## 2 NDZ Comparisons  
In the early days of the dissemination of DG, safe energy generation of the EPS was important. For voltage and frequency variation, which are indicators of EPS accidents such as blackouts, the focus was on disconnecting the DG from the EPS. As DG has been implemented in EPSs with large capacities,  
Figure 1: Description of islanding phenomenon: (**a**) grid-connected mode; (**b**) islanding mode.  
Figure 2: Classification of anti-islanding method.  
a significant loss of DG due to a short disturbance could cause another reliability issue for the EPS. As a result, new international standards, such as IEEE standard 1547-2018, require more sophisticated and complex requirements for grid-connected DGs. For short voltage and frequency disturbances, the ride-through capability was adopted to continue the operation of DG, as shown in Figure 3. These wider voltage and frequency trip windows allow DG to generate electric power even though there is a slight voltage and frequency disturbance. On the other hand, islanding of DG should be prevented in an EPS because it may cause safety issues. Thus, IEEE Std. 1547-2018 requires islanding detection within 2 s without compromise. However, since most anti-islanding methods are based on frequency trip windows, there have been concerns about the reduced effectiveness of anti-islanding under the new standard requirements.  
The relationship between reactive power mismatch \(\Delta Q\) and frequency threshold can be obtained by [22]:  
\[Q_{f}\left[1-\left(\frac{f}{f_{min}}\right)^{2}\right]<\frac{\Delta Q}{P_{ intr}}<Q_{f}\left[1-\left(\frac{f}{f_{max}}\right)^{2}\right] \tag{1}\]  
\[Q_{f}=R\sqrt{\frac{C}{L}}=\frac{\sqrt{|Q_{L}||Q_{C}|}}{P_{R}} \tag{2}\]  
where \(P_{intr}\) is the active power of the DG inverter; \(\Delta Q\) is the reactive power flow from the grid; \(f\) is the grid frequency; \(f_{min}\) and \(f_{max}\) are the under and over frequency thresholds, respectively; and \(Q_{f}\) is a quality factor. The quality factor is defined as the measure of the resonance strength of the islanding test load, as shown in Figure 1a [23].  
With the limit values of the frequency specified in Table 1, the corresponding NDZ was derived. This quantitative NDZ is the basis to calculate the amount of frequency perturbation of the DG inverter, which causes the harmonic distortion of the current. It has been one of the main research targets for detecting islanding with high power quality and low harmonics.  
As shown in Table 1, the islanding test conditions changed to reduce the effect on the EPS by decreasing \(Q_{f}\) from 2.5 to 1. Additionally, the frequency relay settings were changed in a wider direction to prevent nuisance trips. Table 1 shows that NDZ varies by Equation (1) according to the set value of the frequency trip settings and the value of \(Q_{f}\). Among the NDZ ranges of the three different standards, IEEE Std. 1547-2018 shows the largest NDZ because it has the widest frequency trip settings. Under the wide range of frequency trip settings, the current disturbance command of AIM must increase to make the frequency move out of the range when islanding occurs. Since this disturbance appears as the current distortion, harmonic components increase or displacement power factor decreases, resulting in  
Figure 3: A simplified ride-through capability required in IEEE Std. 1547–2018: (**a**) voltage ride-through profile; (**b**) frequency ride-through profile (default setting).  
poor power quality. Thus, this paper presents a correlation-based AIM that does not depend on the frequency trip.