In this paper, we investigate energy-aware real-time scheduling algorithms with speed change constraints. A processor is equipped with variable \emph{clock frequency} (\emph{speedy}) feature and is used to schedule a set of given jobs with deadlines. Each speed change involves time/energy overhead and recent studies show that it also impacts negatively the processor's \emph{lifetime reliability}. Motivated by this, we study theoretical energy-aware scheduling problems with consideration of number and cost of speed changes. We associate a cost with each speed change to reflect its negative impact on the processor's lifetime reliability. We design speed schedules to satisfy all jobs' deadlines and optimize the energy consumption and the total cost incurred due to speed changes. Four related problems based on this framework are considered. We develop algorithms that perform arbitrarily close to the optimal and we also analyze their time complexities.