## 4 Simulation and Experimental Results
### Simulation Model of an Inverter Connected to a Three-Phase Unbalanced Power Grid
In this way, the energy unbalance is not alleviated, but aggravated, and then the three-phase voltage unbalance is also aggravated. Therefore, the conventional strategy does not have the ability to achieve three-phase energy mutual aid and is not suitable for a three-phase unbalanced power grid. In Figure 11, the maximum value of \(\text{I}_{\text{C}}\) is slightly higher than that of \(\text{I}_{\text{A}}\) or \(\text{I}_{\text{B}}\), but the measured RMS value of \(\text{I}_{\text{C}}\) is lower than that of \(\text{I}_{\text{A}}\) or \(\text{I}_{\text{B}}\) in Table 2. This is because the conventional control strategy is designed based on three-phase voltage balance, and waveform distortion will occur under the condition of three-phase voltage unbalance. As can be seen in Figure 11, the three-phase grid currents \(\text{I}_{\text{A/B/C}}\) have different degrees of distortion, resulting in different proportions between the RMS and the maximum values. In Table 2, \(\epsilon_{\text{U2}}\) is the negative sequence voltage unbalance factor, which is the ratio of the RMS of the negative sequence component and the RMS of the positive sequence \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Physical Quantities**} & **Symbol** & **Measured Value** \\ \hline \multirow{3}{*}{RMS of three-phase voltage at connection point} & \(V_{\text{PCC\_A}}\) & 217.3 V \\ \cline{2-3}  & \(V_{\text{PCC\_B}}\) & 217.3 V \\ \cline{2-3}  & \(V_{\text{PCC\_C}}\) & 201.6 V \\ \hline Three-phase unbalance degree & \(\epsilon_{\text{U2}}\) & 5.2\% \\ \hline \multirow{3}{*}{RMS of inverter three-phase grid current} & \(I_{\text{A}}\) & 10.23 A \\ \cline{2-3}  & \(I_{\text{B}}\) & 10.23 A \\ \cline{2-3}  & \(I_{\text{C}}\) & **9.898 A** \\ \hline \multirow{3}{*}{Three-phase output power of the inverter} & \(P_{\text{A}}\) & 2223 W \\ \cline{2-3}  & \(P_{\text{B}}\) & 2223 W \\ \cline{1-1} \cline{2-3}  & \(P_{\text{C}}\) & 1995 W \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation results of the conventional control strategy. Figure 11: Simulation results of a conventional inverter connected to a three-phase unbalanced power grid. component. There is no zero-sequence component in the system, so the unbalance factor of the zero-sequence component is not considered. Simulation Results of an Inverter Connected to a Three-Phase Unbalanced Grid with the Proposed Control Strategy  
The simulation in Section 4.2 is compared to the simulation in this section. The two sections present the differences between the conventional method and the proposed method under the circumstance of a three-phase unbalanced grid. Applying the inverter control strategy proposed in this paper and aimed at the three-phase voltage balance in Section 3.5, the waveform of three-phase voltage and three-phase grid current can be obtained under the same simulation conditions, as shown in Figure 12. The RMS values of each parameter and the grid power are shown in Table 3.  
In Figure 12, the upper column shows the three-phase voltage V\({}_{\text{PCC\_A/B/C}}\) waveform of the PCC, and the lower column shows the three-phase grid current \(\text{I}_{\text{A/B/C}}\) waveform of the inverter. As can be seen from the auxiliary line in Figure 12, applying the proposed control strategy, when the load power of Phase C is greater than those of Phase A and Phase B, the grid current \(\text{I}_{\text{C}}\) of the inverter is greater than \(\text{I}_{\text{A}}\) or \(\text{I}_{\text{B}}\), resulting in the equal voltage of the three-phase V\({}_{\text{PCC\_A/B/C}}\). In Table 3, the numerical differences of grid current and grid power of ABC three-phase voltage can be clearly identified. Due to the larger load power of Phase C, the inverter reduces the grid current of Phase A and B, and improves the grid current of Phase C, which realizes three-phase energy mutual aid and achieves three-phase voltage balance. Figure 12: Simulation results of an inverter connected to a three-phase unbalanced power grid with the proposed control strategy.