# Voltage Ride through Control Strategy of Modular Multilevel Converter under Unbalanced Voltage Sag
## 4 Simulation Results and Analysis  
The entirety of the modeling of the MMC and the design of the control strategy were accomplished in MATLAB/Simulink software in order to monitor the system performance. The nominal parameters which were used for the simulation of power electronic converter and controller are shown in Table 1. The reference amounts for the real and reactive powers were defined and then applied. The steady-state performance of the MMC regulated by the fuzzy sliding mode control strategy was investigated in this set of tests. The capacitor voltages which are related to upper and lower cells of Phase A are illustrated in Figure 3. Considering Equation (3), the control input made the SM voltage track the reference value (5892 V) properly, as depicted in Table 2. As observed, with the help of the proposed nonlinear control method, the MMC operated stably with balanced submodule capacitor voltages when the reference powers were applied. The three-phase line-to-line voltages are shown in Figure 4a, in which four levels of voltage are undoubtedly observable. It is noticeable that during the charging and discharging of the capacitors, the voltage levels varied within acceptable boundaries. The exploited MMC in this study was a conventional MMC and the simulation results obtained prove that the THD of the output voltage was around 7.56%, taking into consideration the ripple in the capacitor voltages. However, the performance of the proposed control of the MMC showed a significant improvement in its reduction of the THD of the output voltage. Moreover, Figure 4b illustrates the AC side currents. As shown, they were balanced and stable during the fault conditions. The THD of the AC currents was less than 1%. Figure 5 shows the Fast Fourier Transform (FFT) analysis of the output voltage under steady-state conditions. As can be observed, the multiples of second fundamental were significantly suppressed. Additionally, the THD was also reduced. The circulating current of the leg in Phase A flow, which circulates through the arms and the DC side of the converter, is illustrated in Figure 6. Due to accurate stabilization of the SM voltage, the circulating current of MMC was suppressed and it balanced the power in the capacitors on the DC side of the MMC. The steady-state simulation confirmed the precise process of the MMC with the proposed technique. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Nominal Parameters**} \\ \hline Submodule (SM) capacitor initial voltage & 5892 V \\ Input DC voltage & 20 kV \\ Rated line-to-line voltage & 10 kV \\ Number of cells per arm & 6 \\ Arm inductance & 1.59 mH \\ Arm resistance & 0.04 m\(\Omega\) \\ Cell capacitance & 100 uF \\ Rated frequency & 60 Hz \\ Carrier frequency & 600 Hz \\ Real power reference & 0.05 MW \\ Reactive power reference & 0.2 MVAr \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for the simulation of the whole system. Figure 3: The upper capacitor voltages of Phase A.  
Figure 4: Three-phase voltages (**a**) and AC side currents (**b**). Figure 5: Fast Fourier Transform (FFT) analysis of the output voltage. Figure 7 demonstrates how the converter replied to the requested active power and reactive power. For this purpose, ramp-up and ramp-down changes were implemented in input power to simulate the behavior of changing the solar irradiation. In this case, the reactive power went up to 0.2 MVAr. It illustrated a matching change in the transferred active and reactive powers. There was also an improvement in the steady-state and transient responses while applying the proposed controller. Supplementary assessment of the proposed controller was performed during grid voltage disturbance. Case (a) (Type B voltage sag) considered a single-line-to-ground (SLG) fault of Phase A, whilst cases (b) and (c) considered a Type C and D sag down to 80% (voltage drops 20%). The specific unbalanced grid voltages and simulation results of cases (a)-(c) are shown in Figure 8.  
Figure 6: The variations of circulating current.