A Subgrid Parameterization for Wind Turbines in Weather Prediction Models with an Application to Wind Resource Limits

A subgrid parameterization is offered for representing wind turbines in weather prediction models. The parameterization models the drag and mixing the turbines cause in the atmosphere, as well as the electrical power production the wind causes in the wind turbines. The documentation of the parameterization is complete; it does not require knowledge of proprietary data of wind turbine characteristics. The parameterization is applied to a study of wind resource limits in a hypothetical giant wind farm. The simulated production density was found not to exceed , peaking at a deployed capacity density of and decreasing slightly as capacity density increased to . 1. Introduction Wind power production in numerical weather prediction models can be either inert or active. In the inert type, the wind speed forecasted for a turbine location can be extracted from the model and used to calculate wind power production, with no impact of the turbines on the weather prediction [1]. In the active type, this impact is included, specifically the drag and turbulence enhancement of the wind turbine acting on the atmosphere [2]. In this paper we offer some details of a wind turbine parameterization appropriate for large wind farms, with many turbines within a grid cell. This paper refines the wind turbine parameterization in [2, 3], effectively offering a simplified and documented alternative to what appeared in WRFv3.3 [4, 5]. Being subgrid, wakes are not explicitly simulated, but rather the momentum loss is immediately diffused across the breadth of the grid cell. The parameterization is adaptable to typical wind turbine characteristics. The giant wind farm of [3] is revisited for the purpose of studying the practical limit to wind power extraction from the atmosphere. Whereas [3] examined the much more subtle effect of the wind farm on precipitation climate statistics, the current study is more straightforward and does not require multidecadal simulations. The simulations use WRFv3.1 with the MYJ boundary layer scheme and horizontal grid spacing. The wind turbine parameterization adds elevated drag and production of turbulent kinetic energy to the MYJ scheme. If a horizontal wind vector is known at the height of wind turbine (in practice, meaning that a suitable average wind vector is known), then the power produced is where is the capacity coefficient and is the rated power output for the particular wind turbine. In the simulations, we focus on and , which roughly brackets the range of potential installations. is constrained by both laws of nature and engineering design.