Abstract：The traditional vector space decoupled (VSD)-based model predictive current control (MPCC) for dual three-phase permanent magnet synchronous motors (PMSM) involves complex selection of harmonic weight coefficients. Dual d-q current control provides an alternative for balancing currents, but it introduces cross-coupling-induced harmonics and limits winding utilization, which can affect fault-tolerant operation. To address these challenges, a model predictive current control strategy based on triple rotational coordinate transformation is proposed. This study develops a mathematical model using the triple coordinate transformation method and examines its relationship with the dual d-q coordinate model and the VSD motor model. The proposed model is analyzed, and its performance is assessed through simulations. The dual three-phase windings of the PMSM are reorganized into a triple virtual stationary coordinate system (3-α-β) based on the phase alignment, which is then transformed into three sets of d-q components using the Park transform. A mathematical model of the motor is formulated within the triple d-q coordinate framework, and a comparative analysis shows that the components are decoupled. It is further demonstrated that the harmonic current components are eliminated when the currents in the triple d-q system are balanced. Simulations are conducted for both VSD-MPCC and the proposed 3dq-MPCC for validation. The simulation results demonstrate the following: VSD-MPCC effectively suppresses harmonic currents while considering the motor's dynamic performance. However, it involves a complex process for selecting weight coefficients. (1) steady-state performance comparison. In terms of phase current, the 3dq-MPCC control method consistently exhibits superior sinusoidal characteristics, lower total harmonic distortion (THD), and reduced harmonic components under varying operating conditions, including low-speed and light-load, high-speed and light-load, and high-speed and heavy-load scenarios. Under low-speed and light-load conditions, the phase current THD of 3dq-MPCC is 6.47%, significantly lower than the 11.09% observed in VSD-MPCC. Moreover, the H5 and H7 harmonic components are reduced by 1.37% and 0.79%, respectively. Similar trends are observed under high-speed conditions. For example, at high-speed and light-load, 3dq-MPCC achieves a THD of 12.15%, compared to 20.50% for VSD-MPCC. Under high-speed and heavy-load conditions, the respective THD values are 4.16% and 6.98%. The motor speed fluctuation analysis further underscores the control advantages of 3dq-MPCC. At 300 r/min under low-speed and light-load conditions, the speed fluctuation range of 3dq-MPCC is only 0.2 r/min, much smaller than the 1.6 r/min of VSD-MPCC. At high-speed and light-load (800 r/min) and high-speed and heavy-load conditions, the speed fluctuation ranges of 3dq-MPCC are 0.7 r/min and 0.5 r/min, respectively, compared to 2.2 r/min and 1.8 r/min for VSD-MPCC. Additionally, the harmonic space current trajectory analysis confirms the superior harmonic suppression capability of 3dq-MPCC. Across all three conditions, the harmonic current trajectory range of VSD-MPCC is significantly larger than that of 3dq-MPCC. For example, under low-speed and light-load conditions, the maximum harmonic current trajectory range of VSD-MPCC reaches 1.5 A, while that of 3dq-MPCC is only 0.6 A. Similar differences are observed under high-speed conditions. (2) Dynamic Performance Comparison Under dynamic conditions (e.g., motor start at no load, a set speed of 600 r/min, load torque increased to 200 N·m at 0.1 s, then suddenly reduced to 100 N·m at 0.2 s): In terms of the phase current dynamic response, VSD-MPCC stabilizes at 0.104 s following a transient period of approximately 0.004 s after a fluctuation at 0.1 s. In contrast, 3dq-MPCC stabilizes at about 0.102 s, with a transient duration of only 0.002 s and a smaller fluctuation range. For the Q-axis current dynamic response, VSD-MPCC requires about 0.004 s to stabilize, while 3dq-MPCC stabilizes in approximately 0.002 s with significantly smaller fluctuations. In the speed dynamic response, the transient process of VSD-MPCC lasts about 0.003 s, while that of 3dq-MPCC is shorter at 0.0025 s, with a comparatively smaller fluctuation range. The simulation results demonstrate a comparison between the proposed 3dq-MPCC and the traditional VSD-MPCC in terms of steady-state and dynamic characteristics, focusing on phase current, motor speed, harmonic current trajectory, and Q-axis current. The proposed 3dq-MPCC eliminates the complexity associated with selecting harmonic weight coefficients in VSD-MPCC, thereby simplifying the control strategy. Furthermore, the results indicate that 3dq-MPCC effectively suppresses harmonic currents and achieves favorable steady-state and dynamic performance.
储炜, 林黄达, 易新强. 基于三重旋转坐标变换的双三相永磁同步电机模型预测电流控制策略[J]. 电工技术学报, 2024, 39(zk1): 51-63.
Chu Wei, Lin Huangda, Yi Xinqiang. Model Predictive Current Control Strategy for Dual Three-Phase Permanent Magnet Synchronous Motors Based on Triple Rotating Coordinate Transformation. Transactions of China Electrotechnical Society, 2024, 39(zk1): 51-63.
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2024, Vol. 39 
