The present paper further develops and experimentally validates the
previously published idea of estimating the wind inflow at a turbine rotor
disk from the machine response. A linear model is formulated that relates one
per revolution (1P) harmonics of the in- and out-of-plane blade root bending
moments to four wind parameters, representing vertical and horizontal shears
and misalignment angles. Improving on this concept, the present work exploits
the rotationally symmetric behavior of the rotor in the formulation of the
load-wind model. In a nutshell, this means that the effects on the loads of
the vertical shear and misalignment are the same as those of the horizontal
quantities, simply shifted by
The ability to control a system is often intimately linked to the awareness of the surrounding environment. For a wind turbine, the environment is represented by the wind inflow, which is characterized by speed, direction, shears, veer, turbulence intensity, presence of impinging wakes, etc. Such parameters have a profound effect on the response of a single wind turbine as well as on clusters of interacting machines within a power plant. Better awareness of the wind environment can be translated into better turbine-level and plant-level operation and control.
The current standard equipment mounted on board wind turbines for the measurement of the wind inflow is composed of one or more anemometers and wind vanes, typically located at hub height, either on the nacelle or on the spinner. Even when properly calibrated, all such devices suffer from one inherent unavoidable limitation: they provide measurements at the single point in space where they are located. As such, they are necessarily blind to all wind characteristics that imply wind variations across the rotor disk. Alternative sensors are represented by lidars, which are, however, not yet routinely installed on board wind turbines because of cost, availability, reliability, effects due to weather conditions and lifetime issues. In this sense, current wind turbines have only a very limited awareness of the environment in which they operate.
The concept of the “rotor as a sensor” was developed to address the limitations of current wind measurement devices. The idea is conceptually very simple: changes in the wind inflow produce changes in the wind turbine response. If the wind-response map is known, one can then measure the response (for example, in the form of loads and/or accelerations) and estimate the inflow by inverting the map.
Various formulations have been proposed for this concept
Despite the more than promising results reported in
To address this issue, the present work exploits the rotationally symmetric behavior of
the rotor. In fact, the effect caused by a horizontal shear on the rotor response is the
same as that caused by a vertical shear, only shifted by
The paper is organized as follows. Section
The wind inflow is characterized in terms of four so-called wind states, which are
defined as the vertical (upflow) and horizontal (yaw) misalignment angles
The wind states are defined with respect to a nacelle-attached reference frame
Definition of the four wind states used for parameterizing the wind field over the rotor disk.
Notice that the formulation of
Looking at Eq. (
In this work, the linear model of
To identify the model coefficients
Once the model expressed by Eq. (
By considering the rotational symmetry of the rotor, the number of unknown coefficients
in
The term
The advantage of this approach is not only in the reduced number of unknown model coefficients, but, most importantly, in the reduced datapoints necessary for identification. In fact, by eliminating the coefficients of horizontal shear and upflow angle, one can use tests in which only yaw misalignment angle and vertical shear are changing. Therefore, since the model is linear and depends on two parameters, a minimum of only three operating conditions is required for identification.
The proposed method was first tested by numerical simulations, using the model of a
horizontal-axis three-bladed 3 MW wind turbine. The machine has a rotor diameter of
93 m; a hub height of 80 m; 4.5
Turbulent simulations were run for a duration of 10 min, according to standard practice.
The 1P harmonics were computed by the Coleman and Feingold transformation
Two observation models were identified. The first is the linear formulation of
The two models were then tested and compared in turbulent wind conditions. Three
different combinations of inflow angles and shears (not included in the identification
set) were considered, each using four different turbulent realizations, for a total of 12
tests performed at each given wind speed and turbulence intensity (TI).
Figures
Mean absolute error
Standard deviation
Next, the proposed formulation was tested using an aeroelastically scaled wind turbine
operated in a boundary layer wind tunnel. The scaled model represents a three-bladed
horizontal-axis wind turbine with a hub height of about 1.8 m, a rotor diameter of 2 m
and a rated wind speed of 6 m s
Test matrix for the wind tunnel experiments. Symbol “
Tests were performed in the boundary layer test section of the wind tunnel of Politecnico
di Milano
Wind states observed for different steady inflow conditions: yaw misalignment
For various wind speeds, several tests were performed for different combinations of yaw
misalignment, vertical shear and upflow angle as reported in Table
Mean absolute error
A total number of 174 different conditions were tested. The entire set of experiments was
then divided into two subsets. The first one was used for identifying the observer model,
and it contains two combinations of vertical shear and misalignment angle per wind speed,
with an upflow of 6
To validate the performance of the observer, the machine response during each test was
averaged over a time window of 180 s in order to estimate the corresponding mean inflow
parameters. The length of the time window is dictated in this case not only by the need
to average out turbulent fluctuations, but also by the dynamic characteristics of this
particular closed-return wind tunnel. Figure
Finally, to better understand the performance of the observer, mean inflow parameters
were estimated and compared to the respective ground truth for each test not included in
the identification set. For each wind speed, such mean errors were averaged over the
number of tests and reported in Fig.
Comparing the experimental results with the numerical ones in the low TI cases (equal to
3.8 % and 5 %, respectively), one should notice that the mean estimation errors
present the same range of accuracy, as one can appreciate by comparing
Fig.
Following the work presented in
The performance of the proposed rotationally symmetric model was tested both in
simulation and with an aeroelastically scaled wind turbine model in a boundary layer wind
tunnel. Results indicate no significant difference in the accuracy of the new
rotationally symmetric formulation with respect to the original one, even if the number
of tests required for identification is significantly decreased. The expected mean error
in the angle estimation is less than 1 and 2.5
Data can be provided upon request. Please con-tact the corresponding author Carlo L. Bottasso (carlo.bottasso@tum.de).
All authors equally contributed to this work.
The authors declare that they have no conflict of interest.
This work has been partially supported by the CL-Windcon project, which receives funding from the European Union Horizon 2020 research and innovation program under grant agreement No. 727477. This work was supported by the German Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open Access Publishing Program. Edited by: Sandrine Aubrun Reviewed by: two anonymous referees