This paper focuses on economical operation of a microgrid (MG) in real-time. A novel dynamic energy management system (EMS) is developed to incorporate efficient management of energy storage system (ESS) into MG real-time dispatch while considering power flow constraints and uncertainties in load, renewable generation and real-time electricity price. The developed dynamic energy management mechanism does not require long-term forecast and optimization or distribution knowledge of the uncertainty, but can still optimize the long-term operational costs of MGs. First, the real-time scheduling problem is modeled as a finite-horizon Markov decision process (MDP) over a day. Then, approximate dynamic programming (ADP) and deep recurrent neural network (RNN) learning are employed to derive a near optimal real-time scheduling policy. Last, using real power grid data from California Independent System Operator (CAISO), a detailed simulation study is carried out to validate the effectiveness of the proposed method.