The problem of the second wind turbine – a note on a common but flawed wind power estimation method

F Gans,L M Miller,A Kleidon

doi:10.5194/esd-3-79-2012

Abstract

Abstract. Several recent wind power estimates suggest that this renewable energy resource can meet all of the current and future global energy demand with little impact on the atmosphere. These estimates are calculated using observed wind speeds in combination with specifications of wind turbine size and density to quantify the extractable wind power. However, this approach neglects the effects of momentum extraction by the turbines on the atmospheric flow that would have effects outside the turbine wake. Here we show with a simple momentum balance model of the atmospheric boundary layer that this common methodology to derive wind power potentials requires unrealistically high increases in the generation of kinetic energy by the atmosphere. This increase by an order of magnitude is needed to ensure momentum conservation in the atmospheric boundary layer. In the context of this simple model, we then compare the effect of three different assumptions regarding the boundary conditions at the top of the boundary layer, with prescribed hub height velocity, momentum transport, or kinetic energy transfer into the boundary layer. We then use simulations with an atmospheric general circulation model that explicitly simulate generation of kinetic energy with momentum conservation. These simulations show that the assumption of prescribed momentum import into the atmospheric boundary layer yields the most realistic behavior of the simple model, while the assumption of prescribed hub height velocity can clearly be disregarded. We also show that the assumptions yield similar estimates for extracted wind power when less than 10% of the kinetic energy flux in the boundary layer is extracted by the turbines. We conclude that the common method significantly overestimates wind power potentials by an order of magnitude in the limit of high wind power extraction. Ultimately, environmental constraints set the upper limit on wind power potential at larger scales rather than detailed engineering specifications of wind turbine design and placement.

Highlights

Several recent studies have quantified large-scale or global wind power availability by extrapolating kinetic energy availability from measured wind speeds
We assume a hub-height wind velocity of vhub = 10 m s−1 in the absence of wind turbines, which results in an accelerating force of Facc = 0.168 Ws m−3 and a wind velocity at the top of the atmospheric boundary layer (ABL) of vtop = 12.8 m s−1
The kinetic energy fluxes for this scenario in the absence of wind turbines (Fturbine = 0) are: Jin = 2.15 W m−2 and Jtransfer = 1.68 W m−2, which is the total input of kinetic energy into the ABL and hub-height level

Summary

Introduction

Several recent studies have quantified large-scale or global wind power availability by extrapolating kinetic energy availability from measured wind speeds (Archer and Jacobson, 2005; Sta. Maria and Jacobson, 2009; Lu et al, 2009; Liu et al, 2008; Leithead, 2007). We will collectively refer to these studies as the “common method”. This methodology can be generally described as follows: 1. Observations of wind velocities, v, are derived for a large spatial area from a collection of surface stations 2. Technical specifications for a turbine are used to specify the rotor height, rotor-swept area, and velocity dependent power characteristics

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Conclusion