Application of Soft Computing Methods for Economic Dispatch in Power Systems
Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.
[1] B. H. Chowdhury and S. Rahman, "A review of recent advances in
economic dispatch," IEEE Trans. Power Systems, vol. 5, no. 4, pp. 1248-
1259, Nov. 1990.
[2] A. J. Wood and B. F. Wollenberg, Power generation operation and
control, 2nd ed. John Willy and Sons, 1996.
[3] A. I. Selvakumar and K. Thanushkodi, "A new particle swarm optimization
solution to nonconvex economic dispatch problems," IEEE Trans.
Power Systems, vol. 22, no. 1, pp. 42-51, Feb. 2007.
[4] M. A. Abido, "A novel multiobjective evolutionary algorithm for environmental
economic power dispatch," Electric Power Systems Research,
vol. 65, no. 1, pp. 71-81, April 2003.
[5] K. P. Wong and Y. W. Wong, "Genetic and genetic/simulated -annealing
approaches to economic dispatch," Proc. Inst. Elect. Eng., Gen., Transm.,
Distrib., vol. 141, no. 5, pp. 507-513, Sept. 1994.
[6] N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, "Evolutionary
programming techniques for economic load dispatch," IEEE Trans.
Evolutionary Computations, vol. 7, no. 1, pp. 83-94, Feb. 2003.
[7] W. M. Lin, F. S. Cheng, and M. T. Tsay, "An improved tabu search for
economic dispatch with multiple minima," IEEE Trans. Power Systems,
vol. 7, no. 1, pp. 83-94, Feb. 2003.
[8] J. Cai, X. Ma, L. Li, Y. Yang, H. Peng, and X. Wang, "Chaotic ant swarm
optimization to economic dispatch," Electric Power System Research,
vol. 77, no. 10, pp. 1373-1380, Aug. 2007.
[9] J. B. Park, K. Lee, J. Shin, and K. Y. Lee, "A particle swarm optimization
for economic dispatch with nonsmooth cost functions," IEEE Trans.
Power Systems, vol. 20, no. 1, pp. 34-42, Feb. 2005.
[10] Z. Gaing, "Particle swarm optimization to solving the economic dispatch
considering the generator constraints," IEEE Trans. Power Systems,
vol. 18, no. 3, pp. 1187-1195, Aug. 2003.
[11] D. N. Jeyakumar, T. Jayabarathi, and T. Raghunathan, "Particle swarm
optimization for various types of economic dispatch problems," Int. J
Electr. Power and Energy system, vol. 28, no. 1, pp. 36-42, Jan. 2006.
[12] M. R. Alrashidi and M. E. El-Hawary, "A survey of particle swarm
optimization applications in power system operations," Electric Power
Components and Systems, vol. 34, no. 12, pp. 1349 - 1357, Dec. 2006.
[13] D. Goldberg and K. Deb, A Comparative Analysis of Selection Schemes
Used in Genetic Algorithms. Morgan Kaufmann, San Mateo, California,
1991, ch. Foundations of Genetic Algorithms, pp. 69-93.
[14] W. M. Spears and K. A. De Jong, "On the virtues of parameterized uniform
crossover," in Proceedings of the Fourth International Conference
on Genetic Algorithms, R. K. Belew and L. B. Booker, Eds., Morgan
Kaufmann, 1991.
[15] F. Herrera, M. Lozano, and J. L. Verdegay, "Tackling realcoded genetic
algorithms:operators and tools for behavioural analysis," Artificial Intelligence
Review, vol. 12, no. 4, pp. 265-319, 1998.
[16] D. E. Goldberg, "Realcoded genetic algorithms, virtual alphabets, and
blocking," Complex Systems, vol. 5, pp. 139-167, 1991.
[17] J. Kennedy and R. Eberhart, "Particle swarm optimization," in Proc.
IEEE Intl. Conf. on Neural Networks, Perth, Australia, 1995, pp. 1942-
1948.
[18] Y. Shi and R. Eberhart, "Parameter selection in particle swarm optimization,"
in Proceedings of 7th Annual Conference on Evolution
Computation, 1998, pp. 591-601.
[19] J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence. Morgan
Kaufmann,San Francisco, 2001.
[20] K. M. Passino, "Biomimicry of bacterial foraging for distributed optimization
and contro," IEEE. Control System Magazine, pp. 52-67, June
2002.
[21] M. Dorigo, "Optimization, learning and natural algorithms," Ph.D.
dissertation, Dipartimento di Elettronica, Politecnico di Milano, IT, 92.
[22] A. Colorni, M. Dorigo, and V. Maniezzo, "Distributed optimization by
ant colonies," in proc. of the First European Conf. on Artificial Life.
Elsevier Science, 92, pp. 134-142.
[23] M. Dorigo, V. Maniezzo, and A. Colorni, "The ant system:optimization
by a colony of cooperating agents," IEEE Trans. System, Man, and
Cybernetics-Part B, vol. 26, no. 1, pp. 1-13, Feb. 1996.
