Solving Security-Constrained Optimal Power Flow Using Analytical Benders' Cuts

With the increasing complexity of power systems, faster methods for power system reliability analysis are needed. We propose a novel methodological approach to solve a DC security-constrained optimal power flow (SCOPF) with a probabilistic operational criterion that reduces computational time by using Benders decomposition in the formation of analytical Benders‘ cuts and the Sherman-Morrison-Woodbury identity in contingency power flow calculation. To model the expected operational cost, the objective function uses a probabilistic operational criterion consisting of contingency probabilities. The case study suggests that in a 500-node system, the total run time is reduced by 99.2% and solver optimization time is reduced by 89.5% when compared to solving the problem as a monolith, all the while ensuring reliable system operation considering short- and long-term post-contingency limits and reducing the operational costs, compared to a preventive ‘N-1’ strategy.