# A Multilevel Switched Capacitor Inverter with Reduced Components and Self-Balance
## 4 Topology Extension and Comparison
### Comparison Analysis  
To assess the pros and cons of the proposed SCMLI, a comprehensive contrast with other 13-level topologies is shown in Table 4. Items which are compared include the number of power elements, the number of DC sources, the number of drivers (\(N_{\text{driver}}\)), the voltage gain, the total standing voltage (TSV), and the extensibility of SCMLIs. The cost function in [16] is defined as follows  
\[\text{CF}= \left(N_{\text{switch}}+N_{\text{driver}}+N_{\text{diode}}+N_{ \text{capacitor}}+\alpha\frac{\text{TSV}}{G}\right)\times\frac{N_{\text{dc}}}{ 13}, \tag{31}\]  
where \(\alpha\) is the \"weighing factor\" reflecting the proportion of TSV in the cost function, which is considered to be 0.5 or 1.5. Therefore, the multilevel inverters with a lower cost function have a better performance.  
It can be concluded from Table 4 that the multilevel inverter in [10] can achieve 13-level output with less components, but the voltage gain is only of 2, which is the same as the inverter in [11]. The topology in [16] requires more components in the extended structure. In addition, the above three topologies use two DC sources, which also leads to a high CF value. The inverter in [18] uses a single source to achieve the high-voltage gain. However, the H-bridge will increase the voltage stress of the switches.  
Compared with the above topologies, TSV is significantly reduced in [19; 20; 21; 22], but their voltage gain is no more than 3, and the application range is limited. Due to plenty of elements being used, the inverter in [23] has a higher CF. The 13-level inverters in [24; 25; 26; 27] and [29] can achieve a six-fold voltage gain. The inverter in [24] has a lower CF value when \(\alpha=0.5\), while the inverter in [25] has a lower CF value when \(\alpha=1.5\), because they have a different TSV.  
Although the proposed multilevel inverter has a higher TSV, it uses fewer power devices to achieve a six-fold voltage gain. Due to the fact that the proposed inverter has five switch pairs operating in complementary states, fewer drivers are needed to control the switches, and the lowest value of \(N_{\text{driver}}\) can be achieved. Compared with the inverters in [24; 25; 26; 27; 29], the proposed topology with good extensibility can easily increase the output  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{\(N_{\text{dc}}\)} & \multirow{2}{*}{\(N_{\text{switch}}\)} & \multirow{2}{*}{\(N_{\text{driver}}\)} & \multirow{2}{*}{\(N_{\text{diode}}\)} & \multirow{2}{*}{\(N_{\text{capacitor}}\)} & \multirow{2}{*}{\(G\)} & \multirow{2}{*}{**TSV**} & \multicolumn{2}{c}{**CF**} \\ \cline{5-8}  & & & & & & & & & \(\alpha\) = 0.5 & \(\alpha\) = 1.5 & \\ \hline
[10] & 2 & 11 & 7 & 1 & 1 & 2 & 39 & 4.577 & 7.577 & No \\
[11] & 2 & 14 & 11 & 0 & 2 & 2 & 32 & 5.384 & 7.846 & No \\
[16] & 2 & 14 & 14 & 2 & 4 & 3 & 34 & 6.103 & 7.846 & Yes \\
[18] & 1 & 10 & 8 & 10 & 5 & 6 & 43 & 2.814 & 3.365 & Yes \\
[19] & 1 & 12 & 8 & 2 & 4 & 1.5 & 15 & 2.385 & 3.154 & Yes \\
[20] & 1 & 12 & 7 & 4 & 4 & 3 & 13 & 2.243 & 2.577 & No \\
[21] & 1 & 14 & 13 & 2 & 4 & 3 & 18 & 2.769 & 3.230 & Yes \\
[22] & 1 & 13 & 11 & 1 & 3 & 3 & 17 & 2.372 & 2.808 & Yes \\
[23] & 1 & 29 & 29 & 5 & 5 & 6 & 29 & 5.416 & 5.788 & Yes \\
[24] & 1 & 13 & 9 & 2 & 3 & 6 & 39 & 2.327 & 2.827 & No \\
[25] & 1 & 14 & 10 & 1 & 3 & 6 & 33 & 2.365 & 2.788 & No \\
[26] & 1 & 15 & 12 & 0 & 3 & 6 & 35 & 2.532 & 2.981 & No \\
[27] & 1 & 12 & 6 & 4 & 3 & 6 & 36 & 2.154 & 2.615 & No \\
[29] & 1 & 13 & 9 & 2 & 3 & 6 & 32 & 2.282 & 2.692 & No \\ Proposed & 1 & 12 & 6 & 2 & 3 & 6 & 38 & 2.013 & 2.500 & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison with other 13-level SCMLIs.  
levels and acquire a higher voltage gain, which is conducive to applying more scenarios. Moreover, it can be seen that the CF of the proposed 13-level switched-capacitor inverter is lowest regardless of whether \(\alpha\) is 0.5 or 1.5, which also confirms that the proposed topology has a better overall performance.