In this paper, the user–base station (BS) association problem is addressed to reduce grid consumption in heterogeneous cellular networks (HetNets) powered by hybrid energy sources (grid and renewable energy). The paper proposes a novel distributed control scheme inspired by population games and designed considering both atomicity and non-anonymity – i.e., describing the individual decisions of each agent. The controller performance is considered from an energy–efficiency perspective, which requires the guarantee of appropriate qualityof-service (QoS) levels according to renewable energy availability. The efficiency of the proposed scheme is compared with other heuristic and optimal alternatives in two simulation scenarios. Simulation results show that the proposed approach inspired by population games reduces grid consumption by 12% when compared to the traditional best-signal-level association policy.