A method for preliminary rotor design – Part 2: Wind turbine Optimization with Radial Independence

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 (CP) and load coefficient (CT, CFM) 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 R̃→∞. The increase in power and AEP is in this case ΔP=50 % and ΔAEP=70 %, with a baseline being 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 ΔR=7.9 % as well as a power increase of ΔP=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 ΔR=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.