Discrete-Time Modeling of Interturn Short Circuits in Interior PMSMs

TL;DR

This work develops a discrete-time description for interturn short circuits in interior PMSMs with concentrated windings by applying a matrix-exponential discretization to a comprehensive continuous-time dq-model that includes radial permanent-magnet flux and wye-connected, series-parallel windings. The method treats the electrical velocity as a time-varying parameter within sampling intervals and introduces a perturbation-based extension to incorporate motor-connection resistance, yielding a robust, stable update law for healthy and fault currents and the electromagnetic torque. Validation on a lab testbed with a fault-insertion unit demonstrates that the derived DTM accurately replicates measured waveforms and outperforms a forward-Euler discretization, especially under fast dynamics and higher fault severity. The resulting approach is suitable for real-time fault diagnosis and model-based mitigation in EV drive-trains and can generate large datasets for training diagnostic neural networks, while acknowledging some inductive-coupling simplifications between adjacent phase segments.

Abstract

This article describes the discrete-time modeling approach for interturn short circuits in interior permanent magnet synchronous motors with concentrated windings that facilitate model-based fault diagnostics and mitigation. A continuous-time model incorporating universal series-parallel stator winding connection and radial permanent magnet fluxes is developed in the stator variables and transformed into the rotor reference frame, including also the electromagnetic torque. The transformed model undergoes discretization using the matrix exponential-based technique, wherein the electrical angular velocity and angle are considered time-varying parameters. The resulting model is subsequently expanded to consider the motor connection resistance via perturbation techniques. In the laboratory experiments, we validate the dynamical properties of the derived model by comparing its outputs with the experimental data and waveforms generated by the forward Euler-based discrete-time approximation.

Figures (6)

• Figure 1: The shorted phase $x$ equivalent circuits: (a) full; (b) algebraically reduced; (c) with reduced currents directly related to $u_x$.
• Figure 2: The testbed with the experimental motor.
• Figure 3: The internal structure of the experimental motor.
• Figure 4: The layout of the experiments.
• Figure 5: The model-to-measurement comparison across the operating conditions.