Power Curve Model Research Articles

Wind Power Curve Model Combining Smoothed Spline with First-Order Moments and Density-Adjusted Wind Speed Strategy

Given the variety of potential application scenarios, it is crucial to develop wind power curves that are more accurate, smoother, efficient, and applicable across a wider range of contexts. To this end, a wind power curve model combining smoothed spline with first-order moments (FOM) and density-adjusted wind speed (DAWS) strategy is proposed in this paper. First, the DAWS strategy is employed to consider the influence of meteorological factors on the wind power curve by adjusting wind speed. This strategy reduces the root mean square error (RMSE) by 5.81%-6.17% and the mean absolute error (MAE) by 5.84%-6.44% without adding complexity to the model. Secondly, FOM is proposed as a substitute for the original data during the modeling process. This approach reduces the number of operations on the similar data, resulting in a reduction of modeling time by 48.11%-99.89%. Furthermore, the impact on model accuracy is minimal. Finally, a the wind power curve model based on smooth spline is constructed, which exhibits superior smoothness, a broader range of generalizability, enhanced model accuracy, and reductions in RMSE by 5.67%-23.87% and MAE by 4.79%-22.35% in comparison to the control method.

A Bayesian approach to estimate the capacity factor of offshore wind farms on the Brazilian coast

This work presents a Bayesian approach for inferring the capacity factor of an offshore wind farm. The calculation of the capacity factor depends on the power curve model and the probabilistic wind speed model, which in this work follows a Weibull distribution, whose scale and shape parameters are estimated using a Bayesian approach where the priors are independent gamma distributions, the likelihood is the Weibull distribution, and the posteriors are obtained by Hamiltonian Monte Carlo. The application of the described methodology is illustrated through a case study of an offshore wind power project located on the Northern coast of the Rio de Janeiro State, Brazil.

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.

A method for cleaning wind power anomaly data by combining image processing with community detection algorithms

Current methodologies for cleaning wind power anomaly data exhibit limited capabilities in identifying abnormal data within extensive datasets and struggle to accommodate the considerable variability and intricacy of wind farm data. Consequently, a method for cleaning wind power anomaly data by combining image processing with community detection algorithms (CWPAD-IPCDA) is proposed. To precisely identify and initially clean anomalous data, wind power curve (WPC) images are converted into graph structures, which employ the Louvain community recognition algorithm and graph- theoretic methods for community detection and segmentation. Furthermore, the mathematical morphology operation (MMO) determines the main part of the initially cleaned wind power curve images and maps them back to the normal wind power points to complete the final cleaning. The CWPAD-IPCDA method was applied to clean datasets from 25 wind turbines (WTs) in two wind farms in northwest China to validate its feasibility. A comparison was conducted using density-based spatial clustering of applications with noise (DBSCAN) algorithm, an improved isolation forest algorithm, and an image-based (IB) algorithm. The experimental results demonstrate that the CWPAD-IPCDA method surpasses the other three algorithms, achieving an approximately 7.23% higher average data cleaning rate. The mean value of the sum of the squared errors (SSE) of the dataset after cleaning is approximately 6.887 lower than that of the other algorithms. Moreover, the mean of overall accuracy, as measured by the F1-score, exceeds that of the other methods by approximately 10.49%; this indicates that the CWPAD-IPCDA method is more conducive to improving the accuracy and reliability of wind power curve modeling and wind farm power forecasting.

Modeling the effect of wind speed and direction shear on utility‐scale wind turbine power production

AbstractWind speed and direction variations across the rotor affect power production. As utility‐scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations, and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility‐scale wind turbine. In the field measurements of the utility‐scale turbine, discrete combinations of speed and direction shear induce changes in power production of −19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over‐performance and increasing magnitudes of direction shear to greater under‐performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub‐models. To further assess the influence of complex, non‐monotonic wind profiles, we also drive the models with best‐fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time‐varying, non‐monotonic wind shear affects wind power production.

