A Learning to Optimize Approach to Accelerating Distributed Optimal Power Flow Solving

As power systems continue to scale, a fast and accurate distributed optimal power flow solver becomes crucial for effective power system dispatch. This work proposes a Learning to Optimize (L2O) approach to accelerate the distributed optimal power flow solving. The final convergence values of global variables and Lagrange multipliers of the Alternating Direction Method of Multipliers (ADMM) are estimated, which serve as its warm-start solution. A Long Short-Term Memory-Variational Auto-Encoder (LSTM-VAE) model is developed as the core model to estimate the convergence value. The LSTM part processes high-dimensional temporal characteristics of global variables and Lagrange multipliers, extracting their latent temporal patterns to generate low-dimensional representations. Subsequently, VAE decoder part reconstructs these compressed latent vectors back to the high-dimensional asymptotic convergence values of ADMM variables. A novel loss function is designed in the form of a quadratic sum penalty term to incorporate the constraint violations of the Lagrange multipliers. Additionally, a two-stage training data generation strategy is proposed to efficiently generate substantial data in a limited amount of time. The effectiveness of the proposed approach is evaluated using the modified IEEE 123-bus system, a synthetic 500-bus system, and a 793-bus system.