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In the future, communications networks are expected to become less an end itself than a means to an end by exploiting them not only for telecommunications per se but also across other relevant economic sectors in order to reap larger benefits from interdisciplinary research across traditional borders, e.g., an increased overall reduction of greenhouse gas emissions across multiple sectors such as energy and transportation, as envisioned by the future Smart Grid. The two main quality attributes of a Smart Grid communications infrastructure are reliability and latency, as defined in IEEE P2030. This paper proposes to aggregate triple-play and Smart Grid services into a converged fiber-wireless (FiWi) broadband access network based on low cost Ethernet passive optical network (EPON) and wireless mesh networks. We first show that, as the load of the FiWi network increases, performance degradation in terms of packet drop and latency of Smart Grid applications occurs due to the lack of quality-of-service (QoS) protection. To mitigate this problem, we propose an adaptive admission control algorithm to provide QoS support for FiWi Smart Grid communications networks. Simulation results show that the proposed admission control enables QoS guarantees for triple-play applications as well as future Smart Grid applications over the same FiWi infrastructure.