the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Stochastic Gradient Descent for Wind Farm Optimization
Julian Quick
Pierre-Elouan Rethore
Mads Mølgaard Pedersen
Rafael Valotta Rodrigues
Abstract. It is important to optimize wind turbine positions to mitigate potential wake losses. To perform this optimization, atmospheric conditions, such as the inflow speed and direction, are assigned probability distributions according to measured data, and these conditions are propagated through engineering wake models to estimate the annual energy production (AEP). This study presents stochastic gradient descent (SGD) for wind farm optimization, which is an approach that estimates the gradient of the AEP using Monte Carlo simulation, allowing for the consideration of an arbitrarily large number of atmospheric conditions. This method does not require that the atmospheric conditions be discretized, in contrast to the typical rectangular quadrature approximation of AEP. SGD is demonstrated using wind farms with square boundaries, considering cases with 25, 64, and 100 turbines, and the results are compared to a deterministic optimization approach. It is shown that SGD finds a larger optimal AEP in substantially less time than the deterministic counterpart as the number of wind turbines is increased.
Julian Quick et al.
Status: final response (author comments only)
- RC1: 'Comment on wes-2022-104', Ahmad Vasel-Be-Hagh, 31 Dec 2022
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RC2: 'Comment on wes-2022-104', Anonymous Referee #2, 03 Jan 2023
The paper is well written and explores an idea worth considering. My main concern is the omission of discussions surrounding accuracy.
- operating on continuous PDFs isn't so much of an advantage as it is made out to be. And really pretty much any of the UQ methods could be thought of acting on a continuous input (the discretization can be considerred part of the method, in the same way that random sampling is part of the method of MC).
- the literature review on SGD has good detail, but the lit review is light on other topics that this paper is based on. Namely, the proposed approach is a gradient-based one and there is no discussion of any prior work in this regard, other than the reference to the review paper by Herbert-Accero (which is a somewhat ironic choice as that review paper shows very few gradient-based approaches and is pretty dismissive of the approach in general).
- Algoirthm 1 could use more introduction. Although I am already familiar with SGD, as noted by the authors it is not in regular use by the wind farm optimization community and so needs more explanation than just an algorithm dump.
- The SGD method notes a mix of AD and finite difference, but in the determinisitic approach it is not stated how you compute the derivatives and of course this will affect the time performance.
- Nowhere is the accuracy of the method shown. Undoubtedly MC can be much faster than a dense rectangule rule, but of course the real question is at what level of accuracy? One would like to see how many random samples are required to achieve the same accuracy.
- I realize this is somewhat difficult to directly compare as you are using a stochastic gradient and so allowing for inaccuracy is built into the method, but this is still a topic that one should be more transparent on. Especially since the main comparison is a very dense rectangle rule combined with SLSQP. I don't have a problem with that choice, but lots of things are faster than that combination. It shows promise, but must be careful on concluding anything more than that.
- The plots on different learning rates, and the discussion on how hyperparameters were selected are appreciated.Citation: https://doi.org/10.5194/wes-2022-104-RC2 -
RC3: 'Comment on wes-2022-104', Anonymous Referee #3, 26 Jan 2023
General comments
This manuscript proposes the application of the stochastic gradient descent (SGD) method from deep learning to the wind farm optimization problem, which maximizes annual energy production (AEP) with respect to wind turbine location. It is claimed that this work is the first such application, and it shows results demonstrating significant reduction in computation time for a small set of test cases. The manuscript is generally well-written, and the writing is concise.
Specific comments
Results are presented for three wind farms of different sizes, with 20 optimizations each with randomized initial designs. The authors are also asked to consider different wind farm shapes. Since there are some tuning parameters in the algorithm (and some tuning was required to achieve favorable results), a concern is whether significant problem-specific tuning is required. Demonstrating consistent results with different wind farm shapes (beyond just the one rectangular domain) would be very compelling.
There is clearly a cost to the reduction in computation time since constraints are not exactly satisfied. Could the authors comment on the degree of constraint violation and its significance, considering a range of different problems? Perhaps it would be helpful to visualize a Pareto front of computation time versus constraint violation, varying eta_T.
Julian Quick et al.
Julian Quick et al.
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