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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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

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TM301.2

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	Zhang Qinpei
	Li Jian
	Lu Yang
	Wu Linghao
	Yang Kai
	Sun jiawei

Cite this article:

Zhang Qinpei,Li Jian,Lu Yang等. Research on discretization model of induction motor for low switching-to-fundamental frequency ratio traction system[J]. Transactions of China Electrotechnical Society, 0, (): 117-117.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.222046 OR https://dgjsxb.ces-transaction.com/EN/Y0/V/I/117

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