Uncertainty Quantification and Control in Power System Security and Operation Via Data-Driven Polynomial Chaos Expansion Based Methods

The global energy situation is shifting towards renewable energy sources (RESs) to promote sustainability and reduce fossil fuel reliance.This shift brings uncertainties from volatile RESs and new forms of loads (e.g., electric vehicles), challenging power system operation and security.Addressing these challenges, this thesis aims to leverage a surrogate modeling method, namely the polynomial chaos expansion method, to systematically investigate and mitigate the impacts of uncertainties on power system transfer capability and economic dispatch (ED).The overarching goal is to offer vital guidance for ensuring and enhancing the security of power systems while maximizing the utilization of transmission assets and economic benefits, considering the high uncertainty level of current and future power grids.The thesis first studies the impacts of uncertainties brought by volatile RESs, random loads, and unforeseen equipment outages on power system available transfer capability (ATC), a crucial index in power system security analysis.By exploiting polynomial chaos theory and moment-based methods, a data-driven sparse polynomial chaos expansion (DDSPCE) method is developed for probabilistic total transfer capability (PTTC) and ATC assessment.Notably, without requiring preassumed probability distributions of random inputs, the proposed DDSPCE directly exploits data for estimating the probabilistic characteristics of PTTC (e.g., mean, variance, probability density function (PDF), and cumulative distribution function (CDF)), based on which the ATC with a certain confidence level can be readily calculated.An integrated sparse framework further enhances its computational efficiency and accuracy.Simulations on the modified IEEE 118-bus system and the modified PEGASE 1354-bus system validate the DDSPCE method's efficacy in PTTC evaluation.Furthermore, the results underscore the significance of incorporating discrete uncertainties, like equipment outages, in both PTTC and ATC assessments.The thesis then delves into the impacts of uncertainties, especially from wind power, on ED, a critical aspect of the power system daily operation.A DDSPCE-based surrogate modeling method is developed to estimate the probabilistic characteristics of ED solutions, including their mean, variance, and distribution functions.The developed method can handle extensive random inputs without their predefined probability distributions.Extensive simulation results on an integrated electricity and gas system (IEGS) using real-life wind power data validate the efficiency and effectiveness of the proposed method in quantifying the impacts of uncertainties on the ED solutions, even when the ED solutions are multimodal.These results highlight the DDSPCE method's efficacy and efficiency in addressing general and complex scenarios.First and foremost, I would like to convey my profound appreciation to my supervisors, Professor Xiaozhe Wang and Professor Franc ¸ois Bouffard, for their unwavering support and guidance throughout my Ph.D. studies.In particular, I am profoundly thankful to my primary supervisor, Professor Xiaozhe Wang.She provided me with invaluable professional guidance and valuable suggestions as well as financial support for my Ph.D. studies and personal development.Also, I would like to express my great thanks for her encouragement to be confident, whether during exams, research seminars, public speaking occasions, or job searching.

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