Economic/Emission Load Dispatch Using Artificial Bee Colony Algorithm

Economic/Emission Load Dispatch Using Artificial Bee Colony Algorithm

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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 Economic/Emission Load Dispatch Using Artificial Bee Colony Algorithm S. Hemamalini1 and Sishaj P Simon1 1 National Institute of Technology/ Department of Electrical and Electronics Engineering, Tiruchirappalli, India Email: s_hemamalini@ rediffmail.com and sishajpsimon@ nitt.edu Abstract—This paper presents an application of the Kermanshahi et al. [6] used the sum of a quadratic artificial bee colony (ABC) algorithm to multi-objective and an exponential term. Nanda et al. [7] tried to find optimization problems in power system. A new multi- the best compromise between the conflicting targets of objective artificial bee colony (MOABC) algorithm to minimum cost and minimum emission by means of solve the economic/ emission dispatch (EED) problem is proposed in this paper. Non-dominated sorting is suitable multi-objective procedures. Granelli et al. [8] employed to obtain a Pareto optimal set. Moreover, fuzzy proposed an emission constrained dynamic dispatch decision theory is employed to extract the best procedure. It minimizes fuel cost during a pre-selected compromise solution. A numerical result for IEEE 30-bus time horizon and thoroughly takes into account the test system is presented to demonstrate the capability of environmental constraints. King et al. [9] reported an the proposed approach to generate well-distributed improved Hopfield Neural Network (NN) for the Pareto-optimal solutions of EED problem in one single economic environmental dispatch problem. Wong and run. In addition, the EED problem is also solved using the Yuryevich [10] developed an evolutionary weighted sum method using ABC. Results obtained with programming based algorithm using emission as the proposed approach are compared with other techniques available in the literature. Results obtained problem constraints. Das and Patvardhan [11] proposed show that the proposed MOABC has a great potential in a multi-objective stochastic search technique (MOSST) handling multi-objective optimization problem. based on real coded Genetic Algorithm (GA) and Simulated Annealing (SA) using single criterion Index Terms— Artificial Bee Colony algorithm, economic function optimization. Abido [12] presented a genetic emission dispatch, fuzzy decision, Pareto-optimal algorithm based multi-objective technique, where multiple nondominated solutions can be obtained in a I. INTRODUCTION single run. In [13], Abido developed a multi-objective evolutionary algorithm that determined the Pareto The basic economic dispatch problem is to optimal set simultaneously using the strength Pareto minimize the total generation cost among the evolutionary algorithm. A comparison of committed units satisfying all unit and system equality nondominated sorting genetic algorithm [NSGA], and inequality constraints. However, the thermal power niched Pareto genetic algorithm [NPGA], and strength generation process produces harmful emission, which Pareto evolutionary algorithm (SPEA) have been done must be minimized for the environmental in [14] for the environmental/economic electric power consideration. Many works are in literature as to solve dispatch problem. the emission/economic dispatch problems. Several In this paper, a novel implementation of the multi- options are proposed to reduce unit emissions like objective optimization problem accompanied by installing cleaning equipments, changing to fuel with swarming intelligence approach is considered to obtain less pollutants or dispatching with emission a best compromise solution between cost and emission considerations [1]. The first two methods involve more minimization. The EED problem is solved using the cost and thereby the third method is preferred. ABC algorithm considering the objectives separately M.R.Gent and J.W.Lamont [2] have proposed a method and as single objective using the weighted sum method. for on-line steam unit dispatch that results in the The feasibility of the proposed method is demonstrated minimum NOx emissions. They had used a combination on IEEE 30-bus test system. The results of MOABC of a straight line and an exponential term for the total are compared with the weighted sum method and with NOx emission. J.Zahavi and L.Eisenberg [3] used a that of the results available in literatures. second order polynomial for representing NOx emission. J.H.Talaq, E.El Hawary et al [4] gave a II. PROBLEM FORMULATION summary of economic environmental dispatching algorithms. A.A.El-Keib, H.Ma et al [5] describes a Environmental/economic load dispatch involves the general formulation of the economic dispatch problem simultaneous optimization of fuel cost and emission based on the requirements of Clean Air Act objectives that are conflicting in nature satisfying the Amendments of 1990. system and unit equality and inequality constraints. The general problem formulation is as follows. 27 © 2010 ACEEE DOI: 01.ijepe.01.02.06
