Solving the Economic Dispatch Problem by Using Differential Evolution

This paper proposes an application of the differential evolution (DE) algorithm for solving the economic dispatch problem (ED). Furthermore, the regenerating population procedure added to the conventional DE in order to improve escaping the local minimum solution. To test performance of DE algorithm, three thermal generating units with valve-point loading effects is used for testing. Moreover, investigating the DE parameters is presented. The simulation results show that the DE algorithm, which had been adjusted parameters, is better convergent time than other optimization methods.

Authors:

• S. Khamsawang
• S. Jiriwibhakorn

Keywords:

• Differential evolution
• Economic dispatch problem
• Valve-point loading effect
• Optimization method.

References:

[1] A.J Wood and B.F. Wollenberg, "Power generation operation and
control", John Wiley and Sons, New York, 1984.
[2] B. H. Chowdhury and S. Rahman, "A review of recent advances in
economic dispatch," IEEE Trans. Power Syst, vol. 5, no. 4, pp. 1248-
1259, 1990.
[3] H.T. Yang, P.C. Yang and C.L. Huang. "Evolutionary programming
based economic dispatch for units with non-smooth fuel cost functions,"
IEEE Trans. Power Syst, vol. 11, no. 1, pp. 112-118, 1996.
[4] A. Immanuel Selvakumar and K. Thanushkodi, "A new particle swarm
optimization solution to nonconvex economic dispatch problem," IEEE
Trans. Power Syst, vol. 22, no. 1, pp. 42-51, 2007.
[5] W.M. Lin, F.S. Cheng and M.T. Tsay, "Improved tabu search for
economic dispatch with multiple minima," IEEE Trans. Power Syst, vol.
17, no. 1, pp. 108-112, 2002.
[6] S. Khamsawang, C. Boonseng ans S. Pothiya, "Solving the economic
dispatch problem with tabu search algorithm," In: Proceeding of the
IEEE International Conference on Industrial Technology 2002,
Bangkok, Thialand, pp. 274-278, 2002.
[7] Wong KP, Wong YW. "Genetic and Genetic/Simulated - Annealing
approaches to economic dispatch," IEE Proc.Gener Transm. Distrib, vol.
141, no. 5, pp. 507-513, 1994.
[8] D.C. Walters and G. B. Sheble "Genetic algorithm solution of economic
dispatch with valve point loading," IEEE Trans. Power Syst, vol. 8, no.
3, 1993.
[9] D. E. Goldberg, Genetic Algorithms in Search, Optimization and
Machine Learning, MA: Addison-Wesley Publishing Company Inc.,
1989.
[10] K.P. Wong 'Solving power system optimization problems using
simulated annealing', Engng Applic. Artif.Intell. vol. 8, no. 6, pp. 665-
670, 1996.
[11] J.S. Al-Sumait, A.K AL-Othman and J.K. Sykulski, "Application of
pattern search method to power system valve-piont economic dispacth",
Int. J. Electr Power Energy Syst (2007),
doi:10.1016/j.ijepes.2007.06.016
[12] N. Sinha, R. Chakrabarti and P.K. Chattopadhyay "Evolutionary
programming techniques for economic load dispatch," IEEE Trans. Evol.
Comput, vol. 7, no. 1, pp. 83-94, 2003.
[13] R. Storn and K.V. Price, "Differential evolution a simple and efficient
heuristic for global optimization over continuous space," J. Global
Optim, vol. 11, no. 4, pp. 341-359, 1997.
[14] K.V. Price, R.M. Storn, J.A. Lampinen, "Differential evolution; A
practical approach to global optimization," Springer Berlin, Heidelberg,
2005.
[15] R. Storn, "System design by constraint adaptation and differential
evolution," IEEE Trans. Evol. Comput, vol. 3, no. 1, pp. 22-34, 1999.
[16] D.T. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S. Rahim and M. Zaidi.
"The bees algorithm, a novel tool for complex optimisation problems".
Proc 2nd Int Virtual Conf. Intelligent Prod. Mach. and Syst, Oxford,
Elsevier, pp.454-459, 2006.
[17] J.F. Kenedy and R.C. Eberhart, "particle swarm optimization," In: Proc
IEEE international conference on neural networks, vol. 4, pp. 1942-
1948, 1995.
[18] M. Clerc and J.K. Kenedy, "The particle swarm: Explosion, stability and
convergence in a multi - dimensional complex space," IEEE Trans. Evol.
Comput, vol. 2, no. 3, pp. 91-96, 1998.