## 2 Proposed Test System  
A modified IEEE-13 node network was used to perform the study of protection in the presence of SE. This network has the capacity of 5_MVA_ which supplies power to feed balanced and unbalanced loads. It is operated at a 60 Hz frequency and voltage levels of 0.48 kV and 4.16 kV [13,14]. This network was modified by incorporating a solar PV system with a capacity of 1 MW at node 680 using a transformer XSPV and overhead line with a length of 5 km, as illustrated in Figure 1. The positive and zero sequence resistances of this line are 0.1153 and 0.413 \(\Omega\)/km, respectively. The positive and zero sequence inductances of the line are 1.05\(e^{-3}\) and 3.32\(e^{-3}\) H/km, respectively. The positive and zero sequence capacitances of the line are 11.33\(e^{-9}\) and 5.01\(e^{-9}\) F/km, respectively. Figure 1: IEEE-13 node test power system incorporating solar PV plant. Three phase overhead (OH) lines and underground (UG) cables were used is this network for the proposed study, as illustrated in Table 1. OH lines used configuration 601, for which the impedance matrix (\(Z_{601}\)) is given by the relation (1) in \(\Omega\)/km. The UG cable used the configuration 606, for which the impedance matrix (\(Z_{606}\)) is given by the relation (2) in \(\Omega\)/km. Positive and zero sequence capacitance magnitudes of 1.57199 nF/km and 1.3398 nF/km, respectively, were used for configuration 601 of OH line. These values used for configuration 606 of the UG cable are each equal to 15.96979 uF/km. All the loads are considered as three-phase balanced whose details are provided in Table 2. The lengths of all OH lines and UG cables are the same as those used in the network of the original test system [15; 16]. \[Z_{601}= \begin{bmatrix}0.2153+j0.6325&0.0969+j0.3117&0.0982+j0.2632\\ 0.0969+j0.3117&0.2097+j0.6511&0.0954+j0.2392\\ 0.0982+j0.2632&0.0954+j0.2392&0.2121+j0.6430\end{bmatrix}  \tag{1}\]  
\[Z_{606}= \begin{bmatrix}0.4960+j0.2773&0.1983+j0.0204&0.1770+j0.0089\\ 0.1983+j0.0204&0.4903+j0.2511&0.1983+j0.0204\\ 0.1770+j0.0089&0.1983+j0.0204&0.4960+j0.2773\end{bmatrix}  \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Node A** & **Node B** & **Length of Feeder (m)** & **Configuration of Feeder** \\ \hline
632 & 645 & 152.40 & 601 \\ \hline
632 & 633 & 152.40 & 601 \\ \hline
633 & 634 & 0 & XFM \\ \hline
645 & 646 & 91.440 & 601 \\ \hline
650 & 632 & 609.60 & 601 \\ \hline
684 & 652 & 243.84 & 606 \\ \hline
632 & 671 & 609.60 & 601 \\ \hline
671 & 684 & 680.00 & 601 \\ \hline
671 & 692 & 0 & Switch \\ \hline
684 & 611 & 91.44 & 601 \\ \hline
692 & 675 & 152.40 & 606 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test System Feeder Data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nodes** & **Load Model** & **Load** & **Capacitor Banks** \\ \hline  & & **kW** & **kVAr** & **(kVAr)** \\ \hline
634 & Y-PQ & 400 & 290 \\ \hline
645 & Y-PQ & 170 & 125 \\ \hline
646 & Y-PQ & 230 & 132 \\ \hline
652 & Y-PQ & 128 & 86 \\ \hline
671 & Y-PQ & 1155 & 660 \\ \hline
675 & Y-PQ & 843 & 462 & 600 \\ \hline
692 & Y-PQ & 170 & 151 \\ \hline
611 & Y-PQ & 170 & 80 & 100 \\ \hline
632-671 & Y-PQ & 200 & 116 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test System Load Data. The test feeder was integrated to the grid using a substation transformer (XSST). The transformer used between nodes 633 and 634 was designated as XFM. The details of transformer parameters are tabulated in Table 3.  
Protection relay (PR-1) was installed near node 650 of the test system to disconnect the test network from the grid due to fault event. The currents were recorded and continuously processed using the proposed algorithm and tripping signals were given to the circuit breaker (CB) during the faulty event. A protection relay (PR-2) was also installed near the node 680 to isolate the solar PV plant during the faulty condition. However, as per the actual requirement of the system, the protection relay may be installed at any node of the test system. The proposed algorithm works well for all the locations.