## 4 Case Study: Eastern Regions of South Korea  
In Korea, when a total blackout occurs, the whole system is divided into seven regions to restore the whole system (Figure 6). Each subsystem has at least one black start unit and pre-assigned paths. Black start units are usually hydroelectric power or pumped storage power. If a blackout occurs, the black start unit and pre-assigned paths are restored first. After the black start unit and pre-assigned paths are restored, the rest of the generators are ordered to be restored. In this section, we assume that a total blackout has occurred, and we choose one subsystem, which is the eastern regions, among the subsystems to restore it. The black start unit and pre-assigned  
Figure 5: Flow chart of generator start-up sequence. Figure 6: Korean power systems. paths are restored first, and the rest of the generators in the eastern regions are ordered to be restored. To find the restoration sequence of the rest of the generators, the information on the generators and the charging currents of the transmission lines are used. Table 1 shows the information about the generators in the eastern regions. It does not display the exact name of the generators due to confidentiality. G6 is a black start unit, and its capacity is 280 MW. The rest of the 19 generators are non-black start units. In the table, there is information about 20 generators, such as the capability and ramping rate in MW/h, to calculate the start-up time for the next units. In order to determine the GSS, the time taken to energize each generator is calculated. The generator that takes the shortest time to start is selected as the next generator. When the time is calculated, the restoration time of the transmission lines to the generator and the restoration time of the transformers to the generator are considered together, and the charging current of the transmission lines and transformers is used. Figure 7 illustrates the adjacency matrix of the eastern regions. The bus numbers are re-assigned to generate the adjacency matrix. Using this matrix, we can consider the shortest path to the non-black start unit. Table 2 shows an example of the GSS in the eastern regions of South Korea. \(ST_{\text{GEN}}\) means the start-up time for each generator, and \(ETLr\) is the energizing time of the transmission lines and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Generator** & _Capacity_ (MW) & _Rr_ (MW/h) & \(P_{\text{start}}\) (MW) & \(T_{\text{start}}\) (h)** \\ \hline G1 & 183 & 24.5 & 0.18 & 0.55 \\ G2 & 186 & 24.5 & 0.14 & 1.05 \\ G3 & 830 & 28.  
transformers for restoring the generator. Total means the total time taken to restore the generator, including the time taken to restore the transmission lines and transformers. The highlighted cells are the generators that are selected as the next units in each step. In the eastern regions, the pre-assigned paths are G6 (Black start unit) \(\rightarrow\)58\(\rightarrow\)6\(\rightarrow\)19\(\rightarrow\)20\(\rightarrow\)30\(\rightarrow\)25\(\rightarrow\)26\(\rightarrow\)29\(\rightarrow\)73\(\rightarrow\)G20, and G6 is started as the black start unit in the first step. In the second step, G20 is started as well. Afterwards, we calculate the total times for all available generators and compare them. In the third step, G7, which has the shortest total time, is restored. At the end of the third step, the total times of all generators are compared again, and in the next step, G8 is restored. G7-G9 are sequentially restored, since these are located near each other and are the same type. In the same way, the restoration sequence is repeated until the available generators exist in the systems. Table 3 shows the results of the simulation. According to the strategy, the generator start-up sequence (GSS) is determined using generator characteristic data and the enhanced Dijkstra algorithm. All the generators in the system are restored sequentially, and at each restoration step, the system conditions are reflected to calculate time taken.