PLANT DESIGN AND ENERGY PRODUCTION ESTIMATION - Wind Resource Assessment: A Practical Guide to Developing a Wind Project - page 247

Here, the sum is over M , the number of masts, v pij is the predicted speed at point
p for direction i based on mast j , d pj is the distance between the point and the
same mast, and C is a smoothing constant that prevents the equation from becoming
undefined very close to a mast. Since most wind flow models do not perform this
type of blending, it is usually necessary to write a software to do it. Another approach
used by some analysts is to estimate the energy production for each turbine using one
mast at a time and then to blend the estimates “offline” in a spreadsheet program.
Distance-weighted blending is relatively easy, but is it the best approach? Not
necessarily. It assumes implicitly that the uncertainty associated with the prediction
from any given mast depends strictly on the distance to that mast. 2 As noted in
Chapter 13, however, distance is only one factor influencing the accuracy of wind
flow modeling. The modeling uncertainty and, therefore, the appropriate blending
weight also depend on the similarity of topographic and other conditions between the
point and the mast. For example, if the point were on a ridgetop, it might be better
to give a ridgetop mast more weight in the adjustment than a mast down the slope,
even if the latter were closer. Although an approach based on topographic similarity
and other factors is more defensible, it is also more difficult to put into practice,
as it requires an understanding of how the modeling uncertainty varies with these
factors (3).

16.7.3 Wake Modeling
Wake modeling remains an area of active research because of the great complexity
and wide range of scales of turbine-atmosphere interactions. While the basic physical
equations are well understood, a complete numerical solution to the wake problem
remains beyond the capability of today's computers.
Two early-generation models, the Park and EV models, are currently in wide use,
and a third class of model, the so-called deep-array models designed for large projects,
has recently appeared.

Park and Modified Park Models. The Park model was developed in the mid
1980s (4) and has been implemented in the WAsP software as well as in most wind
plant design programs. It characterizes a turbine wake by two parameters: the width
and the speed deficit relative to the free-stream speed. The width D is assumed to be
initially equal to the rotor diameter and to grow linearly with distance downstream:

D ( x ) = D 0 ( 1 + 2 kx ) (16.7)

2 The connection between distance and uncertainty is implied by statistical theory, which holds that inde-
pendent measurements of the same quantity should be combined in a weighted average, where the weight
accorded each measurement is inversely proportional to its uncertainty squared. It can be shown that the
new estimate produced this way has the lowest possible uncertainty. Substituting distance for uncertainty
yields the standard distance-weighted blending method.