## 1 Introduction  
Nowadays, power grids face many challenges. New technology enables the grid integration of different renewable energy sources (RESs), which has led to bi-direction power flow and voltage overshoot [1]. The injection of intermittent power into the traditional distribution network has resulted in many problems, and new approaches, including ones that address the allocation strategy, control system, and power grid structure, are needed [2]. Optimization-based power dispatch and battery energy storage systems (BSSs) are frequently used to overcome the poor power quality caused by RESs. However, such approaches may not be efficient in the areas where the output of discrete generators (DGs) cannot be greatly changed and the surplus power generated by the RESs is large. Under such conditions, the optimization of power grid structure can be a promising choice due to its relatively low cost, high flexibility, and efficiency. Research related to the structure of the power grid can be divided into two types according to the problem being solved. Algorithms for network reconfiguration have been proposed to solve the bi-direction power flow and reduce the power loss in networks [3; 4; 5; 6; 7; 8; 9]. In this approach, a network with loops is designed and switches are used to reconfigure the network so that different radial network is obtained in the running process to re-direct the power flow. The aim of a network reconfiguration is to reduce the total power losses and different optimization algorithms that are applied, including the Particle Swarm Optimization (PSO), Invasive Weeds Optimization (IWO), and Cuckoo Search Algorithm (CSA) [3; 4; 5]. To address the issue of power losses, the network survivability index was introduced as a measurement of the redundancy, and the Ant Colony Algorithm (ACA) was used to optimize the survivability index and power losses [6]. To achieve a better convergence property, the Big Bang-Big Crunch (BB-BC) [7] algorithm was used, and a mutation step was added to the Big Crunch process. The optimal power losses can be obtained with the modified BB-BC algorithm [8]. In one study [9], a distributed approach was proposed to reconfigure the network based on open shortest path first (OSPF) routing protocol. In that research, the physical architecture was proposed, and the Dijkstra Algorithm was used to obtain the optimal radial configuration. Algorithms for the network partition were proposed to solve the computational complexity caused by the expansion of the network [10; 11; 12; 13; 14; 15; 16; 17]. A large network is partitioned into several clusters in which the supply and demand is balanced, cohesiveness is high, and inter-connection is low so that the control strategy can be applied to each cluster in parallel. Network partitioning requires a distance matrix indicating the dependency of any two nodes. Commonly the differential of the voltage as a function of the power was used as the distance matrix, and the traditional k-means algorithm was applied to achieve the clusters [10]. In one study [11], the usage of the spectral clustering in a power grid was analyzed, and several weight matrixes were proposed and compared. With the normalized Laplacian matrix and its eigenvalues, the first k eigenvectors were chosen to perform the k-means analysis. Similarly, spectral analysis has been applied to address this issue [12], where both the active and reactive matrixes were considered. Instead of using k-means, the Self-Organizing Map (SOM) algorithm was used so that the number of clusters could be learned from the data. A modified community detection algorithm was used to optimize the network partition. An unbiased performance index was proposed with the knowledge of structure and power supply condition in each cluster to determine the quality of the algorithm so that auto-termination of the algorithm was ensured [13].