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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 A. Multi objective EED Problem Formulation where a solution x is a vector of n decision variables: T The objective function of the non-linear constrained x = [ x1 , x 2 ,...x n ] ,restricting each decision variable EED problem is formulated as in (1) to consider the to take a value within a lower and an upper bound and cost of generation Fc and the emission control level E simultaneously. fi is the ith objective function. The terms g j (x) and Minimize F [Fc(P), E(P)] (1) h k (x) are called constraint functions. There are M  g (P) = 0, Subject to  objective functions and each objective function can be h (P) ≤ 0.  either minimized or maximized. where g is the system equality constraint, h is the A. Pareto optimality inequality constraint and P is the set of variables to be optimized. Having several objective functions, the aim is to find good compromises (or “trade-offs”) rather than a B. Objective Functions single solution as in global optimization. The popular Fuel Cost Function : nondominated sorting procedure is used in this paper, to find multiple Pareto optimal solutions in a multi- The fuel cost characteristics of each generator unit i, is objective optimization problem. represented by a quadratic equation as given in (2). N Fc = ∑ (a i + b i Pi + c i Pi2 ) $ B. Fast nondominated sorting approach (2) i =1 To obtain Pareto optimal set of solutions a where ai, bi, ci are the fuel cost coefficients of ith unit, N nondominated sorting algorithm proposed by Deb [15] is the number of generating units, P imin is the minimum is used. The approach is based on several layers of generation limit of ith unit in MW, Pi is the power output classifications of the individuals as suggested by of ith unit in MW and Fc is the total fuel cost in $. Goldberg [16]. The population is ranked based on Emission Function : nondomination wherein all nondominated individuals The emission from each unit depends on the power are classified into one category. Then this group of generated by that unit. This is modeled as a sum of a classified individuals is ignored and another layer of quadratic and an exponential function [2]. nondominated individuals is considered. The process N 2 continues until all individuals in the population are E = ∑(α i + β i Pi + γ i Pi + ζ i exp(d i Pi )) ton (3) classified. Since individuals in the first front have the i=1 where αi, βi, γi, ζi and di are the emission coefficients of maximum fitness value, they always get more copies the generator i, and E is the total emission function in than the rest of the population. This allows searching ton. for nondominated regions, and results in convergence of the population toward such regions. C. Constraints C. Reducing Pareto set by calculating crowding 1. Equality constraint: distance Real power balance constraint N In some problems, the Pareto optimal set can be ∑ P = PD + PL (4) extremely large or even contain an infinite number of i =1 i 2. Inequality constraint : solutions. In this case, reducing the set of Real power generation limit nondominated solutions without destroying the characteristics of the trade-off front is desirable from Pimin ≤ Pi ≤ Pimax i = 1,2,..N (5) the decision maker’s point of view. Crowded distance estimation approach [15] is employed to reduce the where PD is the total load demand in MW, P L is the total Pareto set to manageable size. transmission loss in MW and Pimax is the maximum generation limit of ith unit in MW. D. Best compromise solution To extract the best compromise solution from a set III. MULTI-OBJECTIVE OPTIMIZATION of Pareto solutions in minimizing two conflicting The multi-objective optimization problem in its general objectives, fuzzy based mechanism is used. Due to the form is as follows: imprecise nature of the decision maker’s judgement, Minimize fi (x) i=1,2,…M; (6) the ith objective function of a solution in the Pareto optimal Fi is represented by a membership function μ i g j (x) = 0, j = 1,2,...J;  [17] defined as in (7). Subject to  h k (x) ≤ 0, k = 1,2,...K;  x imin ≤ x i ≤ x imax , i = 1,2...n; 28 © 2010 ACEEE DOI: 01.ijepe.01.02.06
