Physics-informed neural network with adaptive activation for power flow

Abstract

We introduce a physics-informed neural network for power flow (PINN4PF) that effectively captures the nonlinear dynamics of large-scale modern power systems. The proposed neural network (NN) architecture consists of two important advancements in the training pipeline: (A) a double-head feed-forward NN that aligns with power flow (PF), including an activation function that adjusts to the net active and reactive power injections patterns, and (B) a physics-based loss function that partially incorporates power system topology information through a novel hidden function. The effectiveness of the proposed architecture is illustrated through 4-bus, 15-bus, 290-bus, and 2224-bus test systems and is evaluated against two baselines: a linear regression model (LR) and a black-box NN (MLP). The comparison is based on (i) generalization ability, (ii) robustness, (iii) impact of training dataset size on generalization ability, (iv) accuracy in approximating derived PF quantities (specifically line current, line active power, and line reactive power), and (v) scalability. Results demonstrate that PINN4PF outperforms both baselines across all test systems by up to two orders of magnitude, not only in terms of direct criteria, e.g., generalization ability, but also in terms of derived physical quantities.