Wind Turbine Power Curve Modeling Research Articles

A comprehensive approach to wind turbine power curve modeling: Addressing outliers and enhancing accuracy

This research presents a comprehensive approach to improving the accuracy of wind turbine power curve (WTPC) modeling. The WTPC is a critical tool for monitoring wind turbine performance and estimating wind power potential, but current models have limited ability to capture the complex relationship between wind speed and power output. To address these limitations, this study implements a dual-pronged refinement of WTPC modeling. First, an innovative data preprocessing technique is introduced, using a 97 % confidence interval around a KNN-estimated WTPC constructed using the Laplace distribution to meticulously eliminate prominent outliers. Second, a novel WTPC modeling approach based on quantile regression is adopted, accounting for the asymmetric error characteristics in the loss function. Four distinct quantile regression models are developed, including three tree-based algorithms - decision trees, random forests, and gradient boosting - and a deep learning-based quantile regression neural network. Comparative analysis against ten established parametric and nonparametric techniques confirms the superiority of the proposed models, with the decision tree quantile regression model achieving the lowest validation errors. The proposed techniques are validated on two real-world datasets from operational wind turbines in Turkey and China, demonstrating significant improvements in WTPC modeling accuracy compared to conventional methods. Overall, this study successfully presents a comprehensive modeling approach that addresses outliers and leverages quantile regression to significantly enhance WTPC accuracy.

Conditional monitoring and fault detection of wind turbines based on Kolmogorov–Smirnov non-parametric test

This research presents a new method for conditional monitoring based on the wind turbine power curve. The Kolmogorov-Smirnov (K-S) distribution test is employed in the assessment of turbine data and the detection of abnormality (faults) in wind turbines. The process begins with anomaly detection and filtration of faulty SCADA data by a quantile-based filtration approach. Suitable data comprising wind speed, air density, ambient temperature, and pitch angle are utilized in the development of wind turbine power curve models that represents actualities within wind farms. The radial basis function (RBF), multi-layer Perceptron (MLP), and gradient boosting (GBR) methods utilized for model development are compared for predictive accuracy using Mariano-Preve test. The null hypothesis assumes equal predictive ability (EPA); if rejected, an algorithm compares the coefficients of correlation of the models and selects the closest to one (unity). The most accurate model is utilized for the creation of a bin-wise distribution from past data, and bin-wise confidence levels from the plot of wind speed and output power. Cochran’s method was utilized to validate the minimum sample size that will possess a sampling distribution similar to that of the population, and a fault is detected if there is a reasonable difference between the sample distribution and population distribution. The K-S test, having a null hypothesis of equivalent distributions, signals a fault if the null hypothesis is rejected. Two wind turbine SCADA datasets associated with two fault events are used for the assessment of our method. The results indicate that our method effectively discovers abnormalities in power output relating to increased bearing temperature and reduced generator rpm, thereby aiding in the detection of faults long before they occur.

Performance Comparison of Metaheuristic Optimization-Based Parametric Methods in Wind Turbine Power Curve Modeling

Performance Comparison of Metaheuristic Optimization-Based Parametric Methods in Wind Turbine Power Curve Modeling

A multivariable wind turbine power curve modeling method considering segment control differences and short-time self-dependence

Multivariable wind turbine power curve model is crucial for the performance degradation evaluation of wind turbine. However, the existing models have low modeling accuracy without considering the wind energy capture difference caused by segment control, and the inputs cannot represent the actual wind energy resources owing to the neglect of the short-term self-dependence of environmental parameters, which makes it difficult to ensure the performance degradation evaluation accuracy of wind turbine. To address these problems, a multivariable wind turbine power curve modeling method considering segment control differences and short-time self-dependence is proposed. First, an abnormal data cleaning method based on timing matching and bidirectional quartile algorithm is proposed to clean the abnormal data. Then, the multivariate wind turbine power curve model based on piece-wise regression of multiple environmental parameters is constructed, and applied to the performance degradation evaluation of wind turbine. The results demonstrated that the proposed abnormal data cleaning method can effectively solve the problem that the data categories of transition region between abnormal and normal data cannot be identified. Meanwhile, the proposed multivariable wind turbine power curve model can effectively improve the modelling accuracy and ensure the performance degradation evaluation accuracy of wind turbine under different wind energy resources.

