Gradient Networks for Universal Magnetic Modeling of Synchronous Machines

TL;DR

This paper introduces a physics-informed neural network architecture that models the magnetic behavior of synchronous machines by learning energy gradients, ensuring physical consistency, data efficiency, and applicability in control tasks.

Contribution

The paper proposes a novel gradient network-based neural architecture that accurately models magnetic behavior in synchronous machines, incorporating physical laws directly into the learning process.

Findings

Accurately models magnetic behavior with limited data

Ensures physically consistent and smooth outputs

Enables robust model inversion and control applications

Abstract

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into the fundamental machine equations, enabling accurate modeling of the nonlinear and coupled electromagnetic constitutive relationship. By learning the gradient of the magnetic field energy, the model inherently satisfies energy balance (reciprocity conditions). The proposed architecture can universally approximate any physically feasible magnetic behavior and offers several advantages over lookup tables and standard machine learning models: it requires less training data, ensures monotonicity and reliable extrapolation, and produces smooth outputs. These properties further enable robust model inversion and optimal trajectory generation, often needed in control applications. We validate the proposed approach using measured and finite-element method (FEM) datasets from a 5.6-kW permanent-magnet (PM) synchronous reluctance machine. Results demonstrate accurate and physically consistent models, even with limited training data.