## 6 Various Criteria for Assessing the Power Quality and Efficiency of the Studied System
### Power Quality
#### 6.1.4 DCB Overcharging  
DTLI configurations, supplied by two isolated and symmetrical voltage sources (with a voltage ratio of \(1:1\), i.e., both converters use the same voltage level), designed to improve output voltage quality by enabling three-level operation, represented a significant advance in terms of output voltage quality [155]. However, to further improve voltage quality, configurations with two isolated but asymmetrical voltage sources (with a voltage ratio of \(2:1\)) were introduced, allowing a four-level operation [67]. However, the use of these asymmetrical sources introduced a potential overcharging problem, particularly at the DC bus capacitor (DCB-C) (see Figure 19). The overcharging problem is related to the phase current flowing in the DCB-C during the modulation process. This current is made up of the components \(i_{a}\), \(i_{b}\), and \(i_{c}\), as shown in Figure 19. Depending on the specific switching states, these currents can cause the DCB-C to overcharge. To better understand these scenarios, Figure 20 shows different cases of current flow in the DCB-C, using colors to indicate the path of phase current flow. Green represents the \(i_{a}\) current, red the \(i_{b}\) current, and blue the \(i_{c}\) current. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{N}^{\circ}\) & **Vectors** & **ZSV Levels** \\ \hline \hline
1 & \(V_{18}V_{J7}\) & \(-V_{dc}\) \\ \hline
2 & \(V_{18}V_{J4}\), \(V_{18}V_{j6}\), \(V_{18}V_{j2}\), \(V_{15}V_{J7}\), \(V_{13}V_{J7}\), \(V_{11}V_{J7}\) & \(-2V_{dc}/3\) \\ \hline
3 & \(V_{18}V_{\bar{5}}\), \(V_{18}V_{3}\), \(V_{15}V_{J4}\), \(V_{13}V_{J4}\), \(V_{18}V_{J1}\), \(V_{15}V_{J2}\), \(V_{13}V_{J6}\), \(V_{13}V_{J2}\), & \(-V_{dc}/3\) \\  & \(V_{14}V_{\bar{7}}\), \(V_{11}V_{J4}\), \(V_{11}V_{j6}\), \(V_{11}V_{j2}\), \(V_{16}V_{\bar{7}}\), \(V_{2}V_{\bar{7}}\), \(V_{2}V_{\bar{7}}\), \(V_{5}V_{\bar{6}}\) & \(-V_{dc}/3\) \\ \hline
4 & \(V_{11}V_{\bar{3}}\), \(V_{16}V_{\bar{4}}\), \(V_{2}V_{\bar{7}}\), \(V_{4}V_{1}V_{\bar{5}}\), \(V_{13}V_{\bar{5}}\), \(V_{2}V_{\bar{6}}\), \(V_{4}V_{\bar{6}}\), \(V_{3}V_{\bar{1}}\), & \\  & \(V_{15}V_{\bar{1}}\), \(V_{4}V_{\bar{7}}\), \(V_{2}V_{\bar{5}}V_{\bar{3}}\), \(V_{36}V_{\bar{7}}\), \(V_{2}V_{\bar{7}}V_{\bar{7}}\), \(V_{8}V_{\bar{8}}\), \(V_{11}V_{\bar{1}}\), \(V_{15}V_{\bar{5}}\), & 0 \\  & \(V_{14}V_{\bar{4}}\), \(V_{3}V_{\bar{3}}\), \(V_{2}V_{\bar{7}}\), \(V_{11}V_{\bar{1}}\) & \\ \hline
5 & \(V_{15}V_{\bar{8}}\), \(V_{13}V_{\bar{8}}\), \(V_{14}V_{\bar{5}}\), \(V_{4}V_{\bar{3}}\), \(V_{1}V_{\bar{8}}\), \(V_{2}V_{\bar{5}}\), \(V_{16}V_{\bar{3}}\), \(V_{12}V_{\bar{3}}\), & \\  & \(V_{\bar{i}\pi}V_{\bar{4}}\), \(V_{\bar{i}4}V_{\bar{1}}\), \(V_{\bar{i}6}V_{\bar{1}}\), \(V_{\bar{i}2}V_{\bar{1}}\), \(V_{\bar{i}7}V_{\bar{6}}\), \(V_{\bar{i}7}V_{\bar{2}}\), \(V_{\bar{i}6}V_{\bar{7}}\) & \(V_{\bar{i}6}V_{\bar{7}}\) \\ \hline
6 & \(V_{14}V_{\bar{9}}\), \(V_{16}V_{\bar{9}}\), \(V_{2}V_{\bar{1}}V_{\bar{9}}\), \(V_{\bar{7}}V_{\bar{7}}\), \(V_{\bar{7}}V_{\bar{3}}\), \(V_{\bar{7}}V_{\bar{7}}V_{\bar{1}}\) & \(2V_{dc}/3\) \\ \hline
7 & & \(V_{dc}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ZSV switching vector variations. For example, in Figure 20a, current \(i_{a}\) acts on the positive pole of the DCB-C for the switching state \(\left(V_{1}V_{1}\right)\). However, for the switching state \(\left(V_{2}V_{7}\right)\), shown in Figure 20b, no current flows through the DCB-C. Figure 20c,d show the current flows resulting from switching states \(\left(V_{1}V_{6}\right)\) and \(\left(V_{2}V_{3}\right)\), respectively. In the case of the \(\left(V_{2}V_{3}\right)\) state, the \(i_{b}\) current flows in the positive polarity of the DCB-C, while, for the \(\left(V_{1}V_{6}\right)\) switching state, it flows in the negative polarity of the DCB-C. These currents are referred to as \(+i_{b}\) and \(-i_{b}\), respectively. * Solving the overcharging problem When addressing the issue of overcharging in DTLI systems, the literature typically presents two main approaches.