Probabilistic modelling of wind turbine power curves with application of heteroscedastic Gaussian Process regression

Abstract There exists continued interest in building accurate models of wind turbine power curves for better understanding of performance or assessment of the condition of the turbine or both. Better predictions of the power curve allow increased insight into the operation of the turbine, aid operational decision making, and can be a key feature of online monitoring and fault detection strategies. This work proposes the use of a heteroscedastic Gaussian Process model for this task. The model has a number of attractive properties when modelling power curves. These include, removing the need to specify a parametric functional form for the power curve and automatic quantification of the variance in the prediction. The model exists within a Bayesian framework which exhibits built-in protection against over-fitting and robustness to noisy measurements. The model is shown to be effective on data collected from an operational wind turbine, returning accurate mean predictions ( 1 % normalised mean-squared error) and higher likelihoods than a corresponding homoscedastic model.

[1]  M S Mohan Raj,et al.  Modeling of wind turbine power curve , 2011, ISGT2011-India.

[2]  Mostafa Modiri-Delshad,et al.  Development of an enhanced parametric model for wind turbine power curve , 2016 .

[3]  Yuesheng Xu,et al.  Universal Kernels , 2006, J. Mach. Learn. Res..

[4]  A. Immanuel Selvakumar,et al.  A comprehensive review on wind turbine power curve modeling techniques , 2014 .

[5]  Antonio Messineo,et al.  Monitoring of wind farms’ power curves using machine learning techniques , 2012 .

[6]  Volker Tresp,et al.  A Bayesian Committee Machine , 2000, Neural Computation.

[7]  J. Cidrás,et al.  Review of power curve modelling for wind turbines , 2013 .

[8]  Qinghua Hu,et al.  Wind Power Curve Modeling and Wind Power Forecasting With Inconsistent Data , 2019, IEEE Transactions on Sustainable Energy.

[9]  Charles R. Farrar,et al.  The fundamental axioms of structural health monitoring , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  A. E. Maguire,et al.  Performance monitoring of a wind turbine using extreme function theory , 2017 .

[11]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[13]  Arno Solin,et al.  Hilbert space methods for reduced-rank Gaussian process regression , 2014, Stat. Comput..

[14]  David Barber,et al.  Bayesian reasoning and machine learning , 2012 .

[15]  David Infield,et al.  Incorporating air density into a Gaussian process wind turbine power curve model for improving fitting accuracy , 2018, Wind Energy.

[16]  Andrés Feijóo,et al.  Reformulation of parameters of the logistic function applied to power curves of wind turbines , 2016 .

[17]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[18]  A. Kusiak,et al.  Modeling wind-turbine power curve: A data partitioning and mining approach , 2017 .

[19]  David Infield,et al.  Comparison of advanced non‐parametric models for wind turbine power curves , 2019, IET Renewable Power Generation.

[20]  Alexander G. de G. Matthews,et al.  Scalable Gaussian process inference using variational methods , 2017 .

[21]  Keith Worden,et al.  A Performance Monitoring Approach for the Novel Lillgrund Offshore Wind Farm , 2015, IEEE Transactions on Industrial Electronics.

[22]  Jianfei Cai,et al.  Large-Scale Heteroscedastic Regression via Gaussian Process , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Shuhui Li,et al.  Using neural networks to estimate wind turbine power generation , 2001 .

[24]  Zoubin Ghahramani,et al.  A note on the evidence and Bayesian Occam's razor , 2005 .

[25]  Marc Peter Deisenroth,et al.  Distributed Gaussian Processes , 2015, ICML.

[26]  Temple F. Smith.  Occam's razor , 1980, Nature.

[27]  Arno Solin,et al.  Variational Fourier Features for Gaussian Processes , 2016, J. Mach. Learn. Res..

[28]  A. Immanuel Selvakumar,et al.  Wind Farm Power Prediction Based on Wind Speed and Power Curve Models , 2018 .

[29]  Benas Jokšas,et al.  Non-linear regression model for wind turbine power curve , 2017 .

[30]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[31]  N. Dervilis,et al.  Aspects of structural health and condition monitoring of offshore wind turbines , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[32]  Carl E. Rasmussen,et al.  Understanding Probabilistic Sparse Gaussian Process Approximations , 2016, NIPS.

[33]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[34]  Frank Sehnke,et al.  Wind turbine power curve modeling based on Gaussian Processes and Artificial Neural Networks , 2018, Renewable Energy.

[35]  V. Di Dio,et al.  Modelling and analysis of real-world wind turbine power curves: Assessing deviations from nominal curve by neural networks , 2019 .

[36]  Miguel Lázaro-Gredilla,et al.  Variational Heteroscedastic Gaussian Process Regression , 2011, ICML.

[37]  Richard E. Turner,et al.  A Unifying Framework for Sparse Gaussian Process Approximation using Power Expectation Propagation , 2016, ArXiv.

[38]  Peter Cheeseman,et al.  Bayesian Methods for Adaptive Models , 2011 .

[39]  Antoine Tahan,et al.  Wind turbine power curve modelling using artificial neural network , 2016 .

[40]  A. O'Hagan,et al.  Curve Fitting and Optimal Design for Prediction , 1978 .

[41]  Michalis K. Titsias,et al.  Variational Learning of Inducing Variables in Sparse Gaussian Processes , 2009, AISTATS.

[42]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[43]  Radford M. Neal.  Priors for Infinite Networks , 1996 .

[44]  Ho-Young Kwak,et al.  Wind turbine power curve modeling using maximum likelihood estimation method , 2019, Renewable Energy.

[45]  Wenbo Xu,et al.  Particle swarm optimization with particles having quantum behavior , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[46]  Charles R. Farrar,et al.  Structural Health Monitoring: A Machine Learning Perspective , 2012 .

[47]  Li Li,et al.  Uncertainty estimation for wind energy conversion by probabilistic wind turbine power curve modelling , 2019, Applied Energy.

[48]  V. K. Sethi,et al.  Critical analysis of methods for mathematical modelling of wind turbines , 2011 .

[49]  Jaehoon Lee,et al.  Deep Neural Networks as Gaussian Processes , 2017, ICLR.