[24] L. M. Gambardella and M. Dorigo, "An ant colony system hybridized
with a new local search for the sequential ordering problem," INFORMS
Journal on Computing, vol. 12, no. 3, pp. 237-255, July 2000.
[25] S. Kamali and J. Opatrny, "Posant: A position based ant colony routing
algorithm for mobile ad-hoc networks," in Proc. Third International
Conference on Wireless and Mobile Communications,ICWMC 07, March
2007.
[26] L. Chen, J. Shen, L. Qin, and J. Fan, A Method for Solving Optimization
Problem in Continuous Space Using Improved Ant Colony Algorithm,
Y. Shi, W. Xu, and Z. Chen, Eds. Springer Berlin / Heidelberg, 2004,
vol. 3327/2005.
[27] M. Kong and P. Tian, Ant Colony Optimization and Swarm Intelligence.
Springer-Verlag, 2006, vol. 4150/2006, ch. A Direct Application of Ant
Colony Optimization to Function Optimization Problem in Continuous
Domain, pp. 324-331.
[28] K. Socha and M. Dorigo, "Ant colony optimization for continuous
domains," 2006, article in press: Eur. J. Oper. Res.
[29] M. Dorigo, M. Birattari, and T. Stutzle, "Ant colony optimization
artificial ants as a computational intelligence technique," IEEE COMPUTATIONAL
INTELLIGENCE MAGAZINE, pp. 28-39, 2006.
[30] http://www.ee.washington.edu/research/pstca/.
[31] O. Alsac and B. Stott, "Optimal load flow with steady-state security,"
IEEE Trans. Power Apparatus Systems, vol. PAS-93, no. 3, pp. 745-751,
May 1974.
[32] http://www.pserc.cornell.edu/matpower/.
[33] J. Hazra and A. K. Sinha, "Congestion management using multi objective
particle swarm optimization," IEEE Trans. Power Systems, vol. 22,
no. 4, pp. 1726-1734, Nov. 2007.
[34] Y. Liu and K. M. Passino, "Biomimicry of social foraging bacteria for
distributed optimization: Models,principles, and emergent behaviors1,"
Journal of Optimization Theory and Applications, vol. 115, no. 3, pp.
603-628, Dec. 2002.
[1] B. H. Chowdhury and S. Rahman, "A review of recent advances in
economic dispatch," IEEE Trans. Power Systems, vol. 5, no. 4, pp. 1248-
1259, Nov. 1990.
[2] A. J. Wood and B. F. Wollenberg, Power generation operation and
control, 2nd ed. John Willy and Sons, 1996.
[3] A. I. Selvakumar and K. Thanushkodi, "A new particle swarm optimization
solution to nonconvex economic dispatch problems," IEEE Trans.
Power Systems, vol. 22, no. 1, pp. 42-51, Feb. 2007.
[4] M. A. Abido, "A novel multiobjective evolutionary algorithm for environmental
economic power dispatch," Electric Power Systems Research,
vol. 65, no. 1, pp. 71-81, April 2003.
[5] K. P. Wong and Y. W. Wong, "Genetic and genetic/simulated -annealing
approaches to economic dispatch," Proc. Inst. Elect. Eng., Gen., Transm.,
Distrib., vol. 141, no. 5, pp. 507-513, Sept. 1994.
[6] N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, "Evolutionary
programming techniques for economic load dispatch," IEEE Trans.
Evolutionary Computations, vol. 7, no. 1, pp. 83-94, Feb. 2003.
[7] W. M. Lin, F. S. Cheng, and M. T. Tsay, "An improved tabu search for
economic dispatch with multiple minima," IEEE Trans. Power Systems,
vol. 7, no. 1, pp. 83-94, Feb. 2003.
[8] J. Cai, X. Ma, L. Li, Y. Yang, H. Peng, and X. Wang, "Chaotic ant swarm
optimization to economic dispatch," Electric Power System Research,
vol. 77, no. 10, pp. 1373-1380, Aug. 2007.
[9] J. B. Park, K. Lee, J. Shin, and K. Y. Lee, "A particle swarm optimization
for economic dispatch with nonsmooth cost functions," IEEE Trans.
Power Systems, vol. 20, no. 1, pp. 34-42, Feb. 2005.
[10] Z. Gaing, "Particle swarm optimization to solving the economic dispatch
considering the generator constraints," IEEE Trans. Power Systems,
vol. 18, no. 3, pp. 1187-1195, Aug. 2003.
[11] D. N. Jeyakumar, T. Jayabarathi, and T. Raghunathan, "Particle swarm
optimization for various types of economic dispatch problems," Int. J
Electr. Power and Energy system, vol. 28, no. 1, pp. 36-42, Jan. 2006.
