Wind Turbine Power Curve Modeling Research Articles

Wind Turbine Power Curve Modelling Based on Hybrid Relevance Vector Machine

Wind turbine power curve (WTPC) is important for energy assessment, condition monitoring and abnormal detection. In recent years, researchers proposed a number of WTPC modelling approaches to continuously improve the model performance. In this paper, Relevance Vector Machine (RVM) is applied for WTPC modelling for the first time. Combine single-input RVM and multi-input RVM, this paper proposes a hybrid RVM method (HRVM) to further improve the fitting accuracy. Firstly, we analyse the features of model outputs of both single-input RVM and multi-input RVM. According to the analysis, the confidence interval of single-input RVM is used to limit the power output range of multi-input RVM. At last, SCADA data collected from three wind turbines are used to test the model performance. The results show that, compared with typical WTPC model approaches, HRVM achieves a good balance between fitting accuracy and computation cost.

Gaussian processes with logistic mean function for modeling wind turbine power curves

The wind turbine power curve (WTPC) is a mathematical model built to capture the input-output relationship between the generated electrical power and the wind speed. An adequately fitted WTPC aids in wind energy assessment and prediction since the actual power curve will differ from that provided by the manufacturer due to a variety of reasons, such as the topography of the wind farm, equipment aging, and multiple system faults. As such, this paper introduces a novel approach for WTPC modeling that combines Gaussian process (GP) regression, a class of probabilistic kernel-based machine learning models, and standard logistic functions. This semi-parametric approach follows a Bayesian reasoning, in the sense of maximizing the marginal likelihood to learn the parameters and hyperparameters through a variational sparse approximation to the GP model. Using real-world operational data, the proposed approach is compared with the state-of-the-art in WTPC modeling and with an alternative probabilistic approach based on generalized linear models and logistic functions. Finally, we evaluate the proposed model in its extrapolation ability for unmodelled data.

Gaussian mixture models for site-specific wind turbine power curves

A probabilistic method for modelling empirical site-specific wind turbine power curves is proposed in this paper. The method is based on the Gaussian mixture model machine learning algorithm. Unlike standard wind turbine power curve models, it has a user-selectable number (N) and type of input features. The user can thus develop and test models with a combination of measured, derived or predicted input features relevant to wind turbine power-output performance. The proposed modelling approach is independent of the site location where the measurable input features (i.e. wind speed, wind direction, air density) are collected. However, the specific models are location and turbine dependent. An N-feature wind turbine power curve model developed with the proposed method allows us to accurately estimate or forecast the power output of a wind turbine for site-specific field conditions. All model parameters are selected using a k-fold cross-validation method. In this study, five models with different numbers and types of input features are tested for two different wind farms located in Ireland. The power forecast accuracy of the proposed models is compared against each other and with two benchmarks, parametric wind turbine power curve models. The most accurate models for each of the sites are identified.

A Review on Wind Turbine Deterministic Power Curve Models

Over the last decades, wind energy has been arising as one of the most promising sources for the future of energy supply, and this trend should be reinforced in the future due to the foreseeable environmental and climatological catastrophe. Therefore, all technologies and issues regarding its development are relevant. Among them, research on wind turbine power curve modeling is of importance for stakeholders and researchers because it allows them to easily obtain information about the amount of power and energy that can be captured from the primary resource, i.e., the wind. The task can be simplified by means of the use of wind turbine power curve models, and many researchers have been presenting their contributions on the topic in parallel with such a development. In this paper, a review on the formulation of wind turbine deterministic power curve models is presented.

Wind turbine power curve modeling based on interval extreme probability density for the integration of renewable energies and electric vehicles

Accurate modeling of the wind turbine power curve (WTPC) is crucial for calculating the theoretical wind power for the integration of renewable energies and electric vehicles. However, existing WTPC modeling methods cannot simultaneously guarantee high modeling accuracy and efficiency for data samples with a large amount of accumulated abnormal data. To address this problem, this paper presents a WTPC modeling method based on interval extreme probability density, which does not require complicated and time-consuming abnormal data cleaning and can significantly improve the modeling efficiency while guaranteeing high modeling accuracy. To verify the applicability and validity of the proposed method, firstly, WTPC models were constructed using actual operation data from 12 wind turbines in a Chinese wind farm and were compared with the manufacturer’s power curve and with WTPC modeling methods based on abnormal data cleaning algorithms. Secondly, the theoretical wind power was calculated and compared with the commonly used manufacturer’s power curve. The results demonstrated that the proposed WTPC modeling method has high modeling accuracy and efficiency and can improve the calculation accuracy of the theoretical wind power effectively, providing more reliable data support for the integrated planning of renewable energies and electric vehicles in nearby regions.

