The optimal reactive dispatch problem with discrete control variables and limited control adjustments

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 limiting the number of controls allowed to change. This approach actually allows considering discrete variables as continuous in a modified problem, and, at the same time, providing a smaller number of control adjustments to implement over a time period. Numerical tests with IEEE benchmark test-systems with up to 300 buses are carried out in this study, and the 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.