ScienceDirect. A Comparative Study of Solution of Economic Load Dispatch Problem in Power Systems in the Environmental Perspective

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1 Available online at ScienceDirect Procedia Computer Science 48 (2015 ) International Conference on Intelligent Computing, Communication & Convergence (ICCC-2015) (ICCC-2014) Conference Organized by Interscience Institute of Management and Technology, Bhubaneswar, Odisha, India A Comparative Study of Solution of Economic Load Dispatch Problem in Power Systems in the Environmental Perspective Sarat Kumar Mishra a, Sudhansu Kumar Mishra b * a Assistant Professor, Padmanava College of Engineering, Rourkela, Odisha, India b Assistant Professor, Birla Institute of Technology, Mesra, Ranchi, Jharkhand, India Abstract A power system with many generating units should run under economic condition. The operating cost must be minimized for any feasible load demand. However, along with the cost, the environmental emissions should also be considered, that make it multiobjective optimization problem. In this paper, we have used the standard IEEE test bus systems as a model power system for solving the economic load dispatch (ELD) problem considering different size of system. A comparison of simulation output is made between the results obtained by applying conventional Newton Raphson and Lagrangian multiplier (LM)algorithms and proposed genetic algorithm (GA). From the simulation results, it is observed that, the proposed GA based approach provides better compromised solutions between the two objectives i.e. cost and emission effectively The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility of scientific committee of Missouri University of Science and Technology. Peer-review under responsibility of scientific committee of International Conference on Computer, Communication and Convergence (ICCC 2015) * Corresponding author. Tel.: ; address: mishra.sarat@gmail.com The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of scientific committee of International Conference on Computer, Communication and Convergence (ICCC 2015) doi: /j.procs

2 Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) Keywords:Economic load dispatch, Emission, EED. 1. Introduction The economic load dispatch problem is the schedule of generation of the individual units which minimizes the total operating cost of a power system while meeting the total load plus transmission losses within generator limits. The schedule of generation for the various generators in the system to satisfy the minimum operating cost condition for a particular load is called generation scheduling.the total cost of generation is dependent on the operating efficiencies of the generators, fuel cost and transmission losses. The fuel cost for the generator i supplying a real power P Gi can be expressed as (1) where a i, b i and c i are constants.the emission function for the generator iis given by where,α i, β i, γi are constants found from the emission property of the generator. The objective of the ELD problem is to minimize the total cost with some constraints. The generation should be equal to the total demand plus losses where, P D is the total load demand and P L is the total transmission loss is given by Kron s formula The constants B ij, B i0 and B 00 are dependent on the impedance parameters of the transmission lines of the power system. The generation should be within the minimum and maximum limits The Economic Emission Dispatch (EED) problem has two objective functions to be minimized. The problem can be written as: Subject to: where the equality constraint is given by and the inequality constraints are given by

3 98 Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) Related work Traditionally the problem of ELD was solved by using Gauss-Siedel or Newton-Raphson methods in combination with Lagrangian multiplier method [1, 2]. The problem with these methods is that the convergence depends on initial guess, size of the system and the possibility of local minima. The fuzzy optimization was implemented to solve the same challenging problem [5-7]. However, all these aforementioned papers solve this problem using single objective optimization techniques. These methods required the algorithm to run many times to get all the Pareto optimal points. To solve this challenging and interesting problem researchers have proposed multiobjective optimization algorithm such as particle swarm optimization, non-dominated sorting genetic algorithm etc. and solved the problem at one run [9-15]. In this paper, we have applied three techniques of weighted sum approach to solve this problem. B.Y. Qu et al. have applied multi-objective evolutionary programming to solve environmental economic dispatch problem [16]. A.Bhattacharya et al. have applied gravitational search algorithm for multi-objective optimal power flow in [17] 3. Methodology The traditional approach [1] involves the determination of schedule of generation using lambda iteration. Here, we have adopted the surrogate worth trade off analysis method to solve the ELD problem Algorithm for Surrogate worth Trade-off Analysis: The surrogate worth trade off algorithm can be applied to the ELD problem in the following steps. Step 1: Read input data i.e., bus data, line data and constraints. Step 2: Minimize the fuel cost F C to get F Cmin (use GA) and determine the corresponding transmission loss F LatFCmin. Step 3: Minimize F L to get F Lmin and corresponding cost F CatFLmin. Step 4: Determine L K =F LatFCmin -F Lmin Step 5: Choose and assume a suitable no. of steps, say 15. Step 6: Set index I=1, K=0 Step 7: Vary F L from F Lmin in steps of so that and get the corresponding cost F CK. Step 8:IncrementKby 1. Step 9: IfK 2; go to next step; else go to step vii Step 10: Find trade off function between F C and F L as Step 11: Find the average value of F C and F L for the interval where is constant. and Step 12: Calculate the marginal rate of substitution Step 13: Compute the surrogate worth function Step 14: Increment I to I+1 Step 15: Check if I 2; if yes go to next step; else go to step vii. Step 16: Check if W CLI has changed sign; if yes go to next step; else go to step vii Step 17: Find the value of F C at W CLI =0 on the plot W CLI vsf C. This cost is the best compromise cost. This point gives the best economic dispatch condition.for considering environmental emission in to account along with the cost, we assign a weight to cost and another to emission so that the objective function becomes where w c +w L =1. The value of w c and w L are decided basing on the importance of the objectives.the function F T can be minimized using GA subject to the constraints laid earlier using the same algorithm. 4. Simulation and Results

