## 2 Materials and Methods
Figure 3: \(Cont.\)  
On the other hand, the main concern can be highlighted regarding rapid normal frequency fluctuations when the penetration level of DG's will increase. This can tend to the maloperation of passive methods. Maloperation of relay can be expected at severe sensitive settings and less setting that can result in large NDZ. The main aim of performance analysis is to determine the power indices that can observe the minor disturbances proficiently. The performance analysis of power system parameters has assured the capability of a selected parameter in terms of moderate threshold setting without causing maloperation of the scheme. Parameter used without performance analysis could be vulnerable to maloperation. The selected parameter gives a clear picture that it will give a maloperation-less strategy and differentiate islanding from a non-islanding operation. Our proposed method has nearly zero NDZ because we avoid a less sensitive threshold setting. Hence, without performance analysis of power system parameters selection of threshold is very difficult. Assessment of passive indices presented above demonstrates that voltage phase angle (VPA) has the best capability in terms of performance and sensitivity among all other passive parameters. Therefore, VPA is employed in the islanding detection process. The flow chart of the proposed strategy is shown in Figure 4. The proposed method measures absolute VPA at every half cycle. The strategy is activated when Equation (1) is satisfied:  
\[(\text{VPA})_{\text{measured}}<(\text{VPA})_{\text{threshold}} \tag{1}\]  
where \((\text{VPA})_{\text{measured}}\) is the measured absolute mean value and \((\text{VPA})_{\text{threshold}}\) is the predefined threshold. For \((\text{VPA})_{\text{threshold}}\), phase magnitudes of VPA during islanding and \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Grid Profiles**} & \multicolumn{2}{c}{**Load Profiles**} & \multicolumn{2}{c}{**DG Profiles**} \\ \cline{2-7}
**Testing Situations** & **P (MW)** & **Q (MVar)** & **P (MW)** & **Q (MVar)** & **P (MW)** & **Q (MVar)** \\ \hline Islanding (small mismatch) (P.M) & 0.001 & 0.001 & 2.001 & 0.821 & 2.000 & 0.820 \\ Islanding (large mismatch) (L.M) & 1.930 & 1.920 & 3.960 & 2.110 & 2.030 & 0.200 \\ Load increment (L.I) & 0.001 & 0.001 & 2.001 & 0.821 & 2.000 & 0.820 \\ Load decrement (L.D) & 1.340 & 1.320 & 3.350 & 1.740 & 2.020 & 0.420 \\ Capacitor energization (C.E) & 0.001 & 0.001 & 2.001 & 0.821 & 2.000 & 0.820 \\ Capacitor de-energization (C.D) & 0.670 & 0.680 & 2.670 & 0.970 & 2.030 & 0.670 \\ Motor starting (M.S) & 0.001 & 0.001 & 2.001 & 0.821 & 2.000 & 0.820 \\ Motor unloading (M.U) & 0.840 & 0.820 & 2.840 & 1.590 & 2.030 & 0.760 \\ Fault switching (F.S) & 0.001 & 0.001 & 2.001 & 0.821 & 2.000 & 0.820 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Testing scenarios. Figure 3: Comparison of parameters magnitudes/phase vs. considered islanding and non-islanding event (**a**) voltage (**b**) frequency (**c**) active power (**d**) reactive power (**e**) power factor (**f**) voltage phase angle. non-islanding is measured at power mismatches. Then a comparison of phase magnitudes of islanding and non-islanding is made so that which event shows higher or lower magnitudes. For our study, islanding events magnitudes are lower than the non-islanding events. That's why Equation (1) has been developed. The threshold selection is based on the specifications of the power system and has been found using the hit and trial process. Magnitudes/phase of the balanced or unbalanced three-phase signal is calculated with the help of sequence analyzer block in MATLAB/SIMULINK environment. The positive, negative and zero sequence components can be examined one by one or can be in combined formed at PCC (point of common coupling) and is expressed by Equation (2):  
\[\left[ \begin{array}{c}\mathrm{V_{1}}\\ \mathrm{V_{2}}\\ \mathrm{V_{0}}\end{array} \right]=\frac{1}{3}\left[ \begin{array}{ccc}1&1&1\\ 1&a&a^{2}\\ 1&a^{2}&a\end{array} \right]\left[