Predicting power ramps from joint distributions of future wind speeds
- 1Department of Statistics, Universität Innsbruck, Innsbruck, Austria
- 2Department of Atmospheric and Cryospheric Sciences, Universität Innsbruck, Innsbruck, Austria
- 3MeteoServe Wetterdienst GmbH, Innsbruck, Austria
- 4Department of Mathematics, Universität Innsbruck, Innsbruck, Austria
- 1Department of Statistics, Universität Innsbruck, Innsbruck, Austria
- 2Department of Atmospheric and Cryospheric Sciences, Universität Innsbruck, Innsbruck, Austria
- 3MeteoServe Wetterdienst GmbH, Innsbruck, Austria
- 4Department of Mathematics, Universität Innsbruck, Innsbruck, Austria
Abstract. Power ramps are sudden changes in turbine power and must be accurately predicted to minimize costly imbalances in the electrical grid. Doing so requires reliable wind speed forecasts, which can be obtained from ensembles of physical numerical weather prediction (NWP) models through statistical postprocessing. Since the probability of a ramp event depends jointly on the wind speed distributions forecasted at multiple future times, these postprocessing methods must not only correct each individual forecast but also estimate the temporal dependencies among them. Typically though, crucial dependencies are adopted directly from the raw ensemble and the postprocessed forecast is limited to the tens of members computationally feasible for an NWP model.
We extend statistical postprocessing to include temporal dependencies using novel multivariate Gaussian regression models that forecast 24-dimensional distributions of next-day hourly wind speeds at three offshore wind farms. The continuous joint distribution forecast is postprocessed from an NWP ensemble using flexible generalized additive models for the components of its mean vector μ and for parameters defining the forecast error covariance matrix Σ. Modeling these parameters on predictors which characterize the empirical joint distribution of the NWP ensemble allows forecasts for each hour and their temporal dependencies to be adjusted in one step. Wind speed ensembles of any size can be simulated from the postprocessed joint distribution and transformed into power for computing high-resolution ramp predictions that outperform state-of-the-art reference methods.
Thomas Muschinski et al.
Status: open (until 24 Jul 2022)
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RC1: 'Comment on wes-2022-48', Anonymous Referee #1, 30 Jun 2022
reply
Comments on manuscript wes-2022-48 Submitted on 20 May 2022
"Predicting power ramps from joint distributions of future wind speeds"
byThomas Muschinski, Moritz N. Lang, Georg J. Mayr, Jakob W. Messner, Achim Zeileis, and Thorsten Simon
The paper describes an improved methodology for the probabilistic
forecast of hourly wind speeds on a forecast horizon of one day. Focus
of the work is the prediction of power ramps, i.e, the strong increase or
decrease of wind power over a time window of one or more hours. Basis
of such predictions is typically an ensemble of physics-based
numerical wheather predictions (NWP), which is the transformed into
wind power predictions using idealized wind turbine power curves.The authors address the temporal multi-point correlation structure of
wind speeds and their forecasts as one crucial problem to improve
probabilistic forecasts. Together with existing methods they introduce
their own approach to explicitly model the joint multivariate
distributions of hourly wind speeds with respect to their mutual
temporal dependencies. This new approach of Multivariate Gaussian
Regression (MGR) has previously been published in a journal on
statistics and econometry, and is consequently described only shortly.The main part of the paper performs a detailed comparison of the
various methods at the example of one power ramp event measured at the
German FINO 1 platform in 2019. The proposed method of MGR outperforms
the other appraoches in the comparison.The paper addresses a highly relevant problem in wind power
forecasting, namely the so-called power ramps. Moreover, with the
temporal multi-point correlation structure of wind speeds the authors
address one of the central and most demanding challenges of the field
and of atmospheric flows in general. Their approach is promising and
the given example is convincing.Technically, the paper is well written and well readable. The
structure is clear and comprehensive. English language style is
fluent, precise, and, as far as I can say, correct. Results are
presented clearly and with very appropriate graphics. References are
given whereever necessary.The reviewer is an expert neither in NWP nor in the advanced
mathematical approaches of the paper. However, in my eyes this paper
makes an important contribution, and it is almost ready for
publication.
General remarks:The demonstration of the proposed method using just one single example
of a power ramp is quite limited. However, given the length of the
paper of already 20 pages, more examples do not seem to make sense.
Could the authors comment on the performance of the method for more
examples, or, elaborate on possibilities of a wider evaluation?
Specific remarks:P. 3 L. 85: The bi-linear interpolation between grid points is
assumably widely used and probably also accepted. However, it is knwon
to reduce fluctuation amplitudes. It would be helpful to have any
estimate to what extent that effect is present for the given case.
Technical remarks:P. 3 L. 77: The phrase "but observations generally far from zero" does
not seem to make sense. Please double-check.P. 17 L. 355: Inserting a "that" after "ensure" would be helpful,
although (to my understanding) not strictly necessary. -
CC1: 'Comment on wes-2022-48', Jethro Browell, 01 Jul 2022
reply
This article addresses a timely issue in energy forecasting, is well written and an interesting read.
The proposed approaches are reasonable and it is very nice to have a comparison between modelling temporal correlation and the elements of the Cholesky decomposition. The former has nice links to previous work on modelling wind speed and power using varying coefficient time series models, and the more recent and more general approach proposed in [J. Browell, C. Gilbert and M. Fasiolo, "Covariance Structures for High-dimensional Energy Forecasting", XXII Power Systems Computation Conference, 2022, and Electric Power Systems Research]. The latter has the benefit of additional flexibility, but I find it much more difficult to interpret the elements of the Cholesky decomposition - can you offer any insight into this?
The results are compelling, and the ramp-based forecast evaluation is very useful. I do wonder if looking at additional multivariate scoring rules would provide further insight into the differences in performance of the ensemble forecasts, similarly rank histograms may also help verify the correctness (or not) of temporal dependency structures. On a related issue, how can we tell if the difference in forecast performance is due to genuinely more accurate dependency modelling, or if covariance models correcting deficiencies in the marginal predictive distributions?
Regarding the wind power evaluation, the power curve applied is that of an individual turbine and has a very sharp cut-out characteristic, but in reality wind farms do not exhibit this property and it is usual to see a smooth cut-out characteristic. This is especially true when considering hourly wind speed rather than the (approximately) instantanous wind speed that manufacturer power curved as based on. How sensitive are results to this?
In several equations pseudo code is mixed with mathematical symbols. I think it would be clearer and improve readability if only mathematical symbols were used.
Thomas Muschinski et al.
Thomas Muschinski et al.
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