# Fault Location and Restoration of Microgrids via Particle Swarm Optimization
## 5 Numerical Results and Discussions
### Grid-Tied Operation  
Table 3 illustrates the simulation results of the sample system and the scenarios assumed in Section 5.1 according to the proposed fault location and service restoration algorithms in this study. The network topologies, voltage error values near the fault line segment, and convergence characteristics including the fault location and restoration objective functions in Equations (16) and (17) that correspond to each scenario are illustrated in Figure 7a-c.  
In Scenario 1, a three-phase bolted short-circuit fault occurs in line segment 702-703, which is between buses 702 and 703. Fault is detected in line segment 702-703 according to the minimal value of the voltage deviation in the **VEM** using the proposed fault location algorithm (Equation (16)). The proposed service restoration algorithm is used to restore power supply to the un-faulted area. Therefore, according to the convergence of the numerical results of the objective function and the related constraints (Equations (17)-(19)), the switch between line segment 708-709 is opened, and two tie switches (i.e., S39 and S40) are closed to form the network topology (Figure 7a). The service restoration percentage  
\begin{table}
\begin{tabular}{c c c c} \hline
**Scenario** & **Fault Type** & **Fault Point between Two Buses** \\ \hline Scenario 1 & Three-phase short-circuit bolted fault & 702–703 \\ Scenario 2 & Three-phase short-circuit bolted fault & 702–703, 727–703 \\ Scenario 3 & Three-phase short-circuit bolted fault & 702–703, 727–703, 710–734 \\ \hline \end{tabular}
\end{table}
Table 2: Fault point assumption of each scenario.  
Figure 6: Co-analysis and simulation platform.  
is 100% because of the fault that occurs in the line segment, and the operations of the tie switches successfully restore electricity service. The power loss is 62.47 kW in this radial type topology, and all the line currents and bus voltages satisfy their limits.  
Figure 7: Cont.  
In Scenario 2, the fault type is the same as that in Scenario 1, that is, a double fault occurring in line segments 702-703 and 727-703. These two fault points are detected by two minimal values in the **VEM**. The switch between line segment 708-733 is opened, and three tie switches, namely, S38, S39, and S40, are closed to form the network topology, as shown in Figure 7b. Similar to Scenario 1, the service restoration percentage is 100%, the power loss is 61.47 kW, all the line currents are less than 300 A, and the bus voltages are within 0.95-1.05 pu. The simulation results illustrate that the combined fault location and restoration approach is capable of dealing with double-point fault conditions.  
In Scenario 3, a triple fault occurs in line segments 702-703, 727-703, and 710-734. These multiple fault points are detected by three minimal values in the **VEM**. The switch between line segment 708-733 is opened, and four tie switches, namely, S37, S38, S39, and S40, are closed to form the network topology, as shown in Figure 7c. Similarly, the service restoration percentage is 100%, the power loss is 60.46 kW, and all the line currents and the bus voltages do not violate these limits. The outcomes demonstrate that the proposed approach is capable of multiple-point fault detection, isolation, and restoration.