Real-time systems, ranging from small portable devices or embedded systems to more complex general-purpose computers, are designed to satisfy various of real-time computation. It is the most important to guarantee all the requests will be satisfied correctly in time. Rate monotonic algorithm is the most well-known real-time scheduling algorithm in the periodic task model. It not only has high schedulability, but also has a tight utilization bound to easily check whether the task set is feasible. In rate monotonic algorithm, a task will be executed once in each period, but the start time of execution might be different in each period. On the contrary, for tasks scheduled using pinwheel model, the execution schedule in each period will be always the same. Therefore, pinwheel scheduling model is very suitable for real-time systems which need high predictability. The pinwheel scheduling model transforms the task periods into harmonic numbers shorter than or equal to the original periods and provides many advantageous scheduling features. However, not all tasks allow to do the transformation and some would like to be executed according to their original periods. In this paper, we discuss how to solve the problem and give an application in power-aware real-time scheduling, where we can see the pinwheel model is very important in current embedded system design with power-aware requirement.