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| Inductance Identification and Sensorless Control of PMSM Based on Separation of High-Frequency Current Components |
| Zhu Yuan1, Xu Shihan1, Meng Ling1, Jin Changming2, Wang Weida2 |
1. School of Automotive Studies Tongji University Shanghai 201804 China;
2. Geely Automobile Research Institute (Ningbo) Co. Ltd Ningbo 315300 China |
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Abstract The high-frequency injection method is widely used for inductance identification and low-speed sensorless control of permanent magnet synchronous motors. However, no existing research realizes both functions simultaneously through a shared injection sequence. This paper proposes a current component- separation method based on high-frequency square-wave injection to identify the d- and q-axis incremental inductances and the coupling inductance online. The high-precision sensorless control can be achieved without position sensors. The method has been validated on both interior three-phase and surface dual three-phase (30-degree phase shift) permanent magnet synchronous motors.
The paper introduces a mathematical representation of cross-coupling inductance into the voltage model in the synchronous rotating frame and establishes a traditional reactance model as a reference. A novel four-stage square-wave voltage-injection waveform is designed. By tuning voltage amplitude coefficients, the waveform enables clear separation of self-excited and coupling-excited current components, and averaging is used to suppress high-frequency disturbances.
To mitigate loss of estimation accuracy due to position uncertainty, a correction method for the angular deviation between the injection reference frame and the actual synchronous rotating frame is developed. By modeling the coupling-excited current and deriving the relation between the cross-coupling angle and the d- and q-axis currents, an online fitting strategy is proposed. A cross-coupling angle map is created from real position sensor input.
For dual three-phase motors, a harmonic subspace-based inductance identification path is established via vector space decomposition. High-frequency voltage is injected into this subspace, and inductance is identified using the same component separation strategy.
Different sensorless control structures are developed for different motor types. For interior-motors with high saturation and strong coupling, dual-axis injection in the synchronous rotating frame is used, and a corrected third-order control structure is implemented based on cross-coupling current. For surface dual three-phase motors, a phase-locked loop in the stationary reference frame estimates position directly from response current without angle compensation.
Experimental validation is carried out on a 35 kW three-phase motor and a 400 W dual three-phase motor test bench. Tests include accuracy under static and dynamic conditions, position tracking performance, and convergence speed during step current. The proposed method exhibits reliable real-time performance with inductance estimation error under 6%, convergence within 10 ms, and position error below 10 degrees.
The theoretical foundation of the proposed method is developed based on the voltage equations in the synchronous rotating reference frame. In theory, different multiphase motor configurations (such as five-phase, seven-phase, and multi-three-phase machines) differ only in neutral-point currents and harmonic-order plane currents, which do not affect the current-voltage equations in the synchronous rotating frame. Therefore, variations in winding configurations, power ratings, or saliency ratios do not affect the applicability of the proposed method. However, the coupling relationship between the cross-coupling angle and the injection reference frame makes the calibration process dependent on a physical position sensor. Achieving high-accuracy calibration of the cross-coupling angle under sensorless conditions remains to be further investigated.
In conclusion, the proposed high-frequency square-wave injection and current-separation method enables accurate inductance estimation and sensorless control, which is suitable for deployment in automotive-grade motor controllers.
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Received: 18 June 2025
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2026, Vol. 41 
