## 3 Common-Mode Voltage Analysis  
The use of transformers in the PV grid-connected systems guarantees isolation and eliminates the leakage current. These systems are expensive, heavy, bulky and low efficiency [51]. The current trend is focused on removing this device (transformer), in order to eliminate the aforementioned disadvantages [52]. However, removing the transformer is a new challenge, as the leakage current arises in the system. The leakage current is mainly affected by the variation of the voltage in common mode over time [53]. Taking as an example an inverter without transformer with complete bridge topology for a residential PV system connected to the single-phase grid, the equivalent CM circuit of Figure 5 is considered. \begin{table}
\begin{tabular}{c l} \hline \hline
**Standard** & **Description** \\ \hline IEC 61683:2000 & \begin{tabular}{l} Photovoltaic systems—Power conditioners—Procedure form a suring efficiency. It establishes the measurement procedure, test conditions and method of calculating the performance of a photovoltaic inverter (both isolated and grid connection). \\ \end{tabular} \\ \hline EN50530:2000 & \begin{tabular}{l} Overall efficiency of grid-connected photovoltaic inverters. Test methods for measuring static and dynamic efficiency of PV inverters. Based on the IEC61683 standard, new test conditions are added and the concept of inverter performance is redefined, including the MPPT system as a factor to be considered. \\ \end{tabular} \\ \hline IEC61727:2004 & \begin{tabular}{l} Characteristics of Utility Interface. It applies to PV systems interconnected to an electrical distribution network and operating in parallel with it. In these systems, the use of solid-state inverters with anti-island systems and various interconnection requirements of PV systems to the grid is defined. \\ \end{tabular} \\ \hline EN50524 & \
\begin{tabular}{l} Datasheet and nameplate for photovoltaic inverters. Define the nameplate that a PV inverter must have and the information contained in it. \\ \end{tabular} \\ \hline IEC62109 &
\begin{tabular}{l} Safety of power converters for use in photovoltaic power systems. Its purpose is to ensure that the design and construction methods used are safe for the operator and the surrounding area. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standards applicable to PV inverters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
\begin{tabular}{c} THD \textless{}5\% each \\ harm \textless{}2\% \\ \end{tabular} & \textgreater{}0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Standards in selected IEAcountries [43]. The analysis presented in [54], assumes that the negative (N) terminal of PV is the reference point and the midpoints of the bridge leg (1) and (2) as output terminals. From the definitions of differentiation mode, \(V_{CM}\) and \(V_{DM}\) is related as follows:  
\[V_{CM}=\frac{V_{1N}-V_{2N}}{2} \tag{7}\]  
\[V_{DM}=V_{1N}-V_{2N} \tag{8}\]  
where: \(V_{CM}\) is the common voltage, \(V_{DM}\) is the differential voltage, \(V_{1N}\) is the voltage between (1) and (N) and \(V_{2N}\) is the voltage between (2) and (N). Taking into account Equations (7) and (8), \(V_{1N}\) and \(V_{2N}\) are expressed as:  
\[V_{1N}=\frac{V_{CM}+V_{DM}}{2} \tag{9}\]  
\[V_{2N}=\frac{V_{CM}-V_{DM}}{2} \tag{10}\]  
The scheme in the Figure 6 illustrates the diagram of a current full-scale leakage analytical model considering the parasitic branch. where: \(V_{CM-DM}\) indicates the influence of the differential mode voltage to the common-mode voltage. Figure 5: Equivalent circuit of a common-mode single-phase transformerless topology [54]. Figure 6: Simplest common-mode model for single-phase grid-connected inverter. At this point, it is seen that the common-mode voltage has a marked influence on the leakage current.