## 3 The Proposed Method  
As analyzed in the previous section, the amount of change in reactive power for detecting islanding operation by the standards should be increased by up to 13% of the rated power of the solar unit inverter. In this paper, the anti-islanding method with small reactive power variations (RPVs) in a grid-supported environment is presented by proposing an islanding detection indicator without depending on OF/UF thresholds. The magnitude of the injected reactive power is proposed as a change in the phase angle defined in the basic concept of power factor in Equation (3). As shown in Equation (4), the phase angle deviation is designed to use the positive feedback according to the frequency deviation for two consecutive periods. While the grid is connected to DG, the frequency fluctuation for two consecutive cycles is not large and has a very small value due to the frequency sensing error. Therefore, only a very small change in reactive power occurs before islanding occurs. However, when islanding occurs, a small amount of reactive power change causes a corresponding frequency change, which needs to be designed to exceed the threshold value of the frequency relays. As introduced in the previous section, since the latest technical standards require a wider set value of the frequency relay, the size of the reactive power that needs to be changed to detect islanding operation is relatively large, which is a problem. Therefore, in this paper, an islanding detection indicator that can detect islanding operation for even minute-long fluctuations in reactive power is presented as the correlation parameters in Equation (5). \[\text{Power factor}=\frac{1}{\sqrt{1+THD_{i}^{2}}}\cos(\theta_{RPV})=\frac{1} {\sqrt{1+THD_{i}^{2}}}\cos\left\{\tan^{-1}\left(\frac{Q_{RPV}}{P_{inv}}\right)\right\} \tag{3}\]  
\[\theta_{RPV}[k]=k_{p}\times\left(freq[k-n]-freq[k-n-1]\right) \tag{4}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Standard** & **Non Detection Zone as \(\frac{\Delta P}{P}\)** & **Non Detection Zone as \(\frac{\Delta Q}{P}\)** \\ \hline IEEE Std. 1547-2003 & \(-30.6\%\leq\frac{\Delta P}{P}\leq 300\%\) & \(-2.4\%\leq\frac{\Delta Q}{P}\leq 1.6\%\) \\ IEEE Std.1547-2018 & \(-30.6\%\leq\frac{\Delta P}{P}\leq 394\%\) & \(-12.8\%\leq\frac{\Delta Q}{P}\leq 6.3\%\) \\ KS C 8564-2015 & \(-30.6\%\leq\frac{\Delta P}{P}\leq 300\%\) & \(-2.4\%\leq\frac{\Delta Q}{P}\leq 1.6\%\) \\ KS C 8564-2021 & \(-30.6\%\leq\frac{\Delta P}{P}\leq 300\%\) & \(-10.8\%\leq\frac{\Delta Q}{P}\leq 4.8\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Non-detection zone analysis by standards. \[C_{P}[k]=\sum\limits_{n=0}^{n=N-1}k_{C}(\theta_{RPV}[k-n]-\theta_{RPV}[k-n-1]) \tag{5}\] \[\times((freq[k-n]-freq[k-n-1]))\]  
where \(Q_{RPV}\) is the injected reactive power, \(P_{intv}\) is the inverter output effective power, \(k_{p}\) is the positive feedback gain, \(freq[k]\) is the measured frequency at the time instant \(k\), \(C_{p}\) is the correlation parameter, and \(k_{c}\) is the scaling factor. Before islanding occurs, the frequency of the inverter voltage is maintained robustly by the power grid, so the frequency is determined regardless of the reactive power fluctuations by the proposed method. Thus, the proposed correlation parameter has a value close to 0, even considering the sensing error when the inverter is connected to the grid. On the other hand, after islanding occurs, the frequency changes in the same direction by the variation of the proposed reactive power, which increases the value of the proposed correlation parameter. When the calculated correlation parameter reaches the designed threshold, it is determined as an islanding operation, and the inverter stops. The author has previously proposed an islanding detection technique using a correlation index based on an AFD method rather than reactive power variations. The previously proposed islanding operation detection method using correlation based on the AFD method has a problem of inherently generating harmonic components while the grid frequency changes [22].