FP-QF: A Matrix-Inversion-Free AC Power Flow Solver for Differentiable ML Pipelines

Newton-Raphson (NR) is the de facto choice for enforcing AC power flow feasibility in machine-learning-for-OPF pipelines, but it requires Jacobian assembly and matrix factorisation at every iteration, making it expensive in differentiable training loops and sensitive to poor ML initialisations. We propose the \textbf{Fixed-Point Quadratic-Form (FP-QF)} solver: an iterative, matrix-inversion-free method that derives closed-form quadratic voltage updates at each bus. FP-QF integrates directly into an ML pipeline as either a post-processing step or a differentiable training layer. Experiments on IEEE 30- and 118-bus systems show reliable convergence and faster performance than Newton–Raphson when hot started from ML predictions.