# A Review of Modular Multilevel Converters for Stationary Applications
## 2 MMC Topologies
### Overall Topologies
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Performance** & **HBSM** & **FBSM** & **SCSM** & **NPCSM** & **FCSM** & **CDSM** & **HSM** & **CCSM** \\ \hline No. of & & & & & & & & \\ diodes & & & & & & & & \\ Max. voltage & \(v_{c}\) & \(v_{c}\) & \(v_{c}\) & 2 \(v_{c}\) & 2 \(v_{c}\) & 2 \(v_{c}\) & 2 \(v_{c}\) & 2 \(v_{c}\) \\ Bipolar & No & Yes & Yes & No & No & Yes & Yes & Yes \\ operation & DC fault & & & & & & & \\ DC locking & & & & & & & & \\ Power losses & Low & High & Low & Moderate & Low & Moderate & Moderate \\ Cost & Low & Moderate & High & High & High & High & High & High \\ Control & Low & Low & Low & High & High & Low & Low & High \\ complexity & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. chopper cells or bridge cells on account of the selection of submodules. They can be further split into single-star, single-delta, double-star, double-delta, and triple-star based on star and delta count. The configuration circuits are shown in Figure 5.  
Single-star and single-delta are the basic structures in the subfamily of star/delta-configured MMCs. They have three strings of submodules connected in either star or delta configuration. A single-star MMC is preferred in applications such as power compensators (STATCOM) and battery energy storage systems. Double-star and double-delta include two-star or delta-configured clusters connected by a DC source/load. They can realize the bidirectional current conversion of DC-AC or AC-DC. A double-star is widely used in MMC industries such as HVDC transmission and motor drive systems. A triple-star MMC [67] is comprised of three star-connected clusters, i.e., nine branches. It is well-known as a \"modular multilevel matrix converter\" (M3C) [68; 69; 70]. Figure 4d,e are the two same presentations for triple-star MMC or M3C. It is capable of converting AC to AC directly between the bidirectional three-phase power system confronted with traditional AC-DC-AC indirect conversion, which is similar to back-to-back configuration [71] and involves two three-phase MMCs including twelve branches. It has superior performance for the medium-voltage and high-power motor drive system with regenerative braking. Figure 4: Overall single-phase configurations topologies: (**a**) Symmetric hybrid MMC; (**b**) Bifurcate MMC; (**c**) PC-MMC; (**d**) AC-MMC. In recent years, researchers developed a new topology for MMC referred to hexagonal MMC or Hexverter [72]. The Hexverter consists of six arms connected in a hexagonal circuit, and each arm is alternatively connected to one phase of two three-phase AC networks, as shown in Figure 5f. This novel topology can achieve direct AC-AC conversion with a further reduced number of branches and components when compared with triple-star MMC or M3C. This converter is advantageous when applied in applications such as low-frequency wind turbines. However, the Hexverter has limited reactive power provision capability at some operation points, together with injected common-mode voltage, which is not expected in some applications such as motor drives. Therefore, another hexagonal topology called Hex-Y [73, 74] is proposed based on the Hexverter. Except for the retaining hexagon circuit, three star-connected branches are added within  
Figure 5: MMC arm configurations: (**a**) Single-star MMC; (**b**) Single-delta MMC; (**c**) Double-star MMC; (**d**) Triple-star MMC; (**e**) M3C; (**f**) Hexverter; (**g**) Hex-Y. the hexagon, as shown in Figure 5g. A comparison for low-frequency mode was carried out between the Hex-Y and the M3C due to their identical number of branches. Simulation results indicate that the Hex-Y has a lower peak and RMS currents for low frequency below 5 Hz, and beyond 5 Hz, these turn to be higher than the M3C. The Hex-Y has flat torque-speed characteristics with low frequency. It is applicable for both fields which operate at low frequency and require full power capability in a wide frequency spectrum.