# Current Harmonic Suppression Algorithm for Asymmetric Dual Three-Phase PMSM
## 1 Introduction  
With the wide application of power electronic converters, the motor drive system is no longer limited by the phase number of a traditional three-phase power supply, and the multi-phase motor drive system has been widely concerned [1; 2; 3; 4; 5]. The six-phase motor has attracted more and more attention because of its close connection with the traditional three-phase motor. The asymmetric dual three-phase permanent magnet synchronous motor has greater advantages because of smaller torque ripples [5; 6]. It has two sets of three-phase windings with isolated neutral points, which are spatially shifted by 30 degrees, as shown in Figure 1.  
Figure 1: Two sets of three-phase windings. The vector space decomposition (VSD) method is widely adopted for the control of an asymmetric dual three-phase permanent magnet synchronous motor (ADT-PMSM) [7; 8]. According to the dimensions of current control, the control methods based on the VSD can be divided into two kinds: two-dimension current control [9; 10] and four-dimension current control [11; 12; 13]. Two-dimension current control only establishes the current closed-loop control strategy in the \(\alpha\)-\(\beta\) subspace where electromechanical energy conversion takes place, while an open-loop control strategy is adopted in the \(x\)-\(y\) subspace. The fifth and seventh harmonic voltages due to the dead time effects of inverter will cause large harmonic currents. So, the two-dimension current control cannot achieve the desired results, while the four-dimension current control can control the currents of two subspaces separately. A current closed-loop control strategy is set up in the \(x\)-\(y\) subspace to make the harmonic currents 0, which can compensate for the dead-time effects and the nonlinearities of the inverter [13]. In References [14; 15], by suitably selecting the voltage vectors from the divided vector groups into one sampling period, the current harmonics can be reduced compared to the Switching Table based Direct Torque Control (ST-DTC) drive. However, this method can only avoid injecting harmonic voltages into the \(x\)-\(y\) subspace. However, the dead time and nonlinearities of the inverter are not considered. Methods based on a proportional-integral (PI) controller due to its simple structure and well-known characteristics are employed in the \(x\)-\(y\) subspace. However, the fifth and seventh current harmonics are only suppressed to some extent due to its limited bandwidth [16]. Accordingly, a multiple synchronous frame (MSF) scheme based on a PI controller in several synchronous frames (SF) in parallel (one per harmonic) is employed to eliminate the current harmonics in multi-phase machines, which can attain zero steady-state error at different harmonics. However, the computational burden is heavy. In [13; 16; 17], a resonant controller is employed in an anti-synchronous frame rotating with the negative sequence fundamental frequency in the \(x\)-\(y\) subspace to suppress the current harmonics, but the discretization errors of the poles are not considered. In the field of current harmonics suppression of three-phase motor drives, extensive research has been conducted. Methods based on voltage-second balance theory classify the causes that distort the voltages. By offline measurement of the dead time, the turn-on/off time, and the nonlinearities including the forward voltage drop of the switching device and voltage drop of freewheeling diode, the compensation voltages can be calculated [18; 19; 20]. However, these parameters are varied with the junction temperature of the inverter, motor load, speed, and some other factors. Accordingly, online methods are proposed in [21], but these methods add computational burden to the algorithm and require a lookup table to search for the corresponding parameters under certain operating points. Besides, these above-mentioned schemes need the accurate polarities of phase currents [18; 19; 20; 21].