Summary in my words and general critique
========================================
The paper deals with methods to calculate yield for an airborne wind energy system (AWES).
Because AWES operate at a range of altitudes, wind shear and speed development (aka the wind profile) above 200m play a role in estimating the power output at a given site.
For every instantaneous wind profile, different trajectories are optimal and hence generalizing the output into a power curve that - together with wind statistics at a given site - could be used to estimate yield is difficult.
This is what happens in the sections of the paper:
a) Wind profile classification
Two sites (on-shore and off-shore) are chosen and wind profile simulation data is assembled.
This data is classified into clusters (10 for visualization, 20 for later evaluations) which results in e.g. 10 centroid profile shapes which group all similar occurring instantaneous profiles of the site and that time span and are the "mean" profile in a least-squares sense.
These can be seen in Figs A1 and A2.
From these clusters, three specific profiles from the (mean wind speed sorted simulation data) are chosen: the 5th, 50th and 95th percentile one. I am not sure, but to me this sounds to encompass one that is close to the centroid (50th) and two edge cases. Looking at Figs A1 and A2 it is also clear that each cluster covers a rather large set of wind speeds.
This set of chosen profiles is then assumed to cover "the range of operational wind conditions", so we have 3x20=60 profiles to work with.
b) Power output at each profile
For all 60 profiles, a trajectory optimization is run for a 20m² model of an AWES based on the Ampyx AP2. To use the profiles in the optimization routine, it seems the profiles were sampled at some points and polynomial fits with unknown variation form the actual profile were generated (see red colored line Fig.A3 a), showing only the polynomial where the optimizer has chosen to fly at).
This results in 60 Power outputs for the 60 profiles.
The optimization is also run assuming two different logarithmic profiles with wind speeds at 10m in 2m/s steps.
In addition, a very simple power output formula was used and denoted "QSM", neglecting non-crosswind conditions, retraction, mass. I assume the optimal altitude for this formula and the given profile was chosen, but this is not stated.
In addition, a simple wind-turbine formula ("WT") was evaluated at these profiles at a hub-height of 100m (cubic until constant).
c) Comparisons
Now, we could have compared the power output at all 60 profile shapes and discuss where they differ and why.
We could also calculate the yield by somehow assuming that the total wind conditions could be separated into these 60 profiles with each assigned a fraction of the year.
A similar approach to that last sentence is done for the AEP value "AWEScluster" in section 6.4: The whole year (that is all simulated profiles) are looked at and the power output calculated using the three powers calculated within the cluster the profile belongs to. There, it is assumed that the power can be calculated by inter/extrapolating over mean wind speed, where we have the three cases as base points. This results then in the total power output and should be the "ground truth" as there is no more accurate way to calculate power and yield for the AWES - unless one does more simulations at different profiles.
For now, nothing has been said about defining a reference altitude, and of course the machine yield at a specific site is not determined by any arbitrary definition of a reference altitude.
c-1) Power curve
Instead of using this approach for all, there is the notion of a power curve introduced in Fig13.
In a) and b) for each profile, the power output is printed over the wind speed "at operating height", which is not clearly defined but probably is the mean altitude while we reel-out (?) or maybe also the mean wind speed while operating in reel-out (?). At least that is what I assume based on Fig14, there is however the sentence: "We chose average wind speed between 100 and 400 m as reference wind speed (abscissa)"
The same is plotted for "WT", which operates at constantly 100m and - sorted by wind speed - is continuously increasing but obviously not smooth due to the nature of the 60 profiles.
The "QSM" is plotted as well and is probably operating also at its optimal altitude which the paper states to be higher than the optimized one. Because they all operate at different altitudes - which for every profile means significantly different wind speed at 100m or any other altitude - they are not directly comparable.
The graph also includes the logarithmic optimization cases - which are also not directly comparable.
c-2) Wind statistics
To do something with these power curve plots akin to classical yield estimation form wind turbine power curves, the wind speed frequency of mean wind speed from 100-400m over all discrete wind profiles in all sets are plotted (bars) - which of course differs from the frequency at 100m (red). Rayleigh distributions are plotted for comparison and match the bars rather well.
The last plot now tries to estimate (fractional) yield per wind bin by multiplying power and frequency. This only makes sense if the power curve for the AWES would also have been plotted over this mean wind speed - so either this is the case (which would be weird because the k_onshore=20 line is looking like the z=z_operating line in Fig14) and the yield is somewhat correct (though arbitrarily simplified instead of directly relying on the frequency of the profiles over the year) - or the yield is wrong.
Fig14 adds to the confusion by comparing frequency definitions of the wind data: A histogram of the mean wind speed between 100 and 400m is compared to the constant 100 - but also to the mean at z=z_operating which is hard to define since the operating height is only defined via the optimization of a specific profile and therefore only available for the 60 profiles, not over the whole year - but maybe this is somehow extrapolated from this data?
Because the system stays the same, the total yield of the AWES at these two sites should be the same disregarding any definition of reference height - save for any rounding and binning errors one may add later. But because here the binning of wind speed takes place over all clusters the connection between the occurrence of the wind profile and its power output is lost depending on the definition, resulting in distinct AEP yields in Fig15.
