SOLUTION OF ECONOMIC DISPATCH PROBLEM USING POLAR BEAR OPTIMIZATION ALGORITHM
DOI:
https://doi.org/10.4314/jfas.v11i2.1Keywords:
Polar Bear Optimization algorithm (PBO); Economic Dispatch of Electrical Power (EDEP); meta-heuristic; population based algorithms.Abstract
Polar Bear optimization (PBO) algorithm is a newly developed meta-heuristic optimization algorithm that is inspired by the hunting behavior of polar bears in nature. PBO is a population based algorithm that combines three distinct features of optimization strategies to create a unique solution namely local search, global search and dynamic population. In this paper PBO algorithm is applied to solve economic dispatch problem of electrical power for both convex and non-convex systems. The proposed technique is tested on four IEEE benchmarks systems and the results obtained are compared with other techniques available in literature. Comparison of results obtained proved its success in reducing cost and computation time as compared to other techniques.
Downloads
Download data is not yet available.
References
[1] El-Keib, A. A., Ma, H., & Hart, J. L. (1994). Environmentally constrained economic dispatch using the LaGrangian relaxation method. IEEE Transactions on Power Systems.1994 ;9 (4):1723 - 1729 .
[2] Fan, J. Y., & Zhang, L. Real-time economic dispatch with line flow and emission constraints using quadratic programming. IEEE Transactions on Power Systems. 1998; 13 (2):320-325
[3] Chen, C. L., & Wang, S. C. Branch-and-bound scheduling for thermal generating units. IEEE Transactions on Energy Conversion.1993; 8 (2): 184 - 189.
[4] Aravindhababu, P., & Nayar, K. R. Economic dispatch based on optimal lambda using radial basis function network. International Journal of Electrical Power & Energy Systems.2002 ; 24 (7): 551-556.
[5] Dodu, J. C., Martin, P., Merlin, A., & Pouget, J. An optimal formulation and solution of short-range operating problems for a power system with flow constraints. Proceedings of the IEEE. 1972 ; 60 (1): 54 - 63 .
[6] Parikh, J., & Chattopadhyay , D. A multi-area linear programming approach for analysis of economic operation of the Indian power system. IEEE Transactions on Power Systems.1996; 11 (1): 52 - 58.
[7] Nanda, J., Hari, L., & Kothari, M. L. Economic emission load dispatch with line flow constraints using a classical technique. IEE Proceedings - Generation, Transmission and Distribution. 1994; 141 (1): 1-10.
[8] Liang, Z. -X., & Glover, J. D. A zoom feature for a dynamic programming solution to economic dispatch including transmission losses. IEEE Transactions on Power Systems 1992; 7 (2): 544 - 550.
[9] Holland, J. H. Genetic Algorithms. Scientific American.1992;Vol. 267 (1): 66-73.
[10] Toksari, M. D. Ant colony optimization for finding the global minimum. Applied Mathematics and Computation.2005;176 (1):308-316.
[11] Price, K., Storm, R. M., & Lampinen, J. A. Differential Evolution: A Practical Approach to Global Optimization. Springer Science & Business Media 2006..
[12] Karaboga, D., & Basturk, B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization. 2007;39 (3):459–471.
[13] Eberhart , R., & Kennedy, J. A new optimizer using particle swarm theory. Proceedings of the Sixth International Symposium in Micro Machine and Human Science. Nagoya, Japan. Oct 1995;39-43
[14] Yang , X.-S., & Deb, S. Cuckoo Search via Lévy flights. Nature & Biologically Inspired Computing, . Coimbatore, India. Dec 2009
[15] Yang, X.-S. Firefly Algorithm, Lévy Flights and Global Optimization. Research and Development in Intelligent Systems XXVI. Springer,. London. Oct 2009.
[16] F.Merrikh-Bayat. The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature. Applied Soft Computing. Aug 2015; 33: 292-303.
[17] Mirjalili, S. The Ant Lion Optimizer. Advances in Engineering Software. 2015; 89:80-98.
[18] Mirjalili, S. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems. 2015; 89: 228-249.
[19] Rashedi, E., Nezamabadi-pour, H., & Saryazdi, S. GSA: A Gravitational Search Algorithm. Information Sciences.2009;179 (13):2232-2248.
[20] Hatamlou, A. Black hole: A new heuristic optimization approach for data clustering. Information Sciences.2013; 222: 175-184.
[21] Rao, R. V. Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations.2016; 7 (1): 19-34.
[22] Yang, X.-S. A New Metaheuristic Bat-Inspired Algorithm. In P. D. González J.R., Nature Inspired Cooperative Strategies for Optimization (NICSO). Studies in Computational Intelligence, Springer.2010;284.
[23] Gandomi, A. H., & Alavi, A. H. Krill herd: A new bio-inspired optimization algorithm. Communications in Nonlinear Science and Numerical Simulation.2012;17 (12): 4831-4845.
[24] Mirjalili, S., & Lewis, A. The Whale Optimization Algorithm. Advances in Engineering SoftwareAdvances in Engineering Software.2016; 95: 51-67.
