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Uncertainty Quantification for Optimal Power Flow Problems

Mühlpfordt, Tillmann; Hagenmeyer, Veit; Faulwasser, Timm

Abstract:
The need to de‐carbonize the current energy infrastructure, and the increasing integration of renewables pose a number of difficult control and optimization problems. Among those, the optimal power flow (OPF) problem—i.e., the task to minimize power system operation costs while maintaining technical and network limitations—is key for operational planning of power systems. The influx of inherently volatile renewable energy sources calls for methods that allow to consider stochasticity directly in the OPF problem. Here, we present recent results on uncertainty quantification for OPF problems. Modeling uncertainties as second‐order continuous random variables, we will show that the OPF problem subject to stochastic uncertainties can be posed as an infinite‐dimensional L$_{2}$‐problem. A tractable reformulation thereof can be obtained using polynomial chaos expansion (PCE), under mild assumptions. We will show advantageous features of PCE for OPF subject to stochastic uncertainties. For example, multivariate non‐Gaussian uncertainties can be considered easily. Finally, we comment on recent progress on a Julia package for PCE.


Verlagsausgabe §
DOI: 10.5445/IR/1000100419
Veröffentlicht am 02.03.2021
Originalveröffentlichung
DOI: 10.1002/Pamm.201900087
Dimensions
Zitationen: 1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Automation und angewandte Informatik (IAI)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 11.2019
Sprache Englisch
Identifikator ISSN: 1617-7061, 1617-7061
KITopen-ID: 1000100419
HGF-Programm 37.06.01 (POF III, LK 01) Networks and Storage Integration
Erschienen in Proceedings in applied mathematics and mechanics
Verlag Wiley-VCH Verlag
Band 19
Heft 1
Seiten Art.Nr. e201900087
Vorab online veröffentlicht am 18.11.2019
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