# Fault Location and Restoration of Microgrids via Particle Swarm Optimization
## 1 Introduction  
Microgrids (MGs) can be regarded as a \"set of load clusters, distributed generations (DGs), and energy storage systems\" [1; 2; 3]. In terms of the traditional power grid, MGs are the partial active networks in distribution systems. Therefore, the type and ownership of MGs can vary considerably, such as utility and customer MGs. Utility MGs include distribution substations, main transformers, full feeders, partial feeders, or distribution transformer-level MGs. However, regardless of their type, MGs are capable of operating in grid-tied and islanding modes through the point of common coupling, which is the connection point between the MGs and the main grid that is created by a static switch. Traditional passive distribution networks, which do not have DG interconnection, spend more than half an hour on fault detection, isolation, and restoration (FDIR). As a result of the high penetration of DGs in feeders to form active distribution networks, large amounts of data are available and are received by the feeder dispatch control center or distribution dispatch control center; consequently, the FDIR concept in distribution contingencies is different, in which rigorous fault current calculation approaches are proposed by DGs [4; 5; 6; 7]. Besides, the advanced information and communication techniques in FDIR are proposed to restore power to as many systems as possible and to reduce power restoration time after the occurrence of feeder faults in a radial-type feeder arrangement [8; 9; 10]. In the past few decades, many customers in rural distribution networks served by power companies have experienced long power outages, especially those in upstream networks. A recent, possible solution for rapid and effective restoration is to operate these feeders asMGs because DGs composed of photovoltaics and wind power are interconnected in rural distribution feeders. The key points of FDIR in MGs for outages attributed to overhead conductors or underground cables are fault location and restoration algorithms; therefore, IEEE Std C37.114 [11] and EPPRI [12] have presented essential data and approaches for distribution fault location. [PERSON] et al. [13] proposed fault detection and location in a microgrid using mathematical morphology and recursive least-square methods to detect and classify the faults in microgrids. [PERSON] et al. [14] proposed a method for early detection and area location of short-circuit faults in microgrid based on the relationship between the first peak value of fault current wavelet energy spectrum. [PERSON] et al. [15] also presented a fault detection, classification, and localization method that is based on a multi-resolution analysis of the discrete wavelet transform and a Taguchi-based artificial neural network. [PERSON] et al. [16] proposed an effective ground fault location scheme using unsynchronized data for multi-terminal lines; this scheme does not require the data from each terminal to be synchronized. [PERSON] et al. [17] presented a joint power restoration approach in active distribution networks that combines DG local restoration and switcher operation-based restoration to enhance self-healing. [PERSON] et al. [18] proposed an intelligent fault classification and location identification method for microgrids using discrete orthonormal Stockwell transform (DOST)-based optimized multi-kernel extreme learning machine (MKELM). [PERSON] et al. [19] proposed a decentralized outage detection algorithm that uses AMI meters to obtain the total number of customers and the total amount of lost load in the outage area. The ability to perform a black start is vital for MGs. Hence, [PERSON] et al. [20] proposed a parallel restoration strategy that considers the characteristics of DGs for MG black starts. These state-of-the-art studies presented power restoration approaches in modern active distribution networks and revealed that MGs are distinct from traditional passive radial-type networks.