## Abstract

A novel wind turbine rotor optimization methodology is
presented. Using an assumption of radial independence it is possible to
obtain an optimal relationship between the global power (*C*_{P}) and load coefficient (*C*_{T}, *C*_{FM})
through the use of Karush–Kuhn–Tucker (KKT) multipliers, leaving an
optimization problem that can be solved at each radial station
independently. It allows solving load constraint power and annual energy
production (AEP) optimization problems where the optimization variables
are only the KKT multipliers (scalars), one for each of the
constraints. For the paper, two constraints, namely the thrust and blade
root flap moment, are used, leading to two optimization variables.

Applying the optimization methodology to maximize power (*P*)
or annual energy production (AEP) for a given thrust and blade root
flap moment, but without a cost function, leads to the same overall
result with the global optimum being unbounded in terms of rotor
radius (R̃ ) with a global optimum being at *R*→∞. The increase in powee and AEP is in this case Δ*P*=50% and ΔAEP=70%, with a baselinebeing the BETZ optimum rotor.

With
a simple cost function and with the same setup of the problem, a
power-per-cost (PpC) optimization resulted in a power-per-cost increase
of ΔPpC=4.2 % with a radius increase of Δ*R*=7.9 % as well as a power increase of Δ*P*=9.1 %. This was obtained while keeping the same flap moment and reaching a lower thrust of ΔT=−3.8 %. The equivalent for AEP-per-cost (AEPpC) optimization leads to increased cost efficiency of ΔAEPpC=2.9 % with a radius increase of Δ*R*=17 % and an AEP increase of ΔAEP=13 %, again with the same, maximum flap moment, while the maximum thrust is −9.0 % lower than the baseline.

Original language | English |
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Journal | Wind Energy Science |

Volume | 6 |

Issue number | 3 |

Pages (from-to) | 917-933 |

Number of pages | 17 |

ISSN | 2366-7443 |

DOIs | |

Publication status | Published - 2021 |