Sparse Heteroscedastic Multiple Spline Regression Models for Wind Turbine Power Curve Modeling

An accurate wind turbine power curve (WTPC) plays a vital role in wind power forecasting and wind turbine condition monitoring. There are two major shortcomings of current WTPC models that prevent more accurate WTPC estimation, limited nonlinear fitting ability and the lack of in-depth understanding of the complex characteristics of WTPC. This paper proposes two novel regression models to overcome these two disadvantages simultaneously. First, they make use of multiple spline regression models (MSRM) with different basis functions and different numbers of knots to describe the complex nonlinear relationship between wind speed and wind power. Moreover, sparse prior distributions help avoid the adverse effects of redundant mapping features and useless basis functions on the model performance. Second, they embed the heteroscedasticity of WTPC modeling into MSRM based on Gaussian and Student's t-distributions, respectively. Finally, two sparse heteroscedastic MSRM with Gaussian and Student's t-distributions will be constructed and named as SHMSRM-G and SHMSRM-T, respectively. We compare the proposed models with fifteen benchmark models, and find that they can generate more accurate WTPCs than the others in different seasons and different wind farms. Thus, it is important to consider the complex nonlinear fitting ability and heteroscedasticity together in constructing accurate WTPC models.

Wind turbine power curve modeling for reliable power prediction using monotonic regression

Wind turbine power curve modeling plays an important role in wind energy management and power forecasting and it is often done based on parametric or non-parametric methods. As wind-power data are often noisy, even after polishing data using proper methods, fitted wind turbine power curves could be very different from the theoretical ones that are provided by manufacturers. For example, it might be the case that the theoretical wind turbine power curve is a non-decreasing function of speed but the fitted statistical model does not necessarily meet this desirable property. In this paper, we present two nonparametric techniques based on tilting method and monotonic spline regression methodology to construct wind turbine power curves that preserve monotonicity. To measure the performance of our proposed methods, we evaluate and compare our estimates with some commonly used power curve fitting methods based on historical data from a wind farm in Manitoba, Canada. Results show that monotone spline regression performs the best while the tilting approach performs similar to the methods we studied in this paper with the benefit of finding a curve that is more similar to the theoretical power curve.

Daily condition monitoring of grid-connected wind turbine via high-fidelity power curve and its comprehensive rating

With development of grid-connected wind power, data-driven wind turbine power curve (WTPC) becomes vital for many valuable applications whereas it is hugely affected by the potential outliers in supervisory control and data acquisition (SCADA) system. In this paper, high-fidelity WTPC modeling and its application on condition monitoring are deeply studied. Firstly, through irregular space-division and nonlinear space-mapping, stepwise data cleaning procedure is proposed. On this basis, the cleaned data are used for high-fidelity modeling where optimized least square support vector machine (LSSVM) is chosen for deterministic WTPC modeling and conditional kernel density estimation (CKDE) is selected for uncertainty modeling after comparison where the models are updated via the sliding time window mechanism. Using the consistency of historical data-driven models in a certain future time window, a daily condition monitoring system, including daily multi-index system and improved fuzzy comprehensive evaluation method (FCEM), is established to monitor future wind turbine condition. Finally, measured data from a wind farm in north China are acquired for validation. The results show that the outliers are effectively cleaned for high-fidelity WTPC modeling. The daily condition monitoring system including daily raw data preprocessing, multi-index system and FCEM algorithm can provide efficient daily rating score.

Comparative Analysis for Interval Modeling Algorithms of Wind Turbine Power Curve

Considering the stochastic uncertainty of wind power generation, joint estimation of wind turbine power curve (WTPC) in point and interval forms is carefully studied in this paper. Firstly, inducing factors of uncertain data and outliers types in measured data are analyzed to show necessity of uncertainty modeling of WTPC. Then, theoretical principles of different methods for WTPC modeling such as Gaussian Bin method, kernel density estimation (KDE), conditional kernel density estimation (CKDE), conditional probability via Copula, Gaussian process regression (GPR) and relevance vector machine (RVM), are seriously straightened up. Their theoretical essences are discussed and compared in depth. Subsequently, evaluation indexes for point and interval estimations of WTPC are defined to quantify modeling performance. Finally, using measured data from actual 1.5MW variable-speed variable-pitch (VSVP) wind turbines, simulations are executed to show diversities of these methods and their features are discussed from different views. Meanwhile, their potential application scenarios and usage strategies are carefully analyzed, including wind power prediction and operational performance evaluation of wind turbine in an infinite-time-horizon form or a sliding-window form. It is helpful to enhance development of WTPC modeling techniques.

