An NLP penalty-based strategy for handling discrete controls for Volt/Var optimization in distribution systems

This paper proposes a nonlinear programming (NLP) penalty-based strategy for solving the Volt/Var optimization (VVO) problem in distribution systems, formulated in a mixed integer nonlinear programming (MINLP) form. The VVO consists, basically, in determining the settings of the control variables of switched capacitor banks and on-load tap changer (OLTC) transformers located at substations to minimize daily energy losses. For this, the original problem is modified as a multi-period NLP problem with continuous and discrete variables. In the proposed approach, for solving such a problem, the discrete variables are considered as continuous in the modified problem. Numerical tests with 69 and 135-bus distribution systems were carried out in this study. Then, the obtained results were compared with the ones obtained from the continuous relaxation of the original problem and the rounded-off solutions. This strategy applied to the resolution of the VVO problem provides good feasible solutions for the original MINLP problem.