High-Precision Standstill Flux Linkage Identification for Synchronous Reluctance Motors Based on Gradient Projection and Implicit Inductance Modeling

Abstract

Accurate standstill flux-linkage identification of synchronous reluctance motors (SynRMs) is challenged by voltage-integration errors and optimization interference between data fitting and physical constraints. This paper develops a compact physics-informed neural network (PINN), whose implicit secant-inductance architecture enforces the zero-flux condition and dq-axis parity symmetries by construction. Its training objective combines flux-fitting mean-square error, Maxwell reciprocity, and two axis-wise discrete voltage-equation residuals. Pairwise projecting conflicting gradient (PCGrad) removes conflicting gradient components among these four weighted objectives before parameter update. Following current-injection prealignment, self- and cross-saturation data are acquired by standstill hysteresis voltage injection without mechanical rotor locking or continuous position feedback. The dynamometer-derived constant-speed flux map is excluded from gradient training and serves only as a common external benchmark. Experiments on a 0.55 kW SynRM yield a three-seed average benchmark mean absolute error (MAE) of 0.01248±0.00254 Wb, the lowest among the evaluated neural and function-fitting models. For the complete multi-physics objective, PCGrad reduces the average benchmark MAE by 17.4% relative to direct gradient summation. Ablation studies verify the complementary contributions of reciprocity, the discrete voltage equation, and gradient projection. The resulting direct current-to-flux mapping provides a compact and physically consistent magnetic model for model-based motor-control applications. The implementation code and datasets are available at [https://github.com/KrisCCeng/SynRM-PINN.git].