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The standard way to solve the static economic dispatch problem with transmission losses is the penalty factor method. The problem is solved iteratively by a Lagrange multiplier method or by dynamic programming, using values obtained at one iteration to compute penalty factors for the next until stability is attained. A new iterative method is proposed for the case where transmission losses are represented by a quadratic formula (i.e., by the traditional B-coefficients). | Yugoslav Journal of Operations Research 12 (2002), Number 2, 157-166 A SEPARABLE APPROXIMATION DYNAMIC PROGRAMMING ALGORITHM FOR ECONOMIC DISPATCH WITH TRANSMISSION LOSSES Pierre HANSEN, Nenad MLADENOVI] GERAD and Ecole des Hautes Etudes Commerciales Montr›al (Qu›bec), Canada Abstract: The standard way to solve the static economic dispatch problem with transmission losses is the penalty factor method. The problem is solved iteratively by a Lagrange multiplier method or by dynamic programming, using values obtained at one iteration to compute penalty factors for the next until stability is attained. A new iterative method is proposed for the case where transmission losses are represented by a quadratic formula (i.e., by the traditional B-coefficients). A separable approximation is made at each iteration, which is much closer to the initial problem than the penalty factor approximation. Consequently, lower cost solutions may be obtained in some cases, and convergence is faster. Keywords: Economic dispatch, transmission losses, B-coefficients, penalty factors, separable approximation, dynamic programming. 1. INTRODUCTION Due to the enormous costs involved, optimizing the use of equipment for power generation and transmission is a lasting concern. Given several thermal or hydro units, often with different characteristics, one must decide how to distribute the load considered between them. This problem, called economic dispatch, has been much studied, both in the static and dynamic cases. It is discussed at length in the book of Wood and Wollenberg [6] Power generation, operation and control, an enlarged second edition of which has recently appeared. The standard way to solve the static case with transmission losses is the penalty factor method. The problem is solved iteratively by a Lagrangian multiplier method or by dynamic programming, using values obtained at one iteration to compute penalty factors for the next until stability is attained. 158 P. Hansen, N. .
