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Uncertainty Quantification via Polynomial Chaos Expansion – Methods and Applications for Optimization of Power Systems

Mühlpfordt, Tillmann


Fossil fuels paved the way to prosperity for modern societies, yet alarmingly, we can exploit our planet’s soil only so much. Renewable energy sources inherit the burden to quench our thirst for energy, and to reduce the impact on our environment simultaneously. However, renewables are inherently volatile; they introduce uncertainties. What is the effect of uncertainties on the operation and planning of power systems? What is a rigorous mathematical formulation of the problems at hand? What is a coherent methodology to approaching power system problems under uncertainty? These are among the questions that motivate the present thesis that provides a collection of methods for uncertainty quantification for (optimization of) power systems.

We cover power flow (PF) and optimal power flow (OPF) under uncertainty (as well as specific derivative problems). Under uncertainty---we view "uncertainty" as continuous random variables of finite variance---the state of the power system is no longer certain, but a random variable. We formulate PF and OPF problems in terms of random variables, thusly exposing the infinite-dimensional nature in terms of L2-functions. ... mehr

Volltext §
DOI: 10.5445/IR/1000104661
Veröffentlicht am 13.01.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Automation und angewandte Informatik (IAI)
Publikationstyp Hochschulschrift
Publikationsjahr 2020
Sprache Englisch
Identifikator KITopen-ID: 1000104661
HGF-Programm 37.06.01 (POF III, LK 01) Networks and Storage Integration
Verlag Karlsruher Institut für Technologie (KIT)
Umfang XIII, 191 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Informatik (INFORMATIK)
Institut Institut für Automation und angewandte Informatik (IAI)
Prüfungsdatum 10.12.2019
Schlagwörter power systems, optimization, uncertainty quantification, polynomial chaos expansion, chance constraints, power flow, optimal power flow
Referent/Betreuer Hagenmeyer, V.
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