The use of state estimation technique offers a means of estimating the effective wind speed based solely upon the measurements of the turbine. Such wind speed estimations are crucial for turbines to calculate the reserved power for ancillary services. Nonetheless, the system observability or the possibility of estimating the wind speed is influenced by various down-regulation strategies. Thus, this paper investigates the system observabilities of turbines in different down-regulating conditions via the use of the empirical observability Gramian. In addition, wind speed estimators are constructed for each control strategy using an extended Kalman filter approach. Subsequently, each estimation performance is evaluated from the assessments of the Gramians and high-fidelity turbine simulations. The results reveal that it is more difficult to reconstruct the wind estimate from measurements of the turbine operating in torque-based than rotor-speed-based down-regulation strategies.