A Robust Penalty-Based Approach to Optimal Reactive Power Dispatch With Discrete Controls

The efficient handling of a significant number of discrete variables in large mixed integer non-linear programming (MINLP) problems is challenging due to the combinatorial explosion. This paper proposes a novel tailored approximation approach to handle discrete control variables in the scope of the specific MINLP problem of optimal reactive power dispatch, that targets maximizing generators' reactive power reserves, in the AC security-constrained optimal power flow (SCOPF) framework. The two key features of the proposed approach are: (i) convert discrete variables to a binary format to reduce the combinatorial space, and (ii) approximate binary variables with continuous ones using a nonlinear square penalized Fischer-Burmeister function, smoothening in the objective function the nonlinear complementarity constraints which model binary variables. The benefits and computational requirements of the outlined approach have been evaluated on a 60-node model of the Nordic32 system.