# 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.

 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 Nachgewiesen in Dimensions
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