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Uncertainty Quantification for Optimal Power Flow Problems
Author(s) -
Mühlpfordt Tillmann,
Hagenmeyer Veit,
Faulwasser Timm
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900087
Subject(s) - mathematical optimization , computer science , renewable energy , gaussian , uncertainty quantification , key (lock) , optimization problem , electric power system , stochastic programming , stochastic optimization , polynomial chaos , power (physics) , mathematics , monte carlo method , engineering , machine learning , statistics , physics , electrical engineering , computer security , quantum mechanics
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.