Robust Approximation of Chance Constrained DC Optimal Power Flow under Decision-Dependent Uncertainty

  • We propose a mathematical optimization model and its solution for joint chance constrained DC Optimal Power Flow. In this application, it is particularly important that there is a high probability of transmission limits being satisfied, even in the case of uncertain or fluctuating feed-in from renewable energy sources. In critical network situations where the network risks overload, renewable energy feed-in has to be curtailed by the transmission system operator (TSO). The TSO can reduce the feed-in in discrete steps at each network node. The proposed optimization model minimizes curtailment while ensuring that there is a high probability of transmission limits being maintained. The latter is modeled via (joint) chance constraints that are computationally challenging. Thus, we propose a solution approach based on the robust safe approximation of these constraints. Hereby, probabilistic constraints are replaced by robust constraints with suitably defined uncertainty sets constructed from historical data. The uncertainty sets are calculated by encompassing randomly drawn scenarios using the scenario approach proposed by Margellos et al. (IEEE Transactions on Automatic Control, 59 (2014)). The ability to discretely control the power feed-in then leads to a robust optimization problem with decision-dependent uncertainties, i.e. the uncertainty sets depend on decision variables. We propose an equivalent mixed-integer linear reformulation for box uncertainties with the exact linearization of bilinear terms. Finally, we present numerical results for different test cases from the Nesta archive, as well as for a real network. We consider the discrete curtailment of solar feed-in, for which we use real-world weather and network data. The experimental tests demonstrate the effectiveness of this method and run times are very fast. Moreover, on average the calculated robust solutions lead only to a small increase in curtailment, when compared to nominal solutions.

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Author:Kevin-Martin Aigner, Jan-Patrick Clarner, Frauke Liers, Alexander Martin
Document Type:Preprint
Date of Publication (online):2020/05/12
Date of first Publication:2020/05/12
Release Date:2020/05/12
Tag:OR in energy; chance constrained programming; decision-dependent uncertainty; optimal power flow; robust optimization
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Zuse-Institut Berlin (ZIB)
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International