Although considerable advances have been made in single microgrid (MG) systems, the problem of cooperation among MGs and the macrogrid has attracted considerable interest only recently. As in wireless communications systems, exploiting the temporal, spatial, and technological diversities in multiple cooperative MGs could bring about more efficient power generation and distribution. This paper investigates a hierarchical power scheduling approach to optimally manage power trading, storage, and distribution in a smart power grid with a macrogrid and cooperative MGs. We first formulate the problem as a convex optimization problem and then decompose it into a two-tier formulation. The first-tier problem jointly considers user utility, transmission cost, and grid load variance, while the second-tier problem minimizes the power generation and transmission cost, and exploits distributed storage in the MGs. We develop an effective online algorithm to solve the first-tier problem and prove its asymptotic optimality, as well as a distributed optimal algorithm for solving the second-tier problem. The proposed algorithms are evaluated with trace-driven simulations and are shown to outperform several existing schemes with considerable gains.