Large fluctuations in locational marginal prices

T. Nesti, J. Moriarty, A. Zocca, B. Zwart

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Abstract

© 2021 The Author(s).This paper investigates large fluctuations of locational marginal prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form P(LMP∉∏i=1n[αi-,αi+]), where LMP is the vector of LMPs at the n power grid nodes, and α -, α+∈Rn are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply-demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modelling uncontrollable renewable generation. We use techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations, and are validated numerically on the IEEE 14-bus test case. This article is part of the theme issue 'The mathematics of energy systems'.
Original languageEnglish
Article number20190438
Pages (from-to)1-16
Number of pages16
JournalPhilosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences
Volume379
Issue number2202
DOIs
Publication statusPublished - 26 Jul 2021

Bibliographical note

16 pages, 10 figures

Funding

Competing interests. We declare we have no competing interests. Funding. This research is supported by NWO VICI grant no. 639.033.413, NWO Rubicon grant 680.50.1529 and EPSRC grant no. EP/P002625/1 and EP/R014604/1, and partially supported by a grant from the Simons Foundation. Acknowledgements. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme ‘The mathematics of energy systems’ when work on this paper was undertaken.

FundersFunder number
Simons Foundation
Engineering and Physical Sciences Research CouncilEP/R014604/1, EP/P002625/1
Nederlandse Organisatie voor Wetenschappelijk Onderzoek680.50.1529, 639.033.413

    Keywords

    • math.OC
    • cs.SY
    • eess.SY
    • math.PR
    • physics.soc-ph

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