低载波比牵引系统的感应电机特征根离散化模型研究

doi:10.19595/j.cnki.1000-6753.tces.222046

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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角的稳态误差,严重时甚至出现发散不收敛现象。针对上述问题,本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, 离散化方法, 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 condition . The traditional reduced order discrete model cannot be applied to the control system due to the large discretization error. To address this issue, this paper proposes an eigenvalue based discrete model of induction motor, which still has good steady-state accuracy and transient tracking performance under low switching-to-fundamental frequency ratio. At the same time, a quantitative analysis method of discretization error based on Bode diagram is proposed, and the error magnitude of the proposed model and the traditional discretization model in the observation amplitude and phase of magnetic linkage is quantitatively compared.
Firstly, the mathematical model of the induction motor is modeled in the continuous domain by means of 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, as a result of which, the eigenvalue based discrete model of induction motor is derived. At the same time, 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 continuous model as the evaluation standard, the error of the traditional discrete model and the proposed discrete model 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 obvious observation error, while the observed current of the eigenvalue based discrete model has small observation error. When the switching-to-fundamental frequency ratio is seven, the observed current of the second-order bilinear model can maintain stability, but the observed current amplitude and phase have large errors, while the observed current of the characteristic root discretization model can well track the actual synchronous sampling current. In terms of dynamic observation accuracy, in the process of speed reduction, the zero-order holder discrete model has a certain amplitude and phase deviation in current observation, whose maximum amplitude deviation is up to 30%, and the deviation disappears after the speed enters the steady state. By comparison, the eigenvalue based discrete model has good performance in both transient and steady speed.
The following conclusions can be drawn from the simulation and experimental results: 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 the process of speed reduction.

Key words： Induction machine discretization method transfer function Bode plot low switching-to-fundamental frequency ratio

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研究和技术开发。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研究。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, 0, (): 117-117. 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, 0, (): 117-117.

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