## 4 Discussion  
### Simulation Results  
First, numerical simulations are conducted in MATLAB/Simulink (R2021b) environment in order to evaluate the effectiveness of the proposed VSG-based control with the improved CVB method. The obtained results are also compared to the conventional PQ decoupled control with the CVB method. All simulations are performed using the parameters listed in Table 1.  
Figure 5 presents the simulation results of two control strategies applied to the MMC, namely CVB-PQ control and CVB-VSG control. The waveforms of current and voltage in the steady-state operation of the MMC and the grid are shown in Figures 5a and 5b, respectively. The estimated capacitor voltages of phase A SMs are illustrated in Figures 5c and 5d for CVB-PQ control and CVB-VSG control, respectively. When there is a change in injected power to the grid, the capacitor voltages of the SMs deviate to adjust to an equilibrium state, as demonstrated by Figure 5e. The voltage fluctuations of SMs in the same arm are identical and complementary between the upper \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Simulation** & **Experimental** \\ \hline DC voltage (VDC) & 400 V & 100 V \\ AC voltage (VAC) & 155 V & 30 V \\ AC frequency & 50 Hz & 50 Hz \\ Power active & 6–7.5–9 Kw & 100–120 W \\ Number of SMs per arm & 2 & 2 \\ Capacitor value for a SM & 50 mF & 3.3 mF \\ Arm inductance/arm resistor & 1 mH/0.5 \(\Omega\) & 10 mH/0.5 \(\Omega\) \\ Phase inductor/phase resistor & 20 mH/0.5 \(\Omega\) & 20 mH/0.5 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electrical power system parameters. and lower arms. The voltage fluctuation range of the SMs is 198.2 V to 198.35 V for CVB-VSG control and 195 V to 195.4 V for CVB-PQ control. The circulating currents of both CVB-PQ control and CVB-VSG control are presented in Figure 5f. The fluctuation of the circulating current is \(-3.4\) A to 3.4 A for CVB-PQ control and \(-1.2\) A to 1.1 A for CVB-VSG control. Furthermore, as shown in Figure 5g,h, the DC current is more stable in the case of CVB-VSG control compared to CVB-PQ control. It is observed that the fluctuations in the DC current for CVB-VSG control are smaller (10 A to 20 A) compared to CVB-PQ control (from \(-2\) A to 26 A). Figure 5i clearly demonstrates that the active and reactive powers follow the power references. However, an important observation is that the response time of CVB-VSG control is significantly shorter than that of CVB-PQ control during a power reference change. Regarding the total harmonic distortion (THD) of the alternating currents, it is low in the case of CVB-VSG control compared to CVB-PQ control, as highlighted in Figure 6.  
Table 2 presents the results in numerical form of the relevant measures and indicators used to evaluate the performance of the CVB-VSG and CVB-PQ control methods. This enables a precise analysis and a better understanding of the performance of the two control methods. It becomes easier to identify the advantages and disadvantages of each control method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control** & **THD** & \(\mathbf{\Delta}\)**Idc** & \(\mathbf{\Delta}\)**Icirc** & \(\mathbf{\Delta}\)**Vc** & **Vcref–Vcstm** \\ \hline CVB-PQ & 0.45\% & 28 A & 6.8 A & 0.4 V & 4.8 V \\ CVB-VSG & 0.17\% & 10 A & 2.3 A & 0.15 V & 1.7 V \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation results of CVB-PQ and CVB-VSG. Figure 5: Simulation results of applying CVB\(-\)VSG control and CVB\(-\)PQ control to the MMC. (**a**) Three\(-\)phase voltages and currents of the MMC. (**b**) Three\(-\)phase voltages and currents of the grid. (**c**) Estimation of the voltages of the SM capacitor of phase A by the CVB\(-\)PQ control. (**d**) Estimation of the voltages of the SM capacitor of phase A by the CVB-VSG control. (**e**) Estimation and measurement of phase A SM capacitor voltages for both commands. (**f**) Phase A circulating current. (**g**) Average value of DC current. (**h**) DC current. (**i**) Active and reactive power.