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.

翻译：本文提出了一种基于物理信息神经网络的饱和同步电机动态建模方法，适用于包含空间谐波的情况。我们引入了一种将梯度网络直接嵌入基本电机方程的架构，从而能够精确建模非线性耦合的电磁本构关系。通过学习磁场能量的梯度，该模型本质上满足能量平衡（互易条件）。所提出的架构能够通用逼近任何物理可行的磁行为，相比查表法和标准机器学习模型具有多项优势：所需训练数据更少，保证单调性和可靠的外推能力，并产生平滑输出。这些特性进一步支持鲁棒的模型反演和最优轨迹生成，这在控制应用中常属必需。我们使用来自一台5.6千瓦永磁辅助同步磁阻电机的实测数据与有限元法数据集对所提方法进行了验证。结果表明，即使在有限训练数据下，该方法仍能建立精确且物理一致的模型。