Uncertainty quantification of infinite aligned wind farm performance using non-intrusive polynomial chaos and a distributed roughness model

Uncertainty of wind farm parameters can have a significant effect on wind farm power output. Knowledge of the uncertainty-produced stochastic distribution of the entire wind farm power output and the corresponding uncertainty propagation mechanisms is very important for evaluating the uncertainty effects on the wind farm performance during wind farm planning stage and providing insights on improving the performance of the existing wind farms. In this work, the propagation of uncertainties from surface roughness and induction factor in infinite aligned wind farms modeled by a modified distributed roughness model is investigated using non-intrusive polynomial chaos. Stochastic analysis of surface roughness indicates that 30% uncertainty can propagate such that there is up a 8% uncertainty in the power output of the wind farm by affecting the uncertainty in the position of the individual wind turbines in the vertical boundary layer profile and uncertainty in vertical momentum fluxes which replenish energy in the wake in large wind farms. Induction factor uncertainty of the wind turbines can also have a significant effect on power output. Not only does its uncertainty substantially affect the vertical boundary layer profile, but the uncertainty in turbine wake growth which affects how neighboring turbine wakes interact. We found that optimal power output in terms of reduction of uncertainty closely correlates with the Betz limit and is dependent on the mean induction factor.