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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 1 Fi ≤ Fimin amount of the new food source is higher than that of  the previous one then the bee remembers the new  Fi max − Fi μ i =  max Fimin < Fi < Fimax (7) position and forgets the old one. Once the employed  Fi − Fimin  bees complete their search process, they share the 0 Fi ≥ Fimax nectar information of the food sources and their max position information with the onlooker bees on the where Fi and Fimin are the maximum and minimum dance area. The onlooker bees evaluate the nectar values of the ith objective function respectively. For information and choose a food source depending on the each nondominated solution k, the normalized probability value associated with that food source using membership function μk is calculated as (10). M k fit i ∑ μi Pi = = m=1 k i N μ M j (8) e ∑ ∑ μi ∑ fit (10) j=1i =1 j=1 j where m is the number of nondominated solutions. The where fiti is the fitness value of the solution i which is best compromise solution is the one having the proportional to the nectar amount of the food source in the position i and Ne (i.e. Npop/2 ) is the number of food maximum of μ k . sources which is equal to the number of employed bees, ne. Now the onlookers produce a modification in E. Weighted sum method the position selected by it using (11) and evaluate the In the EED problem, the cost function and nectar amount of the new source. emission function are weighted according to their (11) relative importance and converted into a single vij = x ij + φij (x ij − x kj ) objective function as in (9). Min f = wFc + (1 − w)E (9) where k ∈ {1, 2,…., ne} and j ∈ {1, 2, …,D} are where Fc is the fuel cost function, E is the emission randomly chosen indexes. Although k is determined function and w is the weighting coefficient in the range randomly, it has to be different from i. φij is a random 0 to1. When w=0, the function is an emission function number between [-1, 1]. It controls the production of and when w=1, the function is a fuel cost function. A neighborhood food sources. If the nectar amount of the trade-off can be obtained when w is varied from zero to new source is higher than that of the previous one, the one. onlookers remember the new position; otherwise, it retains the old one. In other words, greedy selection IV.OVERVIEW OF ARTIFICIAL BEE COLONY ALGORITHM method is employed as the selection operation between Artificial Bee Colony (ABC) is one of the most old and new food sources. recently defined algorithms by Dervis Karaboga [18], If a predetermined number of trials does not improve [19] in 2005. It has been developed by simulating the a solution representing a food source, then that food intelligent behavior of honeybees. In ABC system, source is abandoned and the employed bee associated artificial bees fly around in a multidimensional search with that food source becomes a scout. The number of space and the employed bees choose food sources trials for releasing a food source is equal to the value of depending on the experience of themselves. The ‘limit’, which is an important control parameter of onlooker bees choose food sources based on their nest ABC algorithm. The limit value usually varies from mates experience and adjust their positions. Scout bees 0.001neD to neD. If the abandoned source is xij, fly and choose the food sources randomly without j ∈ ( 1,2 ,...D) then the scout discovers a new food using experience. Each food source chosen represents a source xij using (12). possible solution to the problem under consideration. (12) The nectar amount of the food source represents the xij = x j min + rand (0,1) × ( x j max − x j min ) quality or fitness of the solution. The number of employed bees or the onlooker bees is equal to the number of food sources or possible solutions in the where x j min and x j max are the minimum and maximum population. A randomly distributed initial population is limits of the parameter to be optimized. There are four generated and then the population of solutions is control parameters used in ABC algorithm. They are subjected to repeated cycles of the search process of the the number of employed bees, number of unemployed employed bees, onlookers and scouts. An employed or onlooker bees, the limit value and the colony size. bee or onlooker probabilistically produces a Thus, ABC system combines local search carried out modification on the position in her memory to find a by employed and onlooker bees, and global search new food source (solution) and evaluates the nectar managed by onlookers and scouts, attempting to amount (fitness) of the new food source. If the nectar balance exploration and exploitation process [20]. 29 © 2010 ACEEE DOI: 01.ijepe.01.02.06
