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. KEYWORDScontrol of wind turbines, extremum-seeking control, large-eddy simulations, logarithmic power feedback INTRODUCTIONWind turbines work over a wide range of conditions and have a long operating life. Thus, the optimal settings for the parameters of the control system may change from initial design specifications. For instance, turbine aging, local topography, and atmospheric conditions affect the turbine performance. In these cases, tuning the control parameters to the site-specific operating conditions can reduce power losses and/or excessive loads at low cost.Extremum seeking control (ESC) has been proposed to tune control system parameters for wind turbines. 1-3 The ESC is well suited for power maximization below rated conditions because it requires feedback of the power signal only, and it is essentially a model-free algorithm that can be commissioned with data from the turbine step response and knowledge of the spectral characteristics of the wind fluctuations. The convergence rate of the basic ESC depends on the magnitude of the gradient of the performance index 3 with respect to the control parameters (eg, generator torque gain, blade pitch angles, yaw angle). For a turbine in below-rated conditions (region II), the power is the performance index. The rotor power is proportional to the power available in the wind, which in turn is proportional to the cube of the effective wind speed. Thus, the gradient of the power signal with respect to the ESC control parameters, is also roughly proportional to the power available in the wind, which can vary from very little power (cut-in wind speed) to almost rated power (close to rated wind speed).* This wide variation in available wind power results in unpredictable performance of the gradient-based ESC algorithm, with slow convergence at low wind spee...

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