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

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.

Corrigendum: Observation-based solar and wind power capacity factors and power densities (2018 Environ. Res. Lett. 13 104008)

“…Wind's mean power density in 2016 was 0.90 W e m −2 . This observed mean is consistent with estimates based on atmospheric theory and modeling (Gustavson 1979, Keith et al 2004, Wang and Prinn 2010, Miller et al 2011, Gans et al 2012, Jacobson and Archer 2012, Marvel et al 2012, Adams and Keith 2013, Miller et al 2015, Miller and Kleidon 2016 which predicted that large-scale wind power densities would be under 1.0 W e m −2 and also that power densities will decrease with increasing size of the wind farm installation. This observed mean power density is much smaller than many common estimates (Archer and Jacobson 2005, Lu et There are two main reasons for these discrepancies in wind power density.…”

Observation-based solar and wind power capacity factors and power densities

“…Wind's mean power density in 2016 was 0.90 W e m −2 . This observed mean is consistent with estimates based on atmospheric theory and modeling (Gustavson 1979, Keith et al 2004, Wang and Prinn 2010, Miller et al 2011, Gans et al 2012, Jacobson and Archer 2012, Marvel et al 2012, Adams and Keith 2013, Miller et al 2015, Miller and Kleidon 2016 which predicted that large-scale wind power densities would be under 1.0 W e m −2 and also that power densities will decrease with increasing size of the wind farm installation. This observed mean power density is much smaller than many common estimates ( There are two main reasons for these discrepancies in wind power density.…”

“…Maria and Jacobson 2009, Jacobson and Delucchi 2011. Smaller estimates of 0.5-1.0 W e m −2 emerge from analysis that considers turbine-atmosphere interactions(Gustavson 1979, Keith et al 2004, Wang and Prinn 2010, Miller et al 2011, 2015, Gans et al 2012, Jacobson and Archer 2012, Marvel et al 2012…”

ESD Reviews: Thermodynamic optimality in Earth sciences. The missing constraints in modeling Earth system dynamics?

“…An approach looking at the limits to convert kinetic to electrical energy, comes from the set of papers by Miller et al 2011; Gans et al (2012);Miller et al (2015); Miller and Kleidon (2016). They looked at electrical energy generated by wind turbines.…”