Outer-approximation method for security constrained unit commitment

In this study, the authors present an outer-approximation method to solve the mixed-integer non-linear security constrained unit commitment problem. The main idea lies in solving sequentially a set of mixed-integer linear programs (MILP) to obtain lower bounds (LBs) of the global optimum and perform function evaluations on the incumbent solution of the MILP problem to obtain upper bounds (UBs). The algorithm stops when the LB and UB are sufficiently close. The authors also present a heuristic method that builds on the proposed framework to improve the quality of the solution obtained from the piecewise linear method. The authors show through a set of numerical examples the performance of this approach.