## 5 Restoration Plan Strategy after a Blackout in a Wide Area or a Country
### Case Studies
#### 5.4.2 Case Study 2: The IEEE-68 Bus System  
In order to further verify the effectiveness of the proposed algorithm, the same work is carried out for the IEEE-68 bus system [89], which contains 16 generators. There are 4 BS units and 12 NBS units among the 16 generators, the data of which are presented in Table 9. G14, G1, G9, and G3 are BS units in islands 1, 2, 3, and 4, respectively. All the other units are NBS units. After calculation by the proposed algorithm, the optimal network skeleton for each island is shown in Figure 10 with colored solid lines. Table 10 shows the restoration sequence and the corresponding restoration paths. For this scenario, we assume that all thermal units are in hot start time and the system load is 3750 MW. The total available production is 4940 MW, making the system generation high enough. The total restoration time is 57.5 min. During that time, all the units and the loads were restored successfully. Comparing the A* Algorithm with the resilience-oriented service restoration modeling proposed in [90], it is proved that it is more efficient. In [90], the proposed technique is validated in the IEEE-69 bus system (comparable to the IEEE-68 bus system of the current work) and the restoration time comes up to hours.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Island 1**} & \multirow{2}{*}{**BS Unit**} & \multirow{2}{*}{**NBS Unit**} & \multirow{2}{*}{**Critical Loads to be Restored**} & \multirow{2}{*}{**Cranking Path (Bus No.)**} \\ \cline{3-3} \cline{5-5}  & & G1 & & 37\(\rightarrow\)25\(\rightarrow\)2\(\rightarrow\)30 \\ \cline{3-3} \cline{5-5} Island 1 & & G8 & G9 & 25 & 25\(\rightarrow\)26\(\rightarrow\)29\(\rightarrow\)38 \\ \cline{3-3} \cline{5-5}  & & G10 & & 2\(\rightarrow\)1\(\rightarrow\)39 \\ \hline Island 2 & G3 & G2 & 6 & 32\(\rightarrow\)10\(\rightarrow\)11\(\rightarrow\)6\(\rightarrow\)31 \\ \hline \multirow{3}{*}{Island 3} & \multirow{3}{*}{G7} & G6 & & 36\(\rightarrow\)23\(\rightarrow\)22\(\rightarrow\)35 \\ \cline{3-3} \cline{5-5}  & & G5 & 23 & 22\(\rightarrow\)21\(\rightarrow\)16\(\rightarrow\)19\(\rightarrow\)20\(\rightarrow\)34 \\ \cline{3-3} \cline{5-5}  & & G4 & & 19\(\rightarrow\)33 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Cranking paths from BS unit to NBS unit.  
Figure 9: Optimal restoration path using the A* Algorithm for the IEEE-39 bus system.  
Figure 10: Optimal restoration path using the A* Algorithm for the IEEE-68 bus system.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Node No.** & **Generator** & **Generator Type** & **Output (MW)** & **Starting Time (min)** & **BS Unit** \\ \hline
53 & G1 & Hydro & 140 & 1.5 & YES \\ \hline
54 & G2 & Gas & 430 & 3.5 & NO \\ \hline
55 & G3 & Hydro & 130 & 1.6 & YES \\ \hline
56 & G4 & Wind & 100 & 3.4 & NO \\ \hline
57 & G5 & Gas & 520 & 4.8 & NO \\ \hline
58 & G6 & Gas & 560 & 4.7 & NO \\ \hline
59 & G7 & Wind & 200 & 4.1 & NO \\ \hline
60 & G8 & Gas & 520 & 4.8 & NO \\ \hline
61 & G9 & Hydro & 160 & 1.7 & YES \\ \hline
62 & G10 & Wind & 300 & 4.2 & NO \\ \hline
63 & G11 & Wind & 200 & 4.1 & NO \\ \hline
64 & G12 & Gas & 430 & 3.5 & NO \\ \hline
65 & G13 & Wind & 100 & 3.4 & NO \\ \hline
66 & G14 & Gas & 520 & 4.8 & YES \\ \hline
67 & G15 & Wind & 200 & 4.3 & NO \\ \hline
68 & G16 & Gas & 430 & 3.5 & NO \\ \hline \end{tabular}
\end{table}
Table 9: Data generators for the IEEE-68 bus system and its classification.