Enhancing Reliability in Wind Turbine Power Curve Estimation

Accurate power curve modeling is essential to continuously evaluate the performance of a wind turbine (WT). In this work, we characterize the wind power curves using SCADA data acquired at a frequency of 5 min in a wind farm (WF) consisting of five WTs. Regarding the non-parametric methods, we select artificial neural networks (ANNs) to make curve estimations. Given that, we have the curves provided by the manufacturer of the WTs given by some very precisely measured pair of wind speed and power points. We can evaluate the difference between the manufacturer characterization and the ones estimated with the data provided by the SCADA system. Before the estimation, we propose a method of filtering the anomalies based on the characteristics provided by the manufacturer. We use three-quarters of the available data for curve estimation and one-quarter for the test. One WT suffered a break in the test part, so we can check how the test estimates reflect this problem in its wind-power curve compared to the estimations obtained in the WTs that worked adequately.

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.

Wind power curve modeling: A probabilistic Beta regression approach

Wind turbine power curves play a key role in various aspects during the life of a wind farm. Typical uses range from wind power forecasting to wind turbine condition monitoring. This paper addresses the identification of probabilistic models of wind power curves from observed data. The main challenge is the need to handle a statistical distribution of wind energy whose shape not only may be highly skewed, but can also change with wind speed. To address these issues, we resort to the framework of Generalized Linear Models (GLMs), proposing a Beta regression approach, with constant or variable dispersion and an appropriate preconditioning step. The proposed methodology was tested on three real SCADA measurements retrieved from public datasets, including a comparison with Quantile Regression Forests (QRFs), also in terms of robustness to outliers. The results suggest that Beta regression can be a valuable resource in the development of probabilistic models for wind energy, as it provides a high degree of flexibility while preserving an interpretable structure.

Usage of Statistical Techniques to Monitor the Performance of Wind Turbines

Calculating the yearly energy output, which keeps the balance between both the generation and consumption of electricity, is made easier with the use of wind energy production estimates for grid interfaces. Effective wind speed forecasting is crucial for achieving this goal. In this research, linear statistical models of prediction Generalized Autoregressive Score (GAS), GAS model with exogenous variable x (GASX), and Autoregressive Integrated Moving Average (ARIMA) are the models used to estimate wind speed accurately. Additionally, the modeling of non-linear time-series data has been done using the Non-Linear GASX (NLGASX) statistical predictive modeling method. Additionally, the REctified Linear Unit (RELU), Softmax, Hyperbolic Tangent (TANH), and Sigmoid modeling approaches are used to optimize the suggested NLGASX model. In comparison to existing models, the suggested optimized NLGASX approach performs significantly better. In order to anticipate wind power, the wind power curve modeling additionally takes wind speed as an input. The estimated wind power has been used to determine the yearly energy

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.

A novel ultra short-term wind power prediction model based on double model coordination switching mechanism

Ultra-short-term wind power provides technical support for unit control and scheduling to optimize the power system. Wind fluctuation is the main factor that makes it difficult to accurately predict wind power output. To improve the power prediction accuracy of the wind power fluctuation period, a combined prediction model that can automatically switch between two models is proposed. For small fluctuations in wind speed, we construct a sequence-to-sequence model that integrates temporal and spatial attention mechanisms for power prediction. The prediction model switches to the wind power curve model when the wind speed fluctuates significantly, which reflects the static characteristics of the unit. We determine the appropriate wind speed fluctuation threshold on the verification set, so that the two prediction models can coordinate the switchSimulation experiments were carried out on the data set provided by a wind farm in Inner Mongolia, China. The normalized RMSE of the forecast in the future 4h is 0.1405.

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.

Comparative analysis of different methods in estimating wind speed distribution, and evaluation of large‐scale wind turbine performance in Rahva‐Bitlis, Turkey

AbstractIn this study, wind characteristics and electricity generation potential from wind energy were investigated in the Bitlis‐Rahva region in eastern Turkey. Ten‐minute wind data from the Bitlis meteorological station were used in the study. The determination of the wind speed (WS) distribution was carried out using the WindPRO program together with the Weibull and Rayleigh distributions. R2, RMSE, and χ2 goodness‐of‐fit tests were used to measure the accuracy of the velocity distribution process. A digital elevation model of the power generation site was created to evaluate wind data and predict turbine performance. Wind power generation performance was evaluated using five different wind turbines (WTs). A power curve model was developed for the WTs to determine the capacity for energy generation. According to the error tests, it has been determined that the results obtained with the WindPRO program can represent the observed wind data most accurately. The results from the WindPRO program analysis showed an average annual WS of 3.26 m/s and a power density of 49.77 W/m2. Increasing height was found to increase WS and power density. The prevailing wind direction was found to be South‐Southwest with a frequency value of 27.5%. The largest capacity factor was obtained from the WT with the largest rotor diameter and rated power. Out of all the WTs examined, the turbine with the largest rated power and rotor diameter produced the greatest amount of energy. According to the capacity factor values calculated for the selected WTs, the region is not considered efficient for wind energy investments. However, as WS and power density increase with increasing altitude, it is thought that different higher parts of the region may be more efficient in terms of wind energy utilization.

