# Novel Common-Mode Current Suppression Method in Transformerless PV Grid-Connected System
## 3 Proposed Novel CM Internal Loop Method to Suppression CM Current
### Proposed Novel Dual CM Internal Loop to Suppress CM Currents  
Based on single CM internal loop, this paper proposes to set up the novel RC branch between the EMI filter side and the dc negative bus, which can be named as double CM internal loop, as shown in Figure 7. The \(R_{5}\)-\(C_{5}\), \(R_{6}\)-\(C_{6}\), \(R_{7}\)-\(C_{7}\) and \(R_{8}\)-\(C_{8}\) branches are connected to the inverter, the EMI filter side and the dc negative bus side to form a dual CM internal loop, respectively.  
In Figure 7, since the value of grounded Y capacitor is usually very small compared with the parasitic capacitance, the Y capacitor of the EMI filter is ignored [15]. Figure 8 shows the CM equivalent circuit with a double CM internal loop, where \(C_{5\text{-}6}\), \(R_{5\text{-}6}\), \(C_{7\text{-}8}\), and \(R_{7\text{-}8}\) are described.  
\[C_{5\text{-}6}=C_{5}+C_{6} \tag{17}\]  
\[R_{5\text{-}6}=R_{5}R_{6}/(R_{5}+R_{6}) \tag{18}\]  
\[C_{7\text{-}8}=C_{7}+C_{8} \tag{19}\]  
Figure 5: The single-phase PV grid-connected system with single common-mode inner loop.  
Figure 6: The equivalent common-mode circuit with single common-mode inner loop.  
Figure 7: The single-phase PV grid-connected system with double common-mode inner loops.  
For the second order LC circuit, the resonant frequency \(f_{\rm res1}\) and \(f_{\rm res2}\) are derived as [16]:  
\[f_{\rm res1}=\frac{1}{2\pi\sqrt{(L_{1-2}+L_{\rm cm1})\cdot(C_{1-2}+C_{\rm PV})}} \tag{21}\]  
\[f_{\rm res2}=\frac{1}{2\pi\sqrt{L_{\rm cm2}\frac{C_{\rm PV}C_{1-2}}{C_{1-2}+C_{ \rm PV}}}} \tag{22}\]  
Capacitors \(C_{1}\) and \(C_{2}\) should satisfy \(f_{\rm res1}\) and \(f_{\rm res2}\)[8]:  
\[10f_{\rm grid}\leq f_{\rm res1}\leq f_{\rm sw}/10 \tag{23}\]  
\[3f_{\rm res1}\leq f_{\rm res2}\leq f_{\rm sw}/2 \tag{24}\]  
where \(f_{\rm grid}\) is the grid frequency and \(f_{\rm sw}\) is the switching frequency of the inverter.  
Figure 6 shows the single CM internal loop. Let \(f_{\rm res1}\) = 1.5 kHz and \(C_{\rm PV}\) = 0.5 uF. According to the experimental platform, the filter parameters are set as \(L_{\rm cm1}=L_{\rm cm2}\) = 1.3 mH and \(L_{1}=L_{2}\) = 1 mH. The calculated value of \(C_{1}\) and \(C_{2}\) is 2.88 uF. In practical application, the value of \(C_{1}\) and \(C_{2}\) is 2.7 uF, therefore \(f_{\rm res2}\approx\) 6.5 kHz, which meet the requirements of Equation (24).  
In Figure 8, for the CM equivalent circuit, the resonant frequencies \(f_{\rm res3}\) and \(f_{\rm res4}\) are derived as:  
\[f_{\rm res3}=\frac{1}{2\pi\sqrt{L_{1-2}(C_{5-6}+C_{\rm PV}+C_{7-8})}} \tag{25}\]  
\[f_{\rm res4}=\frac{1}{2\pi\sqrt{(L_{\rm cm1}+L_{\rm cm2})\frac{(C_{\rm PV}+C_{ 7-8})C_{5-6}}{C_{5-6}+C_{\rm PV}+C_{7-8}}}} \tag{26}\]  
where \(f_{\rm res3}\) = 1.5 kHz, \(f_{\rm res4}\) = 6.5 kHz, and \(C_{\rm PV}\) = 0.5 uF. According to Equations (25) and (26), \(C_{5}=C_{6}=0.1\) uF and \(C_{7}=C_{8}=1.1\) uF. The resistance R in the RC branch is mainly to suppress the resonance of CM circuit and to suppress leakage current. According to Equations (27)-(29), \(R_{5}=R_{6}=22\)\(\Omega\), \(R_{7}=R_{8}=7.4\)\(\Omega\).  
\[R_{5-6}=\frac{\left(C_{\rm eq}+\sqrt{C_{\rm eq}+1}\right)\sqrt{L_{1-2}}}{2C_{ \rm eq}\sqrt{C_{\