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When dependability of systems with a large number of components is a concern, being able to model and analyze their properties, especially non-functional ones, in a formal and automated way becomes essential. Often, however, the application of formal methods and automated reasoning is seen by practitioners as complex and time consuming. Compositional techniques can help modify this belief. In this paper we show how a compositional modeling and verification technique can be applied to the analysis of distributed systems with numerous interacting nodes. We automate the proof by exploiting a SAT-based tool. We demonstrate the validity of the resulting approach by applying it to an autonomic service-based system that manages, in a coordinated peer-to-peer manner, electricity consumption in a geographical area. In particular, we show that in this case the time needed for performing the proof is remarkably shorter than in the case in which we adopt a non-compositional approach.