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

Abstract

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 %.

A fast-running physics-based wake model for a semi-infinite wind farm

“…Due to the assumption of the fixed height of the capping inversion, however, the vertical displacement of the flow above the farm does not generate gravity waves in the capping inversion. This simplification may lead to errors in cases where gravity waves induce non-negligible pressure gradients at the turbine hub-height level (Allaerts & Meyers 2017, 2019Lanzilao & Meyers 2023;Stipa et al 2023). The precursor simulations are run without the turbines for a period of 10 h (36 000 s) to obtain a quasi-steady state.…”

“…Luzzatto-Fegiz & Colm-cille 2018;Bempedelis, Laizet & Deskos 2023). Other multi-scale models characterised the farm-atmosphere interaction and farm-scale blockage effects caused by meso-scale phenomena such as gravity waves (Allaerts & Meyers 2019;Stipa et al 2023). The coupling between the different scales in these models usually involves an iterative process or the numerical solution of governing equations.…”

An LES Model for Wind Farm-Induced Atmospheric Gravity Wave Effects Inside Conventionally Neutral Boundary Layers

“…Using LES, the impact of gravity waves on the flow around wind farms has been subject of investigation by Allaerts and Meyers (2017); Lanzilao and Meyers (2022b); Stipa et al (2023b); Lanzilao and Meyers (2023), who all assumed a conventionally neutral boundary layer (CNBL). This is characterized by a neutral stratification within the ABL, followed by a positive potential temperature jump ∆θ across the inversion layer and by a stable free atmosphere with linear lapse rate γ aloft.…”

“…Although the 3LM was the first study to incorporate AGW effects into predictions of the wind farm power losses, it lacked a local coupling between the mesoscale and turbine scales, failing to address the effects of gravity wave induced pressure gradients inside the wind farm and in the wake. Recently, Stipa et al (2023b) proposed a new localized coupling strategy between the 3LM and conventional wake models, referred to as the multiscale coupled model (MSC), capturing all features of the wind farm interaction with atmospheric gravity waves for CNBLs.…”

“…The proposed approach addresses the wave reflection problem inherently, eliminating the need for these specialized boundary conditions. We utilize the recently developed multi-scale coupled (MSC) model of Stipa et al (2023b) to estimate the vertical boundary layer displacement triggered by the wind farm, and apply the deformation to the domain of an LES that extends only to the inversion layer. We validate our AGW modeling technique for two distinct free atmosphere stability conditions, comparing it to the traditional approach in which AGWs are fully resolved using a domain extending several kilometers into the free atmosphere.…”