A Nonlinear Decoupled Modeling Method of Linear Induction Motor Propulsion System with Segmented Stator
Xu Fei1,2,3, Shi Liming1,2,3, Li Zixin1,2,3, Li Yaohua1,2,3
1. State Key Laboratory of High Density Electromagnetic Power and Systems Institute of Electrical Engineering Chinese Academy of Sciences Beijing 100190 China; 2. University of Chinese Academy of Sciences Beijing 100049 China; 3. Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology QILU ZHONGKE Jinan 250100 China
Abstract The linear induction motor with a segmented stator (LIM-SS) has great potential for ultra- high-speed electromagnetic propulsion. However, simulating the system’s electromagnetic transient feature in real time poses challenges due to rapid time-varying coupling characteristics between the stator and rotor, zero-crossing thyristor switching current, and varying cable impedance. Mathematical modeling methods for high-speed linear motors mainly include the field-circuit joint operation mathematical model and lumped parameter equivalent circuit mathematical model. While the field-circuit joint operation mathematical model can accurately simulate the system's electromagnetic transient characteristics, it requires extensive computational time and cannot operate in real-time. The lumped parameter equivalent circuit mathematical model is more efficient but struggles to accurately represent the nonlinear characteristics of linear motors. Therefore, this paper proposes a decoupling modeling method for the nonlinear characteristics of the LIM-SS propulsion system. Firstly, this paper analyzes the electromagnetic transient characteristics of the LIM-SS propulsion system under the conditions of the thyristor switching process, rotor entering, and leaving the stator segment. According to the multi-phase motor space vector decoupling modeling method, the system energy conversion characteristics are divided into three parts: effective conversion, invalid conversion, and power supply. The cable voltage drop is moved into the motor leakage inductance part as the stator invalid electromechanical energy conversion part, which effectively avoids the problem of computational divergence caused by the differential term of inductance when calculating the thyristor voltage. Secondly, this paper proposes a virtual rotor flux modeling method for the virtual invalid electromechanical energy conversion part of the linear motor rotor. From the perspective of the rotor, the mutual inductance between the stator and the rotor of the linear induction motor is a constant, which effectively avoids the problem of state equation computational divergence when the coverage ratio is at a continuous non-differentiable point. Finally, a decoupling mathematical model of the LIM-SS propulsion system is proposed based on the multi-phase motor stator space-vector decoupling modeling and virtual rotor flux method. The thyristor’s switching state is judged by the switch command and the current zero crossing point. The stator coverage ratio realizes the mutual decoupling operation of the mathematical model of each stator segment, and the FPGA hardware acceleration realizes the system's small-step real-time calculation. The results of the hardware-in-the-loop test indicate that the traditional mathematical model's numerical calculation diverges as the cable length increases. However, the decoupling modeling method can maintain a constant virtual rotor flux in a steady state, thus avoiding real-time calculation divergence. The simulation results align with the theoretical analysis, achieving a real-time calculation step as low as 500 ns. The steady-state variation between the prototype experimental results and the hardware-in-the-loop simulation results is less than 7%. This difference primarily stems from the dynamic characteristics of the power semiconductor device switching process and the disparity in inductance of each phase from a disconnected structure of linear motor stator. The following conclusions are drawn. (1) The decoupling modeling method equates the cable voltage drop to the electromechanical energy conversion part in the motor. (2) The virtual rotor flux method regards the coupling inductance between the stator and the mover of the linear induction motor as a constant. (3) The constructed mathematical model can realize real-time and accurate characterization of multiple working conditions, such as power supply switching and stator-rotor coupling changes of the stator segmented linear induction motor propulsion system. The results provide a modeling basis for high-performance control of ultra-high-speed linear motor propulsion systems.
Xu Fei,Shi Liming,Li Zixin等. A Nonlinear Decoupled Modeling Method of Linear Induction Motor Propulsion System with Segmented Stator[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 1023-1033.
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2025, Vol. 40 
