Open AccessOptimization of turbine design in wind farms with multiple hub heights, using exact analytic gradients and structural constraints
Author(s) -
Stanley Andrew P.J.,
Ning Andrew,
Dykes Katherine
Publication year - 2019
Publication title -
wind energy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.743
H-Index - 92
eISSN - 1099-1824
pISSN - 1095-4244
DOI - 10.1002/we.2310
Subject(s) - turbine , tower , wind power , wake , marine engineering , wind gradient , wind shear , environmental science , wind speed , meteorology , wind direction , wind profile power law , engineering , structural engineering , physics , aerospace engineering , electrical engineering
Wind farms are generally designed with turbines of all the same hub height. If wind farms were designed with turbines of different hub heights, wake interference between turbines could be reduced, lowering the cost of energy (COE). This paper demonstrates a method to optimize onshore wind farms with two different hub heights using exact, analytic gradients. Gradient‐based optimization with exact gradients scales well with large problems and is preferable in this application over gradient‐free methods. Our model consisted of the following: a version of the FLOw Redirection and Induction in Steady‐State wake model that accommodated three‐dimensional wakes and calculated annual energy production, a wind farm cost model, and a tower structural model, which provided constraints during optimization. Structural constraints were important to keep tower heights realistic and account for additional mass required from taller towers and higher wind speeds. We optimized several wind farms with tower height, diameter, and shell thickness as coupled design variables. Our results indicate that wind farms with small rotors, low wind shear, and closely spaced turbines can benefit from having two different hub heights. A nine‐by‐nine grid wind farm with 70‐meter rotor diameters and a wind shear exponent of 0.08 realized a 4.9 % reduction in COE by using two different tower sizes. If the turbine spacing was reduced to 3 diameters, the reduction in COE decreased further to 11.2 % . Allowing for more than two different turbine heights is only slightly more beneficial than two heights and is likely not worth the added complexity.