Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

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) with non-smooth cost function. 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 three different test systems. 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). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.

[1]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[2]  A. Ebenezer Jeyakumar,et al.  A modified hybrid EP–SQP approach for dynamic dispatch with valve-point effect , 2005 .

[3]  Robert Michael Lewis,et al.  Pattern Search Methods for Linearly Constrained Minimization , 1999, SIAM J. Optim..

[4]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[5]  K.S. Swarup,et al.  Particle swarm optimization for security constrained economic dispatch , 2004, International Conference on Intelligent Sensing and Information Processing, 2004. Proceedings of.

[6]  P. K. Chattopadhyay,et al.  Evolutionary programming techniques for economic load dispatch , 2003, IEEE Trans. Evol. Comput..

[7]  O. SIAMJ.,et al.  ON THE CONVERGENCE OF PATTERN SEARCH ALGORITHMS , 1997 .

[8]  Antti J. Koivo,et al.  Security Evaluation in Power Systems Using Pattern Recognition , 1974 .

[9]  G. Sheblé,et al.  Genetic algorithm solution of economic dispatch with valve point loading , 1993 .

[10]  P. Toint,et al.  A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds , 1991 .

[11]  M. J. Short,et al.  Neural networks approach for solving economic dispatch problem with transmission capacity constraints , 1998 .

[12]  G. Sheblé,et al.  Power generation operation and control — 2nd edition , 1996 .

[13]  Chanan Singh,et al.  ATAVISTIC GENETIC ALGORITHM FOR ECONOMIC DISPATCH WITH VALVE POINT EFFECT , 2002 .

[14]  N. Chen,et al.  Direct Search Method for Solving the Economic Dispatch Problem Considering Transmission Capacity Constraints , 2001, IEEE Power Engineering Review.

[15]  H.K. Youssef,et al.  Power system security with the consideration of economic dispatch , 1994, Proceedings of MELECON '94. Mediterranean Electrotechnical Conference.

[16]  Venansius Baryamureeba,et al.  PROCEEDINGS OF WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY, VOL 8 , 2005 .

[17]  Mohammad Ali Abido,et al.  A neural network-based approach for on-line dynamic stability assessment using synchronizing and damping torque coefficients , 1996 .

[18]  Chao-Lung Chiang,et al.  Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels , 2005 .

[19]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[20]  Mohammad Shahidehpour,et al.  Market operations in electric power systems , 2002 .

[21]  Robert Michael Lewis,et al.  A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds , 2002, SIAM J. Optim..

[22]  Hosam K. M. Youssef,et al.  Genetic based algorithm for security constrained power system economic dispatch , 2000 .

[23]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[24]  V. Torczon,et al.  Direct search methods: then and now , 2000 .

[25]  Rung T. Bui,et al.  Real Power Rescheduling and Security Assessment , 1982, IEEE Transactions on Power Apparatus and Systems.

[26]  A. Ebenezer Jeyakumar,et al.  Hybrid PSO–SQP for economic dispatch with valve-point effect , 2004 .

[27]  Y. W. Wong,et al.  Thermal generator scheduling using hybrid genetic/simulated-annealing approach , 1995 .

[28]  Robert Michael Lewis,et al.  Pattern Search Algorithms for Bound Constrained Minimization , 1999, SIAM J. Optim..