[25] Serani, A., & Diez, M. Dolphin Pod Optimization. In G. P. Nicosia (Ed.), Machine Learning, Optimization, and Big Data, MOD 2107. 10710. Volterra, Italy,Springer. Sep 2017.
[26] Cochocki , A., & Unbehauen , R. Neural Networks for Optimization and Signal Processing. New York, NY, USA: John Wiley & Sons, Inc. 1993
[27] Uymaz, S. A., Tezel, G., & Yel, E. Artificial algae algorithm (AAA) for nonlinear global optimization. Applied Soft Computing.2015;31:153-171.
[28] Mirjalili, S., Mirjalili, S. M., & Lewis, A. Grey Wolf Optimizer. Advances in Engineering Software.2014; 69: 46-61.
[29] Polap, D., & Wozniak, M. Polar Bear Optimization Algorithm: Meta-Heuristic with Fast Population Movement and Dynamic Birth and Death Mechanism. . Symmetry.2017; 203-223.
[30] Wood, , A. j., & Wollenberg, B. F. Power Generation, Operation, and Control. New York: Wiley.1996
[31] Kamboj, V. K., BathJ. , S. K., & Dhillon, S. Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer. Neural Computing and Applications.2016; 27 (5): 1301–1316.
[32] Kamboj, V. K., Bhadoria, A., & Bath, S. Solution of non-convex economic load dispatch problem for small-scale power systems using ant lion optimizer. Neural Computing and Applications.2017; 28.(8): 2181-2192.
[33] Bestha, M., Reddy, K. H., & Hemakeshav, O. Economic Load Dispatch Downside with Valve - Point Result Employing a Binary Bat Formula. International Journal of Electrical and Computer Engineering.2014; 4 (1):101-107.
[34] Mallikarjuna, B., Reddy, K. H., & Hemakesha, O. Economic Load Dispatch with Valve - Point Result Employing a Binary Bat Formula. International Journal of Electrical and Computer Engineering (IJECE).2014; 4 (1): 101-107.
[35] Pothiya , S., Ngamroo , I., & Kongprawechnon, W. Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints. Energy Conversion and Management.2008; 49:506-516.
[36] Adarsh , B. R., Raghunathan, T., Jayabarathi , T., & Yang , X.-S. Economic dispatch using chaotic bat algorithm. Energy.2016; 96: 666-675.
[37] Saka, M., Eke, I., Tezcan, S. S., & Taplamacioglu, M. C. Economic Load Dispatch Using Vortex Search Algorithm. 4th International Conference on Electrical and Electronics Engineering. Ankara, Turkey. 2017
[38] Secu, D. C. A new modified artificial bee colony algorithm for the economic dispatch problem. Energy Conversion and Management.2015;89: 43-62.
[39] Chaturvedi, K. T., Pandit, M., & Srivastava, L. Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch. IEEE Transactions on Power Systems.2008; 23 (3): 1079-1087.
[2] Fan, J. Y., & Zhang, L. Real-time economic dispatch with line flow and emission constraints using quadratic programming. IEEE Transactions on Power Systems. 1998; 13 (2):320-325
[3] Chen, C. L., & Wang, S. C. Branch-and-bound scheduling for thermal generating units. IEEE Transactions on Energy Conversion.1993; 8 (2): 184 - 189.
[4] Aravindhababu, P., & Nayar, K. R. Economic dispatch based on optimal lambda using radial basis function network. International Journal of Electrical Power & Energy Systems.2002 ; 24 (7): 551-556.
[5] Dodu, J. C., Martin, P., Merlin, A., & Pouget, J. An optimal formulation and solution of short-range operating problems for a power system with flow constraints. Proceedings of the IEEE. 1972 ; 60 (1): 54 - 63 .
[6] Parikh, J., & Chattopadhyay , D. A multi-area linear programming approach for analysis of economic operation of the Indian power system. IEEE Transactions on Power Systems.1996; 11 (1): 52 - 58.
[7] Nanda, J., Hari, L., & Kothari, M. L. Economic emission load dispatch with line flow constraints using a classical technique. IEE Proceedings - Generation, Transmission and Distribution. 1994; 141 (1): 1-10.
[8] Liang, Z. -X., & Glover, J. D. A zoom feature for a dynamic programming solution to economic dispatch including transmission losses. IEEE Transactions on Power Systems 1992; 7 (2): 544 - 550.
[9] Holland, J. H. Genetic Algorithms. Scientific American.1992;Vol. 267 (1): 66-73.
[10] Toksari, M. D. Ant colony optimization for finding the global minimum. Applied Mathematics and Computation.2005;176 (1):308-316.
[11] Price, K., Storm, R. M., & Lampinen, J. A. Differential Evolution: A Practical Approach to Global Optimization. Springer Science & Business Media 2006..
[12] Karaboga, D., & Basturk, B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization. 2007;39 (3):459–471.
[13] Eberhart , R., & Kennedy, J. A new optimizer using particle swarm theory. Proceedings of the Sixth International Symposium in Micro Machine and Human Science. Nagoya, Japan. Oct 1995;39-43
[14] Yang , X.-S., & Deb, S. Cuckoo Search via Lévy flights. Nature & Biologically Inspired Computing, . Coimbatore, India. Dec 2009
[15] Yang, X.-S. Firefly Algorithm, Lévy Flights and Global Optimization. Research and Development in Intelligent Systems XXVI. Springer,. London. Oct 2009.
