## 4 Harmonic Suppression Method  
### The Traditional Harmonic Suppression Method  
The main methods to counteract the impact of harmonic voltages in the AC bus on rectifiers include the use of the PI controllers, resonant elements, and quasi-PR(QPR) controllers [22; 23; 24; 25; 26; 27; 28; 29]. According to Figure 6, their transform function of the inner current loop controllers \(G_{\text{PI}}(s)\), \(G_{\text{RE}}(s)\) and \(G_{\text{QPR}}(s)\) are, respectively, presented in (12), (13) and (14). \[G_{\text{PI}}(s)=k_{\text{p}}+\frac{k_{i}}{s} \tag{12}\]  
\[G_{\text{RE}}(s)=k_{\text{pRE}}+\sum\limits_{i=2}^{l}\frac{k_{\text{rRE}i} \omega_{i}^{2}}{s^{2}+\omega_{i}^{2}} \tag{13}\]  
\[G_{\text{QPR}}(s)=k_{\text{PQPR}}+\frac{2k_{\text{QPR}}\omega_{\text{c}}s}{s^{ 2}+2\omega_{\text{c}}s+\omega_{\text{n}}^{2}} \tag{14}\]  
where \(\omega_{\text{n}}\) is the resonant frequency, \(\omega_{\text{k}}\) is \(k\)th harmonic, \(k_{\text{p}}\)\(k_{\text{pRE}}\) and \(k_{\text{PQPR}}\) are proportional coefficients, \(k_{\text{i}}\) is an integral coefficients, and \(k_{\text{rRE}i}\) and \(k_{\text{rQPR}}\) are resonance coefficients. \(\omega_{\text{c}}\) is the cut-off frequency of the QPR controller. When using the inner current loop with the aforementioned three types of controllers, their diagrams of the inner current loop are shown in Figures 7-9, respectively. Figure 8: The control diagram of a current loop with the FI controller. Figure 7: The control diagram of a current loop with the PI controller. As shown in (11) and Figure 7, as long as there are harmonics present, \(m\) will not be zero. No matter how the \(k_{\rm p}\) and \(k_{\rm i}\) are adjusted, the harmonic components cannot be eliminated. Therefore, the PI controller is not suitable for suppressing the impact of harmonic voltages in the AC bus on the HPR. Based on Figure 8, the open-loop transfer function of the inner current loop with the resonance coefficients is  
\[H_{\rm RE}(s)=\frac{k_{\rm PRE}}{sL+r}+\sum_{i=2}^{l}\frac{k_{\rm rREi}\omega_{ i}^{2}}{(s^{2}+\omega_{i}^{2})(sL+r)} \tag{15}\]  
The performance of the resonant elements controller is affected by \(k_{\rm PRE}\) and \(k_{\rm rREI}\). Therefore, it is necessary to plot the Bode diagrams for three different values of \(k_{\rm PRE}\) and \(k_{\rm rREI}\) to analyze. Set the filter order n = 8, the first value set \(k_{\rm PRE}\) = 1, \(k_{\rm rRE2}\) = \(k_{\rm rRE3}\) = \(k_{\rm rRE4}\) = \(k_{\rm rRE5}\) = \(k_{\rm rRE6}\) = \(k_{\rm rRE7}\) = \(k_{\rm rRE8}\) = 1, the second value set \(k_{\rm PRE}\) = 0.35, \(k_{\rm rRE2}\) = 1, \(k_{\rm rRE3}\) = 0.1, \(k_{\rm rRE4}\) = 0.5, \(k_{\rm rRE5}\) = 0.7, \(k_{\rm rRE6}\) = 2, \(k_{\rm rRE7}\) = 1.3, \(k_{\rm rRE8}\) = 1.9, the third value set \(k_{\rm PRE}\) = 10, \(k_{\rm rRE2}\) = 10, \(k_{\rm rRE3}\) = 3.1, \(k_{\rm rRE4}\) = 3.2, \(k_{\rm rRE5}\) = 1.3, \(k_{\rm rRE6}\) = 2.6, \(k_{\rm rRE7}\) = 1.8, \(k_{\rm rRE8}\) = 0.3. The bode diagram is presented in Figure 10.  
From Figure 10, it can be seen that the high gain at the harmonic frequencies indicates that the resonant elements have a good suppression effect on harmonics. However, in the case of the first and third values, the fundamental frequency will experience a leading phase shift, which is detrimental to the stability of the system. Therefore, the selection of coefficients has become a rather critical issue. Small deviations can cause the system to become unstable. The harmonic spectrum in RSHPES is very rich [30; 31; 32], including integer multiple harmonics, interharmonics, and ultraharmonics. Figure 10 only illustrates the  
Figure 10: The Bode diagrams of the resonant elements controller for three different values. Figure 9: The control diagram of a current loop with the QPR controller. suppression capability of the resonant elements on integer multiple harmonics, and cannot eliminate the impact brought by interharmonics and ultraharmonics.