This dissertation studies two important models in the field of the distributed generation technologies to provide resiliency to the electric power distribution system. In the first part of the dissertation, we study the impact of assessing a Combined Cooling Heating Power system (CCHP) on the optimization and management of an on-site energy system under stochastic settings. These mathematical models propose a scalable stochastic decision model for large-scale microgrid operation formulated as a two-stage stochastic linear programming model. The model is solved enhanced algorithm strategies for Benders decomposition are introduced to find an optimal solution for larger instances efficiently. Some observations are made with different capacities of the power grid, dynamic pricing mechanisms with various levels of uncertainty, and sizes of power generation units. In the second part of the dissertation, we study a mathematical model that designs a Microgrid (MG) that integrates conventional fuel based generating (FBG) units, renewable sources of energy, distributed energy storage (DES) units, and electricity demand response. Curtailment of renewable resources generation during the MG operation affects the long-term revenues expected and increases the greenhouses emission. Considering the variability of renewable resources, researchers should pay more attention to scalable stochastic models for MG for multiple nodes. This study bridges the research gap by developing a scalable chance-constrained two-stage stochastic program to ensure that a significant portion of the renewable resource power output at each operating hour will be utilized. Finally, some managerial insights are drawn into the operation performance of the Combined Cooling Heating Power and a Microgrid.