## 2 Theoretical Study of Serial Submodule RMVSC  
### Serial Submodule RMVSC Topology  
Figure 1 illustrates the m-level (m = n + 1) novel RMVSC topology. The currents \(I_{\text{A}}\), \(I_{\text{B}}\) and \(I_{\text{C}}\) represent the ac currents of the RMVSC. The ac currents \(I_{\text{D}i}\) and \(I_{\text{Y}i}\) (\(i\) = A, B, C) correspond to the D and Y main bridge, respectively. The phase voltages \(U_{\text{D}}\) and \(U_{\text{Y}A}\) correspond to the D and Y windings on the transformer's valve side, respectively. The reinjection voltages \(U_{\text{J}\text{D}}\) and \(U_{\text{J}\text{Y}}\) correspond to the D and Y bridges, respectively. The dc currents \(I_{\text{d}\text{c}\text{D}}\) and \(I_{\text{d}\text{c}\text{Y}}\) correspond to the D and Y main bridges, respectively. The voltage \(U_{\text{dc}}\) denotes the dc voltage. The voltage \(U_{\text{rA}}\) denotes the A-phase voltage. SM refers to the half-bridge submodule. The transformation ratios of the Y/D and Y/Y transformers are K\({}_{\text{n}}\):\(\sqrt{3}\) and K\({}_{\text{n}}\):1, respectively.  
The RMVSC topology is divided into two components: the main bridge circuit and the reinjection circuit. The main bridge circuit is configured as a 12-pulse voltage source converter and is further divided into two sections: the Y main bridge (connected to the Y/Y transformer) and the D main bridge (connected to the Y/D transformer). The reinjection circuit comprises dynamically connected submodules in series. The Y reinjection circuit is cascaded at both ends of the Y main bridge circuit, while the D reinjection circuit is cascaded at both ends of the D main bridge circuit. Each submodule is capable of generating two voltage levels (1 and 0) by altering the switch state. By adjusting the number of submodules and the on-off intervals, any m-level linear reinjection voltage waveform can be synthesized.  
The main bridge circuit operates using a 180\({}^{\circ}\) conduction method with a switching frequency of 50 Hz. Given that the reinjection voltage cycle is 60\({}^{\circ}\), the minimum required switching frequency for the reinjection circuit is 300 Hz. The Y and D reinjection circuit is triggered synchronously with the Y and D main bridge, maintaining a 30\({}^{\circ}\) phase difference between them. Each reinjection circuit modulates the dc voltage across the main bridge into a linear multilevel reinjection voltage by adjusting the linear combination of connected sub-modules. The Y and D reinjection voltages are superimposed in series with the grid-side windings of the transformers via the main bridge converter, yielding an ac output voltage waveform characterized by high power quality and low harmonic distortion. Additionally, during the commutation period of the main bridge converter, the reinjection circuit enables a ZVS interval for the main bridge switches, facilitating operation at a reduced switching frequency and minimizing voltage spikes. Consequently, the power electronic switches require only low-capacity absorption circuits, which extend their service life and reduce losses.  
Compared to the cascaded H-bridge RMVSC, the serial submodule reinjection circuit eliminates the need for a large capacitor as a dc voltage support element, instead utilizing multiple submodules to support the dc bus voltage. This approach significantly enhances the advantages of the system in high-voltage and high-power scenarios and reduces the overall equipment volume. By increasing the number of submodules, the number of output voltage waveform levels are elevated, thereby reducing the voltage of the switch while reducing the harmonic distortion rate of the ac voltage and improving power quality.