It is expected that energy harvesting technology will increasingly be deployed to realize autonomous embedded realtime systems such as wireless sensors. In this paper, we consider the problem of jointly scheduling periodic tasks and dynamically arriving hard deadline aperiodic tasks in a monoprocessor system powered with regenerative energy. Our result is an exact admission algorithm in that sense that it accepts every schedulable task based on the amount of available energy and computing capacity. It is assumed that all the accepted tasks are preemptively scheduled according to the optimal algorithm, ED-H which is an energy aware extension of Earliest Deadline First. We also discuss issues concerning the implementation of the admission test.