Solving control-constrained reactive power dispatch with discrete variables

This paper describes the resolution of the optimal reactive dispatch (ORD) problem with respect to voltage magnitudes and taps of on-load tap changing (OLTC) transformers. Although the ORD consists in a large-scale mixed integer nonlinear programming (MINLP) problem due to the discrete nature of some system controls, most papers in technical journals disregard the discrete modeling of such variables. Moreover, from a practical point of view, a trade-off between attaining the optimum of an objective function, satisfying operational constraints and reducing the number of control adjustments is desirable. In this context, this paper is concerned with handling power system discrete control variables by a polynomial discretization function while binary variables associated with limited control adjustments are handled by sigmoid activation function. The polynomial discretization function actually allows considering discrete variables as continuous in a modified problem, and a rule based process with sigmoid function is used for defining the binary variables. Numerical tests with IEEE benchmark test-systems with up to 300 buses are carried out in this study. Results show that the proposed methodology for solving MINLP problems such as the ORD successfully handles discrete control variables while providing a more practical solution for system operators.