Environmental Engineering Reference
In-Depth Information
velocity deficit of the leading upwind turbine. The development of the wake of the second
unit is then calculated and its velocity deficits at the locations of all other units determined.
These are tabulated with the wake deficits from the most-upwind turbine.
This procedure is repeated until the most-downwind turbine has been reached, and
results in the power output of the array for a given combination of wind azimuth, speed,
and turbulence. The calculation must be repeated for differing azimuths (to account for the
annual distribution of wind directions), wind speeds (to account for the annual wind speed
histogram and turbine control characteristics), and ambient turbulence levels (to account for
the varying wake expansion). Conceptually, this procedure provides the performance of all
the turbines in the entire array viewed as a single wind power system. Output power of the
array will be defined as a function of wind speed and turbulence, as it is for a single
turbine. Unlike a single turbine, array output power is also a function of wind direction and
speed variations across the site, taking into account the array geometry and terrain features.
Repeating this process for each wind azimuth, speed, and turbulence level is a
formidable (but not complicated) computational task. The problem of completing the
computation for an array within a reasonable time indicates the merits of a simple,
linearized physical wake model like the one described. It is believed that models with more
fundamental fluid-dynamic features, using more complex rational turbulence models, and
employing finite difference techniques would be prohibitively complex for analyzing an
array of practical size. Such models can, however, be used to validate the simple wake
model for the case of a single turbine and assist in determining any empirical constants.
Analytical Results Obtained with Wake Models
Flat Terrain
From the numerous wake-interference calculations which have been made for the case
of a uniform flow over flat terrain, it has been found that the level of ambient turbulence has
a very large effect on the array energy loss. Typical of the analytical results for simple arrays
on flat terrain are those shown in Figure 6-15. In the course of numerical investigations of
this type, it has been determined that the wake structure within its first four of five diameters
of downwind length does not have a strong effect on its velocity deficit in regions further
downwind, where turbines are likely to be located. Thus, the modelling of the initial potential
core regime (Fig. 6-16) does not need to be very refined, provided it gives the proper initial
state for the fully-developed wake regime.
In the design of a wind power station the normal method is to start with a reasonable
layout for the array, maximizing turbine spacing in the principal flow direction at the
expense of closer spacing in the crosswind direction. This assumes that the case of wind
at right angles to the prevailing wind direction, although involving large losses, does not
occur frequently. Next, the initial layout is examined using the wake interference model
to identify turbines that have particularly poor production because they are in sheltered posi-
tions and to find more favorable locations for these units. Spacing distances are then
perturbed until the maximum (or near-maximum) annual energy production is determined.
Thus the array design is approximately optimized by an iterative process.
Some effort has been devoted to defining a theoretically-exact, optimal arrangement for
simple arrays on flat terrain. Such arrays could not normally be used directly in design,
since each site has its own specific distributions of wind speed and direction. However, the
value of optimal-spacing studies lies in determining the sensitivity of array energy output
to changes in spacing from the theoretical optimum.
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