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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 V. IMPLEMENTATION OF MOABC FOR EED PROBLEM objective function values of cost and emission within In this section, ABC algorithm [21] is the population. Stringerror is the individual string’s implemented to determine the power output of each error in meeting the power balance constraint, Minerror generating unit for a specified demand. is the minimum constraint error within the population and Maxerror is the maximum constraint error within Algorithm the population. Mincost, Maxcost and Stringcost are The step-by-step procedure for the proposed method is calculated using the objective function (2), Minemis, as follows. Maxemis and Stringemis are calculated using the objective function (3) and Minerror, Maxerror and Step 1: Specify generator cost coefficients, emission Stringerror are calculated using (14). Set the cycle coefficients, generation power limits for each unit and count as one and repeat the following steps till the B-loss coefficients. Initialize the four control maximum cycle number (MCN) which is the parameters of the ABC algorithm and maximum cycle termination criteria is reached. for the termination process. Step 4: Modification of position and selection of site by Step 2: Initialization of population with random employed bees solutions An employed bee produces a modification on the Initialize randomly an initial population position (solution) in her memory for finding a new M = [X1, X 2 ,...., X N pop ]T of Npop solutions or food food source. The new food source is determined by altering the value of any one of the D parameters (old source positions in the multi-dimensional solution food source position), selected randomly using (11) and space where Npop represents the size of population. Each keeping other parameters unchanged. The modified solution X i = [Pi1 Pi2  Pij  PiD ] , (i=1, 2,…, Npop position is then checked for constraints in (4) and (5). If the resulting value violates the constraint, they are set and j=1,2,…,D) is represented by a D-dimensional to the extreme limits. Then, the fitness value of the new vector, where D is the number of parameters to be food source position (new solution) is evaluated using optimized. The elements of each solution vector (13). The fitness of the modified position is compared denoted as xij is the real power output of generating with the fitness of the old position computed in step 3. units and they are distributed uniformly between their If the new fitness is better than the old fitness then the minimum and maximum generation limits using (12). new position is retained otherwise the old one is The individuals generated should be refined to satisfy retained in its memory. Here a greedy selection the constraint as in (4) and (5). Half of the colony size mechanism is employed as the selection operation forms the employed bees. between the old and new position. In case, if fitness Step 3: Evaluation of Fitness of the population value of the new position is less than the old one then a Evaluate the fitness value of each food source positions limit count is set. corresponding to the employed bees in the colony. A Step5: Recruit onlooker bees for selected sites and fitness function as in (13) is used. evaluate fitness Fitness = A[1 − %Cost] + B[1 − %Emis] + C[1 − %Error] (13) After all employed bees complete the search process where A, B and C (>0) are the weighting coefficients, they share the nectar information of the food sources and their position information with the onlooker bees N on the dance area. An onlooker bee evaluates the nectar Error = | ∑ Pi − PL − PD | i =1 (14) information taken from all employed bees and chooses Stringcost − Mincost a food source with a probability Pi using (10) related to %Cost = its fitness value [20]. Maxcost − Mincost (15) Step 6: Modification of position by onlookers Stringemis − Minemis As in the case of the employed bee discussed in step 4, %Emis = Maxemis − Minemis the onlookers produces a modification on the position (16) in its memory using (11) and checks the nectar amount Stringerror − Minerror of the candidate source. If the new food has equal or %Error = Maxerror − Minerror better nectar than the old source, it is replaced with the (17) old one in the memory. Otherwise, the old one is where Stringcost and Stringemis are the individual retained in the memory. Again greedy selection string’s cost and emission values of generation, mechanism is employed as the selection operation Mincost and Minemis are the minimum objective between the old and new position. function values of cost and emission within the Step 7: Now, the position of employed bees and the population. Maxcost and Maxemis are the maximum unemployed bees obtained from step 4 and 6 30 © 2010 ACEEE DOI: 01.ijepe.01.02.06
