Wind farm interaction

Motivation

Over the years offshore wind farms tend to be placed closer together, as already illustrated by OWEZ and Princess Amalia Wind Farm (separated 15 km) in the Netherlands or Horns Rev I and II (separated 23 km) in Denmark. Since these separation distances are between 5 and 10 times the wind farm's horizontal scale, the velocity deficit due to an upstream wind farm may be considerable. If so, energy production loss and mechanical load increase are expected to be significant. For this reason the dedicated planetary boundary layer method MFwWF has been developed, which method computes the interaction between a wind farm and the prevailing wind.

Flow model

The planetary boundary layer method MFwWF is a CFD method that is based on three principles. First, neutral planetary boundary layer flow with wind farming essentially is steady and two-dimensional; where the convective forces, the Coriolis forces, the vertical and spanwise gradients of the turbulent momentum fluxes, and the external forces that represent wind turbines all have the same order of magnitude. Second, a numerical representation of the momentum equations in the form of backward differences allows for an implicit solution of the two horizontal velocity components in vertical direction, iterating on the turbulent viscosity, and a marching solution in the horizontal directions. And third the continuity equation is satisfied by employing the Lagrange multiplier method to the velocity components that satisfy the continuity equation.

Because of its mixed implicit/explicit character the planetary boundary layer method MFwWF is computationally fast and cheap, which is beneficial for applications in wind farm siting studies. In that context MFwWF can be used to estimate the effect of nearby wind farms on the electricity production of a given wind farm.

Effect of a wind farm on the prevailing wind

The planetary boundary layer method MFwWF calculates how a wind farm affects the prevailing wind, or to be more exact, the velocity in a position downstream of a wind farm. To this end wind farm parameters as well as meteorological parameters are considered.

The wind farm parameters include separation distance from and layout of the nearby wind farm, as well as hub height and rotor diameter of the wind turbines in that wind farm. The meteorological parameters include geostrophic velocity, geostrophic height and surface roughness length.

Two of the impact factors are the initial velocity deficit and the velocity recovery distances. The initial velocity deficit is a measure of the energy that is removed from the wind and for that reason a measure of the strength of the wake of the wind farm. The velocity recovery distances - one in downstream direction and the other in spanwise direction relative to the upstream wind direction - measure the distance where the velocity again reaches the upstream value.

As an example the impact of nominal power density and geostrophic velocity on the initial velocity deficit and the downstream velocity recovery distance was studied for a wind farm which consists of 22 wind turbines with a nominal power of 5 MW. The initial velocity deficit relative to the upstream velocity is found to decrease with increasing geostrophic velocity in general, ranging from 6% (at a turbine separation of 14 rotor diameters) to 32% (at a separation of 5 rotor diameters) if the velocity at hub height is halfway cut-in and nominal. In addition, the relative velocity recovery distance is found to decrease with the geostrophic velocity, from a value of 20 at low geostrophic velocities to a limit value near 0 at high geostrophic velocities, and the relative minimum save distance is found to reach a maximum value of the order of the streamwise wind farm length scale (which maximum is reached at geostrophic velocities between 15 m/s and 25 m/s). Finally the relative initial velocity deficit is found to decrease with increasing geostrophic velocity, and the largest absolute initial velocity deficit (of in this case 6.3 m/s) is found to occur when the hub-height velocity is near nominal.

Available code

The code MFwWF calculates the effect of one wind farm on another wind farm by taking the entire planetary boundary layer into account. The method has been validated by using measured data from large offshore wind farms, and is available for application to other wind farms.

Publications

Wind Power Plant North Sea - Wind farm interaction
A.J. Brand,
ECN-E--09-041, September 2009, 53p.

Wind farm design - When other wind farms are close
A.J. Brand,
European Offshore Wind 2009, Stockholm, Sweden, 14-16 September 2009