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Internet based service providers, such as Amazon, Google, Yahoo etc, build their data centers (IDC) across multiple regions to provide reliable and low latency of services to clients. Ever-increasing service demand, complexity of services and growing client population cause enormous power consumptions by these IDCs incurring a major part of their running costs. Modern electric power grid provides a feasible way to dynamically and efficiently manage the electricity cost of distributed IDCs based on the Locational Marginal Pricing (LMP) policy. While recent works exploit LMP by electricity-price based geographic load distribution, the dynamic workload and high volatility of electricity prices induce highly volatile power demand and critical power peak problem. The benefit of cost minimization via geographic load distribution is counterbalanced with the high cost incurred by violating the peak power. In this paper, we study the dynamic control of electricity cost to provide low volatility in power demand and shaving of power peaks. To this end, a Model Predictive Control (MPC) electricity cost minimization problem is formulated based on a time-continuous differential model. The proposed solution minimizes electricity costs, provides low variation in power demand by penalizing the change in workload and alleviates the power peaks by tracking the available power budget. By providing extensive simulation results based on real-life electricity price traces we show the effectiveness of our approach.