In this paper, we present a power-aware, best- effort real-time task scheduling algorithm called PA-BTA that optimizes real-time performance and power consumption. The algorithm considers a timeliness model where task timing constraints are described using Jensen?s benefit functions and a system-level power model. We propose a metric called "Energy and Real-Time Performance Grade" (ERG) to measure real-time performance and power consumption in a unified way. Since the scheduling problem is NP-hard, PA-BTA heuristically computes schedules to maximize ERG, incurring a worst-case computational cost of O(n²). Our simulation results indicate that the algorithm performs close to the optimal algorithm and better than other algorithms considered in the study.