Comparison of Optimum Spline-Based Probability Density Functions to Parametric Distributions for the Wind Speed Data in Terms of Annual Energy Production

Abstract

The common approach to wind energy feasibility studies is to use Weibull distribution for wind speed data to estimate the annual energy production (AEP). However, if the wind speed data has more than one mode in the probability density, the conventional distributions including Weibull fail to fit the wind speed data. This highly affects the technical and economic assessment of a wind energy project by causing crucial errors. This paper presents a novel way to define the probability density for wind speed data using splines. The splines are determined as a solution of constrained optimization problems. The constraints are the characteristics of probability density functions. The proposed method is implemented for different wind speed distributions including multimodal data and compared with Weibull, Weibull and Weibull and Beta Exponentiated Power Lindley (BEPL) distributions. It is also compared with two other nonparametric distributions. The results show that the spline-based probability density functions produce a minimum fitting error for all the analyzed cases. The AEP calculated based on this method is considered to have high fidelity, which will decrease the investment risk.

Frequency Distribution Model of Wind Speed Based on the Exponential Polynomial for Wind Farms

“…(2) Multimodal wind speed distribution To further verify the effectiveness of the exponential polynomial model, we compared it to a study [20] where splines were used as wind speed frequency distribution functions, mainly for multi-modal wind speed distribution. From the simulation results, the model proposed in the literature can adequately fit the measured data, whether for unimodal or multimodal wind speed distribution.…”

“…Loukatou [19] proposed and tested an Ornstein-Uhlenbeck geometric Brownian motion model over continuous time to represent the wind speed, avoiding the problems of using the Weibull distribution model. Elfarra and Kaya [20] designed a novel way to define the probability density for wind speed data using splines and validated that spline-based probability density functions produce a minimum fitting error for all the analysed cases.…”

“…This highly affects the technical and economic assessment of a wind energy project by causing crucial errors. To address this problem, Elfarra and Kaya [20] made use of splines to define the probability density for multimodal wind speed data and proved the validity of the method. In fact, the exponential polynomial model presented in this paper can also fit the frequency distribution of multimodal wind speed.…”

“…In fact, the exponential polynomial model presented in this paper can also fit the frequency distribution of multimodal wind speed. Meanwhile, there are differences in three main points from the literature [20]: (1) The piecewise cubic polynomial is used for constructing a spline in the literature. When optimizing spline coefficients the values of three functions need to be minimised, including the values of function at each node, and its first derivative values at the first and last nodes.…”

Application of Statistical Distribution Models to Predict Health Index for Condition-Based Management of Transformers

“…The main motivation of this study is to introduce a simplified method in order to predict the HI of transformer population that is based on Statistical Distribution Model (SDM) utilizing the individual condition parameter data as a key approach to determine the HI. SDM is chosen, due to its simplicity and adaptability to analyze any sample size data [24]. In addition, it can also identify the independent variables (13 condition parameters) that can affect the predicted HI.…”