Scalable Two-Stage Stochastic Optimal Power Flow via Separable Approximation

This paper proposes a Separable Projective Approximation Routine-Optimal Power Flow (SPAR-OPF) framework for solving two-stage stochastic optimization problems in power systems. The framework utilizes a separable piecewise linear approximation of the value function and learns the function based on sample sub-gradient information. We present two formulations to model the learned value function, and compare their effectiveness. Additionally, an efficient statistical method is introduced to assess the quality of the obtained solutions. The effectiveness of the proposed framework is validated using distributed generation siting and sizing problem in three-phase unbalanced power distribution systems as an example. Results show that the framework approximates the value function with over 98% accuracy and provides high-quality solutions with an optimality gap of less than 1%. The framework scales efficiently with system size, generating high-quality solutions in a short time when applied to a 9500-node distribution system with 1200 scenarios, while the extensive formulations and progressive hedging failed to solve the problem.