  Wind turbines degrade over time, resulting in varying structural,
aeroelastic, and aerodynamic properties. In contrast, the turbine controller
calibrations generally remain constant, leading to suboptimal performance and
potential stability issues. The calibration of wind turbine controller
parameters is therefore of high interest. To this end, several adaptive control
schemes based on extremum seeking control (ESC) have been proposed in the
literature. These schemes have been successfully employed to maximize turbine
power capture by optimization of the $K\omega^2$-type torque controller. In
practice, ESC is performed using electrical generator power, which is easily
obtained. This paper analyses the feasibility of torque gain optimization using
aerodynamic and generator powers. It is shown that, unlike aerodynamic power,
using the generator power objective limits the dither frequency to lower
values, reducing the convergence rate unless the phase of the demodulation ESC
signal is properly adjusted. A frequency-domain analysis of both systems shows
distinct phase behavior, impacting ESC performance. A solution is proposed by
constructing an objective measure based on an estimate of the aerodynamic
power.
