14 Aug 2023
 | 14 Aug 2023
Status: a revised version of this preprint is currently under review for the journal WES.

The Multi-Scale Coupled Model: a New Framework Capturing Wind Farm-Atmosphere Interaction and Global Blockage Effects

Sebastiano Stipa, Arjun Ajay, Dries Allaerts, and Joshua Brinkerhoff

Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally-stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially-heterogeneous background velocity field obtained from a reduced-order meso-scale model. The MSC model is validated against two large-eddy simulations (LES) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. Conversely, in the supercritical regime their propagation speed is less than their advection velocity and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two regimes, but also captures wind farm gravity-wave interaction, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone, even if combined with a local induction model, cannot distinguish between differences in thermal stratification, and are affected by a first-row over-prediction bias that leads to a consistent overestimation of the wind farm power by 13 % to 20 %.

Sebastiano Stipa, Arjun Ajay, Dries Allaerts, and Joshua Brinkerhoff

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comprehensive framework for engineering wind farm models addressing the modular coupling of mesoscale and microscale effects', Javier Sanz Rodrigo, 30 Aug 2023
  • RC2: 'Comment on wes-2023-75', Anonymous Referee #2, 16 Oct 2023
Sebastiano Stipa, Arjun Ajay, Dries Allaerts, and Joshua Brinkerhoff
Sebastiano Stipa, Arjun Ajay, Dries Allaerts, and Joshua Brinkerhoff


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Short summary
This paper introduces the multi-scale coupled (MSC) model, an engineering framework aimed at modeling turbine/wake and wind farm/gravity wave interactions, as well as local and global blockage effects. Comparisons against large eddy simulations show that the MSC model offers a valid contribution towards advancing our understanding of the coupled wind farm/atmosphere interaction, helping refining power estimation methodologies for existing and future wind farm sites.