A GA-Based Approach for Building Regularized Sparse Polynomial Models for Wind Turbine Power Curves

• Haroldo C. Maya UFC
• Guilherme A. Barreto UFC

DOI: https://doi.org/10.5753/eniac.2018.4455

Resumo

In this paper, the classical polynomial model for wind turbines power curve estimation is revisited aiming at an automatic and parsimonious design. In this regard, using genetic algorithms we introduce a methodoloy for estimating a suitable order for the polynomial as well its relevant terms. The proposed methodology is compared with the state of the art in estimating the power curve of wind turbines, such as logistic models (with 4 and 5 parameters), artificial neural networks and weighted polynomial regression. We also show that the proposed approach performs better than the standard LASSO approach for building regularized sparse models. The results indicate that the proposed methodology consistently outperforms all the evaluated alternative methods.

Referências

Betz, A. (1920). Das maximum der theoretisch möglichen ausnützung des windes durch windmotoren. Zeitschrift für das gesamte Turbinenwesen, 26:307–309.

Clifton, A., Kilcher, L., Lundquist, J. K., and Fleming, P. (2013). Using machine learning to predict wind turbine power output. Environmental Research Letters, (8):1–8.

Engelbrecht, A. P. (2007). Computational Intelligence: An Introduction. Wiley, 2nd edition.

Hagan, M. T. and Menhaj, M. (1994). Training feed-forward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks, 5(6):989–993.

Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1):73– 101.

Lee, G., Ding, Y., Genton, M. G., and Xie, L. (2015). Power curve estimation with multivariate environmental factors for inland and offshore wind farms. Journal of the American Statistical Association, 110:56–67.

Li, S., Wunsch, D. C., O’Hair, E., and Giesselmann, M. G. (2001). Comparative analysis of regression and artificial neural network models for wind turbine power curve estimation. Journal of Solar Energy Engineering, 123(4):327–332.

Lydia, M., Kumar, S. S., Selvakumar, A. I., and Kumar, G. E. P. (2014). A comprehensive review on wind turbine power curve modeling techniques. Renewable and Sustainable Energy Reviews, 30:452–460.

Lydia, M., Suresh Kumar, S., Immanuel Selvakumar, A., and Edwin Prem Kumar, G. (2013). Advanced algorithms for wind turbine power curve modeling. IEEE Transactions on Sustainable Energy, 4(3):827.

Manwell, J., McGowan, J., and Rogers, A. (2009). Wind energy explained : theory, design, and application. John Wiley & Sons, Ltd., 2nd edition.

Marciukaitis, M., Zutautaite, I., Martisauskas, L., Joksas, B., Gecevicius, G., and Sfetsos, A. (2017).

Non-linear regression model for wind turbine power curve. Renewable Energy, 113:732–741.

Schmidt, M. (2005). Least squares optimization with L1-norm regularization. Technical report, The University of British Columbia. CS542B Project Report.

Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2):461–464.

Shokrzadeh, S., Jozani, M. J., and Bibeau, E. (2014). Wind turbine power curve modeling using advanced parametric and nonparametric methods. IEEE Transactions on Sustainable Energy, 5(4):1262–1269.

Sohoni, V., Gupta, S. C., and Nema, R. K. (2016). A critical review on wind turbine power curve modelling techniques and their applications in wind based energy systems. Journal of Energy, 2016:1–18.

Storn, R. and Price, K. (1997). Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4):341–359.

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society - Series B, 58(1):267–288.

Wang, J., Zhao, X., Guo, X., and Li, B. (2018). Analyzing the research subjects and hot topics of power system reliability through the Web of Science from 1991 to 2015. Renewable and Sustainable Energy Reviews, 82(1):700–713.