This paper presents a stochastic mixed-integer nonlinear programming model for the optimal energy management system of unbalanced three-phase of alternating current microgrids. The proposed model considers the following random variables: nodal demands, nodal renewable generation and voltage reference at the point of common coupling. Furthermore, the proposed model is aimed at providing resilient energy management system solutions via contingency constraints. The proposed mixed-integer nonlinear programming model is transformed into a mixed-integer linear programming model through a set of linearizations that can be solved via off-the-shelf convex programming solvers. The analyzed microgrid comprises photovoltaic generation, energy storage systems, electric vehicle chargers, direct load control, and non-renewable generation, which operates when the microgrid is in islanded mode. The stochastic nature of the problem is considered through a scenario-based approach. The solution to the model determines the day-ahead operation of the microgrid resources that minimizes the average operational cost. An unexpected islanded operation at any given time is considered via contingency constraints. Tests are performed using data of the real microgrid at the Laboratory of Intelligent Electrical Networks (LabREI), at University of Campinas. Results show that the proposed model produces resilient day-ahead energy management system solutions while minimizing the average operational costs and maximizing the use of local renewable energy sources.