## 1 Introduction
### Related Work  
Various measures of microgrid (MG) system resilience have been explored in the literature. For instance, Reference [7] presents a method for quantifying the resiliency measure for an MG that is based on networking, Failure rate, and weather factor. In the networking perspective, a connectivity metric is specified by determining the connectivity nature between the installed nodes. Other metrics that have been counted which are the load metric, representing the load that has not been disconnected,  
Figure 1: Microgrid system. due to emergency cases, such as weather problems. Failure rate indicated the robustness degree of the system, and weather factor defined the weather impacts on the system's resiliency. The blackout duration of the power system is proposed in Reference [8] as a resiliency measure. This outage may occur due to failure in the distribution system. This paper supposed that the resiliency key of the distributed systems is based on two main factors. These factors are the infrastructure of installed power distributed system, and the restoration priority scheme given by the power company. The proposed measure is tested on a residential electrical power distribution system located in part of the City of Phoenix, Arizona. In Reference [9], the authors evaluated the resiliency measure of the MG during high-impact low-probability (HILP) windstorms. This resiliency measure is mainly based on performance reduction and other normalized metrics that are utilized for the resiliency comparison process under different operation conditions. A real MG test-bed is utilized to investigate and examine the proposed methods. A resiliency quantification technique that mainly aimed to provide a non-interrupted power to the critical load is proposed by Reference [10]. Resiliency estimation is specified as a decision-making problem with multiple measures. It has been quantified through this study by utilizing two approaches, which are: Graph-theoretic approach and Choquet integral. Similar to our work, the simulations of operational contingency scenarios implemented by Reference [10] validate the fact that resiliency of power system depends on the number of paths connecting source units to loads. An advanced Code-Based Metric is implemented by [PERSON] [11] to quantify the resiliency measure of the power distribution system. This resiliency metric is specified via the simulation process that is based on steady-state and dynamic simulation tools. As shown in the results, the utilization of the output data from the proposed technique highly supported the reliability factor of the system by choosing the suitable design of the power distribution system. Like our work, the scheme presented by [PERSON] [11] can be scalable to different power systems topologies. The concept of Transportable Energy Storage System (TESS) is utilized by [PERSON] [12] during the investigation of the proposed resiliency metric. The authors of this paper proposed a post-disaster recovery scheme that involved the scheduling process of the TESS, and, in turn, generated resources in MGs to meet cost reduction purpose. The proposed recovery scheme is developed as mixed-integer linear programming. An environment of a modified 33-bus test system with three MGs and four TESSs is utilized to test and analyze the proposed model. The authors of Reference [13] studied the resiliency level of different control systems inside an MG network. They also proposed a Cyber-Physical Resilience Metric (CPRM) that is based on utilizing the vulnerability data to specify the system status for monitoring and management purposes. In order to test the proposed metric and study its impact on resiliency, a case study that is relevant to Ukraine cyber-attack is presented. In our work, we have reviewed some recent strategies on resiliency enhancement for MGs. For instance, optimal scheduling of microgrid system is developed by [PERSON] [14] to enhance its resiliency.