Power dissipation has constrained the performance boosting of modern computer systems in the past decade. Dynamic power management has been widely applied to change the system (or device) state dynamically to reduce the power consumption. This paper explores how to effectively reduce the energy consumption to handle event streams with hard real-time guarantees. We adopt Real-Time Calculus to describe the event arrival and resource service by arrival curves and service curves in the interval domain, respectively. We develop online algorithms to adaptively control the power mode of the device, postponing the processing of arrival events as late as possible. Profited from the worst-case interval-based abstraction, our algorithms can on one hand tackle arbitrary event arrivals (even with burstiness) and on the other hand guarantee hard real-time requirements in terms of both timing and backlog constraints. We also present simulation results to demonstrate the effectiveness of our algorithms.