An explainable AI framework for robust and transparent data-driven wind turbine power curve models

In recent years, increasingly complex machine learning methods have become state-of-the-art in modelling wind turbine power curves based on operational data. While these methods often exhibit superior performance on test sets, they face criticism due to a perceived lack of transparency and concerns about their robustness in dynamic, non-stationary environments encountered by wind turbines. In this work, we address these issues and present a framework that leverages explainable artificial intelligence methods to gain systematic insights into data-driven power curve models. At its core, we propose a metric to quantify how well a learned model strategy aligns with the underlying physical principles of the problem. This novel tool enables model validation beyond the conventional error metrics in an automated manner. We demonstrate, for instance, its capacity as an indicator for model generalization even when limited data is available. Moreover, it facilitates understanding how decisions made during the machine learning development process, such as data selection, pre-processing, or training parameters, affect learned strategies. As a result, we obtain physically more reasonable models, a prerequisite not only for robustness but also for meaningful insights into turbine operation by domain experts. The latter, we illustrate in the context of wind turbine performance monitoring. In summary, the framework aims to guide researchers and practitioners alike toward a more informed selection and utilization of data-driven wind turbine power curve models.

Interval model of a wind turbine power curve

The wind turbine power curve model is critical to a wind turbine’s power prediction and performance analysis. However, abnormal data in the training set decrease the prediction accuracy of trained models. This paper proposes a sample average approach-based method to construct an interval model of a wind turbine, which increases robustness against abnormal data and further improves the model accuracy. We compare our proposed methods with the traditional neural network-based and Bayesian neural network-based models in experimental data-based validations. Our model shows better performance in both accuracy and computational time.

Multivariate wind power curve modeling using multivariate adaptive regression splines and regression trees.

Wind turbine power curve (WTPC) serves as an important tool for wind turbine condition monitoring and wind power forecasting. Due to complex environmental factors and technical issues of the wind turbines, there are many outliers and inconsistencies present in the recorded data, which cannot be removed through any pre-processing technique. However, the current WTPC models have limited ability to understand such complex relation between wind speed and wind power and have limited non-linear fitting ability, which limit their modelling accuracy. In this paper, the accuracy of the WTPC models is improved in two ways: first is by developing multivariate models and second is by proposing MARS as WTPC modeling technique. MARS is a regression-based flexible modeling technique that automatically models complex the nonlinearities in the data using spline functions. Experimental results show that by incorporating additional inputs the accuracy of the power curve estimation is significantly improved. Also by studying the error distribution it is proved that multivariate models successfully mitigate the adverse effect of hidden outliers, as their distribution has higher peaks and lesser standard deviation, which proves that the errors, are more converged to zero compared to the univariate models. Additionally, MARS with its superior non-linear fitting ability outperforms the compared methods in terms of the error metrics and ranks higher than regression trees and several other popular parametric and non-parametric methods. Finally, an outlier detection method is developed to remove the hidden outliers from the data using the error distribution of the modeled power curves.

Improvement in output power assessment by wind turbine power curve modeling based on data mining

The accurate assessment of wind turbine output power is crucial in the process of sizing wind farms. Typically, this assessment is based on the manufacturer’s characteristic power curve, which relates wind speed to power output. However, the manufacturer’s power curve is often an idealized representation that may not accurately reflect the actual power output of the turbine under real-world conditions. To address this limitation, various techniques have been employed to develop more precise power curves, including curve fitting, artificial intelligence, probabilistic models, and Gaussian processes. This paper introduces a novel method for modeling the power curve that takes into account the specific conditions at the wind turbine’s location. The method involves transforming wind speed data into a graph that resembles the phase space commonly used in statistical mechanics. By applying the k-means algorithm to this phase space, clusters of wind speeds can be identified. Furthermore, the corresponding clusters of wind turbine output power can be determined based on the identified wind speed clusters. These clusters of power data provide valuable information for constructing a more accurate power curve using an adjustment function. By utilizing this method, the authors demonstrate a significant improvement in the accuracy of power output estimation compared to relying solely on the manufacturer’s power curve. The proposed approach considers the unique characteristics of the wind speed data and incorporates them into the modeling process, resulting in a more reliable representation of the turbine’s power output. This advancement represents a significant step forward in optimizing the sizing of wind farms and ensuring their efficient operation.

