This paper studies two energy management problems under uncertainties for a grid-connected microgrid. The problems are motivated by practical microgrid applications such as peak power shaving and frequency regulation. These applications require constraints on the microgrid energy output, which is uncertain due to the integration with renewable resources and random loads. Both problems are formulated as chance constrained programming problems to systematically incorporate uncertainties. We also show that the resulting chance constrained programming problems can both be solved using linear programming. The proposed formulation and solution are verified by two case studies originated from real world applications.