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.

Short-Term Wind Speed and Power Forecasting for Smart City Power Grid With a Hybrid Machine Learning Framework

To address foreseeable challenges during the penetration of wind energy into the power grid, including accurate wind power forecasting and smart power generation scheduling, this study proposes a novel short-term wind speed forecasting model, named EMD-KM-SXL, which is based on empirical mode decomposition (EMD), K-means clustering and machine learning, and a new two-stage short-term wind power forecasting model based on wind speed forecasting and wind power curve modeling. The former wind speed forecasting model regards historical wind speed observations as model inputs, and the latter power forecasting model utilizes knowledge augmentation, introducing wind power conversion relationship, environmental factors as well as wind power system status parameters. In the proposed wind speed forecasting model, three machine learning models, including support vector regressor, XGBoost regressor, and Lasso regressor, are employed to forecast three types of frequency components that are generated via EMD and K-means clustering. Then, the wind power curve model is utilized to compute potential outpower based on the predicted wind speed, which is regarded as the first stage of the proposed wind power forecasting model. In the second stage, environmental factors and wind power system status parameters are introduced and an artificial neural network model, considering preliminary predicted power, environmental factors, and wind power system status parameters as model inputs, is built to make final power prediction. Computational results show that proposed models achieve the best performance in terms of wind speed and power forecasting over different forecasting horizons ranging from 10 to 40 minutes, compared with benchmarking methods.

Wind Power Curve Modeling With Large-Scale Generalized Kernel-Based Regression Model

Accurate wind power curves (WPCs) are crucial for wind energy development and utilization, e.g., wind power forecasting and wind turbine condition monitoring. In the era of big data, large-scale datasets make the training of power curve models inefficient, especially for kernel-based models. Furthermore, most models do not take into account the error characteristics of WPC modeling. In this study, a large-scale generalized kernel-based regression model is proposed to solve the above problem. First, a generalized loss function, which can model both symmetric and asymmetric error distributions, is designed for model training. Then, the Nyström technique is employed to get the approximate kernel matrix, based on which an eigenvalue-based kernel regression framework is constructed. Next, a large-scale generalized kernel-based regression model is developed with model parameters tuned using the alternating direction method of multipliers. Before WPC modeling, a three-step data processing method based on isolation forest is designed to process missing data, irrational data, and outliers in the collected data. The WPC modeling results on four large-scale wind datasets demonstrate that the proposed model generates accurate WPCs with high efficiency. Furthermore, the effect of turbulence intensity on WPC modeling and the effectiveness of LSGKRM with multivariate inputs are also verified.

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.

Abnormal data cleaning for wind turbines by image segmentation based on active shape model and class uncertainty

Wind power curve describes the relationship between wind speed and output power of wind turbine. In this paper, we propose a novel image-based abnormal data cleaning algorithm aiming to provide high quality data for wind power curve modeling and relevant applications. For image binarization, a multiscale space is built to determine the optimal scale at which the most stable as well as informative shape representations are extracted. The active shape model is utilized to model the power curve shape and generate a set of segmentation candidates for filtering abnormal data. An energy space is constructed based on class uncertainty map generated from dual feature images and eventually the optimal segmentation boundary is determined by an optimization process. Comparative experiments are conducted over the real-world datasets consisted of 37 wind turbines from two wind farms located in West and East China respectively. The accuracy reaches as high as 0.95, the precision rate P is 0.98, recall rate R is 0.99 and F1-score is 0.96, which demonstrates the superior performance of the proposed method. Besides, the reproducibility and sensitivity analyses are also carried out to assess the algorithm’s performance.