## 4 RMVSC-STATCOM Control Strategy  
When the aforementioned driving pulse sequence is applied in the reinjection circuit of the RMVSC, the switch can operate at a low frequency while maintaining low output voltage harmonic content with no submodule capacitor imbalance issues. Additionally, increasing the number of submodules enables safe and stable operation under high-voltage conditions. This configuration enhances the performance of the RMVSC when employed as a STATCOM. To achieve continuous reactive power control in RMVSC-STATCOM, an appropriate control strategy must be developed. The equivalent circuit model of the RMVSC-STATCOM system is illustrated in Figure 6. The overall system can be modeled as two voltage sources connected via an interconnecting inductance \(L_{s}\), with a phase difference \(\alpha\) between them. Here, \(U_{\mathrm{sA}}\), \(U_{\mathrm{sB}}\), and \(U_{\mathrm{sC}}\) represent the grid voltages, with the grid voltage phase taken as the reference, setting the phase angle to 0. \(U_{\mathrm{rA}}\), \(U_{\mathrm{rB}}\), and \(U_{\mathrm{rC}}\) represent the ac voltages of the RMVSC-STATCOM. For simplification, the reference direction is chosen to be opposite to the grid voltage. \(I_{\mathrm{A}}\), \(I_{\mathrm{B}}\), and \(I_{\mathrm{C}}\) represent the compensation currents; \(\theta\) is the power factor angle; and \(U_{\mathrm{dc}}\) is the dc voltage. The KVL equations for the circuit shown are  
\[U_{si}=j\omega L_{\mathrm{s}}I_{i}+U_{\mathrm{r}i}\hskip 14.226378 pti=A,B,C \tag{17}\]  
The apparent power \(S\) of the RMVSC-STATCOM output for the three phases is  
\[S=3j\frac{U_{\mathrm{s}}(U_{\mathrm{s}}-U_{\mathrm{r}})}{\omega L_{\mathrm{s }}} \tag{18}\]  
The reactive power Q is  
\[Q=\mathrm{Im}(\mathrm{S})=3\frac{U_{\mathrm{s}}(U_{\mathrm{s}}-U_{\mathrm{r}} )}{\omega L_{\mathrm{s}}} \tag{19}\]  
From Equation (19), it is evident that the reactive power transfer of the RMVSC-STATCOM is determined by the ac voltage of the RMVSC. When \(U_{\mathrm{s}}>U_{\mathrm{r}}\) then \(Q>0\), indicating that the RMVSC-STATCOM absorbs reactive power. Conversely, when \(U_{\mathrm{s}}<U_{\mathrm{r}}\), \(Q<0\), indicating that the RMVSC-STATCOM emits reactive power. Thus, the RMVSC-STATCOM enables bidirectional reactive power regulation, providing flexible compensation for the system's reactive power requirements. Figure 6: RMVSC-STATCOM system equivalent model diagram. RMVSC-STATCOM regulates the charging and discharging of the dc-side capacitor by adjusting the firing angle, which in turn determines the dc voltage. This dc voltage subsequently controls the magnitude of the output ac voltage. Consequently, the RMVSC-STATCOM can regulate the transmission of reactive power by modifying the firing angle. The RMVSC-STATCOM control scheme is constructed, as depicted in the control system block diagram shown in Figure 7. The RMVSC-STATCOM controller utilizes a dual-loop control system comprising an outer power loop and an inner current loop. The control strategy is implemented in the _dq_ rotating coordinate system. Initially, the phase-locked loop (PLL) is employed to synchronize with the grid phase. Subsequently, the voltage at the grid connection point and the compensation current are transformed into the _dq_ coordinates. Real-time reactive power is calculated based on instantaneous power theory and is utilized as the feedback parameter \(Q\) for the outer power loop. The RMVSC-STATCOM tracks _Q_* and _I_q* through the outer power loop and inner current loop. As depicted in Figure 8, the control block diagram of the RMVSC-STATCOM illustrates that the outer power loop achieves a grid-side power factor of 1 by tracking _Q_*. The outer power loop generates the reactive current command _I_q*, while active power control is omitted, with _I_q* set to 0. The current control loop then tracks _I_q* and _I_q*, outputting the active and reactive voltage command values _U_d* and _U_q* at the converter port.