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We propose an adaptive power management (APM) algorithm for a data center with an objective to minimize the total cost of power bought from an electrical grid. This APM algorithm is developed for a smart grid environment which is envisioned to be a cooperative, responsive, and economical power system. In particular, APM algorithm takes the spot power price from an electrical grid, the power supply from a renewable power source, and users' demand in terms of application workload processing into account when managing the power consumption. Therefore, an APM algorithm is considered to be the demand side management in a smart grid. To obtain an optimal decision of the APM algorithm, an optimization model based on stochastic programming with multi-stage recourse is developed. This optimization model considers various uncertainties and is able to determine the optimal solution for the APM algorithm. The APM algorithm is evaluated by numerical studies. The numerical results clearly show that the APM algorithm can minimize the power cost of a data center.