期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 301, 期 1, 页码 318-333出版社
ELSEVIER
DOI: 10.1016/j.ejor.2021.10.051
关键词
OR in energy; Optimal power flow; Chance constrained programming; Robust optimization; Decision-dependent uncertainty
资金
- Federal Ministry of Education and Research of Germany [05M18WEB]
- Deutsche Forschungsgemeinschaft(DFG) [Sonderforschungsbereich/Transregio 154]
- Bavarian State Government
This paper proposes a mathematical optimization model and its solution for joint chance constrained DC Optimal Power Flow. The proposed model minimizes curtailment of renewable energy feed-in while ensuring a high probability of transmission limits being maintained. The solution approach is based on robust safe approximation and replaces probabilistic constraints with suitably defined uncertainty sets constructed from historical data. Experimental results demonstrate the effectiveness and efficiency of this method.
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 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 only lead to a small increase in curtailment, when compared to nominal solutions. (c) 2021 Elsevier B.V. All rights reserved.
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