Novel Nonparametric Approaches for Wind and Solar Probability Density Estimation for Power Network Planning Studies

  • Maisam Abdulrahman Wahbah

Student thesis: Doctoral Thesis

Abstract

The accurate estimation of available wind and solar resources at a given site is crucial in network planning and design studies. This requires probabilistic models with adaptive algorithms that accurately estimate the probability distributions of these stochastic renewable resources. The work presented in the thesis addresses this critical challenge of renewables, namely the modeling of the intermittency of generation. Two nonparametric probability density approaches are introduced in this thesis for the first time. The first approach implements a nonparametric combinatorial method for obtaining a Kernel Density Estimation (KDE)-based statistical model. The selection of the KDE bandwidth is optimized with respect to mean integrated absolute error between the true and hypothesized densities. The second approach is based on the application of local linear regression in tandem with a root transformation method. KDE methods, including the proposed combinatorial approach, are not ideally suited for characterizing solar irradiance variability because of the boundary bias problem when estimating the density near the finite end points of its support. To overcome this issue, two hybrid models based on a combination of the parametric Beta distribution and nonparametric KDE models are developed to obtain more reliable statistical models. The accuracy of the aforementioned proposed nonparametric statistical estimation methods is assessed via comparisons with multiple popular parametric and nonparametric models using data obtained at different sites. The performance of the proposed models is evaluated using the Kolmogorov–Smirnov goodness-of-fit test, Coefficient of Determination, and a number of statistical error metrics. Results confirm the suitability and accuracy of the proposed estimation methods for modeling the stochastic behavior of wind and solar resources, with substantial improvements over conventional parametric and nonparametric models.
Date of AwardJun 2019
Original languageAmerican English

Keywords

  • Adaptive estimation
  • kernel density estimation
  • nonparametric regression
  • parametric statistics
  • probability density estimation
  • solar irradiance models
  • wind speed models.

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