Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 48 (2015 ) 96 100 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-769002 b Assistant Professor, Birla Institute of Technology, Mesra, Ranchi, Jharkhand, India-835215 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. 2014 2015 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 (http://creativecommons.org/licenses/by-nc-nd/4.0/). 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.: +91-9861387789; E-mail address: mishra.sarat@gmail.com 1877-0509 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of scientific committee of International Conference on Computer, Communication and Convergence (ICCC 2015) doi:10.1016/j.procs.2015.04.156
Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) 96 100 97 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
98 Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) 96 100 2. 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. 3.1. 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
Sarat Kumar Mishra and Sudhansu Kumar Mishra / Procedia Computer Science 48 ( 2015 ) 96 100 99 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 1 2 3 4 5 LM 173.1103 47.4434 21.0112 14.2895 11.4834 715.51 GA 174.0566 47.3832 20.8597 13.8621 11.1885 715.3374 Table-II Results of multi-objective EED of IEEE 14 Bus system Fuel cost in 1 2 3 4 5 118.0809 60.2286 15.0001 64.0355 10.0048 743.4491 383.1316 Table-III Comparison of individual and multi-objective results of IEEE 14 Bus system Best Cost Best Emission Best Compromise 715.3374 409.2888 761.2230743.4491 382.3803 743.4491 383.1316 Algorithm used Table-IV Economic Load Dispatch results of IEEE 30 Bus system 1 2 3 4 5 6 Total Fuel Cost in LM 150.4562 42.8299 18.5212 10.0000 30.0000 40.0000 780.26 GA 156.3843 42.4571 17.1883 10.0000 29.5702 36.2501 780.120 7 Table-V Results of multi-objective EED of IEEE 30 bus system Fuel cost in Emission in 1 2 3 4 5 6 137.9911 64.0427 15.0002 18.3284 16.5351 39.9526 793.6054 406.5669 Table-VI Comparison of results of IEEE 30 Bus system Best Cost Best Emission Best Compromise 780.1207 419.2238 798.0949 382.3803 793.6054 406.5667 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
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