The reduction of the energy footprint of large and mid-sized IEEE 802.11 access networks is gaining momentum. When operating at the network management level, the availability of an accurate power model of the APs becomes of paramount importance, because different detail levels have a non-negligible impact on the performance of the optimisation algorithms. The literature is plentiful of AP power models, and choosing the right one is not an easy task. In this paper we report the outcome of a thorough study on the impact that various inflections of the AP power model have when minimising the energy consumption of the infrastructure side of an enterprise wireless LAN. Our study, performed on several network scenarios and for various device energy profiles, reveals that simple one- and two-component models can provide excellent results in practically all cases. Conversely, employing accurate and detailed power models rarely offers substantial advantages in terms of power reduction, but, on the other hand, makes the solving algorithms much slower to execute