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| Harmonic Suppression Strategy of Single Frequency Proportional Resonance Controller for Asymmetric Multiphase Motors Based on Harmonic Mapping Law |
| Zhou Hao, Li Hui, Xiang Xuewei, Li Wendong, Chen Siyu |
| State Key Laboratory of Power Transmission Equipment & System Security and New Technology Chongqing University Chongqing 400044 China |
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Abstract The coupling between spatial-harmonic and time-harmonic currents in asymmetric multiphase motors (AMM) increases torque ripple and decreases efficiency, limiting their widespread application. Currently, active harmonic suppression strategies rely on complex filters or observers to extract harmonics and require the construction of numerous proportional resonance (PR) controllers at different frequencies, making the complexity and impracticality of harmonic suppression. Therefore, this paper proposes a single-frequency PR harmonic suppression strategy without filters based on the harmonic mapping law.
Firstly, based on the magnetic electromotive force equivalence principle, the universal space vector decoupling matrixes for AMM are established. Then, a mapping formula for harmonics of different frequency components on the subspaces is established. The general formula is decomposed into two independent components: amplitude and phase. The amplitude and phase mapping law of harmonics on the subspaces is derived according to the characteristics of the two components. Secondly, three criteria are proposed to search for the AMM with the minimum number of phases to ensure the unique mapping of harmonics. Based on the graphical representation of the mapping laws, the mapping trajectories of all harmonics are obtained to optimize the AMM topology and establish the subspaces for harmonic mapping. Then, based on the current phase-shifting method, a virtual AMM is constructed, and harmonics are extracted through the vector decoupling transformation subspaces. Finally, after unifying the frequency through linear space rotation transformation, PR controllers with the same resonant frequency are used to regulate harmonics.
Harmonic extraction and suppression experiments under steady-state and transient conditions are conducted using a dual three-phase motor. The extracted harmonic amplitudes can reach over 92% of the actual harmonics, demonstrating that the proposed algorithm can effectively separate harmonics. In the harmonic suppression experiment, the strategies of no harmonic suppression, current harmonic suppression under multiple synchronous rotating frames, and the proposed harmonic suppression strategy are compared. The proposed strategy decreases the proportions of the 5th, 7th, 11th, and 13th harmonic currents from 13.92%, 5.31%, 4.05%, and 2.96% before suppression to 3.02%, 0.43%, 0.39%, and 1.19%, respectively. The total harmonic distortion (THD) is decreased from 15.36% to 2.86%. Moreover, the harmonic suppression exhibited robustness under various operating conditions across the entire speed range.
The following conclusions can be drawn. (1) There are two harmonic mapping methods: full mapping with equal amplitudes and partial mapping with reduced amplitudes. The phase of mapping components can be divided into the α component leads or lags the β component by π/2. (2) Based on the harmonic mapping law, an optimal AMM topology selection criterion is established, and a virtual AMM is constructed, effectively avoiding the complex and inaccurate problem of harmonic extraction caused by constructing filters or harmonic observers. (3) The features of harmonic pair mapping on the selected subspace are that the difference in frequency order is equal, and the phase sequence is opposite. Thus, linear spatial rotation coordinate transformations are applied to unify frequencies, which enables single-frequency PR controllers with half the number of harmonics to regulate all harmonics.
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Received: 10 April 2024
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2025, Vol. 40 
