Physics-Informed Neural Network of Half-Inverse Gradient Method for Solving the Power Flow

Power flow (PF) analysis is fundamental for power system operation and planning, yet traditional methods like Newton–Raphson face problems in convergence and computational efficiency. While deep learning (DL) offers promising solutions, its “black-box” nature and unstable training dynamics hinder practical adoption. This paper proposes a physics-informed neural network (PINN) framework integrated with a novel half-inverse gradient (HIG) mechanism to address these limitations. First, a systematic study of gradient scaling in PF optimisation found that the lack of enough inverse matrix compensation was the main cause of training instability. Second, we design a residual-driven HIG method that compensates gradient matrices via inverse operations, enabling accelerated convergence while maintaining numerical stability. Third, we develop parameterized voltage variables with differentiable activation functions to enforce hard operational constraints. The HIG optimizer leverages automatic differentiation and truncated singular value decomposition to balance diagonal/non-diagonal gradient information, achieving 99% accuracy in case4gs and case30 studies. Experiments on case118 demonstrate the framework’s scalability, with 65% accuracy compared to about 38% for baseline physics-informed approaches.