## 3 Proposed Service Restoration Scheme
### Optimization-Based Intentional Islanding Scheme  
The proposed intentional islanding scheme utilizes an optimization technique based on genetic algorithm (GA), which is one of the meta-heuristic algorithms inspired by natural selection in order to derive a near-optimal topology of a distribution system. GA is commonly used to find optimal or near-optimal solutions to the problems from the search space which otherwise would have taken a significant amount to solve. It uses crossover and mutation operations to achieve exploration of the search space by creating new solutions. Furthermore, the selection operation is utilized to promote exploitation by identifying good solutions in the population. As a result of iterative GA operations, a wide range of solutions have been reasonably explored, and the near-optimal solution can be derived. The binary-coded GA is utilized since the status of switches (branches) in a distribution system can be easily represented by binary values such as 0 (open) and 1 (closed). Therefore, a single control variable corresponds to the status of one switch, and the number of GA control variables is the same as the number of controllable switching devices in a distribution system. The GA plays the role of searching possible topology candidates in a significantly wide search space due to the large number of controllable switches in a distribution system. Figure 5 shows the flowchart of binary-coded GA, and the details of the algorithm are provided in [29; 30]. Figure 6 shows the flowchart of the proposed optimization-based SR algorithm. First of all, populations representing distribution system topologies are initialized as depicted in Figure 6. The number of variables in a population equals the number of branches, and the variables are randomly encoded by 0 (open) or 1 (closed) except for a faulty section which should be regarded as an open one. Once the populations are created, the proposed algorithm performs the island partitioning process as described in Section 3.1. If an island contains more than two DGs, the penalty is imposed on the corresponding population because it is considered an infeasible solution violating the anti-parallel operation constraint. Otherwise, the load flow analysis is conducted to calculate distribution network quantities such as the magnitude of bus voltages and power losses in an island. Then, the constraints regarding the operational limits of the distribution network shown in Equations (2)-(4) are checked, and the penalty is imposed on the corresponding population in case there is any network constraint violation. If the population satisfies all the constraints, the objective function (\(F\)) is calculated by using Equation (1). The process is iteratively performed for all the populations and terminated after reporting the best SR result when it reaches the  
Figure 4: An example of island partitioning for a simple system: (**a**) sample system configuration; (**b**) tree representation of the sample system. maximum iteration. If the termination condition is not met, the populations are updated by using processes of GA to search for other topology candidates for SR plans. The proposed SR algorithm can derive a near-optimal SR plan with the help of the optimization-based approach using a meta-heuristic algorithm so that the SR solution is regarded as a reliable one concerning optimality. Furthermore, it can significantly improve  
Figure 5: Flowchart of the binary-coded genetic algorithm. Figure 6: Flowchart of the proposed optimization-based SR algorithm. the time required to derive an optimal SR plan as it takes advantage of the anti-parallel operation constraint that narrows down the search space thereby reducing the time to perform load flow analysis and evaluate all candidate topologies. Figure 7 depicts the structure of the SR application using the proposed algorithm in the DAS environment. Three fundamental functions are implemented in the SR application: (1) binary-coded GA, (2) island partitioning scheme, and (3) load flow calculation module.