For optimal operation of microgrids, energy management is indispensable to reduce the operation cost and the emission of conventional units. The goals can be impeded by several factors including uncertainties of market price, renewable generation, and loads. Real-time energy management system (EMS) can effectively address uncertainties due to the online information of market price, renewable generation, and loads. However, some issues arise in real-time EMS as battery-limited energy levels. In this paper, Lyapunov optimization is used to minimize the operation cost of the microgrid and the emission of conventional units. Therefore, the problem is multi-objective and a Pareto front is derived to compromise between the operation cost and the emission. With a modified IEEE 33-bus distribution system, general algebraic modeling system (GAMS) is utilized for implementing the proposed EMS on two case studies to verify its applicability.