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. 

 

The authors present a framework to derive operational states of one wind turbine, based in (linear) correlation metrics of six observables describing the turbine's behavior. Combining these matrices with a k-means algorithm to cluster them, the author identify 5 operational states with distinct dynamical features.

I found this idea interesting to explore frameworks to analyse wind turbine behavior. However, I would suggest to expand the main text to discuss it. In particular, I have the following remarks:

1) At least a more torough description of the parameter when applying the framework should be provided. Namely, how is T determined? Is there an optimal value. balancing trade-off between accuracy and statistical uncertainty?

2) How would such an approach scale with the number of turbines, i.e. applied to a wind farm? Would it enable to also derive large scale operational states of wind farms?

3) The use of linear correlations (only) seems odd in the context of a (highly) non-linear system. I am aware of the previous works by Guhr and co-workers with correlation matrices between stocks, but I wonder why e.g. mutual information or even granger causality matrices were not consider. At least some content at the level of discussion would be in order.

Minor points: 

The authors should in the end make a careful proof-reading, to detect several typos, missed references ("??") and improve the layout of some tables and figures.