Bayesian and Non-Bayesian Models for Multi-Site Dependent Wind Farms
PhD Candidate Vincent Tanoe
By: Vincent Tanoe
PhD Advisor: Dr. Amir Shahirinia
Wednesday, December 14, 2022 at 9:00 AM
PhD Committee
Dr. Amir Shahirinia PhD Advisor
Dr. Paul Cotae Committee Chair
Dr. Nian Zhang Member UDC
Dr. Amin Hajizadeh External Member from Aalborg University
Dr. Oran Alston External Member from Department of Defense
Research Presentation
Renewable energies are of paramount importance when it comes to energy consumption. They provide reliable power sources and fuel diversification, which improves energy security and helps reduce the risk of fuel spillage and the need for imported fuels. They also help preserve the country’s natural resources. Wind energy production must be increased to be able to use them at high capacity. Wind speed is one of the most reliable sources of clean and sustainable electricity supply. The use of wind speed is one of the crucial factors that significantly contribute to the renewal of energy. Enable an enormous benefit from it requires an increase in wind power generation. But the major problem with this increase is the uncertainty inherent in the wind speed. For too long, the issue of uncertainty has been at the center of deep-thinking scientists, researchers, academics, and scholars working on the central question of the usage of wind speed. This uncertainty is due to the day/night cycle caused by the earth’s rotation, and the seasonal changes due to the tilt of the earth’s axis cause changes in the wind speed. So far, the wind speed uncertainty has been presented as a probability distribution. However, the uncertainty of these wind speed models has not yet been considered. This dissertation uses three approaches to thoroughly analyze fifteen wind speed data variables from the National Renewable Energy Laboratory. The data are split into three different sample sizes, namely (hourly 8760, daily 365, and weekly 53).
Firstly, the dissertation applies (i) the non-Bayesian and the Bayesian approaches to study linearity among the data. In this first approach, a correlation matrix method is implemented to select the most correlated variables and use the highest correlated variable among them as the dependent variable. After selecting the dependent variable from the correlation matrix method, we proceeded by applying a Random Forest machine learning technique for the feature selections and considered the most critical features to be used as independent variables in both the non-Bayesian and Bayesian regression models.
Secondly, to ensure that the nature of the uncertainty is carefully analyzed and minimized, we analyzed the variables again to determine their dependencies. To investigate their dependencies, we have applied different dependency models such as R-vine, C-vine, and D-vine copulas on each data size, i.e., hourly, daily, and weekly. The empirical pairwise Kendall Tau values and pairwise copula families are used to assessing the data’s dependencies after the data are normalized. Loglik, AIC, and BIC were used as measurement tools to select the best structure to choose the suitable model.
Finally, to predict the wind data we analyzed through the linearity and dependencies approaches, the dissertation applied the Bayesian Moving Average method to the medium dataset since the medium dataset provided promising results from the precedents analysis. We ran three different equations based on the Bayesian Moving Average. We first determined the most important variables with a higher coefficient based on Post Mean. Second, we used different priors’ models and ran an MCMC model to ensure the best fit of the models. Thus, we used the posterior coefficient density to analyze the entire posterior distribution of the coefficients and compare the expected values of the coefficients. For the prediction, we used the last 165 days of the medium dataset (daily 365).
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