## 5 Case Studies
### Results and Discussions  
Table 3 shows the result of generating TFs for all the switches considered for case studies by using the proposed scheme, and the last 12 integers of an entire TF string are shown in the figure. It can be seen from the result that TFs, represented as serialization of integers, are created for each switch in both the DMS and the duplicated DMS according to the algorithm provided in Figure 5. As we can see in all strings in Table 3, the last integer is calculated as '0' since there is no more child node. It is noted that some switches have a 'count' value of 2 or more, which means that there are other switches with the same TF in the same system. The duplication of TF for different objects occurs due to topological symmetry. The pairs of DG20-DG21 and SW18-SW19 in Figure 12 have the same TFs since each pair is connected symmetrically from the junction. Similarly, the connectivity of switches between SW5 and SW6 causes the same TFs for SW5 and SW6. For switches with the same TF, standard information described in Section 4.2 should be applied to make the switches distinguishable from each other. Table 4 shows the standard information used for solving the TF duplication problem that occurs in the case study and descriptions of each standard information. Data that both systems have in common such as the circuit number of a PAD internal switch (e.g., 1 for local ID of 3) and the pole number of a switch (e.g., 2173G791 for local ID of 18) are selected as the standard information. Table 5 indicates new TFs generated by applying the standard information. \begin{table}
\begin{tabular}{c c} \hline
**Type of Power System Resources** & **Name of Class in CIM** \\ \hline Line Section & \multicolumn{1}{c}{AClinesegment} \\ Internal Switch in PAD Switchgear & Switch \\ Automatic Switch & Switch \\ Manual Switch & Switch \\ Recloser & Recloser \\ Cut-Out-Switch & Fuse \\ Circuit Breaker & Breaker \\... &... \\ Distributed Generation & PowerElectronicsConnection \\ Junction & Junction \\ Load & EnergyConsumer \\ \hline \end{tabular}
\end{table} 
Table 2: Mapping table of power system resources and classes in CIM. Figure 11: Layout of the distribution system considered for case studies. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Local ID** & **Standard Information** & **Description** \\ \hline
3 & 1 & Circuit no. of a PAD internal switch \\
4 & 2 & Circuit no. of a PAD internal switch \\
5 & 3 & Circuit no. of a PAD internal switch \\
6 & 4 & Circuit no. of a PAD internal switch \\
18 & 2173G791 & Pole no. of a switch \\
19 & 2173G792 & Pole no. of a switch \\
20 & 2173G791 & Pole no. of a switch connected to DG \\
21 & 2173G792 & Pole no. of a switch connected to DG \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Standard information and description of switches. Figure 12: A part of the network for case study causing TP duplication. Table 6 shows the result of creating TFs for all the switches in both systems according to the application of the standard information. The TFs for some switches in both systems are newly created by adding the standard information to the original serialization result. It is noted that the count values are changed to '1' for all the switches after applying the standard information to some switches. This means that there are no duplicated TFs in a system so that every switch can have its dedicated property that is distinguishable from other switches in the system. A mapping table can be created by matching local IDs with the same TF. For example, local IDs '2' and '11456' in the DMS are mapped to local IDs '4' and '1' in the duplicated DMS, respectively. If mappings of local IDs for the last object in a system are performed, then a complete local ID mapping table can be derived. Figure 13 shows the number of duplicated TFs in the test system according to the application of the standard information. It is shown in the figure that the number of