# Common-Ground Photovoltaic Inverters for Leakage Current Mitigation: Comparative Review
## 1 Introduction
#### 3.1.1 Generation mechanism of leakage current  
The generation mechanism of leakage current can be explained by representing the above-mentioned single-phase PV system as shown in Figure 2a, where \(v_{1Q}\) and \(v_{2Q}\) are the voltages of the inverter terminals to the reference point \(Q\). Two voltage components, differential-mode (DM) and common-mode (CM) can be identified in terms of \(v_{1Q}\) and \(v_{2Q}\) as follow:  
\[v_{dm}=v_{1Q}-v_{2Q}\;\;\text{and}\;v_{cm}=\left(v_{1Q}+v_{2Q}\right)/2 \tag{2}\]  
The currents of the output inverter terminals, \(i_{1}\) and \(i_{2}\), can be expressed as follow:  
\[i_{1}=i_{dm}+i_{cm}/2\;\;\text{and}\;i_{2}=i_{dm}-i_{cm}/2 \tag{3}\]  
According to (1) and (2), a simple model for the total common-mode voltage (\(v_{cm-total}\)) is shown in Figure 2b, where \(Z_{L-eq}\) is the parallel combination of two lines impedances (\(Z_{L-eq}=\left(\frac{Z_{1}Z_{2}}{Z_{1}+Z_{2}}\right)\)). Thus, the total CMV component (\(v_{cm-total}\)) can be expressed as:  
\[v_{cm-total}=v_{cm}+\frac{v_{dm}}{2}\left(\frac{Z_{1}-Z_{2}}{Z_{1}+Z_{2}}\right) \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Leakage Current Value (mA)** & **Disconnection Time (msec)** \\ \hline
30 & 300 \\
60 & 150 \\
100 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Leakage current limits and their corresponding disconnection times according to VDE 0126-1-1 standard [19]. Figure 2: (**a**) Common-mode equivalent circuit of single-phase grid-connected converter, (**b**) simplified equivalent circuit for the total common-mode voltage. Accordingly, the unsymmetrical of the line impedances (\(Z_{1}\) and \(Z_{2}\)) can produce another source for leakage current. - Mitigation methods of leakage current According to the above analysis, there are mainly three directions that can be adopted to eliminate or minimize leakage currents in single-phase PV connections: - Using of common-mode (CM) chokes: this represents an effective solution to mitigate the leakage current in grid-connected systems [21]. These filters can be connected on either the DC side or the AC side of the inverter. To reduce the required size and weight, a number of configurations have been proposed for magnetic integration of the differential-mode (DM) and common-mode (CM) filters [22]. In these configurations, two types of coils use a common core; according to the DM and CM current directions, some coils attenuate the DM current component, and the other coils attenuate the CM current components. However, these filters introduce a significant increase in cost, size, and weight. In addition, the losses of these coils reduce the overall efficiency. Furthermore, core saturation at high leakage current values worse the overall system performance. Thus, large cores might be needed to avoid such scenario; - Keeping constant CMV: Accordingly, no leakage current can be generated. According to the expression in (3), two conditions must be realized for this purpose: - Equal line impedances (\(Z_{1}\) and \(Z_{2}\)). This requires two filter inductors with independent iron cores, which can result in increased size and cost. - Achieving constant value for CM component expressed in (1). Some effort has been reported in the literature to achieve constant CM component; two main directions are followed: - Modulation-based method [1, 3, 4, 6, 8]. A simple way to realize the constant CM component is to use the full-bridge inverter with the bipolar sinusoidal PWM; this offers a constant CM at half of the DC bus voltage. However, compared to unipolar sinusoidal PWM, such modulation strategy results in high switching losses and high harmonic contents, which need a large filter size. - Converter-based methods (modified full-bridge converters). To keep constant CM when the unipolar modulation is used, a number of topologies have been developed based on the full-bridge inverter, such as the H5 inverter and the HERIC inverter. The main idea of these topologies is the disconnection of PV from the grid during freewheeling mode.