Learning-Accelerated ADMM for Stochastic Power System Scheduling With Numerous Scenarios

The increasing share of uncertain renewable energy sources (RES) in power systems necessitates new efficient approaches for the two-stage stochastic multi-period AC optimal power flow (St-MP-OPF) optimization. The computational complexity of St-MP-OPF, particularly with AC constraints, grows exponentially with the number of uncertainty scenarios and the time horizon. This complexity poses significant challenges for large-scale transmission systems that require numerous scenarios to capture RES stochasticities. This paper introduces a scenario-based decomposition of the St-MP-OPF based on the alternating direction method of multipliers (ADMM). Additionally, this paper proposes a machine learning-accelerated ADMM approach (ADMM-ML), facilitating rapid and parallel computations of numerous scenarios with extended time horizons. Within this approach, a recurrent neural network approximates the ADMM sub-problem optimization and predicts wait-and-see decisions for uncertainty scenarios, while a master optimization determines here-and-now decisions. Additionally, we develop a hybrid approach that uses ML predictions to warm-start the ADMM algorithm, combining the computational efficiency of ML with the feasibility and optimality guarantees of optimization methods. The numerical results on the 118-bus and 1354-bus system show that the proposed ADMM-ML approach solves the St-MP-OPF with 3-4 orders of magnitude speed-ups, while the hybrid approach provides a balance between speed-ups and optimality.