Most of wireless sensors are dynamically changing and execute two types of tasks: hard deadline periodic ones and aperiodic ones with no deadline. The emergence of energy harvesting technologies makes it possible to design self-powered sensors through environmental energy. Nevertheless, classical scheduling techniques need to be reconceived so as to take into account the fluctuating energy source and energy consumptions of tasks. Hence, we firstly describe the called TB-H and TB *-H aperiodic task servers which are extensions of the famous Total Bandwidth server. We show how TB-H and TB *-H permit to provide short response times for the aperiodic tasks by computing adequate virtual deadlines taking into account both time and energy constraints. Our second contribution lies in extensive simulations to bring to light the effectiveness of these two novel Bandwidth based servers in comparison to basic background approaches.