[16] F.Merrikh-Bayat. The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature. Applied Soft Computing. Aug 2015; 33: 292-303.
[17] Mirjalili, S. The Ant Lion Optimizer. Advances in Engineering Software. 2015; 89:80-98.
[18] Mirjalili, S. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems. 2015; 89: 228-249.
[19] Rashedi, E., Nezamabadi-pour, H., & Saryazdi, S. GSA: A Gravitational Search Algorithm. Information Sciences.2009;179 (13):2232-2248.
[20] Hatamlou, A. Black hole: A new heuristic optimization approach for data clustering. Information Sciences.2013; 222: 175-184.
[21] Rao, R. V. Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations.2016; 7 (1): 19-34.
[22] Yang, X.-S. A New Metaheuristic Bat-Inspired Algorithm. In P. D. González J.R., Nature Inspired Cooperative Strategies for Optimization (NICSO). Studies in Computational Intelligence, Springer.2010;284.
[23] Gandomi, A. H., & Alavi, A. H. Krill herd: A new bio-inspired optimization algorithm. Communications in Nonlinear Science and Numerical Simulation.2012;17 (12): 4831-4845.
[24] Mirjalili, S., & Lewis, A. The Whale Optimization Algorithm. Advances in Engineering SoftwareAdvances in Engineering Software.2016; 95: 51-67.
[25] Serani, A., & Diez, M. Dolphin Pod Optimization. In G. P. Nicosia (Ed.), Machine Learning, Optimization, and Big Data, MOD 2107. 10710. Volterra, Italy,Springer. Sep 2017.
[26] Cochocki , A., & Unbehauen , R. Neural Networks for Optimization and Signal Processing. New York, NY, USA: John Wiley & Sons, Inc. 1993
[27] Uymaz, S. A., Tezel, G., & Yel, E. Artificial algae algorithm (AAA) for nonlinear global optimization. Applied Soft Computing.2015;31:153-171.
[28] Mirjalili, S., Mirjalili, S. M., & Lewis, A. Grey Wolf Optimizer. Advances in Engineering Software.2014; 69: 46-61.
[29] Polap, D., & Wozniak, M. Polar Bear Optimization Algorithm: Meta-Heuristic with Fast Population Movement and Dynamic Birth and Death Mechanism. . Symmetry.2017; 203-223.
[30] Wood, , A. j., & Wollenberg, B. F. Power Generation, Operation, and Control. New York: Wiley.1996
[31] Kamboj, V. K., BathJ. , S. K., & Dhillon, S. Solution of non-convex economic load dispatch problem using Grey Wolf Optimizer. Neural Computing and Applications.2016; 27 (5): 1301–1316.
[32] Kamboj, V. K., Bhadoria, A., & Bath, S. Solution of non-convex economic load dispatch problem for small-scale power systems using ant lion optimizer. Neural Computing and Applications.2017; 28.(8): 2181-2192.
[33] Bestha, M., Reddy, K. H., & Hemakeshav, O. Economic Load Dispatch Downside with Valve - Point Result Employing a Binary Bat Formula. International Journal of Electrical and Computer Engineering.2014; 4 (1):101-107.
[34] Mallikarjuna, B., Reddy, K. H., & Hemakesha, O. Economic Load Dispatch with Valve - Point Result Employing a Binary Bat Formula. International Journal of Electrical and Computer Engineering (IJECE).2014; 4 (1): 101-107.
[35] Pothiya , S., Ngamroo , I., & Kongprawechnon, W. Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints. Energy Conversion and Management.2008; 49:506-516.
[36] Adarsh , B. R., Raghunathan, T., Jayabarathi , T., & Yang , X.-S. Economic dispatch using chaotic bat algorithm. Energy.2016; 96: 666-675.
[37] Saka, M., Eke, I., Tezcan, S. S., & Taplamacioglu, M. C. Economic Load Dispatch Using Vortex Search Algorithm. 4th International Conference on Electrical and Electronics Engineering. Ankara, Turkey. 2017
[38] Secu, D. C. A new modified artificial bee colony algorithm for the economic dispatch problem. Energy Conversion and Management.2015;89: 43-62.
[39] Chaturvedi, K. T., Pandit, M., & Srivastava, L. Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch. IEEE Transactions on Power Systems.2008; 23 (3): 1079-1087.
Downloads
Published
2019-03-04
How to Cite
FAYYAZ, S.; AHMAD, A.; BABAR, M. I. SOLUTION OF ECONOMIC DISPATCH PROBLEM USING POLAR BEAR OPTIMIZATION ALGORITHM. Journal of Fundamental and Applied Sciences, [S. l.], v. 11, n. 2, p. 562–577, 2019. DOI: 10.4314/jfas.v11i2.1. Disponível em: https://jfas.info/index.php/JFAS/article/view/261. Acesso em: 30 jan. 2025.
Issue
Section
Articles
Submissions
