## 4 Discussion  
To verify the feasibility of the proposed method, a 3 kW class grid-connected DG inverter system was implemented using PSIM software, as shown in Figure 2. The main circuit design parameters are shown in Table 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Nominal DG inverter effective power, \(P_{intv}\) & 3 [kW] \\ Nominal grid voltage, \(V_{grid}\) & 220 [V] \\ Nominal grid frequency.\(f_{grid}\) & 60 [Hz] \\ Number of phases & Single \\ Allowable frequency range & 56.5 [Hz] \(\leq f\leq\) 62 [Hz] \\ Threshold value for \(C_{p}\) & 6 (when \(N\) = 4, \(k_{c}\) = 100,000, \(k_{p}\) = 0.0056) \\ Local load \(R\), \(L\), \(C\) & \(P_{R}\) = 3 kW, \(Q_{L}\) = 3 kVar, \(Q_{C}\) = 3 kVar \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Electrical specification of the simulation circuit. Figure 2: Simulation circuit for islanding detection test. First, the power quality on harmonics was compared and analyzed for the proposed method and the conventional AFD method. Figure 3 shows how the waveform changes as cf, which is the control target of the AFD technique when the grid is connected, and Table 5 shows its Total Harmonic Distortion (_THDi_) of the current. When the cf value is 0% and there is no disturbance at all, the base _THDi_ is 3.18%, and when the cf value is 5%, the _THDi_ is 5.54%. As cf increases, _THDi_ increases, as the distortion in the fundamental sinusoidal wave increases. Figure 4 shows how the waveform changes as the phase, which is the control target of the proposed method, and Table 5 shows its _THDi_ for the proposed method. It can be seen that the base _THDi_ is 3.18% when the phase disturbance, which is the change in reactive power, is 0%, and the _THDi_ is 3.23% when the phase disturbance is 5%. In other words, it can be seen that even when the phase disturbance increases, there is little change in the _THDi_ because there is no distortion of the fundamental sinusoidal wave component. As suggested in IEEE Std. 1547-2018 and KS C 8564-2021, the anti-islanding performance evaluation is conducted under the worst test condition, in which the power flows to the grid (\(\Delta P\), \(\Delta Q\)) are almost zero since the balance between the DG generation power and the load is made. Figure 5 shows the inverter output voltage (\(V_{inv}\)), current (\(I_{inv}\)), frequency (_Freq_), Correlation parameter (\(C_{p}\)), and phase variation (\(\theta_{RPV}\)) for the grid-connected DG inverter when islanding occurs at 0.4 s. In Mode A1 before islanding occurs, the difference in measured frequency between two consecutive periods is very small, up to 0.007, and the phase angle for the proposed reactive power variation is also very small, close to about 0.004, as shown by Equation (4). Therefore, at this time, it can be confirmed that the _THDi_ in Mode A1 is also maintained at the level of 3.18%, as discussed in the previous section. In addition, in Mode A1, the correlation between the frequency difference and the reactive power variation is very low, and the \(C_{p}\) value stays at the maximum level of 0.08. In Mode A2, after islanding occurs, the frequency fluctuations by the proposed method and the corresponding fluctuations in \(C_{p}\) values are shown. By the reactive power variation technique with positive feedback gain \(K_{p}\) of 0.0056, it can be confirmed that the inverter frequency in the steady state stays around 60.55 Hz. Additionally, it can be seen that \(C_{p}\) in Mode A2 has a maximum value of about 7.45. For these frequency fluctuations, it can be confirmed that islanding cannot be detected under the condition of the frequency relay set value in IEEE Std. 1547-2018 and KS C 8564:2021. Figure 6 shows the waveform that prevents islanding operations by using the proposed technique at about 0.007 s after islanding occurs.