Robust DC Optimal Power Flow with Modeling of Solar Power Supply Uncertainty via R-Vine Copulas
Aigner KM, Schaumann P, von Loeper F, Martin A, Schmidt V, Liers F (2022)
Publication Language: English
Publication Status: Submitted
Publication Type: Journal article, Original article
Future Publication Type: Journal article
Publication year: 2022
Journal
URI: https://link.springer.com/article/10.1007/s11081-022-09761-0
DOI: 10.1007/s11081-022-09761-0
Open Access Link: https://link.springer.com/article/10.1007/s11081-022-09761-0
Abstract
We present a robust approximation of joint chance constrained DC Optimal Power Flow in combination with a model-based prediction of uncertain power supply via R-vine copulas.
It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in.
This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (European Journal of Operational Research, (2021)).
The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets.
The resulting robust optimization problem has a known equivalent tractable reformulation.%, which can be solved with standard software.
To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes.
The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model.
Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts.
The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas.
We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.
Authors with CRIS profile
Kevin-Martin Aigner
Professur für Optimization under Uncertainty & Data Analysis
Alexander Martin
Lehrstuhl für Analytics & Mixed-Integer Optimization
Frauke Liers-Bergmann
Professur für Optimization under Uncertainty & Data Analysis
Related research project(s)
Multi-sector coupled energy system modeling on a regional level (ESM-Regio)
May 1, 2021 - April 30, 2024
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Optimierung der Netzeingriffe (Verteilnetze)
Flächenbezogene Modellierung, Simulation und Optimierung von Solar-Einspeisung, Lastfluss und Steuerung für Stromverteilnetze, unter Berücksichtigung von Einspeisungsunsicherheiten
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Involved external institutions
Germany (DE)How to cite
APA:
Aigner, K.-M., Schaumann, P., von Loeper, F., Martin, A., Schmidt, V., & Liers, F. (2022). Robust DC Optimal Power Flow with Modeling of Solar Power Supply Uncertainty via R-Vine Copulas. Optimization and Engineering. https://dx.doi.org/10.1007/s11081-022-09761-0
MLA:
Aigner, Kevin-Martin, et al. "Robust DC Optimal Power Flow with Modeling of Solar Power Supply Uncertainty via R-Vine Copulas." Optimization and Engineering (2022).
BibTeX: Download