# Current Harmonic Suppression Algorithm for Asymmetric Dual Three-Phase PMSM
## 4 Proposed Current Harmonics Suppression Strategy
### Adaptive Feedback Current Control Loop  
A feedback current control loop is implemented in the anti-synchronous reference frame to eliminate the sixth-order current harmonics. According to Equation (10), the sixth-order current harmonics in the _x1-y1_ coordinate axis can be defined as follows:  
\[\left[ \begin{array}{c}I_{x1}^{6}\\ I_{y1}^{6}\end{array} \right]=\left[ \begin{array}{c}I_{xs}\sin(6w_{e}t)+I_{ xc}\cos(6w_{e}t)\\ I_{ys}\sin(6w_{e}t)+I_{yc}\cos(6w_{e}t)\end{array} \right] \tag{14}\]  
Figure 6: Relationship between the current vector angle and polarities of six-phase currents. The resonant controller can achieve infinite gain at the specific frequency [16; 17; 23], which can be expressed in the s-domain as follows:  
\[G_{R}(s)=K_{R}\frac{s}{s^{2}+\left(hw_{e}\right)^{2}} \tag{15}\]  
where \(h\) is the harmonic order, and \(K_{R}\) is the resonant gain. When the frequency of ac signal is \(hw_{e}\), i.e., s = \(jhw_{e}\), the amplitude can be obtained as  
\[\left|G_{R}(s)\right|_{\mathrm{s=}jhw_{e}}=\sqrt{(\frac{K_{R}hw_{e}}{-w_{e}^{2 }+w_{e}^{2}})} \tag{16}\]  
From Equation (16), it is obvious that the amplitude of \(G_{R}(s)\) is infinite, which can achieve a zero steady-state error of an AC signal at the resonant frequency. However, the gain of the frequency that is not located at the resonant frequency decreases sharply, which will make the control system more sensitive to the change of input signal frequency and may result in system fluctuation. In addition, due to the limitation of the accuracy of the digital system, the ideal resonant controller is not easy to implement in digital signal processor (DSP). In order to take advantage of the resonant controller, it is necessary to improve the ideal resonant controller. The improved resonant controller can be employed as  
\[G_{MR}(s)=\frac{K_{R}w_{c}s}{s^{2}+2w_{c}s+\left(hw_{e}\right)^{2}} \tag{17}\]  
where \(w_{c}\) is the cut-off frequency. So, the relationship between output voltage function \(Y(s)\) and current error function \(E(s)\) can be expressed as  
\[G_{MR}(s)=\frac{Y(s)}{E(s)}=\frac{K_{R}w_{c}s}{s^{2}+2w_{c}s+\left(hw_{e} \right)^{2}} \tag{18}\]  
which can also be defined as follows:  
\[\left\{ \begin{array}{c}Y(s)=\frac{1}{s}[K_{R}w_{c}E(s)-V_{1}(s)-V_{2}(s)]\\ V_{1}(s)=2w_{c}Y(s)\\ V_{2}(s)=\frac{\left(hw_{e}\right)^{2}}{s}Y(s)\end{array} \right. \tag{19}\]  
The equivalent schematic block diagram of Equation (19) is shown in Figure 7.  
Figures 8 and 9 show the Bode diagrams of the improved resonant controller. It is obvious that the parameters will influence the system gain and bandwidth. The gain and bandwidth of the improved resonant controller will increase as the parameter \(w_{c}\) increases, but a large \(w_{c}\) will affect the frequency selection characteristics of the controller, while the change of \(K_{R}\) will only influence the gain of the improved resonant controller. It is ideal to choose a larger \(K_{R}\), but the stability and convergence will  
Figure 7: Structure of the improved resonant controller. be affected. So, the best values of \(K_{R}\) and \(w_{c}\) should be determined by comprehensive consideration according to the actual situation of the system. 5 Pulse Width Modulation (PWM) Techniques for the Implementation of Four-Dimensional Current Control  
The block diagram of four-dimensional current control based on the VSD approach is illustrated in Figure 10, which can compensate for nonlinear factors such as dead-time effects. After the feedback current control loop is adopted in both \(\alpha\)-\(\beta\) and \(x\)-\(y\) subspaces, the desired voltages \(u_{\alpha}\), \(u_{\beta}\), \(u_{x}\), and \(u_{y}\) can be acquired. Applying the inverse VSD transformation, the phase voltages after the feedback current control loop can be obtained as follows:  
\[\left[ \begin{array}{cccccccc}U_{AN}^{*}&U_{BN}^{*}&U_{CN}^{*}&U_{DN}^{*}&U_{ EN}^{*}&U_{FN}^{*}\end{array} \right]^{T}=T_{VSD}^{-1}\left[ \begin{array}{cccccccc}U_{ \alpha}&U_{\beta}&U_{x}&U_{y}\end{array}