Two-Stage Optimization Framework Ensuring Stability constraints in Power System Optimal Power Flow

This paper proposes a two-stage optimization framework for integrating stability constraints into optimal power flow (OPF) analysis. First, a hybrid gradient-stochastic search strategy is developed to efficiently locate the stability boundary through coordinated gradient descent and random perturbation mechanisms. Then, a particle swarm algorithm is used to further search for feasible solutions with better economic efficiency along the stability boundary, and a penalty function is used to ensure that the search path meets the stability requirement. A case study based on an improved IEEE-39 node system shows that the framework is able to achieve a scheduling solution with stability guarantee, and the balance between economy and computational efficiency can be achieved by adjusting parameters.