polynomial chaos, annual energy production, uncertainty quantification, wind farm, uncertainty in wind speed and direction, optimization


Careful management of wake interference is essential to further improve Annual Energy Production (AEP) of wind farms. Wake effects can be minimized through optimization of turbine layout, wind farm control, and turbine design. Realistic wind farm optimization is challenging because it has numerous design degrees of freedom and must account for the stochastic nature of wind. In this paper we provide a framework for calculating AEP for any relevant uncertain (stochastic) variable of interest. We use Polynomial Chaos (PC) to efficiently quantify the effect of the stochastic variables—wind direction and wind speed—on the statistical outputs of interest (AEP) for wind farm layout optimization. When the stochastic variable includes the wind direction, polynomial chaos is one order of magnitude more accurate in computing the AEP when compared to commonly used simplistic integration techniques (rectangle rule), especially for non grid-like wind farm layouts. Furthermore, PC requires less simulations for the same accuracy. This allows for more efficient optimization and uncertainty quantification of wind farm energy production.

Original Publication Citation

Padrón, S., Stanley, A. P. J., Thomas, J., Alonso, J. J., and Ning, A., “Polynomial Chaos for the Computation of Annual Energy Production in Wind Farm Layout Optimization,” Journal of Physics: Conference Series, Vol. 753, No. 032021, The Science of Making Torque from Wind, Oct. 2016. doi:10.1088/1742-6596/753/3/032021

Document Type

Conference Paper

Publication Date


Permanent URL


IOP Science




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering

University Standing at Time of Publication

Assistant Professor