In this paper, we design a power-aware distributed access point scheduling algorithm, PowerNap, to enhance power conservation of co-existing multiple access points (APs) each having multiple clients in the same wireless vicinity. This consequently addresses low channel utilization, degraded throughput, and unfairness problems of Wi-Fi networks in an energy-efficient way. PowerNap schedules transmission periods of APs according to their traffic loads to ensure fair access of the medium from their respective clients' perspective. It supports dynamic rescheduling of AP transmission periods to aid client mobility and traffic fluctuations. The scheduling also ensures that no two APs, in a shared environment, wake up their clients at exactly the same time, decreasing data packet collisions and thus increasing network throughput and energy-efficiency. PowerNap achieves decentralization by exploiting single-hop neighborhood information (e.g., traffic loads) only, and thus, it is scalable. Performance evaluations, carried out in ns-3, depict that the effectiveness of the proposed PowerNap algorithm surpasses the state-of-the-art approaches in terms of energy consumption, network throughput, and fairness.