Abstract
Annual energy production (AEP) is commonly used in objective
functions for wind farm layout optimization. AEP is proportional to wind
farm power production integrated over an annual distribution of
free-stream wind conditions. Physics-based estimates of wind farm power
production typically rely on low-fidelity engineering wake models that
approximate the steady-state wind farm flow field. AEP estimates are
then obtained by performing independent simulations for discrete wind
conditions and using rectangular quadrature to account for each
condition’s expected frequency of occurrence. Depending on the number of
simulated discrete wind conditions, this numerical integral could be
hampered by poor accuracy or high computational costs. The FLOWERS AEP
model instead poses an analytical integral of the engineering wake model
over the variable wind conditions, yielding a closed-form, analytical
function for wind farm AEP. This paper derives the analytical functions
for FLOWERS AEP and its derivatives with respect to turbine position,
which are useful for gradient-based wind farm layout optimization, in
non-dimensional form. We then analyze the benefits of the FLOWERS AEP
model over conventional reference models, focusing on its low cost,
adequate wake loss predictions, and smooth design space. We find that
FLOWERS predicts AEP within about 10% of the baseline AEP models in
less than 10% of the computational time. Furthermore, we illustrate how
the FLOWERS design space at relatively low resolution is qualitatively
similar to the reference and yields comparable optimal layouts.
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