Numerical optimisation of a small-scale wind turbine through the use of surrogate modelling

Gareth Erfort, Theodor Willem von Backström, Gerhard Venter


Wind conditions in South Africa are suitable for small-scale wind turbines, with wind speeds below 7 m.s−1. This investigation is about a methodology to optimise a full wind turbine using a surrogate model. A previously optimised turbine was further optimised over a range of wind speeds in terms of a new parameterisation methodology for the aerodynamic profile of the turbine blades, using non-uniform rational B-splines to encompass a wide range of possible shapes. The optimisation process used a genetic algorithm to evaluate an input vector of 61 variables, which fully described the geometry, wind conditions and rotational speed of the turbine. The optimal performance was assessed according to a weighted coefficient of power, which rated the turbine blade’s ability to extract power from the available wind stream. This methodology was validated using XFOIL to assess the final solution. The results showed that the surrogate model was successful in providing an optimised solution and, with further refinement, could increase the coefficient of power obtained.


surrogate modelling; optimization; NURBS; Cp

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Cencelli, N.A. Aerodynamic optimisation of a small-scale wind turbine blade for low windspeed conditions. 2006. Masters thesis, University of Stellenbosch, Stellenbosch, South Africa.

Drela, M. 2001. Xfoil 6.94 user guide. Aeronautics, and Astronautics Engineering, Massachu-setts Institute of Technology, Cambridge, MA, USA.

Hansen, M.O.L. 2008. Aerodynamics of wind turbines. Earthscan.

Ju, Y., Zhang, C. and Ma, L. 2016. Artificial intelli-gence metamodel comparison and application to wind turbine airfoil uncertainty analysis. Advances in Mechanical Engineering, 8(5), p.1687814016647317.

Li, Y.F, Ng, S.H., Xie, M. and Goh, T.N. 2010. A systematic comparison of metamodeling tech-niques for simulation optimization in decision support systems. Applied Soft Computing 10(4): 1257–1273.

Mckay, M.D., Beckman, R.J. and Conover, W.J. 2000. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 42(1): 55–61.

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V. and Vanderplas, J. 2011. Scikit-learn: Machine learn-ing in Python. Journal of Machine Learning Re-search 12(Oct), 2825–2830.

Python Software Foundation. Python language reference, version 2.7.

Salomon, R. 1998. Evolutionary algorithms and gradient search: similarities and differences. IEEE Transactions on Evolutionary Computation 2(2): 45–55.

hao, T. and Krishnamurty, S. 2007. A hybrid method for surrogate model updating in engineer-ing design optimization. ASME. International Design Engineering Technical Conferences and Computers and Information in Engineering Con-ference, Volume 6: 33rd Design Automation Con-ference, Parts A and B():345-370.

Smola, A.J. and Schölkopf, B. 2004. A tutorial on support vector regression. Statistics and computing 14(3): 199–222.

Wessels, F.J.L., Venter, G. and Backstrom, T.W. 2012. An efficient scheme for describing airfoils using non-uniform rational b-splines. ASME. Turbo Expo: Power for Land, Sea, and Air, Volume 6: Oil and Gas Applications; Concentrating Solar Power Plants; Steam Turbines; Wind Energy ():969-977.

Wise, J. 2008. Optimization of a low speed wind turbine using support vector regression. Masters thesis, Stellenbosch University, Stellenbosch, South Africa.

Zhang, Z. 2012. Performance optimization of wind turbines. PhD thesis, University of Iowa, Iowa, USA.



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