Differential adaptive protections considerably improve the resiliency of the electrical microgrid power system, mitigating electrical failures and increasing its flexibility, ensuring the electrical energy supply remains available. The purpose of the paper is to analyze the behavior and, therefore, its suitability as compared to conventional differential protections under multiple fault conditions, the introduction of distributed renewable energy resources, battery storage, and the connection to the main national electric grid for the Pedernales province, in the Dominican Republic, distribution network as a microgrid. The above is highly interesting when one knows how critical electrical protections are in power systems for both low- and high-voltage microgrid systems. Additionally, the frequency behavior is analyzed with the use of a battery energy storage system activated by an adaptive protection scheme. The grid infrastructure is simulated with the PowerFactory DIgSILENT software. In this work, the differential adaptive protection scheme provided better grid stability and a greater than 10 times faster response when compared to the conventional differential protection solution.