Non-Injected Online Inductance Estimation Method for Permanent Magnet Synchronous Motor Based on Virtual Voltage Excitation Coordinate System
Zhou Yangwei1,2, Nie Ziling2,3, Peng Li1, Zou Xudong1, Li Huayu2,3
1. School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China; 2. National Key Laboratory of Science and Technology on Electromagnetic Energy Naval University of Engineering Wuhan 430033 China; 3. East Lake Laboratory Wuhan 430204 China
Abstract：Traditional online inductance identification methods for permanent magnet synchronous motors (PMSMs) based on mean value models often encounter the issue of under-ranking, particularly in low-current or high-load conditions. This paper proposes a novel non-invasive inductance estimation method based on a virtual voltage excitation discrete coordinate system and a switching time-scale motor model. This method utilizes basic inverter switching vectors and current ripple information, eliminating the need for additional current injection or rotor position sensor feedback. It is suitable for control strategies such as direct torque control (DTC) and finite-control-set model predictive direct torque control (FCS-MPDTC), which operate without pulse-width modulation. A differential inductance model in the d-q synchronous reference frame is derived based on the motor's voltage equations. The voltage equation is differentiated between two periods to obtain terms involving current differential and inductance. To remove the dependency on rotor position and low-frequency components such as resistance and back EMF, the model is transformed into a virtual voltage excitation-based x-y coordinate system. In the x-y reference frame, inductance is estimated based on current ripple information without needing rotor position data. The x-y reference frame enables accurate inductance estimation solely from current ripple data. By leveraging the basic switching vectors of the inverter, this method avoids the need for position sensors or additional current injections. The inductance values are calculated using differential current and voltage data from several inverter switching periods. The raw inductance results are filtered using a low-pass filter to reduce noise and ensure stability. Experimental validation shows that the method achieves an average inductance estimation error of less than 4% across a wide range of loads. At 10% load, the estimated d-axis inductance Ld is 7.62 mH, closely matching the offline reference value of 7.61 mH, with an error of less than 0.13%. Similarly, the q-axis inductance Lq is estimated at 18.22 mH, with a reference value of 18.2 mH, yielding an error of less than 0.1%. Even at 120% overload, the Ld estimation error is within 1.89%, while Lq exhibits a larger error of 3.13% due to the magnetic cross-coupling effect. The method demonstrates fast convergence across the whole load range, stabilizing results within 20 ms. Despite variations in q-axis inductance caused by load-dependent magnetic saturation, the system maintains sufficient accuracy for practical applications. The robustness of the proposed method is highlighted by its ability to operate effectively under different load conditions without requiring rotor position feedback. The impact of switching ripple noise is minimized by appropriate filtering, and accuracy is maintained under full working conditions. Cross-coupling compensation based on piecewise fitting can reduce the error to approximately 1%. The following conclusions of the paper are drawn. (1) The virtual voltage excitation discrete coordinate system enables reliable inductance estimation without rotor position feedback or additional current injection. (2) The method’s average inductance estimation error is less than 4%, with a response time of 20 milliseconds, suitable for real-time control applications. (3) Inductance estimation is practical across a wide range of load conditions using current ripple information, with cross-coupling compensation further enhancing accuracy.
周杨威, 聂子玲, 彭力, 邹旭东, 李华玉. 虚拟电压激励离散变换坐标系定向的非注入式永磁同步电机电感在线观测方法[J]. 电工技术学报, 2025, 40(22): 7166-7178.
Zhou Yangwei, Nie Ziling, Peng Li, Zou Xudong, Li Huayu. Non-Injected Online Inductance Estimation Method for Permanent Magnet Synchronous Motor Based on Virtual Voltage Excitation Coordinate System. Transactions of China Electrotechnical Society, 2025, 40(22): 7166-7178.
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