Physics-Informed Neural Networks for Power Systems Warm-Start Optimization

Several studies have demonstrated the potential of machine learning methods to solve optimal power flow problems. However, designing a scalable physics-informed neural network (PINN) model that can improve its performance being trained in diverse scenarios by considering the significance of its several elements remains a challenging task. Here, we propose an approach that leverages the inclusion of physical constraints into the loss function using a penalty factor and the utilization of bounds of optimization variables in the activation functions to enhance the generalization performance of tuned neural networks. The results indicate that this method significantly improves the success rate and computational speed gains of AC-optimal power flow (AC-OPF) calculations, especially when forward predictions are employed as warm-start points. Our PINN models are trained using accurate AC-OPF solutions from slow high-precision interior-point solvers across several power system scenarios. Furthermore, we examine and demonstrate the critical role of adjusting PINN's hyperparameters and architecture design in achieving the optimal tradeoff between empirical error and constraint violation to make accurate and feasible predictions. A combination of stochastic methods and grid search is utilized to establish a reliable and efficient way of performing optimization calculations for a wide range of power systems using collected data. The proposed PINN model offers a promising solution for adapting neural networks to diverse scenarios of a physical problem. Furthermore, it offers a robust methodology for successfully addressing optimal power flow (OPF) problems in power systems.