Physics-Constrained Neural Dynamics: A Unified Manifold Framework for Large-Scale Power Flow Computation

TL;DR

This paper introduces a physics-constrained neural network framework for large-scale power flow computation, leveraging manifold geometry and gradient flow to improve efficiency and physical consistency without requiring labeled data.

Contribution

It presents a novel unsupervised neural method based on manifold geometry and gradient flow, enabling physics-consistent power flow solutions without pre-labeled data.

Findings

Achieves physically consistent power flow solutions

Requires no pre-solving or labeled data

Improves efficiency over traditional methods

Abstract

Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation, while existing deep learning-based power flow solvers mostly rely on supervised learning, requiring pre-solving of numerous cases and struggling to guarantee physical consistency. This paper proposes a neural physics power flow solving method based on manifold geometry and gradient flow, by describing the power flow equations as a constraint manifold, and constructing an energy function \(V(\mathbf{x}) = \frac{1}{2}\|\mathbf{F}(\mathbf{x})\|^2\) and gradient flow \(\frac{d\mathbf{x}}{dt} = -\nabla V(\mathbf{x})\), transforming power flow solving into an equilibrium point finding problem for dynamical systems. Neural networks are trained in an unsupervised manner by directly minimizing physical residuals, requiring no labeled data, achieving true "end-to-end" physics-constrained learning.