A penalty function for reactive power optimization with discrete variables

In this paper, a penalty based model for solving the Reactive Power Optimization (RPO) problem formulated as a Nonlinear Programming (NLP) problem with continuous and discrete variables is proposed. The discrete control variables of the RPO problem are treated as continuous variables and solved with the aid of a penalty polynomial function. The resulting problem is an NLP problem with only continuous variables which solution is equivalent to the solution of the original problem. Efficiency and robustness of the proposed approach have been checked with IEEE 14, 30, 57, 118 and 300-bus test systems. The test results show the viability of the method with good solutions and it successfully attains discrete values for the original discrete variables.