the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Extension of the Langevin power curve analysis by separation per operational state
Abstract. In the last few years, the dynamical characterization of the power output of a wind turbine by means of a Langevin equation has been well established. For this approach, temporally highly resolved measurements of wind speed and power output are used to obtain the drift and diffusion coefficients of the energy conversion process. These coefficients fully determine a Langevin stochastic differential equation with Gaussian white noise. We show that the dynamics of the power output of a wind turbine have a hidden dependency on turbine's different operational states. Here, we use an approach based on clustering Pearson correlation matrices for different observables on a moving time window to identify different operational states. We have identified five operational states in total, for example the state of rated power. Those different operational states distinguish non-stationary behavior in the mutual dependencies and represent different turbine control settings. As a next step, we condition our Langevin analysis on these different states to reveal distinctly different behaviors of the power conversion process for each operational state. Moreover, in our new representation hysteresis effects which have typically appeared in the Langevin dynamics of wind turbines seem to be resolved. We assign these typically observed hysteresis effects clearly to the change of the wind energy system between our estimated different operational states.
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RC1: 'Comment on wes-2024-52', Anonymous Referee #1, 30 May 2024
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The paper shows that the power output dynamics of a wind turbine have a hidden dependency on the turbine's different operational states. By identifying these states using a correlation matrix clustering method, the authors were able to condition the Langevin analysis on the different states. This revealed distinct power conversion behaviors for each state and resolved previously observed hysteresis effects, which were attributed to changes between the operational states. The results emphasize the importance of accounting for the different states to accurately capture the complex dynamics of the wind turbine power generation process.
The message of the manuscript is very interesting and sound. Although the paper is well-written and extremely timely, there are some improvements to consider before final acceptance in WES.1-Add a small subsection about hysteresis effects and how the new analysis is resolving it.
2-Change the naming of the indexing variable k in Eqs. (1)-(3) to avoid any confusion with the k-means clustering method. Unify the notations used for k-mean, k mean.3-Define the diffusion coefficients after Eq. (7) and Eq. (16) to provide a clear explanation of these important parameters.
4-Describe how the optimal bandwidth h of the kernel is estimated, as this can significantly impact the results.
5-Write a short note about the possibility that the diffusion term may change the location of the stable fixed points obtained from the drift term, leading to noise-induced transitions.
6-Discuss the impact of potential jumps in the power output that may be present in the different operational states S=1,...,5.
7-Unify the citation style used throughout the References section.
Citation: https://doi.org/10.5194/wes-2024-52-RC1
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