## 1 Introduction  
A microgrid can be defined as a local power network that integrates distributed energy resources (DERs) to provide grid backup or off-grid power to meet local electricity needs [1, 2]. Recently, MGs have begun to be used as a novel alternative to mitigate some of the difficulties that arise in traditional electrical grids [3]. MGs can be considered as small-scale and controllable electrical distribution networks that are able to operate either connected to or disconnected from the main electrical grid [4]. MGs allow the incorporation of distributed generation (DG), presenting itself as a new and promising solution to meet the needs of the expanding energy consumption. The coordination of electrical protections in MGs with the presence of DG has become a major challenge in modern electrical systems. Distribution networks are changing their traditional behavior due to the presence of DG units that give rise to bidirectional power flows and variable short-circuit levels. In addition, according to [5, 6], microgrid protection systems must face two important aspects that make their operation difficult. The first one is the fact that they may operate either connected to or disconnected from the main AC power supply, and the second one is the intermittency of loads and generators that generates a dynamic behavior. Over-current relays (OCR) have proven to be an effective alternative for the protection of MGs [7, 8]. However, their proper incorporation and coordination still remains a research topic [7, 8, 9]. MGs have changed radial distribution networks into flexible, non-radial systems. Nonetheless, a suitable protection scheme that simultaneously ensures speed, selectivity, and reliability is still one of the most difficult challenges in MG design [10]. Recently, many research efforts have focused on the application of optimization techniques to find a suitable protection coordination scheme that reduces operating times while ensuring reliability and safety [11, 12]. Several authors agree that directional OCRs are a proper alternative for protecting MGs [7]. The authors in [13] presented a methodology for determining the effect on the coordination of directional OCRs when DG units are included. In addition, the problem of coordination of directional OCRs is considered in [14] for distribution networks with high DG participation. In [15], the authors presented a procedure for the coordination of OCRs in which N-1 security criteria were considered. A methodology based on a multi-objective swarm optimization technique for OCR coordination is developed in [16]. The authors in [17] developed a methodology for OCR coordination that has the ability to adapt online according to system operating conditions. An adaptive protection system for OCR coordination is also presented in [18], being mixed a neural network technique with a support vector machine algorithm, which enhances the state recognition in MGs; basically, all network protection settings were dynamically modified to improve network reliability. A novel alternative to the traditional OCR protection coordination is presented in [11]. In this case, the authors propose a new constraint regarding the plug setting multiplier (PSM). In the approach proposed in [11], the optimization model considers real aspects of commercially available relays. The authors in [19] proposed an adaptive protection scheme for OCRs based on the sets of settings available in the relays. They proposed the use of different setting groups, though limited by the capabilities of commercially available relays. In this case, for specifying a setting group, a technique was developed using linear integer programming and particle swarm optimization (PSO). A similar approach to the one proposed in [19] was implemented in [20; 21; 22]. In this case, the authors used unsupervised machine learning techniques to intelligently group operative scenarios to conduct the OCR coordination.