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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). 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

A separable approximation dynamic programming algorithm for economic dispatch with transmission losses