Energy is an essential, but often forgotten aspect in large-scale federated systems. As most of the research focuses on tackling computational and statistical heterogeneity from the machine learning algorithms, the impact on the mobile system still remains unclear. In this paper, we design and implement an online optimization framework by connecting asynchronous execution of federated training with application co-running to minimize energy consumption on battery-powered mobile devices. From a series of experiments, we find that co-running the training process in the background with foreground applications gives the system a deep energy discount with negligible performance slowdown. Based on these results, we first study an offline problem assuming all the future occurrences of applications are available, and propose a dynamic programming-based algorithm. Then we propose an online algorithm using the Lyapunov framework to explore the solution space via the energy-staleness trade-off. The extensive experiments demonstrate that the online optimization framework can save over 60% energy with 3 times faster convergence speed compared to the previous schemes.