## 4 Simulation Results  
The performance of the proposed method was verified using PSIM software under the conditions of IEEE Std. 1547-2018. The key parameters for islanding test are shown in Table 2 and simulation circuit is shown in Figure 6. The local load was chosen as a unity power quality factor for a 3 kW DG inverter system. By adjusting tunable _RLC_ local load, a test condition was implemented for the worst case, the power balance condition between DG generation and local load consumption. The threshold value of the correlation factor was chosen to be 0.0013, which was derived from the value of _cf_ for IEEE Std. 1547-2003. This is to show that the designed _cf_ for IEEE Std. 1547-2003 can also be applied to IEEE Std. 1547-2018 using the proposed method. In other words, the lower _cf_ value, which was designed for IEEE Std. 1547-2003, can be used for IEEE Std. 1547-2018. Figure 7 shows islanding test results when no AIM is applied. When the local loads are almost matched with DG power generation and the grid is disconnected at 0.5 s, the measured frequency is almost maintained to be 60 Hz. Thus, islanding is not detected at all. Figure 8 shows anti-islanding test results when the conventional AFD method with 5% _cf_ is used. Before islanding occurs, the inverter output current is clearly distorted by _cf_, as shown in Figure 8. Once islanding occurs, the frequency of inverter voltage stays still around 60 Hz, because DG source and load power are balanced under the constant _cf_ disturbance. Thus, islanding is not prevented in this case. In the same way, Figure 9 shows anti-islanding test results when AFDPF method is used. Before islanding occurs, it is hard to recognize the distortion of the inverter output current as shown in Figure 9, because the initial value _cf_ for AFDPF method is 1%. After islanding at 0.5 s, the frequency is drifted by _cf_ over 60.5 Hz and then stabilized under 62 Hz. Even though _cf_ is increased by the positive feedback, the frequency variation after islanding is not enough to detect islanding by depending on frequency trip settings. This means that AFDPF method may meet the requirements of anti-islanding under IEEE Std. 1547-2003, whose frequency trip setting is at 60.5 Hz. However, this AFDPF method does not meet the requirement of IEEE Std. 1547-2018 because its frequency trip point is 62 Hz. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Local load \(R\), \(L\), \(C\) power & Quality factor \(Q_{f}=1\) & \(P_{R}=3\) kW \\  & & \(Q_{L}=3\) kVar \\ \hline Single DG inverter nominal power, \(P_{inv}\) & 3 kW \\ \hline Threshold value of correlation parameter, \(C_{p,set}\) & 0.0008 (when N = 5, \(K_{p}=0.02\)) \\ \hline Frequency trip setting & OF: 62 Hz, UF: 56.5 Hz \\ \hline OF: 62 Hz, UF: 56.5 Hz & 56.5 \(<\)_f_ \(<\) 62 Hz \\ \hline Nominal grid voltage, frequency, \(V_{grid}\) & 220 V, 60 Hz single phase \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DG’s key parameters for simulation. Figure 10 shows anti-islanding test results when the proposed method is used. Before islanding occurs, the distortion of the current is small like the AFDPF method since the initial value _cf_ is 1%. In addition, before islanding, the proposed correlation parameter \(C_{P}\) is maintained to be almost zero because frequency is dominated by the rigid grid voltage source, not the chopping fraction. In other words, there is little correlation between _cf_ and frequency before islanding. However, after islanding, the frequency is determined by the chopping fraction with positive feedback. Therefore, the proposed correlation factor starts to increase to be over 0.0013. Therefore, islanding can be prevented by the proposed islanding indicator, \(C_{P}\). Figure 6: Simulation circuit for islanding test. Figure 7: Islanding test results when no anti-islanding method is used. The simulation results are summarized in Table 3. When the grid is connected to DG, the \(\mathit{THD}_{i}\) values of AIM methods are assessed.