A novel data-driven deep learning approach for wind turbine power curve modeling

Existing wind turbine power curve (WTPC) models have limited performance in capturing the complex relationship between wind speed and wind power due to their inadequate nonlinear fitting abilities. Deep learning (DL) excels at describing complex relationships. However, it is typically not applicable to WTPC modeling with a single wind speed input. This study proposes a novel data-driven DL approach mELM-CA-CNN to establish WTPCs based on multiple extreme learning machines (ELMs), channel attention (CA), convolutional neural network (CNN), and Huber loss (HL). First, multiple ELMs map a single wind speed to various high-dimensional feature spaces. Then, CA helps reduce redundant mappings of ELMs. Next, CNN extracts important features from all ELM mappings and models the complex relationship between wind speed and the corresponding power. Finally, the proposed model is trained with the differentiable and robust HL. To reduce the adverse impact of outliers on WTPC modeling, a segmented data cleaning approach based on 3 σ criterion and quartile algorithm is proposed. Comparisons with ten popular WTPC models demonstrate that mELM-CA-CNN obtains the most accurate WTPCs on four wind datasets, showing the superiority of the proposed DL approach. Moreover, the roles of the different modules of mELM-CA-CNN in improving model performance are verified.

Physically meaningful uncertainty quantification in probabilistic wind turbine power curve models as a damage-sensitive feature

A wind turbines’ power curve is an easily accessible form of damage-sensitive data, and as such is a key part of structural health monitoring (SHM) in wind turbines. Power curve models can be constructed in a number of ways, but the authors argue that probabilistic methods carry inherent benefits in this use case, such as uncertainty quantification and allowing uncertainty propagation analysis. Many probabilistic power curve models have a key limitation in that they are not physically meaningful – they return mean and uncertainty predictions outside of what is physically possible (the maximum and minimum power outputs of the wind turbine). This paper investigates the use of two bounded Gaussian processes (GPs) in order to produce physically meaningful probabilistic power curve models. The first model investigated was a warped heteroscedastic Gaussian process, and was found to be ineffective due to specific shortcomings of the GP in relation to the warping function. The second model – an approximated GP with a Beta likelihood was highly successful and demonstrated that a working bounded probabilistic model results in better predictive uncertainty than a corresponding unbounded one without meaningful loss in predictive accuracy. Such a bounded model thus offers increased accuracy for performance monitoring and increased operator confidence in the model due to guaranteed physical plausibility.

Wind resource assessment considering the influence of humidity

The current study presents a wind resource assessment (WRA) approach by combining existing approaches, including wind probability density estimation based on hourly wind speed frequency, wind power density (WPD) and wind energy density (WED), wind turbine (WT) power output and power curve modeling, and annual energy production (AEP). Wind probability density investigation employed various probability density functions (PDF), including parametric probability density functions such as Weibull, Normal, and Gamma, and non-parametric distribution, including Kernel Density Estimator (KDE). The present study also models the influence of humidity on air density for estimating WPD, WT power output, and AEP. The current study validated the proposed approach by conducting case studies for selected sites of remote Indonesian archipelago islands. AEP estimation proposed by this study can assist the site-turbine fitting design, especially for relatively moist locations.

Hybrid Approach for Wind Turbines Power Curve Modeling Founded on Multi-Agent System and Two Machine Learning Algorithms, K-Means Method and the K-Nearest Neighbors, in the Retrieve Phase of the Dynamic Case Based Reasoning

Wind turbine power curve (WTPC) plays an important role for energy assessment, power forecasting and condition monitoring. The WTPC captures the nonlinear relationship between wind speed and output power. Many modeling approaches have been proposed by researches to improve the WTPC model performance. In this paper, we present a hybrid approach of wind turbines power curve modeling based on Case Based Reasoning approach, multi agent system, the K-Means unsupervised machine learning method, and then the supervised machine learning algorithm, which is the K-Nearest Neighbors KNN method. The both of the Machine Learning algorithms, K-means and KNN, are used in the retrieve step of the Dynamic Case Based Reasoning (DCBR) cycle to facilitate the search of wind turbines with similar characteristics to our target case. These wind turbines are first grouped into homogeneous classes and then sorted on the basis of a feature similarity measure using the K-Nearest Neighbors supervised machine learning method. Finally, a set of WTPC with similar characteristics of the target case are proposed.

