In this paper, we investigate the problem of minimizing energy cost for distributed Internet data centers (IDCs) in smart microgrids while taking system dynamics into consideration. Specifically, IDC operators expect to minimize the long-term energy cost with the uncertainties in electricity price, workload, renewable energy generation, and power outage state. At first, we formulate the problem as a stochastic program that captures service request distribution, server provisioning, energy storage management, generator scheduling, power transactions between smart microgrids, and main grids. Second, we use the Lyapunov optimization technique to design an operation algorithm, which enables an explicit tradeoff between energy cost saving and battery investment cost. Finally, the effectiveness of the proposed algorithm is evaluated with practical data.