TY - JOUR
T1 - Numerical NS Equations-Constrained Power Optimization of Wind Turbines Affected by Wake
AU - Akhavan , Yousef
AU - Chen , Michael
AU - Liang , Dong
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 384
EP - 400
PY - 2025
DA - 2025/03
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1017
UR - https://global-sci.org/intro/article_detail/ijnam/23884.html
KW - Wind farm power optimization, the vorticity-velocity Navier-Stokes equation, wake interaction, time-stepping, pattern search, optimization algorithm.
AB - <p style="text-align: justify;">We develop a model for wind farm power optimization while considering the wake
interaction among wind turbines. The proposed model is a Navier-Stokes equations-constrained
optimization model with the objective of maximizing the total power where the operating points
of the turbines are the decision variables, and the three-dimensional vorticity-velocity Navier-Stokes equations of wind speed are among the constraints. Moreover, we develop an efficient
numerical algorithm to solve the optimization model. This algorithm is based on the pattern
search method, the actuator line method and a time-stepping scheme which is used to solve the
vorticity-velocity Navier-Stokes equations. In the numerical experiments, we first compute the
power generation of a commercial wind turbine called WindSpot for different wind speed. It is
shown that the computed power is in a good agreement with the measurements. Then, in the case
of two turbines, we find that by optimizing the turbines’ operation while considering the wake
effect, we can gain an additional 8.11% in the total power when the incoming wind speed on the
boundary is 10 m/s.</p>