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With the explosive growth of user data, AI applications are increasingly affecting people’s lives. To tackle the problems of data privacy and network congestion, people raise their interest in the Federated Learning (FL) framework, which enables Edge Nodes (ENs) to learn a global model without data sharing. However, FL also brings some challenges, including energy consumption restrictions, EN heterogeneity, data imbalance, and so on. These problems may lead to poor convergence accuracy, slow convergence speed, and high energy consumption during FL model training. In this paper, we focus on the performance of the FL model under energy-limited training devices, heterogeneous hardware and unbalanced data, while taking into account the social relationships between the devices. We utilize the Lyapunov optimization technique to convert the original problem into an online optimization problem, and introduce two algorithms to address this online problem. Through our analysis, we demonstrate that the optimal solution to the online problem can approximate the optimal solution to the original problem. Our simulation results validate that our proposed algorithms can achieve great performance while satisfying the energy constraints and outperforms the benchmark algorithms.