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| Compensation Strategy for Static End Effect in Nest-Loop Secondary Linear Doubly-Fed Machine |
| Bao Zhen1, Ge Jian1, Xu Wei1, Zhang Yaping1, Li Weiye2, Lin Guobin3, Su Shihu4, Liu Zhicheng5, Yuan Wenye6 |
1. State Key Laboratory of Advanced Electromagnetic Technology Huazhong University of Science and Technology Wuhan 430074 China;
2. Xiangyang CRRC Motor Technology Co. Ltd Xiangyang 441047 China;
3. Maglev Transportation Engineering R&D Center Tongji University Shanghai 201804 China;
4. CRRC Zhuzhou Motor Co. Ltd Zhuzhou 412001 China;
5. Guangzhou Metro Group Co. Ltd Guangzhou 510330 China;
6. Zhuzhou CRRC Times Electric Co. Ltd Zhuzhou 412001 China |
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Abstract At present, linear induction machines (LIMs) and linear synchronous machines (LSMs) are mainly used for linear traction system adopted to urban rail transit. As a new type of linear machine, the nest-loop secondary linear doubly-fed machine (NLS-LDFM) and its drive system have gradually attracted the attention of scholars for its advantages of adjustable power factor and flexible operation mode. However, the static end effect exists in NLS-LDFM due to the cut-open primary iron core. It generates the pulsating magnetic field which is evenly distributed along the direction of motion. The phenomenon not only leads to two sets of asymmetrical three-phase windings but also direct-coupling between them. Therefore, the static end effect can produce both negative-sequence current and direct-coupling current in the primary windings. Therein, the negative-sequence current can produce negative thrust, which can weaken the average thrust. And the direct-coupling current does not produce effective thrust or active power. Thus, the static end effect will lead to the reduction of power factor and efficiency in the NLS-LDFM.
Firstly, based on the law of static end effect and the working principle of NLS-LDFM, the main components of harmonic current generated by static end effect are analyzed. Most of the harmonic currents generated by the static end effect can be compensated by suppressing the fundamental negative-sequence current and direct-coupling current. Secondly, based on the analysis of static end effect pulsating inductance matrix and direct-coupling mutual inductance matrix, the expression of pulsating electromotive force is derived. It can be compensated to the primary windings as feedforward voltage to suppress the negative-sequence current and direct-coupling current. Thirdly, a mixed second- and third-order generalized integrator (MSTOGI) is used to extract fundamental current and direct-coupling current to improve the compensation accuracy. The corresponding positive- and negative-sequence components are obtained by using instantaneous symmetric component method. Finally, the effectiveness of proposed compensation strategy is verified by simulation and experiment.
The simulation results show that when the static end effect compensation strategy is not adopted, the three-phase current is very asymmetrical, indicating that the negative-sequence current is of high content. After applying the static end effect compensation strategy, the negative sequence current is effectively suppressed and the three-phase current becomes more symmetrical. By fast Fourier transform analysis of C-phase current of power winding, the current content of direct-coupling decreases from 12.0% to 3.1% after compensation. In experiments, the asymmetry of three-phase current in the power winding decreases from 27.7% to 3.9%, and the content of direct-coupling current decreases from 11.4% to 5.8%.
The following conclusions can be drawn from the simulation and experiment analysis: (1) The static end effect of NLS-LDFM will generate harmonic current and negative-sequence current of various frequencies, of which the fundamental negative-sequence current and direct-coupling current are the main components. (2) The proposed current control process based MSTOGI and pulsating voltage feedforward can suppress the fundamental negative-sequence current and direct-coupling current, which can effectively compensate the static end effect in NLS-LDFM.
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Received: 06 June 2022
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2023, Vol. 38 
