# Practical Submodule Capacitor Sizing for Modular Multilevel Converter Considering Grid Faults
## 6 Case Study
### Experimental Verification  
By using the selected components given in Table 4, an experiment platform has been assembled, the structure of which is shown in Figure 10. The platform is formed with three phase-legs. The DC-side voltage of the MMC is provided by a constant DC source. A dSPACE system is used as the controller of the MMC, while an auxiliary DC supply is used to provide power for the sensors and gate drivers in the system. The AC side of the platform is connected to a grid simulator, which is used to generate the grid fault signal. The system operation waveforms during grid fault conditions are shown in Figure 11, where the system state during single-line-to-ground condition and three-phase short-circuit condition is shown in Figure 11a,b, respectively. Due to the symmetrical characteristic, only the SM voltage of upper arm is given.  
It can be seen that the circulating current through each phase-leg is well-suppressed when the system operates in steady-state. During normal operation, the peak-to-peak SM voltage ripple is 3.5 V, which is well constrained within the design limit. During the transient state of both grid fault conditions, an obvious voltage over-shoot appears on each SM capacitor, which is caused by the dynamic response of the control system [30]. In Figure 11a, the maximum SM voltage in three phase-legs is 48.8 V, which is 1.5 V higher than the model-estimated value shown in Figure 9a. For three-phase short circuit condition, the maximum SM voltage is close to the expectation, with only a 1 V difference. These estimation errors are caused by the signal coupling within the MMC control system. However, all SM voltage is limited under 40 V, which proves the effectiveness of the proposed SM capacitor selection method.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Part Number** & **UBY2A681 MHL** \\ \hline Capacitance & 680 μF \\ ESR & 28 m\(\Omega\) at 50 Hz; 14 m\(\Omega\) at 100 Hz \\ Thermal resistance & 1.5 \({}^{\circ}\)C/W \\ Reference lifetime & 3000 h at 125 \({}^{\circ}\)C, 20-50 V \\ \hline \hline \end{tabular}
\end{table}
Table 4: Key parameters of the selected capacitor product.  
\begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{2}{c}{**Normal Operation Point**} \\ \hline Grid voltage & \(V_{d+}=50\) V \\ Grid current injection & \(I_{d+}=5\) A ; \(I_{d+}=0\) \\ Circulating current reference & \(I_{cj}=0.417\) A \\ \hline \multicolumn{2}{c}{**Single-Line-to-Ground Condition**} \\ \hline Grid voltage & \(V^{\prime}_{d+}=33.5\) V \\  & \(V^{\prime}_{d-}=16.5\) V \\ Grid current injection & \(I_{d+}=1.67\) A \\  & \(I^{\prime}_{d+}=2.875\) A \\  & \(I^{\prime}_{d-}=0\) ; \(I^{\prime}_{q-}=-3.5\) A \\ \hline \multicolumn{2}{c}{**Three-Phase Short-Circuit Condition**} \\ \hline Grid voltage & \(V^{\prime}_{d+}=0\) ; \(V^{\prime}_{d-}=0\) \\ Grid current injection & \(I_{d+}=0\) ; \(I^{\prime}_{d+}=4.5\) A \\  & \(I^{\prime}_{d-}=0\) ; \(I^{\prime}_{q-}=0\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Possible operation points of the MMC.  
Figure 11: The experiment waveform of the MMC platform under different grid faults: (**a**) single-line-to-ground condition and (**b**) three-phase short-circuit condition.  
Figure 10: A photo of the down-scale MMC experimental platform.