An Ordinal Optimization Theory-Based Algorithm for Solving the Optimal Power Flow Problem With Discrete Control Variables

Abstract—The optimal power flow (OPF) problem with discrete control variables is an NP-hard problem in its exact formula-tion. To cope with the immense computational-difficulty of this problem, we propose an ordinal optimization theory-based algo-rithm to solve for a good enough solution with high probability. Aiming for hard optimization problems, the ordinal optimization theory, in contrast to heuristic methods, guarantee to provide a top % solution among all with probability more than 0.95. The approach of our ordinal optimization theory-based algorithm consists of three stages. First, select heuristically a large set of candidate solutions. Then, use a simplified model to select a subset of most promising solutions. Finally, evaluate the candidate promising-solutions of the reduced subset using the exact model. We have demonstrated the computational efficiency of our algo-rithm and the quality of the obtained solution by comparing wit