Multivariate Wind Turbine Power Curve Model Based on Data Clustering and Polynomial LASSO Regression

Wind turbine performance monitoring is a complex task because of the non-stationary operation conditions and because the power has a multivariate dependence on the ambient conditions and working parameters. This motivates the research about the use of SCADA data for constructing reliable models applicable in wind turbine performance monitoring. The present work is devoted to multivariate wind turbine power curves, which can be conceived of as multiple input, single output models. The output is the power of the target wind turbine, and the input variables are the wind speed and additional covariates, which in this work are the blade pitch and rotor speed. The objective of this study is to contribute to the formulation of multivariate wind turbine power curve models, which conjugate precision and simplicity and are therefore appropriate for industrial applications. The non-linearity of the relation between the input variables and the output was taken into account through the simplification of a polynomial LASSO regression: the advantages of this are that the input variables selection is performed automatically. The k-means algorithm was employed for automatic multi-dimensional data clustering, and a separate sub-model was formulated for each cluster, whose total number was selected by analyzing the silhouette score. The proposed method was tested on the SCADA data of an industrial Vestas V52 wind turbine. It resulted that the most appropriate number of clusters was three, which fairly resembles the main features of the wind turbine control. As expected, the importance of the different input variables varied with the cluster. The achieved model validation error metrics are the following: the mean absolute percentage error was in the order of 7.2%, and the average difference of mean percentage errors on random subsets of the target data set was of the order of 0.001%. This indicates that the proposed model, despite its simplicity, can be reliably employed for wind turbine power monitoring and for evaluating accumulated performance changes due to aging and/or optimization.

Ensemble offshore Wind Turbine Power Curve modelling – An integration of Isolation Forest, fast Radial Basis Function Neural Network, and metaheuristic algorithm

Offshore wind energy is drawing increased attention for the decarbonization of electricity generation. Due to the unpredictable and complex nature of offshore aero-hydro dynamics, the Wind Turbine Power Curve (WTPC) model is an important tool for power forecasting and, hence, providing a reliable, predictable, and stable power supply. With the development of data-driven approaches, the Artificial Neural Network (ANN) has become a popular method for estimating WTPCs. This paper integrates the Isolation Forest (iForest), Nonsymmetric Fuzzy Means (NSFM) Radial Basis Neural Network (RBFNN), and metaheuristic algorithm to form a novel WTPC model. iForest performed anomaly detection and removal, NSFM RBFNN approximated the WTPC, and the metaheuristic solved NSFM optimization without training RBFNN. Four real-world datasets were used to assess the performance of NSFM RBFNN. According to multiple evaluation metrics and the Diebold-Mariano test, the accuracy of NSFM RBFNN was significantly better than the other competitive neural network-based methods. Additionally, NSFM RBFNN was shown to be more robust to anomalies than competitors, which is highly beneficial for practical applications.

Wind turbine power curve modeling using an asymmetric error characteristic-based loss function and a hybrid intelligent optimizer

Wind energy is one of the most promising solutions to energy crisis and environmental pollution, so it is being developed rapidly. Wind turbine power curves (WTPCs) play an important role in wind energy assessment, turbine condition monitoring, and power grid dispatching. However, there are two challenges in WTPC modeling: model selection and parameter optimization. Many parametric and non-parametric models have been developed to characterize WTPCs, but none can always perform the best due to the complex wind regimes. In this paper, considering the simple structure and interpretability of model parameters, a set of parametric WTPC models is constructed to adapt to the variability of wind regimes, and the optimal candidate will be selected from the set according to their performances. As to the process of parameter optimization, a novel loss function, which considers the asymmetric error characteristic of WTPC modeling, is proposed, and a hybrid intelligent optimization method named GWO-BSA, which makes full use of the advantages of grey wolf optimizer and backtracking search algorithm, is designed. Finally, a novel WTPC modeling strategy, which combines the candidate model set, error characteristic-based loss function, and GWO-BSA, is proposed to obtain better power curves. Experimental results show that (1) GWO-BSA shows faster convergence speed and higher optimization accuracy than single optimization algorithms; (2) the proposed error characteristic-based loss function has better performance than the commonly used symmetric loss functions; and (3) compared with some popular artificial intelligence-based models, the designed WTPC modeling strategy produces better WTPCs under different wind regimes.

Quantile based probabilistic wind turbine power curve model

Wind turbine power curve is an indicator of wind turbine performance and important input of wind farm design or power prediction, therefore can serve the system planning and operation. However, a good power curve model is difficult to obtain because of the uncertain relationship between wind speed and its power output. Existing works focus on a deterministic model or use probabilistic distribution to represent such uncertain relation, which is not easy to be employed by the following decision-makers. This paper presents a novel concept termed as quantile power curve, which generates a series of power curves under any confidence level. Quantile loss based neural network algorithm is proposed to establish the quantile power curve. Index to measure the wind turbine performance and power generation uncertainty is also proposed based on the quantile power curve. Based on the operational data of a Chinese wind farm, the proposed model and index are validated and employed to estimate the wind energy yield when planning a system with wind, solar and electric vehicle charging loads. The results show that quantile power curve provides more comprehensive information about the uncertainty during the power generation process and helps to improve the renewable supply rate to charging loads.

