Wake Losses in Wind Plants – Comparing Several Methods with Measured Wakes
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One of the most important steps in wind project valuation is the estimation of wake losses. Wake impact estimates are usually based on simplified wake models that assume the wind speed recovery downstream from a turbine is a function of the upstream wind speed and turbulent mixing between the reduced momentum in the turbine wake and the wind speed outside the wake, which is assumed to be the same as the upstream wind speed. Newer “large array” models take into account the effect of large wind plants by representing those plants as an increase in surface roughness, which causes added drag on the wind profile and further slows the wind speeds. A third technique, which is widely used in computational fluid dynamics modeling and has recently been added to the Weather Research and Forecast (WRF) model, is to explicitly calculate the turbine forces as a separate term in the momentum equations in addition to modeling the added turbulence in the turbine wake.
A measurement-based calculation of wind plant wake was used to evaluate the accuracy of the three methods. This calculation of wake was based on meteorological data from towers at operating wind plants whose period of record included at least one year before and one year after wind plant construction. Using the pre-construction met data, machine learning methods were used to establish the relationship with a gridded reanalysis dataset, then this relationship was used to extend the pre-build tower data through the entire post-build time period of available met data. The same approach, this time using the post-construction met data, was used to extend the post-build data through the entire pre-build time period of available met data. The differences between these extended, overlapping sets of data were then used to calculate the whole plant wake impacts. The calculated wake losses from this method were significantly larger than the predicted losses from both the simplified wake model and the large plant wake model.
We then simulated winds for an entire year for a dozen wind power plants using WRF. For each wind plant, we ran one simulation without turbines and another with the wind turbines. To calculate power in each run, we extracted WRF wind speeds every 10 minutes for each turbine location and converted those speeds to power using the turbine power curve. The wake impacts were found by taking the difference between the aggregate energy produced in the runs with and without turbines. The turbines of all neighboring wind plants were also included in the WRF runs to make sure that their far-field wakes were taken into account. The WRF-estimated wake impacts tended to be larger than the wake values calculated from the tower data, but for the larger wind farms, these differences were smaller than those of the simplified and large array wake models.
There are several hypotheses to explain why the WRF method is providing a more accurate estimate of turbine wakes. WRF takes into account the variability of the atmospheric vertical temperature profile, which strongly controls the amount of turbulence available to dissipate turbine wakes, whereas the standard wake models assume neutral atmospheric stability. Neutrally stable flows allow more rapid dissipation of wakes than would occur in the more strongly stable conditions typical of the nocturnal boundary layer. Additionally, the calculation of turbine forces on the flow provides an overall drag force that is directly dependent on the size of the wind plant, making a separate parameterization for large wind plants unnecessary. Although WRF is more computationally expensive and may slightly overestimate wake losses, the results of this study show that using WRF to model wind turbines (and nearby existing or planned wind plants) is the best method to ensure that the total waking effect has been appropriately captured. Wind project wake losses make a substantial contribution to understanding wind plant under-performance, and in many cases may be the largest contributor to such under-performance.