## 5 Experimental Results
### Simulation Studies
#### 5.3.1 Test Case 1: The IEEE 39-Bus System  
The IEEE 10-generator and 39-bus system actually represents a 345-kV power network in New England, the United States. The system consists of 10 generators and 46 branches, and its total generated power is 6297.9 MW [36]. To simulate large disturbances in the power system, all time-domain simulations for the IEEE 39-bus system are performed using DIgSILENT PowerFactory [37]. We assume that at \(t=1s\), a three phase-to-ground solid fault happens at bus Node 27, and the fault is  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & \multicolumn{3}{c}{**Separation Boundaries**} & **Inbalance Power (MW)** & **Inbalance Power (Ratio \%)** & **Time** \\ \hline \hline
**Tabsu search** & 15-33, 34-36, 37-34, 34-33, 30-38, 70-24, 24-72, 111-109, 103-105, 10  
If no control actions are taken, it can be seen that the system loses synchronization at about 1.6417 s. Figure 18b indicates that the generator rotor angle curves become two clusters: {38} and {30, 31, 32, 33, 34, 35, 36, 37, 39}. The transient stability of the power system, or whether the system generators can continue to maintain synchronization after suffering large disturbances, is determined by the changing characteristics of the relative angles between generator rotors. Proper control measures should be required at this moment, such as controlled islanding. At about 2 s, the relative angles between the remaining generations have experienced the change from positive to negative 180 degrees, which indicates that the system has lost its transient stability [38]. Accordingly, the node voltage in the power system is usually controlled within [0.95 p.u., 1.05 p.u.]. However, after the fault occurs at time 1 s, the voltages suffer from drastic fluctuations, as shown in Figure 18c, especially for bus Node 38. Similarly, Figure 18d shows that the frequency of Generator 9 at bus Node 38 rises sharply, which means that the rotor speed is increased, widens the angle difference between itself and other generators gradually and eventually leads to instability.  
After the fault happens, we can trip the boundary transmission lines that have been obtained by our tabu search algorithm. The emergency control actions after the system splitting are taken at 2.5 s: load shedding at Bus 29 with 90.72 MW. The system generator angle, voltage and frequency curves are shown in Figure 18f-h. We set the tabu tenure to seven, the number of iterations to 1000 and obtained a solution with the total power imbalance of 79.5 MW within 1 ms. The solution gives an islanding strategy, which disconnects lines 17-27 and 25-26. Therefore, the Nodes 2, 26, 28, 29 and 38 are included in one island, and the rest are included in the other island. We can also see that the two islands are successfully created with frequencies between 1.00 and 1.01 p.u. after 10 s, which is shown in Figure 18h. Similarly, the bus voltage and frequency gradually return to normal levels after 2.39 s. The angles, voltages and frequencies of generators in both islands have reached a steady state. Thus, the validity of our proposed tabu search algorithm can be verified from this perspective.