Perspectives on SCADA Data Analysis Methods for Multivariate Wind Turbine Power Curve Modeling

Wind turbines are rotating machines which are subjected to non-stationary conditions and their power depends non-trivially on ambient conditions and working parameters. Therefore, monitoring the performance of wind turbines is a complicated task because it is critical to construct normal behavior models for the theoretical power which should be extracted. The power curve is the relation between the wind speed and the power and it is widely used to monitor wind turbine performance. Nowadays, it is commonly accepted that a reliable model for the power curve should be customized on the wind turbine and on the site of interest: this has boosted the use of SCADA for data-driven approaches to wind turbine power curve and has therefore stimulated the use of artificial intelligence and applied statistics methods. In this regard, a promising line of research regards multivariate approaches to the wind turbine power curve: these are based on incorporating additional environmental information or working parameters as input variables for the data-driven model, whose output is the produced power. The rationale for a multivariate approach to wind turbine power curve is the potential decrease of the error metrics of the regression: this allows monitoring the performance of the target wind turbine more precisely. On these grounds, in this manuscript, the state-of-the-art is discussed as regards multivariate SCADA data analysis methods for wind turbine power curve modeling and some promising research perspectives are indicated.

Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression

The wind turbine power curve (WTPC) is of great significance for wind power forecasting, condition monitoring, and energy assessment. This paper proposes a novel WTPC modelling method with logistic functions based on quantile regression (QRLF). Firstly, we combine the asymmetric absolute value function from the quantile regression (QR) cost function with logistic functions (LF), so that the proposed method can describe the uncertainty of wind power by the fitting curves of different quantiles without considering the prior distribution of wind power. Among them, three optimization algorithms are selected to make comparative studies. Secondly, an adaptive outlier filtering method is developed based on QRLF, which can eliminate the outliers by the symmetrical relationship of power distribution. Lastly, supervisory control and data acquisition (SCADA) data collected from wind turbines in three wind farms are used to evaluate the performance of the proposed method. Five evaluation metrics are applied for the comparative analysis. Compared with typical WTPC models, QRLF has better fitting performance in both deterministic and probabilistic power curve modeling.

Toward hybrid approaches for wind turbine power curve modeling with balanced loss functions and local weighting schemes

Wind turbine power curves are often used for monitoring the performance of wind turbines and play an important role in wind power forecasting. Various factors such as age of turbines, installed location, air density, wind direction and measurement errors cause non-homogeneity among observed data, which often influences the accuracy of fitted power curves. To overcome this problem, a hybrid estimation approach is proposed, based on weighted balanced loss functions that account for both estimation error and goodness of fit by shrinking estimates toward standardized target models. Two different weighting schemes are developed to incorporate the non-homogeneity of data in the estimation process. The proposed algorithm is compared with commonly used power curve estimation methods based on classical least squares, natural splines, and local linear smoothing methods. The performance of the original and proposed hybrid methods is evaluated using a historical data set collected from a wind farm located in Canada. Results show that hybrid methods can be used as an effective tool to improve the performance of existing power curve modeling approaches. Consequently, proposed methods can facilitate more robust monitoring the performance of wind turbines as well as wind power forecasting.

Wind turbine power curve modeling using radial basis function neural networks and tabu search

Wind turbine power curve (WTPC) modeling is of great importance for performance monitoring. This work proposes a new method for producing highly accurate non-parametric models for wind turbines based on artificial neural networks (ANNs). To achieve this, we employ networks belonging to the radial basis function (RBF) architecture, and feed them with additional important input variables besides wind speed. To further increase modeling accuracy, while at the same time keeping the computational cost at acceptable levels, we introduce a new training algorithm based on the successful non-symmetric fuzzy means (NSFM) approach, which in this work is hybridized with the tabu search (TS) metaheuristic technique, enabling the method to train efficiently datasets of high dimensionality. The resulting method is evaluated on real data from four wind turbines, whereas a comparison with numerous WTPC modeling schemes, including parametric and non-parametric models is conducted. The solution found by the proposed algorithm outperforms the results produced by its rivals in terms of both modeling accuracy and efficiency, while in most cases it also leads to simpler models. The resulting models can be used successfully, not only for accurate WTPC modeling, but also for constructing wind turbine performance analysis tools, e.g. 3-D power curves.