## 4 Simulation and Experimental Results  
### Simulation Model of an Inverter Connected to a Three-Phase Unbalanced Power Grid  
In the Matlab/Simulink environment, the simulation model, as shown in Figure 10, is built, and the main parameters are shown in Table 1.  
The power grid on the right side of Figure 10 is an ideal three-phase balanced power grid, and the line voltage and phase voltage are 380 V and 220 V, respectively. Three-phase loads Rl equal to each other. If the switch is off, the three-phase load is balanced; and if the switch is closed, an additional resistance Re is connected to Phase C, resulting in load unbalance, and further causing voltage unbalance at the PCC. In the distribution network, the resistive characteristic of the line impedance is obviously larger than the inductive characteristic, so the inductive characteristic is ignored in this paper and the line impedance is directly equivalent to pure resistance. The value of line impedance \(Z_{\text{grid}}\) in the simulation is set at 10 \(\Omega\), which is much larger than the real value (m\(\Omega\) level). The purpose is to make the load current produce a noticeable voltage change when flowing through the line impedance, so as to facilitate observation and comparison. Simulation Results of a Conventional Grid-Connected Inverter Connected to a Three-Phase Unbalanced Grid  
When the switch is closed, the extra resistance Re of Phase C is connected to the grid, and the load power of Phase C is significantly higher than those of Phase A and B, resulting in three-phase power unbalance, which in turn causes three-phase voltage unbalance on \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Physical Quantities**} & **Symbols** & **Values** \\ \hline Line voltage at the head of the grid & \(V_{\text{grid\_AB/BC/CA}}\) & 380 V \\ \hline Phase voltage at the head of power grid & \(V_{\text{phase\_AN/BN/CN}}\) & 220 V \\ \hline The grid frequency & \(f\) & 50 Hz \\ \hline Three-phase load balancing resistance & \(R_{\text{l}}\) & 22 \(\Omega\) \\ \hline Unbalance resistance of phase C & \(R_{\text{e}}\) & 50 \(\Omega\) \\ \hline Three-phase grid impedance & \(Z_{\text{grid}}\) & 10 \(\Omega\) \\ \hline Target current of positive sequence d-axis & \(I_{\text{dref}}\) & 10 A \\ \hline Target current of positive sequence q-axis & \(I_{\text{qref}}\) & 0 A \\ \hline PWM carrier frequency & \(f_{\text{c}}\) & 5000 Hz \\ \hline Inverter DC voltage & V\({}_{\text{dc}}\) & 700 V \\ \hline \multirow{2}{*}{Current loop PI controller} & K\({}_{\text{P\_j}}\) & 30 \\ \cline{2-2}  & K\({}_{\text{l,i}}\) & 600 \\ \hline \multirow{2}{*}{Voltage loop PI controller} & K\({}_{\text{P\_v}}\) & 0.2 \\ \cline{2-2}  & K\({}_{\text{l,v}}\) & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of the simulation model. Figure 10: Simulation model topology. the PCC. In this case, the inverter applies the conventional control strategy, as shown in Figure 2. The three-phase voltage and grid current waveforms are shown in Figure 11. The RMS of each parameter and the grid power are shown in Table 2.  
In Figure 11, 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 \(I_{\text{A/B/C}}\) waveform of the inverter. As can be seen from the auxiliary line in Figure 11, applying the conventional control strategy, when the load power of Phase C is larger than those of Phase A and B, the RMS of \(V_{\text{PCC\_C}}\) is lower than that of \(V_{\text{PCC\_A}}\) or \(V_{\text{PCC\_B}}\), resulting in three-phase voltage unbalance. The numerical difference of ABC three-phase voltage can clearly be seen in Table 2.  
It can also be seen in Table 2 that applying the conventional strategy, when the load power of Phase C is larger than those of Phase A and B, the grid power of the inverter in Phase C is also smaller than those of Phase A and B.