# 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 Current  
Taking the topology shown in Figure 1 as an example, the main components of the CM current are analyzed. The main components of CM current are analyzed from three aspects of CM equivalent circuit, i.e., the CM equivalent model, the modulation of H6 inverter and the load. This section focuses on the generation principle of the high frequency components. The topology with CM suppression capability under ideal conditions can keep the CM voltage as constant. Therefore, there should be no harmonics of modulation frequency. However, the inconsistency of the dynamic process during the opening and closing of the switching device or the inconsistency of the switching device driving signal leads to the change of CM voltages. Figure 4: The most simplified equivalent common-mode circuit. For example, in Figure 1, the bridge of H6 in the positive half cycle modulation process may cause VT\({}_{4}\) to be turned off before VT\({}_{1}\) due to the inconsistency of dynamic process or of the driving signal. Hence, according to Equation (11), \(V_{\text{cm-t}}\) can be depicted as:  
\[V_{\text{cm-t}}=\frac{V_{\text{AO}}{+}V_{\text{BO}}}{2}=\frac{V_{\text{dc}}+0.5 V_{\text{dc}}}{2}=\frac{3V_{\text{dc}}}{4} \tag{12}\]  
where \(V_{\text{cm-t}}\) does not return to \(V_{\text{dc}}/2\) until VT\({}_{1}\) is turned off, which causes the CM voltage to generate the spike. Conversely, if VT\({}_{1}\) is turned off before VT\({}_{4}\), \(V_{\text{cm-t}}\) will produce a sudden change of \(V_{\text{dc}}/4\). In the worst case, the frequency of CM voltage is the same as the modulation frequency of the inverter bridge. The circuit resonance caused by the mode transformation of the inverter bridge makes the CM voltage fluctuate. The inverter adopts the PWM mode; therefore, the CM voltage contains the harmonic of each order. Some specific harmonic makes the impedance of the CM equivalent circuit be pure resistance, or makes the local LC branch to be pure resistance, which will lead to resonance. It can be seen from Equation (5) that the impedance of the CM equivalent circuit is lower in the vicinity of the resonant frequency than in the frequency section of non-resonance, which leads to the larger CM current with the same CM voltage at the resonant frequency. From Equations (2) and (10), due to the asymmetry of the output filter inductance \(L_{1}\) and \(L_{2}\), it can be concluded that the differential mode voltage of the CM circuit loop with the switching frequency is introduced. It is assumed that the inductance difference of \(L_{1}\) and \(L_{2}\) is 10% [14], therefore, \(V_{\text{cm-t}}\) can be depicted as:  
\[V_{\text{cm-t}}=V_{\text{cm}}+V_{\text{dm}}\frac{L_{1}{-}L_{2}}{2(L_{1}{+}L_{ 2})}=V_{\text{cm}}\pm 0.025V_{\text{dm}} \tag{13}\]  
Because of the asymmetry of \(L_{1}\) and \(L_{2}\), the fluctuation component of \(0.025V_{\text{dm}}\) is introduced into the CM voltage. The fluctuation component includes the switching frequency component and the line frequency component. The voltage fluctuation at the output of the PV array resulting from the operation of the Boost circuit causes the CM voltage to fluctuate. Therefore, the CM currents of switching frequency are introduced in the CM circuit loop by these non-ideal factors. The grid can be regarded as the load of the whole PV system. When the grid voltage is not neglected in the CM loop shown in Figure 2, the total voltage is derived as:  
\[V_{\text{cm-t}}=0.5(V_{\text{AO}}+V_{\text{BO}})-0.5V_{g} \tag{14}\]  
From Equation (14), \(V_{\text{cm-t}}\) has the fluctuation component of line frequency and the amplitude is half the amplitude of the grid voltage. Hence, the CM current has a large component of line frequency. In addition, since the inverter uses the PWM modulation, the low-order harmonic components in the CM voltage are inevitably produced. The low-order harmonics cannot be filtered by the passive LC filter and EMI filter. Hence, there is a certain amount of low-order harmonic components in the CM current.