the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Jan 2025
Brief communication: An elliptical parameterisation of the wind direction rose
Abstract. This brief communication presents a parametric model for the wind direction rose, based on ellipse geometry. Such a model supports standardisation and identification of generally representative cases, while also enabling systematic analyses of wind rose “shape” impacts on the benefits of proposed wind farm design and control innovations. Formulations include analytical wind direction rose modelling, model fitting to measured data via gradient descent minimisation of sum-of-square errors, and goodness-of-fit measures. Testing on wind direction data from real offshore wind farms confirms good performance, indicating this parametric model is useful to wind energy research and development efforts.
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RC1: 'Comment on wes-2024-187', Anonymous Referee #1, 17 Feb 2025
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This paper presents a parametric wind direction rose model based on an ellipse and demonstrates how the model, which includes 3 parameters, can be fit to measured wind direction data for a variety of sites. There is little published on parametric wind direction rose models, so this is a novel contribution to the literature. When combined with wind speed distributions, the model could potentially serve as a standard wind rose definition for computing wake losses, lifetime loads from wakes, and wind farm control benefits for a wind farm, similar to how the Weibull distribution is used to model wind speed probabilities for annual energy production and fatigue load calculations for individual turbines. The parameters of the elliptical wind direction rose model could be used to standardize the characterization of wind direction distributions in the wind industry. They could also be varied to explore the sensitivity of wind plant performance, loads, and wind farm control strategies to different wind direction distributions.
The main comment I have is about how the elliptical parameterized wind rose can be made more useful for sites with more complex wind direction distributions. The presented parameterization works well for sites with unimodal wind roses or bimodal wind roses where the prevailing wind directions are in opposite directions, as shown in Fig. 3. However, similar to what is shown in Fig. 3e, there are many sites where the most common wind directions are not 180 degrees apart. To provide another example, in Fig. 3 of Bensason et al. 2021 (https://pubs.aip.org/aip/jrse/article/13/3/033303/285076/Evaluation-of-the-potential-for-wake-steering-for), the most common wind direction sectors are from the northwest and south. It would greatly strengthen the paper to discuss possible extensions of the elliptical wind rose model that could more accurately describe these types of wind direction distributions. For example, could you consider a linear combination of elliptical wind roses with different prevailing wind directions such that the sum of the distributions integrates to 1? This could be a nice solution if the different prevailing wind directions could be included as optimization parameters, rather than being identified manually. Of course the idea behind a parameterized wind rose model is to keep it relatively simple, but considering only wind roses with prevailing wind directions 180 degrees apart might be too much of a simplification for many sites. Among other issues, this could be important when estimating wake losses at a site with long distances between rows of turbines but close spacing in the perpendicular direction. Underrepresenting the likelihood of common wind directions aligned with the close turbine spacing in order to fit the wind rose model to the prevailing direction might cause wake losses to be significantly underestimated.
Comments:
- Pg. 3, ln. 60: Is this equation only supposed to be valid when theta^tilde_1 and theta^tilde_2 are less than or equal to pi/2? If so, please clarify. Also, looking at Fig. 1b, how is y^tilde_+(x) defined for x_2 < x <= x_1? The segment area is no longer bounded by two lines like it is for x < x_2.
- Pg. 4, ln. 82: "not be equally" -> "not equally"
- Section 2.4: Scaling the wind direction probability by 1-f for pi/2 < theta_c,i < 3pi/2 and 1+f for 0 <= theta_c,i < pi/2 or 3pi/2 < theta_c,i <= 2pi causes a sharp discontinuity at theta_c,i = pi/2 and 3pi/2, which doesn’t seem very realistic. Would a smooth (e.g., linear) transition from 1-f to 1+f be more appropriate? One example would be scaling P_el by (1 + f - (2*f/pi)*theta_c,i) for 0 <= theta_c,i < pi. This way you would still get 1 - f for theta_c,i = pi, 1 for theta_c,i = pi/2 and 1 + f for theta_c,i = 0.
- Section 2.5: Could you also optimize the prevailing wind direction theta_prev when fitting a wind rose to empirical data?
- Pg. 6, equation after line 110: in the first two lines, it would clarify the equation if "i" were added as a subscript for P^dagger_g because this represents the probability of the specific bin "i".
- Pg. 6, ln. 115: "The partial derivative del P^dagger_g / del a is readily obtained using del A_theta_1,theta_2 / del a…": To help the reader, it would be good to refer to the specific equations earlier in the text that show how these two partial derivatives are linked. This might require more equations to be numbered.
- Section 3: It would be helpful to discuss the choice of bin sizes shown. What are typical wind direction bin widths for wind roses in the wind industry, for example for energy yield assessments or controls analysis?
- Pg. 7, ln. 130: "the RMSE-scale is dependent on the number of wind direction bins." Couldn't the RMSE be normalized to account for the number of wind direction bins so it can be used to compare the goodness-of-fit for roses with different bin sizes?
- Pg. 7, ln. 131: "Limitations of R^2 should be kept in mind" Please briefly discuss these limitations here.
Citation: https://doi.org/10.5194/wes-2024-187-RC1 -
AC1: 'Reply on RC1', Edward Hart, 20 Feb 2025
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