Demand response is a promising approach to deal with the emerging power generation fluctuations introduced by the increasing amount of renewable energy sources fed into the grid. Consumers need to be able to adapt their energy consumption with respect to the given demand pattern and at the same time ensure that their adaptation (i.e., response) does not interfere with their various operational objectives. Finding, evaluating and verifying adaptation strategies which aim to be optimal w.r.t. multiple criteria is a challenging task and is currently mainly addressed by hand, heuristics or guided simulation. In this paper we carry out a case study of a demand response system with an energy adaptive data center on the consumer side for which we propose a formal model and perform a quantitative system analysis using probabilistic model checking. Our first contribution is a fine-grained formal model and the identification of significant properties and quantitative measures (e.g., expected energy consumption, average workload or total penalties for violating adaptation contracts) that are relevant for the data center as an adaptive consumer. The formal model can serve as a starting point for the application of different formal analysis methods. The second contribution is an evaluation of our approach using the prominent model checker PRISM. We report on the experimental results computing various functional properties and quantitative measures that yield important insights into the viability of given adaptation strategies and how to find close-to-optimal strategies.