The paper describes a formal approach for designing and reasoning about power-constrained, timed systems. The framework is based on process algebra, a formalism that has been developed to describe and analyze communicating concurrent systems. The proposed extension allows the modeling of probabilistic resource failures, priorities of resource usages, and power consumption by resources within the same formalism. Thus, it is possible to model alternative power-consumption behaviors and analyze tradeoffs in their timing and other characteristics. This paper describes the modeling and analysis techniques, and illustrates them with examples, including a dynamic voltage-scaling algorithm.