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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 respectively are combined. The combined colony is Table I sorted based on the nondomination sort. The new BEST FUEL COST OUT OF 20 RUNS colony of employed bees of size Npop/2 is formed and is NSGA NPGA SPEA MOPSO MOAB updated in the Pareto set. [14] [14]] [14] [24] C P1 0.1447 0.1425 0.1279 0.1207 0.0976 Step 8: Abandon sources exploited by the bees P2 0.3066 0.2693 0.3163 0.3131 0.3092 If a solution representing a food source is not improved by a predetermined number of trials, then that food P3 0.5493 0.5908 0.5803 0.5907 0.6123 source is abandoned and the scout discovers a new food P4 0.9894 0.9944 0.9580 0.9769 0.9385 source to be replaced with Xi. The number of trials for P5 0.5244 0.5315 0.5258 0.5155 0.5363 releasing a solution is equal to the value of limit. This P6 0.3542 0.3392 0.3589 0.3504 0.3633 operation is performed using (12). COST 605.946 Step 9: Increment the cycle count. Stop the process if ($/H) 607.98 608.06 607.86 607.79 5 EMISSION the termination criteria is satisfied. Termination criteria (TON/H) 0.2191 0.2207 0.2176 0.2193 0.2180 used in this work is the specified maximum number of LOSS cycles. Otherwise, go to step 4. Npar members of the (MW) - - - - 2.3118 colony belonging to the first front are saved as Pareto optimal solutions. TABLE II BEST EMISSION OUT OF 20 RUNS Step 10: To extract the best compromise solution from NSGA NPGA SPEA MOPSO the Pareto optimal set, fuzzy based mechanism as [14] [14] [14] [24] MOABC discussed in section III (D) is used. P1 0.3929 0.4064 0.4145 0.4101 0.4039 P2 0.3937 0.4876 0.4450 0.4594 0.4484 VI. SIMULATION RESULTS AND DISCUSSIONS P3 0.5818 0.5251 0.5799 0.5511 0.5464 In order to validate the proposed method, the EED P4 0.4316 0.4085 0.3847 0.3919 0.3994 is solved using the proposed method for IEEE 30-bus P5 0.5445 0.5386 0.5348 0.5413 0.5428 system. and has been implemented in MATLAB on a P6 0.5192 0.4992 0.5051 0.5111 0.5253 Pentium-IV, 1GB, 3.4 GHz PC. The maximum size of COST($ 644.168 the Pareto-optimal set is chosen to hold 20 solutions. /H) 638.98 644.23 644.77 644.74 7 EMISSIO The ABC parameters are chosen by trial and error. N (TON/H) 0.1947 0.1943 0.1943 0.1942 0.1942 A. Test Case 1- IEEE 30 bus system LOSS This test system comprises of 6 generators, 41 (MW) - - - - 3.2225 transmission lines and 30 buses. The cost coefficients, Now, the bi-objective optimization problem is solved power generation limits and emission coefficients for using the proposed approach. The result for the best the test case are adapted from [14]. The line data and compromise solution of the combined economic bus data are as given in [22], [23]. In this case, the cost emission dispatch problem is shown in Table III. function is quadratic in nature and the emission Tables I, II and III reveal that the power output of each function includes exponential term. Transmission unit are well within the minimum and maximum limits losses are considered in this problem. The demand of of generation. It can be seen that the proposed approach the system is 283.4 MW. The population size and is superior and preserves the diversity of the maximum number of generations have been selected as nondominated solutions over the trade-off front. 100 and 300, respectively for the system under TABLE III consideration. Limit value is set as 2 and the number of BEST COMPROMISE SOLUTION-CASE 1 employed bees is equal to the number of unemployed NSGA NPGA SPEA MOPSO bees. In order to explore the extreme points obtained by [14] [14] [14] [24] MOABC the proposed approach, fuel cost and emission functions are optimized individually. The result of best P1 0.2935 0.2976 0.2752 0.2367 0.2687 fuel cost and best emission when optimized P2 0.3645 0.3956 0.3752 0.3616 0.3806 individually are given in Table I and Table II. Table I P3 0.5833 0.5673 0.5796 0.5887 0.5780 and II show the results for optimized cost and emission, P4 0.6763 0.6928 0.677 0.7041 0.6726 generation schedule, and losses for economic dispatch and emission dispatch when the two objectives are P5 0.5383 0.5201 0.5283 0.5635 0.5267 optimized individually. Generation schedules for each P6 0.4076 0.3904 0.4282 0.4087 0.4344 unit are given in p.u. on a base of 100 MVA. In Fig. 1 Cost($/h) 617.8 617.79 617.57 615.00 617.1724 convergence characteristics of best fuel cost and best Emission emission are shown. (ton/h) 0.2002 0.2004 0.2001 0.2021 0.1999 Loss ( MW) - - - - 2.7000 31 © 2010 ACEEE DOI: 01.ijepe.01.02.06
