Application of Pattern Search Method to Power System Security Constrained Economic Dispatch

Authors: A. K. Al-Othman, K. M. EL-Nagger

Abstract:

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED). Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using one system. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED).

Keywords: Security Constrained Economic Dispatch, Direct Search method, optimization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333462

References:

[1] R. B. Alder, "Security consideration economic dispatch with participation factors," IEEE Transactions on Power Apparatus and Systems, vol. PAS-96, 1977.
[2] R. T. Bui and S. Ghaderpanah, "Real power rescheduling and security assessment," IEEE Transactions on Power Apparatus and Systems, vol. PAS-101, pp. 2906-15, 1982.
[3] M. EL-Sharkawy and D.Nieebur, "Artificial Neural Networks with application to power systems," IEEE Power Engineering Society, A Tutorial course, 1996.
[4] T. Yalcinoz and M. J. Short, "Neural networks approach for solving economic dispatch problem with transmission capacity constraints," IEEE Transactions on Power Systems, vol. 13, pp. 307-13, 1998.
[5] R. K. Pancholi and K. S. Swarup, "Particle swarm optimization for security constrained economic dispatch," presented at International Conference on Intelligent Sensing and Information Processing. (IEEE Cat. No.04EX783), Chennai, India, pp. 7-12, 2004.
[6] H. K. Youssef and K. M. El-Naggar, "Genetic based algorithm for security constrained power system economic dispatch," Electric Power Systems Research, vol. 53, pp. 47-51, 2000.
[7] C. L. Chen and N. Chen, "Direct search method for solving economic dispatch problem considering transmission capacity constraints," IEEE Transactions on Power Systems, vol. 16, pp. 764-769, 2001.
[8] R. Hooke and T. A. Jeeves, "Direct search solution of numerical and statistical problems," Journal of the Association of Computing Machinery, vol. 8, pp. 212-229, 1961.
[9] R. M. Lewis, V. Torczon, and M. W. Trosset, "Direct search methods: then and now," Journal of Computational and Applied Mathematics, vol. 124, pp. 191-207, 2000.
[10] C. K. Pang, F. S. Prabhakara, A.H.Abid, and A. J. Koivo, "Security evaluation in power systems using pattern recognition," IEEE Trans. on Power Apparatus and Systems, pp. 969-976, 1974.
[11] H. mashhadi, "Pattern recognition technique for fast on-line security assessment of large interconnected power systems," IEEE Trans. on Power System, pp. 3816-3824, 1983.
[12] H. K. Youssef, M.El-Shibini, and G.A.Hazaa, "Some new aspects in power system dynamic security using pattern recognition," presented at Second Middle East Power Conference. MEPCON-92, pp. 308-313, 1992.
[13] H. K. Youssef, M. El-Shibini, and G. A. W. Hazza, "Power system security with the consideration of economic dispatch," presented at the Mediterranean Electrotechnical Conference - MELECON, Antalya, Turkey, pp. 889-892, 1994.
[14] R. M. Lewis and V. Torczon, "Pattern search algorithms for linearly constrained minimization," SIAM Journal on Optimization, vol. 10, pp. 917-941, 1999.
[15] R. M. Lewis and V. Torczon, "Pattern search algorithms for bound constrained minimization," SIAM Journal on Optimization, vol. 9, pp. 1082-99, 1999.
[16] R. M. Lewis and V. Torczon, "A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds," SIAM Journal on Optimization, vol. 12, pp. 1075-89, 2001.
[17] V. Torczon, "On the convergence of pattern search algorithms," SIAM Journal on Optimization, vol. 7, pp. 1-25, 1997.
[18] A. R. Conn, N. I. M. Gould, and P. L. Toint., "A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds," SIAM Journal on Numerical Analysis, vol. 28, pp. 545--572, 1991.
[19] E. Abu-Al-Feilat, M. Bettayeb, H. Al-Duwaish, M. Abido, and A. Mantawy, "A neural network-based approach for on-line dynamic stability assessment using synchronizing and damping torque coefficients," Electric Power Systems Research, vol. 39, pp. 103-110, 1996.
[20] D. C. Walters and G. B. Sheble, "Genetic algorithm solution of economic dispatch with valve point loading," Power Systems, IEEE Transactions on, vol. 8, pp. 1325-1332, 1993.
[21] N. Sinha, R. Chakrabarti, and P. K. Chattopadhyay, "Evolutionary programming techniques for economic load dispatch," Evolutionary Computation, IEEE Transactions on, vol. 7, pp. 83-94, 2003.
[22] K. P. Wong and Y. W. Wong, "Thermal generator scheduling using hybrid genetic simulated-annealing," Generation, Transmission and Distribution, IEE Proceedings-, vol. 142, pp. 372-380, 1995.