Decentralized federated learning (DFL) enables edge devices to collaboratively train models through local training and fully decentralized device-to-device (D2D) model exchanges. However, these energy-intensive operations often rapidly deplete limited device batteries, reducing their operational lifetime and degrading the learning performance. To address this limitation, we apply energy harvesting technique to DFL systems, allowing edge devices to extract ambient energy and operate sustainably. We first derive the convergence bound for wireless DFL with energy harvesting, showing that the convergence is influenced by partial device participation and transmission packet drops, both of which further depend on the available energy supply. To accelerate convergence, we formulate a joint device scheduling and power control problem and model it as a multi-agent Markov decision process (MDP). Traditional MDP algorithms (e.g., value or policy iteration) require a centralized coordinator with access to all device states and exhibit exponential complexity in the number of devices, making them impractical for large-scale decentralized networks. To overcome these challenges, we propose a fully decentralized policy iteration algorithm that leverages only local state information from two-hop neighboring devices, thereby substantially reducing both communication overhead and computational complexity. We further provide a theoretical analysis showing that the proposed decentralized algorithm achieves asymptotic optimality. Finally, comprehensive numerical experiments on real-world datasets are conducted to validate the theoretical results and corroborate the effectiveness of the proposed algorithm.