Model‐based state space controllers require knowledge of states, both measurable and unmeasurable, and state estimation algorithms are typically employed to obtain estimates of the unmeasurable states. For the control of wind turbines, a good estimate of the free mean wind speed is important for the closed‐loop dynamics of the system, and an appropriate level of modelling detail is required to obtain good estimates of the free mean wind speed. In this work, three aerodynamic models based on blade element momentum theory are presented and compared with the aero‐servo‐elastic code HAWC2. The first model, known as quasi‐steady aerodynamics, assumes instant equilibrium of the wind turbine wake, a modelling approach often used by model‐based control algorithms. The second model includes the dynamic wake also known as dynamic inflow and gives a more correct description of the actual physics of the wind turbine wake. The dynamic inflow model includes a number of dynamic states proportional to the number of radial points in the spatially discretised blade formulation. The large number of dynamic states inhibits the use of this model in model‐based control and estimation algorithms. The lack of dynamic inflow in the first model and large number of dynamic states in the second model lead to a third model, a simplified dynamic inflow model, which with only a single dynamic state is still able to capture the most significant dynamics of the more advanced dynamic inflow model. Simulations in the aero‐servo‐elastic code HAWC2 compare the ability to estimate the free mean wind speed when either the first or third model is included in the estimation algorithm. Both a simplified example with a deterministic step in wind speed and full degrees‐of‐freedom simulations with turbulent wind fields clearly show that the inclusion of the dynamic inflow model in the free wind speed estimation algorithm is important for good free mean wind speed estimates.