# Novel Common-Mode Current Suppression Method in Transformerless PV Grid-Connected System
## 2 Analysis of the CM Current of Non-Isolated Grid-Connected PV System  
### Analysis of CM Loop Models  
In the current market, the distributed residential grid-connected PV systems that have the characteristic of non-isolation and low power include two stages with Boost converter and single-phase inverter [11], as shown in Figure 1. In this system, the Boost circuit mainly completes the MPPT function. When the dc bus voltage Vdc is controlled at a constant value, the output side of the front Boost circuit can be equivalent to a voltage source. The inverter circuit completes the conversion from dc to ac, and the topology with the function of CM current suppression is usually adopted [12].  
Figure 1: The two-level single-phase PV grid-connected system considering the parameters.  
In Figure 1, the single-phase PV grid connected system with two stages uses the H6 topology shown in the Box I of the Figure 1. This H6 topology embeds two unidirectional freewheel units into the midpoint of a full bridge inverter, which provide novel freewheel paths and separate battery cells form a grid during free wheeling time. Body diodes with poor performance of active switches are not used so it achieves higher efficiency. Meanwhile, split capacitors are not needed as in topologies with dc bypass structure [13]. In addition to the use of LC filter, the EMI filter with \(L_{\text{cm1}}\), \(C_{\text{Y1}}\), \(C_{\text{Y2}}\), and \(L_{\text{cm2}}\) is added on the output side shown in Box II of the figure. According to the definitions of the CM voltage and the differential mode voltage, the inverter CM voltage \(V_{\text{cm}}\) and differential-mode voltage \(V_{\text{dm}}\) can be obtained as:  
\[V_{\text{cm}}=0.5(V_{\text{AO}}+V_{\text{BO}}) \tag{1}\]  
\[V_{\text{dm}}=V_{\text{AO}}-V_{\text{BO}} \tag{2}\]  
thus  
\[V_{\text{AO}}=V_{\text{cm}}+0.5V_{\text{dm}} \tag{3}\]  
\[V_{\text{BO}}=V_{\text{cm}}-0.5V_{\text{dm}} \tag{4}\]  
In this paper, the high frequency components in the CM current are considered. Therefore, in the CM equivalent circuit, the influence of the grid voltage on the CM circuit is neglected. According to Equations (3) and (4), the CM equivalent circuit of two stages PV grid-connected systems is shown in Figure 2, where \(C_{\text{PV}}\) is the equivalent parasitic capacitance.  
In Figure 2, the CM inductance is located in the differential mode branch. The CM inductance has no influence on the differential signal, therefore, it can be moved to the CM branch. Figure 3 shows the simplified CM equivalent circuit.  
Figure 3: The simplified common-mode equivalent circuit.  
Figure 2: Common-mode equivalent circuit.  
By using the principle of circuit equivalent, the differential mode circuit is equivalently transformed and the branch impedance is calculated. The simplest CM equivalent circuit is shown in Figure 4.  
In Figure 4, \(Z\) is the equivalent impedance of the CM circuit and \(V_{\text{dm-t}}\) is the equivalent differential-mode voltage, expressed as:  
\[Z=j\omega L_{1-2}+j\omega L_{\text{cm1}}+\frac{1}{2j\omega C_{\text{PV}}}+\frac {1}{j\omega C_{1}+1/Z_{1}} \tag{5}\]  
\[V_{\text{dm-t}}=V_{\text{dm}}\frac{L_{1}-L_{2}}{2(L_{1}+L_{2})} \tag{6}\]  
where \(\omega\) is the angular frequency.  
\(Z_{1}\), \(C_{1}\), and \(L_{1\text{-2}}\) are derived as below:  
\[Z_{1} =j\omega L_{\text{cm2}}+R_{\text{g}} \tag{7}\]  
\[C_{1} =C_{\text{Y1}}+C_{\text{Y2}} \tag{8}\]  
\[L_{1-2} =L_{1}L_{2}/(L_{1}+L_{2}) \tag{9}\]  
According to Figure 4, the total voltage of the CM voltage loop \(V_{\text{cm-t}}\) is derived as:  
\[V_{\text{cm-t}}=V_{\text{cm}}+V_{\text{dm}}\frac{L_{1}-L_{2}}{2(L_{1}+L_{2})} \tag{10}\]  
It is assumed that \(L_{1}=L_{2}\). The CM loop voltage \(V_{\text{cm-t}}\) can be depicted as:  
\[V_{\text{cm-t}}=V_{\text{cm}}=0.5(V_{\text{AO}}+V_{\text{BO}}) \tag{11}\]