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Renewable energy enables sensor networks with the capability to recharge and provide perpetual data services. Due to low recharging rates and the dynamics of renewable energy such as solar and wind power, providing services without interruptions caused by battery runouts is nontrivial. Most environment monitoring applications require data collection from all nodes at a steady rate. The objective of this paper is to design a solution for fair and high throughput data extraction from all nodes in the presence of renewable energy sources. Specifically, we seek to compute the lexicographically maximum data collection rate and routing paths for each node such that no node will ever run out of energy. We propose a centralized algorithm and two distributed algorithms. The centralized algorithm jointly computes the optimal data collection rate for all nodes along with the flows on each link, the first distributed algorithm computes the optimal rate when the routing structure is a given tree, and the second distributed algorithm, although heuristic, jointly computes a routing structure and a high lexicographic rate assignment that is nearly optimum. We prove the optimality for the centralized and the first distributed algorithm, and use real test-bed experiments and extensive simulations to evaluate both of the distributed algorithms.