In summary: The comparisons shows (to me) that using these clusters with three candidate profiles to evaluate power output may be a good way to estimate yield by going through the year and calculating power at each profile using the three power outputs of the current cluster (since for increasing clusters the change in AEP becomes smaller - though still significant for the step from 20 to 50). But it does not seem to be a good idea to force this data into a power curve and estimate yield together with some wind histogram. Different definitions, binning, interpolation and so forth introduce quite large differences in yield that are not due to the system but only due to the method. This of course begs for the question: Why do it?
A power curve is a tool that should allow the calculation of yield for a given site. Here, a power curve that is intrinsically linked to the site is proposed - and even there it cannot be used effectively to estimate yield. In comparison, the methodology in [1] describes how one can use a family of power curves for different operating altitudes to estimate yield at arbitrary sites.
However, the methodology to categorize wind conditions into clusters of different shapes is good and potentially a good way to characterize AWES power output. I would propose to
a) Use a wind speed multiplier for each shape
b) Find normalized shapes that allow for a good fit of the whole year of profile shapes
such that f_k(h)*w-f(h) for k shapes is minimal for all f(h) in the year.
Then, one can generate power curves for each k, and together with a histogram of w-k the yield can be reliably calculated. If the k shapes generalize to a large part of available sites, it can then be used at any site. This would also allow the characterization of different sites by "prominent cluster shapes" and the discussion of the shape of power curves (over wind multiplier w) for different shape classes (and why they differ).
While talking about the clusters: If the clusters have such a wide range of wind speeds that one cannot use the centroid for evaluation as a stand-in for the whole cluster (and instead the range must be "sampled" by using three profiles), maybe another way of clustering would have been better anyways?
Now: "Normalization was was not applied in this study to simplify and clarify the clustering procedure as the focus of this manuscript is on the derivation and comparison of power curves." I understand that you decided that this is beyond the scope of this paper. Maybe you should then leave the power curve out of it and simply discuss the AEP from the clustering and evaluation over the year and compare to a wind turbine and QSM if you want?
Most "conclusions" are actually independent of the whole power curve discussion
* "logarithm fits better offshore"
* "the system mostly operates below 400m" (and actually at minimum altitude if not in depower from the looks of it)
* "Rayleigh distribution over-predicts high wind speeds" (I don't see it, but you state it)
and depend purely on either wind analysis alone or how the optimization results look like here.
And a discussion about power curves should follow once a reasonable power curve definition (e.g. as proposed above with normalized profiles and a wind multiplier) is used that enables to estimate yield and can be generalized to other sites.
I might have misunderstood the parts about yield and power curves, and I am sorry for these rather harsh notes. If I did, take these notes as input to rephrase the topic such that I understand the point of the power curves as defined better and feel free to send me more explanations as an answer to this review.
Additional points
=================
* A rather important paper and method (by the author of these lines) has been omitted: [1]. This methodology has been presented on the AWEC2015 and is part of the second edition of the AWE book. There, a family of power curves at different mean altitudes is calculated and used to evaluate best altitudes and AEP for logarithmic as well as arbitrary wind profiles. Looking at the operating altitudes in Fig11 it seems that at least for the blue, red and yellow lines this is a suitable assumption, while the green depower mode increases altitude dramatically during operation and hence might be a candidate to show where this assumption is insufficient. However: it is significantly simpler to calculate and to understand, does not rely on any wind profile families and hence is a "machine-only" description and can actually be used to evaluate AEP for different sites. The paper should sort this alternative methodology from the literature within this paper in the introduction and - at best - show where a "similar altitude and hence wind speed" assumptions leads to significant errors in AEP and a "profile shape" classification leads to improves AEP calculations. This means that one needs to show that the optimized trajectory makes explicit use of the wind shear within its cycle!
* Why are only calculated profiles used? As far as I know, the sites and times are correlating with LIDAR measurement campaigns where detailed measurements are available
* Is it true that the QSM is neglecting force constraints and the retraction phase? Because they can be easily incorporated (calculate or assume reel-in speed and hence time lost even if you want to stick to P=0, increase reel-out speed or elevation in case of force constraint). And neglecting these two things easily explains an increased power output in partial load regime, no complex optimization routines for wind shear assumptions necessary. If you want to show the difference due to wind profile and optimization for those, these factors need to be included.
* For the logarithmic optimization runs: Maybe 2m/s steps at 10m reference height is a bit rough (as this will be steps of 3.3m/s at onshore conditions at 200m altitude). While the plots are noisy enough so that this is probably not so relevant, I would use a finer resolution - if you redo them.
* The usage of the three profiles per cluster in the optimal control problem is not clear to me. In FigA3 it is noted that the difference between the red line and the gray line in A3a) is due to polynomials. But I also assumed that these polynomials would go through all points. So either there are only two points (at 30m(?) and at 220m(?)) which are plotted linearly in gray and somewhat quadratic in red or you removed some points. Either way, the gray line is not showing the wind speed variation used for the optimization algorithm. Please plot the actually used wind profile here as well over all altitudes, not only those that were used by the optimizer. And if they differ drastically from the plotted gray ones maybe talk about why that is and what your thoughts on that are.
Additional notes in the attached PDF as comments.
[1] Ranneberg, Maximilian, et al. "Fast power curve and yield estimation of pumping airborne wind energy systems." Airborne Wind Energy. Springer, Singapore, 2018. 623-641. |