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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 612 0.198 non-convex EED problem. Nondominated sorting Fuel cost 611 0.1975 approach is used to find the Pareto set of solutions. The n ) Emission E is io (to /h size of the Pareto set is maintained by computing the 0.197 610 C s ($ ) o t /h 0.1965 crowding distance, which preserves the diversity of m s n 609 0.196 608 0.1955 the Pareto solutions. To obtain a best compromise 607 0.195 solution from a set of Pareto solutions, fuzzy decision 606 0.1945 theory is used. The feasibility of the proposed method 605 0 50 100 150 200 250 0.194 300 is demonstrated on IEEE 30 bus system. The EED Iteration problem is also formulated as a single objective Fig.1.Convergence of best cost and best emission objective functions. function using weights and solved using the classical weighted sum method. Results obtained depicts that the 0.22 proposed method is well suited to obtain a well- 0.215 distributed Pareto optimal solutions in a single run. In Best compromise (MOABC) addition, the comparison of the results with other Emission (ton/h) 0.21 methods reported in the literature shows the superiority 0.205 of the proposed method and its potential for solving 0.2 non-smooth EED problems in a power system. 0.195 Best compromise (WSABC) 0.19 REFERENCES 600 610 620 630 640 650 Cost ($/h) [1]. J. W. Lamont and E. V. Obessis, “Emission dispatch Fig. 2. Pareto-optimal front of the proposed MOABC approach. models and algorithms for the 1990's,” IEEE Trans. Power Syst., vol. 10, pp. 941-947, 1995. [2]. M. R. Gent and J. W. Lamont, “Minimum emission For comparison, the same conflicting bi-objective dispatch,” IEEE Trans. Power App. Syst., vol. PAS-90, problem is solved with ABC algorithm using weighted pp. 2650-2660, 1971. sum method in which the bi-objective function is [3]. J. Zahavi and L. Eisenberg, “Economic environmental converted into single objective function. In this method power dispatch,” IEEE Trans. SMC-5 (5) (1975) 485- to obtain 20 nondominated solutions, the algorithm is 489. applied 20 times, by varying w between 0 and 1 in [4]. J. H. Talaq, M. E. Ferial, and El-Hawary, “A Summary steps of 0.05. The distribution of the nondominated of environmental/economic dispatch algorithms,” IEEE solutions obtained in a single run using MOABC and in Trans. Power Syst., vol. 9, pp.1508-1516, 1994. 20 runs for weighted sum ABC (WSABC) are shown in [5]. A. A. El-Keib, H. Ma and J. L. Hart, “Environmentally constrained economic dispatch using Lagrangian Fig. 2. In the single objective approach of solving the relaxation method,” IEEE Trans.Power Syst., vol. 9, EED problem, the computation time taken to produce pp.1723-1729, 1994. 20 solutions is 981.78 seconds. However, in the [6]. B. S. Kermanshahi, Y. Wu, K. Yasuda and R. nondominated sorting MOABC method the time taken Yokoyama, “Environmental marginal cost evaluation by to produce 20 solutions is 157.02 seconds. This shows non-inferiority surface,” IEEE Trans. Power Syst., vol.5, that the proposed method is faster than the classical pp. 1151-1159, 1990. weighted sum method. The results for single and bi- [7]. J. Nanda, D. P. Kothari and K. S. Lingamurthy, objective optimization using ABC algorithm is “Economic and emission load dispatch through goal compared in Table IV. It can be seen that, the results programming techniques,” IEEE Trans. Ener. Conv., vol. 3, pp. 26-32, 1988. for weighted sum method are closer to that of the multi- [8]. G.P. Granelli, M. Montagna, G.L. Pasini, and P. objective solutions. However, the computation time is Marannino, “Emission constrained dynamic dispatch,” very large in producing the same number of solutions Electric Power Syst. Res., vol. 24, pp. 56-64, 1992. as in MOABC. [9]. T. D. King, M. E. El-Hawary and F. El-Hawary, TABLE IV “Optimal environmental dispatching of electric power BEST SOLUTIONS FOR SINGLE AND MULTI-OBJECTIVE FUNCTIONS systems via an improved Hopfield neural network model,” IEEE Trans. Power Syst., vol. 10, pp. 1559- No. of Best cost Best Best compromise 