Analytical solution for the cumulative wake of wind turbines in wind farms

Bastankhah, Majid; Welch, Bridget L.; Martínez‐Tossas, Luis A.; King, Jennifer; Fleming, Paul

doi:10.1017/jfm.2020.1037

“…This could be explained by speed up effects: The turbines act as resistances in the flow field and the wind speed in the place of least resistance, between the turbines, increases. The effect has been observed and described in Bastankhah et al (2021) as well for instance. Due to the speed up, the turbines further down stream experience higher wind speeds than the ones in free stream and generate more energy.…”

Section: A2 Averaged Velocity In the Nine Turbine Casementioning

confidence: 78%

The revised FLORIDyn model: Implementation of heterogeneous flow and the Gaussian wake

Becker

¹

,

Ritter

²

,

Doekemeijer

³

et al. 2022

Preprint

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Abstract. In this paper a new version of the FLOw Redirection and Induction Dynamics (FLORIDyn) model is presented. The new model uses the three-dimensional parametric Gaussian FLORIS model and can provide dynamic wind farm simulations at low computational cost under heterogeneous and changing wind conditions. Both FLORIS and FLORIDyn are parametric models which can be used to simulate wind farms, evaluate controller performance and can serve as a control-oriented model. One central element in which they differ is in their representation of flow dynamics: FLORIS neglects these and provides a computationally very cheap approximation of the mean wind farm flow. FLORIDyn defines a framework which utilizes this low computational cost of FLORIS to simulate basic wake dynamics: this is achieved by creating so called Observation Points (OPs) at each time step at the rotor plane which inherit the turbine state. In this work, we develop the initial FLORIDyn framework further considering multiple aspects. The underlying FLORIS wake model is replaced by a Gaussian wake model. The distribution and characteristics of the OPs are adapted to account for the new parametric model, but also to take complex flow conditions into account. To achieve this, a mathematical approach is developed to combine the parametric model and the changing, heterogeneous world conditions and link them with each OP. We also present a computational lightweight wind field model to allow for a simulation environment in which heterogeneous flow conditions are possible. FLORIDyn is compared to SOWFA simulations in three- and nine-turbine cases under static and changing environmental conditions.The results show a good agreement with the timing of the impact of upstream state changes on downstream turbines. They also show a good agreement in terms of how wakes are displaced by wind direction changes and when the resulting velocity deficit is experienced by downstream turbines. A good fit of the mean generated power is ensured by the underlying FLORIS model. In the three turbine case, FLORIDyn simulates 4 s simulation time in 24.49 ms computational time. The resulting new FLORIDyn model proves to be a computationally attractive and capable tool for model based dynamic wind farm control.

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“…Further improvements in active wake control are necessary to increase the efficacy of wake steering, such as closedloop control [22,28,33,38] or machine learning based methods [39]. Additionally, further improvements in flow control models are necessary to capture three dimensional effects such as wake curling [40,41,42], veer [19,43], and stability [22,44].…”

Section: Discussionmentioning

confidence: 99%

Collective wind farm operation based on a predictive model increases utility-scale energy production

Howland¹,

Quesada²,

Martínez³

et al. 2022

Preprint

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Wind turbines located in wind farms are operated to maximize only their own power production. Individual operation results in wake losses that reduce farm energy. In this study, we operate a wind turbine array collectively to maximize total array production through wake steering. The selection of the farm control strategy relies on the optimization of computationally efficient flow models. We develop a physics-based, data-assisted flow control model to predict the optimal control strategy. In contrast to previous studies, we first design and implement a multi-month field experiment at a utility-scale wind farm to validate the model over a range of control strategies, most of which are suboptimal. The flow control model is able to predict the optimal yaw misalignment angles for the array within ±5 • for most wind directions (11-32% power gains). Using the validated model, we design a control protocol which increases the energy production of the farm in a second multi-month experiment by 2.7% and 1.0%, for the wind directions of interest and for wind speeds between 6 and 8 m/s and all wind speeds, respectively. The developed and validated predictive model can enable a wider adoption of collective wind farm operation.

show abstract

“…Further improvements in active wake control are necessary to increase the efficacy of wake steering, such as closed-loop control [22,28,33,38] or machine learning based methods [39]. Additionally, further improvements in flow control models are necessary to capture three dimensional effects such as wake curling [40,41,42], veer [19,43], and stability [22,44].…”

Section: Discussionmentioning

confidence: 99%

Collective wind farm operation based on a predictive model increases utility-scale energy production

Howland

¹

,

Quesada

²

,

Martínez

³

et al. 2022

Preprint

1

0

View full text Add to dashboard Cite

Wind turbines located in wind farms are operated to maximize only their own power production. Individual operation results in wake losses that reduce farm energy. In this study, we operate a wind turbine array collectively to maximize total array production through wake steering. The selection of the farm control strategy relies on the optimization of computationally efficient flow models. We develop a physics-based, data-assisted flow control model to predict the optimal control strategy. In contrast to previous studies, we first design and implement a multi-month field experiment at a utility-scale wind farm to validate the model over a range of control strategies, most of which are suboptimal. The flow control model is able to predict the optimal yaw misalignment angles for the array within ±5 • for most wind directions (11-32% power gains). Using the validated model, we design a control protocol which increases the energy production of the farm in a second multi-month experiment by 2.7% and 1.0%, for the wind directions of interest and for wind speeds between 6 and 8 m/s and all wind speeds, respectively. The developed and validated predictive model can enable a wider adoption of collective wind farm operation.

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Analytical solution for the cumulative wake of wind turbines in wind farms

Abstract: Abstract

Cited by 63 publications

References 51 publications

The revised FLORIDyn model: Implementation of heterogeneous flow and the Gaussian wake

The revised FLORIDyn model: Implementation of heterogeneous flow and the Gaussian wake

Collective wind farm operation based on a predictive model increases utility-scale energy production

Collective wind farm operation based on a predictive model increases utility-scale energy production

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