We formulate optimization problems to study how data centers might modulate their power demands for cost-effective operation taking into account various complexities exhibited by real-world electricity pricing schemes. For computational tractability reasons, we work with a fluid model for power demands which we imagine can be modulated using two abstract knobs of demand dropping and demand delaying (each with its associated penalties or costs). We consider both stochastically known and completely unknown inputs, which are likely to capture different data center scenarios. Using empirical evaluation with both real-world and synthetic power demands and real-world prices, we demonstrate the efficacy of our techniques.