[12] M. R. Alrashidi and M. E. El-Hawary, "A survey of particle swarm
optimization applications in power system operations," Electric Power
Components and Systems, vol. 34, no. 12, pp. 1349 - 1357, Dec. 2006.
[13] D. Goldberg and K. Deb, A Comparative Analysis of Selection Schemes
Used in Genetic Algorithms. Morgan Kaufmann, San Mateo, California,
1991, ch. Foundations of Genetic Algorithms, pp. 69-93.
[14] W. M. Spears and K. A. De Jong, "On the virtues of parameterized uniform
crossover," in Proceedings of the Fourth International Conference
on Genetic Algorithms, R. K. Belew and L. B. Booker, Eds., Morgan
Kaufmann, 1991.
[15] F. Herrera, M. Lozano, and J. L. Verdegay, "Tackling realcoded genetic
algorithms:operators and tools for behavioural analysis," Artificial Intelligence
Review, vol. 12, no. 4, pp. 265-319, 1998.
[16] D. E. Goldberg, "Realcoded genetic algorithms, virtual alphabets, and
blocking," Complex Systems, vol. 5, pp. 139-167, 1991.
[17] J. Kennedy and R. Eberhart, "Particle swarm optimization," in Proc.
IEEE Intl. Conf. on Neural Networks, Perth, Australia, 1995, pp. 1942-
1948.
[18] Y. Shi and R. Eberhart, "Parameter selection in particle swarm optimization,"
in Proceedings of 7th Annual Conference on Evolution
Computation, 1998, pp. 591-601.
[19] J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence. Morgan
Kaufmann,San Francisco, 2001.
[20] K. M. Passino, "Biomimicry of bacterial foraging for distributed optimization
and contro," IEEE. Control System Magazine, pp. 52-67, June
2002.
[21] M. Dorigo, "Optimization, learning and natural algorithms," Ph.D.
dissertation, Dipartimento di Elettronica, Politecnico di Milano, IT, 92.
[22] A. Colorni, M. Dorigo, and V. Maniezzo, "Distributed optimization by
ant colonies," in proc. of the First European Conf. on Artificial Life.
Elsevier Science, 92, pp. 134-142.
[23] M. Dorigo, V. Maniezzo, and A. Colorni, "The ant system:optimization
by a colony of cooperating agents," IEEE Trans. System, Man, and
Cybernetics-Part B, vol. 26, no. 1, pp. 1-13, Feb. 1996.
[24] L. M. Gambardella and M. Dorigo, "An ant colony system hybridized
with a new local search for the sequential ordering problem," INFORMS
Journal on Computing, vol. 12, no. 3, pp. 237-255, July 2000.
[25] S. Kamali and J. Opatrny, "Posant: A position based ant colony routing
algorithm for mobile ad-hoc networks," in Proc. Third International
Conference on Wireless and Mobile Communications,ICWMC 07, March
2007.
[26] L. Chen, J. Shen, L. Qin, and J. Fan, A Method for Solving Optimization
Problem in Continuous Space Using Improved Ant Colony Algorithm,
Y. Shi, W. Xu, and Z. Chen, Eds. Springer Berlin / Heidelberg, 2004,
vol. 3327/2005.
[27] M. Kong and P. Tian, Ant Colony Optimization and Swarm Intelligence.
Springer-Verlag, 2006, vol. 4150/2006, ch. A Direct Application of Ant
Colony Optimization to Function Optimization Problem in Continuous
Domain, pp. 324-331.
[28] K. Socha and M. Dorigo, "Ant colony optimization for continuous
domains," 2006, article in press: Eur. J. Oper. Res.
[29] M. Dorigo, M. Birattari, and T. Stutzle, "Ant colony optimization
artificial ants as a computational intelligence technique," IEEE COMPUTATIONAL
INTELLIGENCE MAGAZINE, pp. 28-39, 2006.
[30] http://www.ee.washington.edu/research/pstca/.
[31] O. Alsac and B. Stott, "Optimal load flow with steady-state security,"
IEEE Trans. Power Apparatus Systems, vol. PAS-93, no. 3, pp. 745-751,
May 1974.
[32] http://www.pserc.cornell.edu/matpower/.
[33] J. Hazra and A. K. Sinha, "Congestion management using multi objective
particle swarm optimization," IEEE Trans. Power Systems, vol. 22,
no. 4, pp. 1726-1734, Nov. 2007.
[34] Y. Liu and K. M. Passino, "Biomimicry of social foraging bacteria for
distributed optimization: Models,principles, and emergent behaviors1,"
Journal of Optimization Theory and Applications, vol. 115, no. 3, pp.
603-628, Dec. 2002.
@article{"International Journal of Electrical, Electronic and Communication Sciences:54596", author = "Jagabondhu Hazra and Avinash Sinha", title = "Application of Soft Computing Methods for Economic Dispatch in Power Systems", abstract = "Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.
", keywords = "Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.", volume = "3", number = "4", pages = "706-6", }
