Evaluation of log-of-power extremum seeking control for wind turbines using large eddy simulations

Abstract

The extremum seeking control (ESC) algorithm has been proposed to determine operating parameters that maximize power production below rated wind speeds (region II). This is usually done by measuring the turbine's power signal to determine optimal values for parameters of the control law or actuator settings. This paper shows that the standard ESC with power feedback is quite sensitive to variations in mean wind speed, with long convergence time at low wind speeds and aggressive transient response, possibly unstable, at high wind speeds. The paper also evaluates the performance, as measured by the dynamic and steady state response, of the ESC with feedback of the logarithm of the power signal (LP-ESC). Large eddy simulations (LES) demonstrate that the LP-ESC, calibrated at a given wind speed, exhibits consistent robust performance at all wind speeds in a typical region II. The LP-ESC is able to achieve the optimal set-point within a prescribed settling time, despite variations in the mean wind speed, turbulence, and shear. The LES have been conducted using realistic wind input profiles with shear and turbulence. The ESC and LP-ESC are implemented in the LES without assuming the availability of analytical gradients.