电工技术学报  2024, Vol. 39 Issue (2): 434-444    DOI: 10.19595/j.cnki.1000-6753.tces.222046
电机及其系统 |
低载波比牵引系统的感应电机特征根离散化模型研究
张钦培1, 李健1, 卢阳1, 吴凌豪2, 杨凯1, 孙佳伟3
1.强电磁工程与新技术国家重点实验室(华中科技大学电气与电子工程学院) 武汉 430074;
2.华中科技大学电气与电子工程学院新型电机与特种电磁装备教育部工程研究中心 武汉 430074;
3.中车大连电力牵引研发中心有限公司 大连 116052
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
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摘要 在大功率和高速电机驱动领域,电机控制系统将运行于低载波比工况。传统的一阶欧拉、二阶双线性等降阶离散化模型在低载波比下由于离散化误差过大,对应的状态观测将出现幅值和相位的稳态误差,严重时甚至出现发散不收敛现象。针对上述问题,该文提出了感应电机特征根离散化模型。通过构建感应电机的复矢量模型状态空间方程,将满秩的状态转移矩阵进行对角化,得到状态转移矩阵的精确离散化结果,该模型在低载波比时仍具有较高的离散化精度。同时,提出了一种基于伯德图的离散化误差定量分析方法,通过定量对比不同离散化模型和连续域模型之间观测变量的幅值和相位误差,从理论上证明了提出方法的优越性。最后,通过仿真和实验验证了上述感应电机特征根离散化模型在低载波比下均具有良好的稳态精度与暂态跟随性能。
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关键词 感应电机离散化模型传递函数伯德图低载波比    
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.
Key wordsInduction machine    discretization method    transfer function    Bode plot    low switching-to- fundamental frequency ratio   
收稿日期: 2022-10-28     
PACS: TM301.2  
通讯作者: 李健, 男,1982年生,研究员,博士生导师,主要研究方向为大功率牵引变流器控制方面的理论和技术开发。E-mail: jianli@hust.edu.cn   
作者简介: 张钦培, 男,1998年生,硕士研究生,主要研究方向为感应电机数学模型与控制策略。E-mail: zqp@hust.edu.cn
引用本文:   
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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