1565, 1995. Objectiv ($) Emission Cost ($) Emissio [10].K. Wong and J. Yuryevich, “Evolutionary programming e (ton) n (ton) based algorithm for environmentally constrained function economic dispatch,” IEEE Trans. Power Syst., vol. 13, s pp. 301-306, 1998. Single 605.6725 0.1942 615.0303 0.2007 Multi 605.9465 0.1942 617.01 0.2000 [11].D. B. Das, and C. Patvardhan, “New multi-objective stochastic search technique for economic load dispatch,” IEE Proc.Gener. Trans., Distr., Vol. 145, pp. 747-752, VII. CONCLUSIONS 1998. The proposed multi-objective ABC algorithm has [12].M. A. Abido, “A new multiobjective evolutionary been applied successfully to solve the bi-objective, algorithm for environmental/economic power dispatch,” 32 © 2010 ACEEE DOI: 01.ijepe.01.02.06
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  ACEEE International Journalon Electrical and Power Engineering, Vol. 1, No. 2, July 2010 IEEE PES Summer Meeting, Vancouver, Canada, [23].R. Yokoyama, S.H. Bae, T. Morita, and H. Sasaki, pp.1263-1268, 2001. “Multiobjective optimal generation dispatch based on [13].M. A. Abido, “Environmental/economic power dispatch probability security criteria,” IEEE Trans. on Power using multiobjective evolutionary algorithms,” IEEE Syst., vol.3, pp.317-324, Feb 1988. Trans. Power Syst., vol. 18, pp. 1529-1537, 2003. [24].M.A. Abido, “Multiobjective particle swarm [14].M. A. Abido, “Multiobjective evolutionary algorithms optimization for environmental/economic dispatch for electric power dispatch problem,” IEEE Trans. Evol. problem,” Electric Power Systems Research,vol. 79, pp. Comput., vol. 10, pp. 315-329, 2006. 1105-1113, July 2009. [15]. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic S. Hemamalini was born in India and received the B. E. algorithm: NSGA-II,” IEEE Trans. Evol. Comput., vol.6, degree in electrical and electronics engineering, and the pp.182-197, 2002. M.Tech. Degree in power systems in 2005 from National [16]. D. E. Goldberg, “Genetic Algorithms in Search, Institute of Technology, Tiruchirapalli, India. She is currently Optimization and Machine Learning,” Addison-Wesley pursuing Ph. D. degree in the Department of Electrical and Publishing Company, Reading, MA, 1989. Electronics Engineering, National Institute of Technology, [17]. M. Sakawa, H. Yano, and T. Yumine, “An interactive Tiruchirapalli, India. fuzzy satisficing method for multiobjective linear Her research interest includes Deregulation of Power System, programming problems and its application,” IEEE Trans. Power System Operations and Control, Optimization Syst., Man, Cybern., vol. SMC-17, pp. 654–661, 1987. techniques in power system. [18].D. Karaboga, “A powerful and efficient algorithm for Sishaj Pulikottil Simon was born in India and received his numerical function optimization: artificial bee colony Bachelors of Engineering (Electrical and Electronics (ABC) algorithm,” Journal of global optimization, vol. Engineering) and Masters of Engineering (Applied 39, pp. 459-471, 2007. Electronics) at Bharathiar University, Coimbatore, India. He [19].B. Basturk and D. Karaboga, “An Artificial Bee colony obtained his Ph.D., (Power System Engineering) at Indian (ABC) algorithm for numeric function optimization,” In Institute of Technology (IIT), Roorkee, India in the year Proceedings of the IEEE swarm intelligence Symposium 2006. Currently he is an Assistant professor in the 2006, Indianapolis, Indiana, USA, pp. 12-14, 2006. Department of Electrical and Electronics Engineering at [20].Dervis Karaboga and Bahriye Basturk, “Artificial Bee National Institute of Technology (NIT) (formerly Regional Colony (ABC) Optimization Algorithm for Solving Engineering College), Tiruchirappalli, Tamil Nadu. Constrained Optimization Problems,” Springer-Verlag, He has taught courses in Basic Electrical Engineering, IFSA 2007, LNAI 4529, pp. 789–798, 2007. Power Systems Planning and Reliability, Artificial [21].S. Hemamalini and Sishaj P Simon, “Economic Load Intelligence and Artificial Neural Networks. His field of Dispatch with Valve-Point Effect Using Artificial Bee interest is in the area of Deregulation of Power System, Colony Algorithm,” XXXII National Systems Power System Operations and Control, Application of Conference, Dec. 17-19, 2008, India, pp. 525-530. Artificial Intelligence, and New Optimization Techniques to [22]. A. S. Farag, S.A. Al-Baiyat, and T.C. Cheng, “Economic Power System. Load Dispatch Multiobjective Optimization Procedures Using Linear Programming Techniques,” IEEE Trans. on Power Syst., vol. 10, pp. 731-738, 1995. 33 © 2010 ACEEE DOI: 01.ijepe.01.02.06