Copula‐based model for wind turbine power curve outlier rejection

Abstract

Power curve measurements provide a conventional and effective means of assessing the performance of a wind turbine, both commercially and technically. Increasingly high wind penetration in power systems and offshore accessibility issues make it even more important to monitor the condition and performance of wind turbines based on timely and accurate wind speed and power measurements. Power curve data from Supervisory Control and Data Acquisition (SCADA) system records, however, often contain significant measurement deviations, which are commonly produced as a consequence of wind turbine operational transitions rather than stemming from physical degradation of the plant. Using such raw data for wind turbine condition monitoring purposes is thus likely to lead to high false alarm rates, which would make the actual fault detection unreliable and would potentially add unnecessarily to the costs of maintenance. To this end, this paper proposes a probabilistic method for excluding outliers, developed around a copula-based joint probability model. This approach has the capability of capturing the complex non-linear multivariate relationship between parameters, based on their univariate marginal distributions; through the use of a copula, data points that deviate significantly from the consolidated power curve can then be removed depending on this derived joint probability distribution. After filtering the data in this manner, it is shown how the resulting power curves are better defined and less subject to uncertainty, whilst broadly retaining the dominant statistical characteristics. These improved power curves make subsequent condition monitoring more effective in the reliable detection of faults.

Data-Driven Wind Turbine Power Generation Performance Monitoring

“…Numerous power curve modeling approaches have been reported in [21][22][23]. In this study, we select two types of profiles, the linear profile and Weibull cumulative distribution function (WCDF) profile, to demonstrate the accuracy and effectiveness of the proposed monitoring framework.…”

A stochastic power curve for wind turbines with reduced variability using conditional copula

“… Given the selected copula function between each candidate form and wind speed, and the selected copula function between each candidate form and wind power, we obtain the conditional cdf of wind power and wind speed. For example, let C P , r ( u P , u r ) and C v , r ( u v , u r ) denote the selected copula functions for wind power and solar radiation, wind speed and solar radiation respectively, we can derive their conditional cdfs by conditioning on u r as follows: Given the conditional cdf of wind power and wind speed as marginal distributions, we fit them into the GMCM by Wang et al through MLE. We further generate 10,000 random samples from the GMCM and transform the random samples back to original scale of the data.…”

“…Using wind speed and azimuth, , we obtain the wind speed data conditioned on wind azimuth using the conditional form of normal copula as follows: where Φ 2 is the cdf of two standard normally distributed random variables with correlation θ , Φ − 1 is the inverse of the standard normal distribution. Given the conditional cdf value of wind power and wind speed as marginal distributions, we fit them into the GMCM by Wang et al through MLE. We further generate 20,000 random samples from the GMCM and transform the random samples back to the original scale of the data.…”

“…Wang et al adopted the Gaussian mixture copula model (GMCM) to model the power curve and claimed to have better goodness of fit than reported in Stephen et al . While the stochastic characteristics between wind power and wind speed are well captured by the copula models proposed in Wang et al ., a large variability between the wind speed and wind power still exists. This substantial variability makes it difficult for monitoring the health condition of wind turbines and affects the accuracy of wind power forecasting.…”

Adaptive robust polynomial regression for power curve modeling with application to wind power forecasting

“…Consequently, it is crucial for forecast accuracy improvement to make the wind power conversion function adaptive and robust. Raw data preprocessing before training is one possible way to handle data quality related problems in power curve modeling . Those methods could mitigate the effect of abnormal data to some extent, but they do not help capturing the time‐varying and scattered properties of the power curve essentially.…”