Wind speed model based on kernel density estimation and its application in reliability assessment of generating systems

Abstract

An accurate probability distribution model of wind speed is critical to the assessment of reliability contribution of wind energy to power systems. Most of current models are built using the parametric density estimation (PDE) methods, which usually assume that the wind speed are subordinate to a certain known distribution (e.g. Weibull distribution and Normal distribution) and estimate the parameters of models with the historical data. This paper presents a kernel density estimation (KDE) method which is a nonparametric way to estimate the probability density function (PDF) of wind speed. The method is a kind of data-driven approach without making any assumption on the form of the underlying wind speed distribution, and capable of uncovering the statistical information hidden in the historical data. The proposed method is compared with three parametric models using wind data from six sites.The results indicate that the KDE outperforms the PDE in terms of accuracy and flexibility in describing the longterm wind speed distributions for all sites. A sensitivity analysis with respect to kernel functions is presented and Gauss kernel function is proved to be the best one. Case studies on a standard IEEE reliability test system (IEEE-RTS) have verified the applicability and effectiveness of the proposed model in evaluating the reliability performance of wind farms.

On Hybridizations of Fourth Order Kernel of the Beta Polynomial Family.

“…where ( ) is the roughness of the kernel, 2 ( ) 2 is the variance or second moment of the kernel function and ( ″ ) = ∫ ″ (x) 2 x is usually referred to as the roughness of the unknown probability density function. There is the usual bias-variance trade-off between the terms of the AMISE, that is, the bias can be reduced while the variance increases and vice versa as a result of the variation in the size of the bandwidth.…”

“…The computational simplicity and efficiency of the kernel density estimator with its easy interpretation of results has contributed to the popularity of the method over other nonparametric density estimation methods. Some recent areas of the application of kernel density estimation include image and video processing (Koloda et al, 2013) and estimation of the direction of wind (Hu et al, 2017). In modeling, kernel density estimation is of immerse applications especially in the construction of probability distributions of observations obtained from a system or process (Martinez and Martinez, 2008) and with applications in data streams of very high speed and large volume (Cao et al,2012).…”

Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions

“…e modality assessment method have been recently applied into various research fields; the BC has been employed in the psychiatry science, public opinion, chemistry, and physics [11,13,[20][21][22], and HDS has been implemented in the brain science, biological science, microbiology, and ecology [23][24][25][26]. Even though there are many applications with multimodality in the engineering fields, the methods of evaluating the multimodality have been rarely applied, and graphical methods such as histograms have been simply employed [3][4][5][6][7][8][9][27][28][29][30][31][32].…”

“…It was verified that the proposed method is more accurate, reliable, and quickly converges to the true unimodality or multimodality through the assessment of multimodality of unimodal, bimodal, and trimodal distributions in simulations and case studies of real measurements and engineering data. Accordingly, the proposed HDS with BC method can improve the accuracy of quantification and propagation such as calculations of variation in dynamic stiffness of rubber mounts [4], reliability-based design optimization of helicopters [8], reliability assessment [32], and fatigue reliability assessment for steel decks [7] through correct identification of data modality. It can be highly likely to be used in the engineering field.…”

Reliability evaluation of integrated electricity–gas system utilizing network equivalent and integrated optimal power flow techniques

“…Reliability evaluations of both electricity systems [8] and gas systems [9,10] have been well studied. However, the integration of electricity and gas systems brings additional complexities and new challenges to the reliability evaluation of IEGS.…”