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The general problem of minimizing the operating cost of a power system by proper selection of the active and reactive productions is formulated as a nonlinear programming problem in accordance with previous work by Carpentier of Electricitéde France. This general problem is particularized to the minimization of transmission line losses by suitable selection of the reactive productions and transformer tap settings. An efficient computational procedure based on the Newton-Raphson method for solving the power-flow equations and on the dual (Lagrangian) variables of the Kuhn and Tucker theorem is discussed. This minimization procedure has been applied successfully to a 500-node system studied by the Bonneville Power Administration for which an effective power-flow program had been developed previously. The dual variables associated with the primary (electrical) variables are obtained in the course of the computation, and their engineering significance for power system design and tariffication is emphasized. The procedure has been extended to the general case of combined active and reactive optimization.
Peschon et al. (Mon,) studied this question.