## Date of Award

May 2015

## Degree Type

Dissertation

## Degree Name

Doctor of Philosophy

## Department

Engineering

## First Advisor

David Yu

## Second Advisor

Ehsan Soofi

## Committee Members

Adel Nasiri, Chiu Tai Law, Junhong Chen

## Keywords

Bayesian Statistics, Power Systems, Probability, Statistical Analysis, Uncertainty, Wind Modeling

## Abstract

A major challenge with the increase in wind power generation is the uncertain nature of wind speed. So far the uncertainty about wind speed has been presented through probability distributions. However, the uncertainty about these wind speed models has not yet been considered. In this dissertation we use the Bayesian approach to taking into account the uncertainty inherent in the wind speed model. Also the existing models that consider the uncertainty of the wind speed primarily view the distributions of the wind speed over a wind farm as being homogeneous. The Bayesian predictive model of the wind speed aggregates the non-homogeneous distributions into a single continuous distribution. Therefore, the result is able to capture the variation among the probability distributions of the wind speeds at the turbines' locations in a wind farm. More specifically, instead of using a wind speed distribution whose parameters are known or estimated, the parameters are considered as random whose variations are according to probability distributions. In order to present the applications of developed uncertain models, we apply both non-Bayesian and Bayesian models to a well-known power systems problem known as Stochastic Economic Dispatching (S-ED). Traditionally, S-ED algorithms incorporate wind speed using a single point from a wind speed distribution to generate the resultant wind power as the input for the ED algorithm to produce the optimal combination of fossil fuel power generation. In this dissertation, we develop a new Stochastic Economic Dispatch algorithm, referred to as SEconD, for capturing the uncertainty induced by the wind speed of the planning target time to economic dispatching output variables. SEconD uses the entire wind speed distribution as the input to generate the resultant wind power distribution rather than just a single point and produces data for estimating the probability distributions of optimal fossil fuel generation outputs, transmission loss, and total cost of power generation. Having distributions of optimal outputs enables a system operator to perform useful statistical analyses of the outputs.

## Recommended Citation

Shahirinia, Amir Hossein, "Probability Models for Wind-Penetrated Power Systems" (2015). *Theses and Dissertations*. 926.

https://dc.uwm.edu/etd/926