Joint Point-Interval Prediction and Optimization of Wind Power Considering the Sequential Uncertainties of Stepwise Procedure

To support high-level wind energy utilization, wind power prediction has become a more and more attractive topic. To improve prediction accuracy and flexibility, joint point-interval prediction of wind power via a stepwise procedure is studied in this paper. Firstly, time-information-granularity (TIG) is defined for ultra-short-term wind speed prediction. Hidden features of wind speed in TIGs are extracted via principal component analysis (PCA) and classified via adaptive affinity propagation (ADAP) clustering. Then, Gaussian process regression (GPR) with joint point-interval estimation ability is adopted for stepwise prediction of the wind power, including wind speed prediction and wind turbine power curve (WTPC) modeling. Considering the sequential uncertainties of stepwise prediction, theoretical support for an uncertainty enlargement effect is deduced. Uncertainties’ transmission from single-step or receding multi-step wind speed prediction to wind power prediction is explained in detail. After that, normalized indexes for point-interval estimation performance are presented for GPR parameters’ optimization via a hybrid particle swarm optimization-differential evolution (PSO-DE) algorithm. K-fold cross validation (K-CV) is used to test the model stability. Moreover, due to the timeliness of data-driven GPR models, an evolutionary prediction mechanism via sliding time window is proposed to guarantee the required accuracy. Finally, measured data from a wind farm in northern China are acquired for validation. From the simulation results, several conclusions can be drawn: the multi-model structure has insignificant advantages for wind speed prediction via GPR; joint point-interval prediction of wind power is realizable and very reasonable; uncertainty enlargement exists for stepwise prediction of wind power while it is more significant after receding multi-step prediction of wind speed; a reasonable quantification mechanism for uncertainty is revealed and validated.

Uncertainty estimation for wind energy conversion by probabilistic wind turbine power curve modelling

This paper proposes probabilistic wind turbine power curve (WTPC) models to quantify the uncertainties of energy conversion and highly scattered relationships of actual wind speed to power. First, new model inputs (i.e. pitch angle and wind direction) and novel data clearing methods are presented to improve the model accuracy, which is rare in the previous studies. Second, the models are established based on three nonparametric algorithms, i.e. Monte Carlo, neural network, and fuzzy clustering. Third, to fill the research gap on model evaluation, the desirable properties of a probabilistic WTPC model are defined as expected variance ratio (EVR), and this index is formulated by calculating the cumulative gaps between the simulated and actual power distribution in each wind speed segment. Data from two Chinese wind farms are used to validate and compare the proposed methods using the mainstream deterministic index and the proposed EVR. Results show that (i) new model inputs and data clearing methods are able to improve the accuracy for probabilistic models regardless of the afterwards modelling method; (ii) fuzzy outperforms other probabilistic models.

Wind Turbine Power Curve Modeling and Monitoring With Gaussian Process and SPRT

The wind turbine power curve is an important indicator of the performance of a wind turbine. Modeling and monitoring the power curve can detect wind turbine operation abnormalities and degradation in a timely manner. First, this paper points out the drawbacks of the standard binned power curve modeling method of IEC-61400-12-1. Multiple factors that influence wind energy capture and power output of a wind turbine are analyzed in detail and used as the power curve model inputs. A multivariable power curve model is constructed with a modified Cholesky decomposition Gaussian process (GP) and validated using wind turbine Supervisory Control and Data Acquisition (SCADA) data. A sequential probability ratio test with two groups of hypotheses is introduced to analyze and detect abnormal changes in GP power curve prediction residuals and thus detect abnormal operation. In order to locate failed components when an alarm is identified, longitudinal and transverse data comparisons are proposed to check the operation of specific components. The modeling and monitoring methods proposed in this paper successfully identify faults and locate the faulty component for two wind turbines with anemometer failure and pitch system failure, respectively.

Incorporating air density into a Gaussian process wind turbine power curve model for improving fitting accuracy

AbstractA power curve conventionally represents the relationship between hub height wind speed and wind turbine power output. Power curves facilitate the prediction of power production at a site and are also useful in identifying the significant changes in turbine performance which can be vital for condition monitoring. However, their accuracy is significantly influenced by changes in air density, mainly when the turbine is operating below rated power. A Gaussian process (GP) is a nonparametric machine learning approach useful for power curve fitting. Critical analysis of temperature correction is essential for improving the accuracy of wind turbine power curves. The conventional approach is to correct the data for air density before it is binned to provide a power curve, as described in the IEC standard. In this paper, four different possible approaches of air density correction and its effect on GP power curve fitting model accuracy are explored to identify whether the traditional IEC approach used for air density correction is most effective when estimating power curves using a GP. Finding the most accurate air density compensation approach is necessary to minimize GP model uncertainty.

