Large fluctuations in locational marginal prices

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

doi:10.1098/rsta.2019.0438

Large fluctuations in locational marginal prices

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

Mathematics

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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 language	English
Article number	20190438
Pages (from-to)	1-16
Number of pages	16
Journal	Philosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences
Volume	379
Issue number	2202
DOIs	https://doi.org/10.1098/rsta.2019.0438
Publication status	Published - 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.

Funders	Funder number
Simons Foundation
Engineering and Physical Sciences Research Council	EP/R014604/1, EP/P002625/1
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	680.50.1529, 639.033.413

Keywords

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

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1098/rsta.2019.0438

2002.11680v1Submitted manuscript, 974 KB

https://arxiv.org/abs/2002.11680

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Large fluctuations in locational marginal prices

Abstract

Bibliographical note

Funding

Keywords

UN SDGs

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