## 3 The Proposed AIM  
As one of the most used AIMs, the active frequency drift (AFD) method with positive feedback has been studied often [24; 25; 26]. Accordingly, this method was applicable to be implemented in a commercial photovoltaic (PV) inverter to meet the requirements of IEEE Std. 1547-2003. As shown in Figure 4, the AFD method uses the chopping fraction, _cf_, as a frequency perturbation parameter, which is defined as the ratio of zero time (\(t_{z}\)) to half of the period of voltage waveform (\(T_{1}\)/2) as follows:  
\[cf=\frac{t_{z}}{(T_{1}/2)} \tag{3}\]  
where \(t_{z}\) is zero time of the inverter current and \(T_{1}\) is a period of voltage waveform. Without the AFD method, the current is controlled to be in phase with the voltage waveform, which results in a unity power factor control. When the AFD method is applied, the frequency of the DG inverter is maintained by the grid voltage when the grid is connected, so there is no frequency variation due to zero time of the AFD reference current. It is important to design an appropriate _cf_ value because harmonic components are generated by the injected AFD current command. When the DG inverter is disconnected from the grid, the AFD current command makes the frequency drift to the frequency trip set value, and the inverter stops [24; 25; 26]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Standard**} & **Over** & **Under** & \multirow{2}{*}{**Clearing Time**} & \multirow{2}{*}{**Condition**} & **Non Detection Zone** \\  & **Frequency** & **Frequency** & & & **as** \(\frac{\Delta\Omega}{P}\) \\  & **[Hz]** & **[Hz]** & & & \\ \hline IEEE Std. & \multirow{2}{*}{60.5} & \multirow{2}{*}{59.3} & \multirow{2}{*}{6 [cycles]} & \(\leq 10\) [kW], & \multirow{2}{*}{\(-\)5.94\%\(\leq\frac{\Delta\Omega}{P}\leq\)**4.12**\%} \\  & & & & & \\ \hline IEEE Std. & \multirow{2}{*}{60.5} & \multirow{2}{*}{59.3} & \multirow{2}{*}{0.16 [s]} & \(\leq 30\) [kW], & \multirow{2}{*}{\(-\)**2.37**\%\(\leq\frac{\Delta\Omega}{P}\leq\)**1.65**\%} \\  & & & & & \\ \hline IEEE Std. & \multirow{2}{*}{62.0} & \multirow{2}{*}{56.5} & \multirow{2}{*}{0.16 [s]} & Default setting, & \multirow{2}{*}{\(-\)**12.77**\%\(\leq\frac{\Delta\Omega}{P}\leq\)**6.35**\%} \\  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Historical frequency trip settings of the distributed generation (DG) inverter. Figure 4: Active frequency drift (AFD) reference current waveform compared with the voltage waveform. If an AFD current disturbance with a fixed _cf_ can be canceled by local load adjustment, the chopping fraction is usually modified with a positive feedback as follows [24]:  
\[cf[k]=cf[k-1]+K_{p}(Freq[k]-Freq[k-1]) \tag{4}\]  
where \(k\) is the present status, \(K_{p}\) is a proportional coefficient, and \(Freq\) is the measured frequency of the voltage. Since the displacement factor (DPF) is 1, the power factor (PF) and the reactive power can be expressed as follows [27]:  
\[PF=\frac{P}{S}=\frac{P}{\sqrt{P^{2}+Q^{2}}}=\frac{1}{\sqrt{1+THD_{i}^{2}}} \tag{5}\]  
\[\frac{Q}{P}=THD_{i} \tag{6}\]  
Since total harmonic distortion of current (\(THD_{i}\)) is directly proportional to _cf_, the amount of reactive power variation (\(Q/P\)) in Equation (6) can be determined by cf. The previous research showed the relationship between _cf_ and \(THD_{i}\) through some experiments [27]. The allowable limit of \(THDi\) (5%) by the standard sets the maximum _cf_ about 5% [27; 28]. In the case of the new IEEE Std. 1547-2018, the amount of perturbation (\(\Delta Q/P_{inv}\)) increases dramatically, as shown in Table 1. Consequently, a higher _cf_ of the AFD method is required to prevent islanding. Thus, it is difficult to use the conventional AFD with positive feedback (AFDPF) by IEEE Std. 1547-2018 because the corresponding \(THD_{i}\) is around 12.77% which is higher than the standard limit [28].