Research on Discretization Model of Induction Motor for Low Switching-to-Fundamental Frequency Ratio Traction System
Zhang Qinpei1, Li Jian1, Lu Yang1, Wu Linghao2, Yang Kai1, Sun jiawei3
1. State Key Laboratory of Advanced Electromagnetic Engineering and Technology School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China; 2. Engineering Research Center of Novel Electrical Machines and Special Electromagnetic Equipment Ministry of Education School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China; 3. CRRC Dalian R&D Co. Ltd Dalian 116052 China
Abstract：In high-power and high-speed motor drives, the control system will operate in low switching- to-fundamental frequency ratio conditions. Due to the large discretization error, the traditional reduced-order discrete model cannot be applied to the control system. Therefore, this paper proposes an eigenvalue-based discrete induction motor model, which still has good steady-state accuracy and transient tracking performance under a low switching-to-fundamental frequency ratio. At the same time, a quantitative analysis method of discretization error based on the Bode diagram is proposed. Firstly, the mathematical model of the induction motor is modeled in the continuous domain using state space description. The full-rank state matrix is diagonalized through the transformation matrix. The elements on the diagonal of the diagonal matrix are the characteristic roots of the corresponding stator and rotor voltage equations of the induction motor. Then, the exact solution of the system matrix can be obtained through the transformation matrix and the diagonal matrix, and the eigenvalue-based discrete model of the induction motor is derived. Moreover, by deducing the z-domain transfer function of flux linkage observation of different discrete models, the Bode diagram is drawn. Taking the Bode diagram of the continuous model as the evaluation standard, the traditional and the proposed discrete models' errors in the magnitude and phase of flux linkage observation is compared. The simulation and experimental results show that in terms of the steady-state observation accuracy, at the electric frequency of about 20 Hz, the observed current of the first-order discretization model has an obvious observation error. In contrast, the observed current of the eigenvalue-based discrete model has a small observation error. When the switching-to-fundamental frequency ratio is seven, the observed current of the second-order bilinear model can maintain stability. However, the observed current amplitude and phase have large errors, while the observed current of the characteristic root discretization model can track the actual synchronous sampling current. Regarding dynamic observation accuracy, in speed reduction, the zero-order holder discrete model has a specific amplitude and phase deviation in current observation. The maximum amplitude deviation is up to 30%, and the deviation disappears after the speed enters the steady state. The eigenvalue-based discrete model has good performance in both transient and steady speeds. The following conclusions can be drawn: (1) The proposed discrete model of the characteristic root of the induction motor can achieve high-precision rotor flux and stator current observation in the full-speed range. When the switching-to-fundamental frequency ratio is as low as five, the observation error of the flux angle is less than 1°. (2) Compared with the zero-order holder discretization model, the proposed eigenvalue-based discrete model has higher current observation accuracy in speed reduction.
张钦培, 李健, 卢阳, 吴凌豪, 杨凯, 孙佳伟. 低载波比牵引系统的感应电机特征根离散化模型研究[J]. 电工技术学报, 2024, 39(2): 434-444.
Zhang Qinpei, Li Jian, Lu Yang, Wu Linghao, Yang Kai, Sun jiawei. Research on Discretization Model of Induction Motor for Low Switching-to-Fundamental Frequency Ratio Traction System. Transactions of China Electrotechnical Society, 2024, 39(2): 434-444.
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2024, Vol. 39 
