Nonlinear Magnetics Model for Permanent Magnet Synchronous Machines Capturing Saturation and Temperature Effects

TL;DR

The paper addresses the challenge of accurately modeling permanent magnet synchronous machines (PMSMs) under magnetic saturation and rotor-temperature variations, which undermine conventional linear flux–current models. It introduces a nonlinear magnetics model that treats the permanent magnet excitation as a current source, with the current–flux relation expressed as $ oldsymbol{i}^r = oldsymbol{h}(oldsymbol{cyr^r}) - oldsymbol{i}_{pm}^r(T_r)$ and an invertible map $ oldsymbol{lambda}^r = oldsymbol{h}^{-1}(oldsymbol{i}^r + oldsymbol{i}_{pm}^r) = oldsymbol{g}(oldsymbol{i}^r + oldsymbol{i}_{pm}^r) $. This decouples saturation from temperature via the temperature-dependent PM current $I_{pm}(T_r)$, enabling adaptive estimation without direct rotor-temperature sensing. The authors derive the rotor-frame dynamics and a torque expression within this framework and validate the approach with FEA across interior, distributed-winding SMPM, and concentrated-winding SMPM designs, as well as experimental data from a high-power SMPM. Results show significantly improved accuracy in saturated and high-temperature conditions, highlighting the method’s potential for real-time control and improved torque performance without explicit temperature measurements.

Abstract

This paper proposes a nonlinear magnetics model for Permanent Magnet Synchronous Machines (PMSMs) that accurately captures the effects of magnetic saturation in the machine iron and variations in rotor temperature on the permanent magnet excitation. The proposed model considers the permanent magnet as a current source rather than the more commonly used flux-linkage source. A comparison of the two modelling approaches is conducted using Finite Element Analysis (FEA) for different machine designs as well as experimental validation, where it is shown that the proposed model has substantially better accuracy. The proposed model decouples magnetic saturation and rotor temperature effects in the current/flux-linkage relationship, allowing for adaptive estimation of the PM excitation.

Figures (24)

• Figure 1: Simplified, single-coil magnetics model of PMSM machine
• Figure 2: Derivation of proposed magnetics model for single-coil. Top left: magnetic circuit model. Top right: Thevenin equivalent of permanent magnet. Bottom left: Combination of magnet and core reluctances. Bottom right: Resulting electric circuit model.
• Figure 3: Representative flux-linkage/current relationship capturing magnetic saturation at two different rotor temperatures. (a) $\lambda-i$ curve. (b) $i-\lambda$ curve.
• Figure 4: Cross-section of Interior Permanent Magnet machine en14092343
• Figure 5: $\vec{\lambda}^r$ - $\vec{i}^r$ mapping of interior permanent magnet machine at different rotor temperatures