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Optimal Power Flow Subject to Non‐Gaussian Stochastic Uncertainties: An L 2 ‐based Approach
Author(s) -
Mühlpfordt Tillmann,
Faulwasser Timm,
Hagenmeyer Veit
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800371
Subject(s) - polynomial chaos , polynomial , mathematical optimization , uncertainty quantification , gaussian , stochastic process , mathematics , propagation of uncertainty , computer science , algorithm , monte carlo method , mathematical analysis , statistics , physics , quantum mechanics , machine learning
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 the 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. Modeling uncertainties as second‐order continuous random variables, the OPF problem subject to stochastic uncertainties can be posed as an infinite‐dimensional L 2 ‐problem. A tractable and exact reformulation thereof can be obtained using polynomial chaos expansion, under mild assumptions. Polynomial chaos as such is a Hilbert space series expansion for random variables that is frequently employed for uncertainty propagation and uncertainty quantification. Polynomial chaos offers several advantages for OPF subject to stochastic uncertainties. For example, multivariate non‐Gaussian uncertainties can be considered straightforwardly. Also, the solutions from polynomial chaos are effectively feedback laws in terms of the realizations of the uncertainty that are determined in a single numerical run.