the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 May 2025
Wind farm inertia forecasting accounting for wake losses, control strategies, and operational constraints
Abstract. Future inverter-based resources (IBRs) must provide grid-forming functionalities to compensate for the declining share of conventional synchronous machines (SMs) in the power generation mix. Specifically, decreasing power system inertia poses a significant challenge to grid frequency stability, as system inertia limits the rate of change of frequency (ROCOF). Conventional grid-following control decouples the physical inertia of wind turbines (WTs) from the grid frequency. Novel grid-forming control methods, such as virtual synchronous machine (VSM) control, provide (virtual) inertia to the system, e.g. by extracting kinetic energy from WTs. Since the grid-forming capability of IBRs depends on volatile operating conditions, future market designs will remunerate inertia provision based on its availability. Thus, estimating grid-forming capabilities of WTs and forecasting inertia of wind farms (WFs) are of interest for both WF and system operators. In this paper, we propose a method to forecast inertia that accounts for wake effects in a WF. The approach is based on mapping forecasted site conditions to each single WT in the WF through a wake model. The resulting inflow conditions are used to predict the WT grid-forming capabilities, taking WT control strategies and operating limits into account.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on wes-2025-72', Anonymous Referee #1, 15 Jun 2025
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RC2: 'Comment on wes-2025-72', Anonymous Referee #2, 21 Jun 2025
The authors present a method to predict the grid-forming capabilities of wind turbines on a wind farm, taking wind turbine control strategies and operating limits into account. Previous work by some of the authors (Anand et al., 2024) forms a basis for forecasting inflow conditions at each wind turbine in a wind farm, incorporating wake effects in the wind farm. The resulting flow conditions are then used in predicting the grid-forming capabilities of the wind turbines. The (Thommessen and Hackl, 2024) paper is cited numerous times throughout the paper in the presentation of the various parts needed for predicting the inertia that wind turbines can provide, and I am not completely sure of the new contributions the authors are providing in this current paper. It would be helpful for the authors to more clearly state what has been done in the past, and what their *new* contributions are with this paper. Are they assembling many pieces from past works, which has never been done before? Are some pieces novel and were required to be developed as the authors were putting together the overall inertia forecasting capability?
While I enjoyed the paper overall, the paper is quite complex and at times difficult to understand and follow. There are often references within the same sentence to an appendix at the end, a figure several pages later in the paper, and a figure that was previously shown several pages earlier in the paper. This cross-referencing to multiple other places in the paper sometimes made it difficult to follow.
In Section 4, the authors present a case study for a wind farm with 12 wind turbines. What is the layout of the wind turbines? This would be useful, for instance, in interpreting the individual wind turbine curves in Figure 14(a).
A few more detailed comments and suggestions for improvement:
- Below Equation (9), the authors state that “The i-th constraint is considered active if c_i = 0, or inactive if c_i > 1.” Should the “1” be a “0”?
- When Figure 2 first appears, the authors state at the beginning of Section 3.4 that “Figure 2 depicts the overall WT modeling and control used in this work.” Figure 2 actually depicts a lot more than the overall WT modeling and control used. It would be useful to the reader if the authors provided an overall description of the rather complex and encompassing Figure 2 when the figure is first introduced, before the various sections that then focus on discussing particular parts of the figure in further detail.
- It would be useful to point out to the reader early on that Appendix J provides a listing of the nomenclature used throughout the paper. I don’t believe Appendix J is ever mentioned in the main text, and at least for me, I didn’t see that Appendix until well into the paper. Indeed, there are many symbols used and it quickly became confusing; and it would have been useful to know of Appendix J before I discovered it much later on my own.
- On page 14, lines 319-320, the authors state “the VSM mechanical model is based on a one-mass model with virtual inertia constant H_v in Eq. (13).” When I look at Eq. (13), I don’t see any H_v, and as a result I am confused and am not sure I am understanding the statement correctly.
- On page 21, lines 498, in the discussion of Fig. 8, the symbol “beta_min” is used. From Fig. 8, panel (c), it appears that this beta_min is 1.1 degrees (green curve). Since there are several other curves in Fig. 8(c) with beta values *smaller* than 1.1 degrees, I would suggest using “beta_finepitch” or some other symbol other than “beta_min” since beta_min is clearly not the minimum beta.
- On page 21, lines 500-501, the authors state that “After the ROCOF changes from negative to positive at t_{s,min} = 3.5s, …” Should that be 2.5s instead? Indeed, later in the same paragraph (line 504), the authors indicate that “t_{s,min} = 2.5s”.
- In Figure 10, on the right plot, the legend has the ordering of Omega_min, dot{M}_{e,max}, M_{e,max}, P_{e, max}. The ordering is then changed in the legends in the left plots of Figures 11 and 12. I would suggest using a common ordering for the legends in all of these plots.
- On page 28, line 607, the authors indicate “P_{set} = 98% (panel b)” but panel (b) has a plot title indicating “P_{set} = 0.96”. It’s not clear which is the actual P_{set}.
- Sometimes closing-quotes show up instead of opening-quotes when quotes are used around “Det”, “Comb Min”, “Simple Opt”, “No Wake”, “Deterministic” in Figures 16-18.
- If possible, please move the legends so that they do not cover the results “bars” in Figures 17-18. It seems there is enough white space in the plots to move the legends to more “optimal” locations that don’t cover any of the results actually being shown.
Citation: https://doi.org/10.5194/wes-2025-72-RC2
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Wind farm inertia forecasting accounting for wake losses, control strategies, and operational constraints Andre Thommessen et al. https://doi.org/10.5281/zenodo.15176373
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