Assessment and Performance Evaluation of a Wind Turbine Power Output

Estimation errors have constantly been a technology bother for wind power management, often time with deviations of actual power curve (APC) from the turbine power curve (TPC). Power output dispersion for an operational 800 kW turbine was analyzed using three averaging tine steps of 1-min, 5-min, and 15-min. The error between the APC and TPC in kWh was about 25% on average, irrespective of the time of the day, although higher magnitudes of error were observed during low wind speeds and poor wind conditions. The 15-min averaged time series proved more suitable for grid management and energy load scheduling, but the error margin was still a major concern. An effective power curve (EPC) based on the polynomial parametric wind turbine power curve modeling technique was calibrated using turbine and site-specific performance data. The EPC reduced estimation error to about 3% in the aforementioned time series during very good wind conditions. By integrating statistical wind speed forecasting methods and site-specific EPCs, wind power forecasting and management can be significantly improved without compromising grid stability.

Wind turbine power curve modeling based on Gaussian Processes and Artificial Neural Networks

Abstract An accurate estimation of the wind turbine power curve is a key issue to the provision of the electricity that the wind farm will transfer to the grid and for a correct evaluation of the performance of each turbine. Artificial Neural Networks (ANN) have proven to be well suited for solving this problem. We propose in this study that including a prior automatic filtering, by means of Gaussian Processes modelling, improves the network performance significantly, and saves substantial time and resources. The aim of this paper is to present a complete method based on Gaussian Processes data pre-filtering and ANN modeling of wind turbine power curves. Results show that this procedure improves the standard ANN modeling and also improves on the widely used IEC-61400 standard (International Electro technical Commission) and other parametric and non-parametric methods. Overall, there is a significant improvement (25%) in root mean square error of predicted power using our proposed model compared to standard methods currently applied.

Wind resource estimation using wind speed and power curve models

Estimation of wind resource in a given area helps in identifying potential sites for establishing wind farm and aids in the calculation of annual energy produced. Estimation of annual energy improves the wind power penetration in the electricity grid and in electricity trading. In this paper, wind resource estimation has been carried out using wind speed forecasting models and wind turbine power curve model. The time series model of wind speed for day ahead forecasting is developed based on linear and non-linear autoregressive models with and without exogenous variables. The daily wind speed data of five different locations in New Zealand have been used for this analysis and the annual energy produced has been obtained. The standard deviation between the mean wind speed of the previous day and the mean wind speed during corresponding day five years and ten years ago has been used as exogenous variables. The neuralnet based non-linear model built using exogenous variables (NLARX) performs better in three locations and wavenet based non-linear model performs better in the remaining two locations. Wind resource is estimated using a wind turbine power curve modeled using a five parametric logistic expression, whose parameters were solved using Differential Evolution (DE).

Wind Turbine Power Curve Modeling Using Advanced Parametric and Nonparametric Methods

Wind turbine power curve modeling is an important tool in turbine performance monitoring and power forecasting. There are several statistical techniques to fit the empirical power curve of a wind turbine, which can be classified into parametric and nonparametric methods. In this paper, we study four of these methods to estimate the wind turbine power curve. Polynomial regression is studied as the benchmark parametric model, and issues associated with this technique are discussed. We then introduce the locally weighted polynomial regression method, and show its advantages over the polynomial regression. Also, the spline regression method is examined to achieve more flexibility for fitting the power curve. Finally, we develop a penalized spline regression model to address the issues of choosing the number and location of knots in the spline regression. The performance of the presented methods is evaluated using two simulated data sets as well as an actual operational power data of a wind farm in North America.

A comprehensive review on wind turbine power curve modeling techniques

Abstract The wind turbine power curve shows the relationship between the wind turbine power and hub height wind speed. It essentially captures the wind turbine performance. Hence it plays an important role in condition monitoring and control of wind turbines. Power curves made available by the manufacturers help in estimating the wind energy potential in a candidate site. Accurate models of power curve serve as an important tool in wind power forecasting and aid in wind farm expansion. This paper presents an exhaustive overview on the need for modeling of wind turbine power curves and the different methodologies employed for the same. It also reviews in detail the parametric and non-parametric modeling techniques and critically evaluates them. The areas of further research have also been presented.