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The impact of potential-based physics models on pricing in energy networks

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Abstract

Pricing of access to energy networks is an important issue in liberalized energy sectors because of the natural monopoly character of the underlying transport infrastructures. We introduce a general pricing framework for potential-based energy flows in arbitrarily structured transport networks. In different specifications of our general pricing model we discuss first- and second-best pricing results and compare different pricing outcomes of potential-free and potential-based energy flow models. Our results show that considering nonlinear laws of physics leads to significantly different pricing results on networks and that these differences can only be seen in sufficiently complex, e.g., cyclic, networks as they can be found in real-world situations.

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Notes

  1. Potentials correspond to squared gas pressures and the potential bounds are chosen such that gas pressure is within 1 bar 70 bar. For the gas network model, all pipes have length \(L = 25\,\text {km}\) and an inner roughness of \(k = 0.05\,\text {mm}\). Furthermore, the compressibility factor is set to 1, the constant mean temperature of gas is 283.15 K and the constant molar mass of gas is \(18.05\,\text {kg kmol}^{-1}\).

  2. https://www.mso.math.fau.de/fileadmin/wima/data_members/schmidt/chao-peck.zip.

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Acknowledgements

The authors thank the Deutsche Forschungsgemeinschaft for their support within projects A05, B07, and B08 in the Sonderforschungsbereich/Transregio 154 “Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks”. This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. Finally, we thank Veronika Grimm and Gregor Zöttl for numerous discussions on the topic of this paper.

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Correspondence to Martin Schmidt.

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Schewe, L., Schmidt, M. The impact of potential-based physics models on pricing in energy networks. Cent Eur J Oper Res 28, 1003–1029 (2020). https://doi.org/10.1007/s10100-019-00616-1

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  • DOI: https://doi.org/10.1007/s10100-019-00616-1

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