Two-scale interaction of wake and blockage effects in large wind farms

Kirby, Andrew C.; Nishino, Takafumi; Dunstan, Thomas D.

doi:10.1017/jfm.2022.979

Cited by 16 publications

(62 citation statements)

References 37 publications

(103 reference statements)

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“…Our method is hence slightly more expensive when m is large. However, the cost of the simulator is often the computational bottleneck, sometimes taking up to tens or hundreds of CPU hours per run; see Behrens and Dias (2015); Kirby et al (2022). As a result, proposing data efficient likelihood-free inference methods Beaumont et al (2009); Gutmann and Corander (2016); Greenberg et al (2019) is still an active research area.…”

Section: Computational Costmentioning

confidence: 99%

“…Although this model is an approximation of the state-of-the-art models that can take around 100 CPU hours per run (see e.g. Kirby et al (2022)), one realisation from this model takes ≈ 2 mins, which is still computationally prohibitive for likelihood-free inference. This example is indicative of the expensive simulators which are widely used in science, and is thus suitable for our method.…”

Section: Large Scale Offshore Wind Farm Modelmentioning

confidence: 99%

“…to hundreds or thousands of CPU hours per simulation; see Niederer et al (2019) for an example in cardiac modelling. Other examples include tsunami models based on shallow water equations that require several GPU hours per run Behrens and Dias (2015), runaway electron analysis models for nuclear fusion devices that require 24 CPU hours per run Hoppe et al (2021), and models of large-scale wind farms that require 100 CPU hours per run Kirby et al (2022). Naturally, the discrepancies popular for likelihood-free inference are those which can be efficiently estimated given samples from two distributions, such as the KL divergence Jiang (2018), Wasserstein distance Peyré and Cuturi (2019); Bernton et al (2019), Sinkhorn divergence Genevay et al (2018), energy distance Nguyen et al (2020), classification accuracy Gutmann et al (2017), or the maximum mean discrepancy, the latter of which is the topic of this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

Bharti¹,

Masha²,

Key³

et al. 2023

Preprint

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Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low-to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

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Section: Computational Costmentioning

confidence: 99%

Section: Large Scale Offshore Wind Farm Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

Bharti¹,

Masha²,

Key³

et al. 2023

Preprint

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“…Kirby et al. (2022) employed the two-scale momentum theory introduced by Nishino & Dunstan (2020) to estimate the power production of large wind farms. This theory splits the multi-scale flow into external and internal subproblems.…”

Section: Overviewmentioning

confidence: 99%

“…Antonini & Caldeira (2021) showed with mesoscale simulations and model calculations that the maximum achievable power output density of wind farms is primarily determined by the strength of the geostrophic wind that drives the boundary layer flow. Kirby, Nishino & Dunstan (2022) introduced a combined theoretical and computational approach to analyse fluid mechanics processes that determine the optimal performance of extended wind farms. This approach provides new estimates for optimal wind power density and a novel way to study the effective efficiency of extended wind turbine arrays.…”

Section: Introductionmentioning

confidence: 99%

Understanding wind farm power densities

Stevens

2023

J. Fluid Mech.

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Kirby et al. (J. Fluid Mech., vol. 953, 2022, A39) adapted the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, A2) to large finite-sized farms. They demonstrated that analytical estimates agree excellently with large eddy simulations, and that the model provides a good upper limit of the power production for a given array density. Crucially, they introduced the concepts of farm-scale losses, caused by the atmospheric response to the whole farm, and turbine-scale losses, owing to internal flow interactions in the wind farm. These two new theoretical concepts offer a novel way to analyse the performance of extended wind farms. For large offshore wind farms, losses at the wind-farm scale are typically twice as high as at the turbine scale. This demonstrates that there is limited potential for layout optimizations of extended arrays. Instead, optimization strategies should focus on developing methods to increase the energy entrainment into the wind farm. This work provides an exciting roadmap for analysing the effective efficiency of large wind farms.

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Data‐driven modelling of turbine wake interactions and flow resistance in large wind farms

et al. 2023

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Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine and (2) by changing the overall flow resistance in the farm and thus the so‐called farm blockage effect. To better predict these effects with low computational costs, we develop data‐driven emulators of the ‘local’ or ‘internal’ turbine thrust coefficient as a function of turbine layout. We train the model using a multi‐fidelity Gaussian process (GP) regression with a combination of low (engineering wake model) and high‐fidelity (large eddy simulations) simulations of farms with different layouts and wind directions. A large set of low‐fidelity data speeds up the learning process and the high‐fidelity data ensures a high accuracy. The trained multi‐fidelity GP model is shown to give more accurate predictions of compared to a standard (single‐fidelity) GP regression applied only to a limited set of high‐fidelity data. We also use the multi‐fidelity GP model of with the two‐scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be used to give fast and accurate predictions of large wind farm performance under various mesoscale atmospheric conditions. This new approach could be beneficial for improving annual energy production (AEP) calculations and farm optimization in the future.

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Two-scale interaction of wake and blockage effects in large wind farms

Cited by 16 publications

References 37 publications

Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

Understanding wind farm power densities

Data‐driven modelling of turbine wake interactions and flow resistance in large wind farms

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