4 Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) Here, we have taken the IEEE standard test system (14 bus and 30 bus) as the power system for the simulation study. The performance comparison has been carried out by applying the conventional Newton-Raphson and Lagrangian multiplier (LM) method [1] and the proposed genetic algorithm. The program was run for 20 times and the averages of the results were taken for comparison. The final Pareto solutions between cost and emission have been found out as shown in Table I to VI. Table-I Economic Load Dispatch results of IEEE 14 Bus system Algorithm used Total LM GA Table-II Results of multi-objective EED of IEEE 14 Bus system Fuel cost in Table-III Comparison of individual and multi-objective results of IEEE 14 Bus system Best Cost Best Emission Best Compromise Algorithm used Table-IV Economic Load Dispatch results of IEEE 30 Bus system Total Fuel Cost in LM GA Table-V Results of multi-objective EED of IEEE 30 bus system Fuel cost in Emission in Table-VI Comparison of results of IEEE 30 Bus system Best Cost Best Emission Best Compromise It is observed from Table-I and IV that the results obtained by using GA has lower operating cost. In Table-III and VI it is seen that for minimum operating cost, the value of emission is high; whereas for minimum emission, the operating cost is high. Therefore, a compromise between the cost and the emission was arrived. 5. Conclusion Genetic algorithm has been successfully applied to find a compromise between the cost and emission of a multiple unit power system. With the help of the evolutionary computing techniques the same multi-unit power

5 100 Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) system can be made to operate with a better voltage profile while running at the best compromised value of cost and emission. Further study in this field include the performance evaluation of proposed technique considering the reactive power limit of generators, real and reactive power flow in the transmission lines etc. References 1. H. Sadaat, Power System Analysis, McGraw-Hill Publishing Company Limited. 2. A.J. Wood, B.F. Wollenberg, Power Generation, Operation and Control, John Wiley & sons, Inc. 3. S. P. Karthikeyan, K. Palanisamy, C. Rani, I. J. Raglend, D. P. Kothari, Security Constrained Unit Commitment Problem with Operational Power Flow and Environmental Constraints, WSEAS Transactions on Power Systems, Vol.-4, Issue-2, pp53-66, Feb K. P. Wong, B. Fan, C. S. Chang, A. C. Liew, Multi-objective Generation Dispatch Using Bi-criterion Global Optimisation, IEE 2nd International Conference on Advances in Power System Control, Operation and Management, Hong Kong, pp , D. Srinivasan, C.S. Chang, A.C. Liew, Multi-objective Generation Scheduling Using Fuzzy Optimal Search Technique, IEE Proc.- Genm. Transm. Disrrib. Vol. 141, No. 3, pp , H. Yan, P. B. Luh, A Fuzzy Optimization-Based Method for Integrated Power System Scheduling and Inter-Utility Power Transaction with Uncertainties, IEEE Transactions on Power Systems, Vol. 12, No. 2, pp , May Y.S. Brar, J. S. Dhillon, D.P. Kothari, Multiobjective Load Dispatch By Fuzzy Logic Based Searching Weightage Pattern, Electric Power Systems Research 63, pp , R. K. Pancholi, K.S. Swarup, Particle Swarm Optimization for Economic Dispatch with Line flow and Voltage Constraints, IEEE Conference on Optimal Operation of Power Systems, pp , l-xI01/$l7.Q IEEE 9. M. A. Abido, Environmental/Economic Power Dispatch Using Multi-objective Evolutionary Algorithms, IEEE Transactions on Power Systems, Vol. 18, No. 4, pp , November R. T. F. A. King, H. C. S. Rughooputh, K. Deb, Evolutionary Multi-Objective Environmental/Economic Dispatch: Stochastic vs. Deterministic Approaches, Kanpur GA Lab Report Number Sudhansu Kumar Mishra,Ganapati Panda, Ritanjali Majhi, A Comparative Performance Assessment of a Set of Multiobjective Algorithms for Constrained Portfolio Assets Selection, Swarm and Evolutionary Computing, Elsevier. Vol. 16, January-2014, pp Sudhansu Kumar Mishra,Ganapati Panda, RitanjaliMajhi. Constrained portfolio asset selection using multiobjective bacteria foraging optimization. Operational Research: An International Journal, Springer, Vol.138. DOI /s , 2014,pp Sudhansu Kumar Mishra, Ganapati Panda, Babita Majhi, Ritanjali Majhi, Improved Portfolio Optimization Combining Multiobjective Evolutionary Computing Algorithm and Prediction Strategy IAENG Conferences-World Congress on Engineering (WCE-2012), 4th -6th July, London, U.K, Y.S. Brar, J.S. Dhillon, D.P. Kothari, Multiobjective Load Dispatch Based on Genetic-Fuzzy Technique, IEEE Conf. on PSCE, pp , S. K. Nayak, K.R. Krishnand, B. K. Panigrahi, P. K. Rout, Application of Artificial Bee Colony to Economic Load Dispatch Problem with Ramp Rate Limits and Prohibited Operating Zones IEEE World Congress on Nature & Biologically Inspired Computing, pp , B. Y. Qu, P. N. Suganthan, V. R. Pandi, B. K. Panigrahi, Multi Objective Evolutionary Programming to Solve Environmental Economic Dispatch Problem, 11th Int. Conf. Control, Automation, Robotics and Vision, Singapore, pp , 7-10th December A. Bhattacharya, P.K. Roy, Solution of multi-objective optimal power flow using gravitational search algorithm IET Gener. Transm. Distrib. Vol. 6, Iss. 8, pp , 2012,