994 [2] Sog.Y.H,wag. G.S.,Wag. P.V.,Johs 1997 Evirometal Ecoomic Dispatch Usig FUZZY Logic cotrolled Geetic Algorithm. IEE proceedigs-geeratio, Trasmissio istributio,vol.144(4) [3] Kit Po Wog, Bie Fa, C.S.Chag, A.C Liew Multi-Objective geeratio dispatch usig Bicriterio global optimisatio, IEEE trasactio o power system, Vol.10, No, November 1995.

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