# Editor report wes-2020-120

## General comments

### Content

I find the discussion of the state of research still too concise. On page 2 of the manuscript past research is shortly listed but not critically discussed at all. I would expect at least one sentence, per published work, to highlight the individual contribution, the pros and cons of it. This would help the reader to position the new contribution of the authors, in the frame of existing work.

When describing the QSS model in Section 4.1 Engineering "reference model" I am missing a discussion of assumptions that lead from the pumping cycle operation with a flight trajectory spanning a large spacial volume, along which the pulling force and reeling motion is converted into electrical energy at the ground, to a single point description for the power P_opt at some reference height z.

In Section 4.4 "Aircraft model" you should stress that this scaling law is for fixed wing AWES only. Although you define the scope to be limited to fixed wing systems, you use the term AWES and a reader who missed this scope definition might misinterpret this section.

### Style

The manuscript still requires a textual improvement. Articles are frequently missing, etc.

The use of citations in the text must be corrected throughout the manuscript. Please refer to, for example, https://libguides.williams.edu/citing/chicago-author-date#s-lg-box-21699945 describing how this is done correctly. I believe that Latex has \citet{} and \citep{} commands to properly implement this standard.

The mixed use of citations and footnotes could be more consistent. Many footnotes can actually be converted into references and included in the bibliography.

When mentioning specific figure, equation, section etc, these terms should start with an upper case letter, e.g. "In Figure 2 it is shown...".

Equation numbers are generally in round brackets. See Latex command \eqref{}.

## Minor comments

p. 2, line 27: "a tether" -> "one or more tethers". Strictly speaking, there are also concepts that emply one or more flying devices.

p. 2, line 44: The use of "They" to start a new paragraph is a bit confusing. Also the "they" in the following sentence. I suggest to either remove the paragraph break, or use "Such approximations" to better connect the two sentences.

p. 3, line 80: "fig" -> "Figure"

p. 3, line 73: "WRF simulation" -> "WRF simulation data"

p. 13, last line: opening bracket is not closed.

p. 14, line 259: In mathematics it is standard to attach an exponent to the variable symbol and not a possible dependency. So, U^3(z) instead of U(z)^3

p. 14, line 263: Start the sentence with "The elevation angle ...".

p. 14, line 264: "air resistance" -> "aerodynamic drag". For clarity I would also write "AWES, comprising kite and tether".

p. 14, line 266: "A tether diameter...".

p. 23, line 447: \zeta is called the "power harvesting factor", not "AWES harvesting factor". Equation (9) is also not introduced. Please add something like "The power harvesting factor is computed as" before the equation.

p. 26, Figure 15: Axis labelling is tiny and hardly readable, unnecessarily. Please increase font size.

p. 27, line 497: Unclear to what "4.7" refers.