## 3 Various System Configurations Studied
### Configuration Type II: Two Isolated DCB Sources  
This topology is the same as that described in Section 3.1. However, it is based on the use of two isolated DCB sources (Type II), as shown in Figure 9.  
This configuration can be divided into two categories: DTLI configurations with symmetrical and asymmetrical voltage sources. As shown in Figure 9, this configuration features two separate DC buses, which are mutually isolated [98, 99, 99, 100, 55, 57, 91, 101, 102, 103, 104, 105, 106, 107, 108]. The isolation of the DC buses prevents the circulation of triple-harmonic currents. The use of the DTLI system, with two DCB sources of unequal values (asymmetrical voltage source), leads to a significant change in the converter operation, compared to the scenario where both DCB sources have equal values (symmetrical voltage source). Figure 10 illustrates the voltage vector generation diagrams for these two cases: one with equal voltage sources and the other with unequal voltage sources \(\left(V_{dc}^{Master}=2V_{dc}^{Slave}\right)\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Vector Name** & \(\mathbf{N}^{\circ}\) **of Vectors** & **Magnitude** \\ \hline Zero vectors & O & 0 \\ \hline Small vectors & ABCDEF & \(2/3V_{dc}\) \\ \hline Intermediate vectors & HJLNQS & \(2/\sqrt{3}V_{dc}\) \\ \hline Large vectors & GIKMPR & \(4/3V_{dc}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Voltage vector groups for DTLIs with a common DCB. Figure 8: Vector diagram of the space of a DTLI. The vector voltage diagrams are derived by considering the complex switching sequences \(S_{i}\) and \(S_{j}\). These sequences are defined for the master inverter \((S_{i1}=1,\,S_{i3}=0,\,S_{i5}=0)\) and for the Slave inverter \(\big{(}S_{j1}=1,\,S_{j3}=1,\,S_{j5}=0\big{)}\), as shown in Figure 3. The output voltages are given by Equation (11), and the corresponding diagrams are provided in Figure 10.  
\[ \begin{cases}V_{i}=V_{dc}^{Master}\overline{S_{x}}+V_{dc}^{Slave}\overline{S_ {y}}\\ V_{j}=V_{dc}^{Master}\overline{S_{y}}+V_{dc}^{Slave}\overline{S_{x}}\end{cases}  \tag{11}\]  
The complex vectors resulting from various switching combinations are used to indicate the direction of the complex voltage vectors' positions. In this context, there are two voltage vectors: one aligned with the \"\(\alpha\)\" axis and the other 60 degrees out of phase with the \"\(\alpha\)\" axis. The amplitude of the voltage vectors is determined by the electrical source value. If the two voltage sources are of equal intensity, the corresponding voltage vectors will have the same magnitude and orientation. However, if the voltages are unequal, such as in a \(2:1\) voltage ratio, additional vectors are generated. These extra vectors can be observed in Figure 10. Further analysis shows that some of these additional vectors may be redundant. By employing asymmetrical voltage sources, these redundant vectors can  
Figure 10: Voltage vector compositions: (**a**) symmetrical voltage source and (**b**) asymmetrical source ratio of (2:1). Figure 9: Configuration of a DTLI powered by a two isolated DCB. be isolated, increasing the number of available output voltage vectors. This provides a broader range of options for generating distinct output voltages. Figure 11a illustrates a spatial vector scheme for a two-level DTLI, utilizing voltage sources with an unequal voltage ratio of \(2:1\). This converter system, with a \(2:1\) voltage ratio, generates \(37\) voltage vectors, which are uniformly and symmetrically distributed in the \(\alpha\beta\) plane. On the other hand, the vector diagram shown in Figure 11b is constructed considering the use of asymmetrical sources with a voltage ratio of \(3:1\). In this converter configuration, \(48\) voltage vectors can be generated. However, these vectors are distributed asymmetrically in the \(\alpha\beta\) plane. It should be noted that, in this arrangement, certain areas present challenges regarding the selection of the three closest vectors. This complexity may introduce additional harmonics into the output waveform.