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Trans. R. Soc. A."],"published-print":{"date-parts":[[2021,7,26]]},"abstract":"<jats:p>\n            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\n            <jats:disp-formula>\n              <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n                <mml:mrow>\n                  <mml:mi mathvariant=\"double-struck\">P<\/mml:mi>\n                <\/mml:mrow>\n                <mml:mrow>\n                  <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">(<\/mml:mo>\n                <\/mml:mrow>\n                <mml:mrow>\n                  <mml:mrow>\n                    <mml:mtext mathvariant=\"bold\">LMP<\/mml:mtext>\n                  <\/mml:mrow>\n                <\/mml:mrow>\n                <mml:mo>\u2209<\/mml:mo>\n                <mml:munderover>\n                  <mml:mo>\u220f<\/mml:mo>\n                  <mml:mrow>\n                    <mml:mi>i<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:munderover>\n                <mml:mo stretchy=\"false\">[<\/mml:mo>\n                <mml:msubsup>\n                  <mml:mi>\u03b1<\/mml:mi>\n                  <mml:mi>i<\/mml:mi>\n                  <mml:mrow>\n                    <mml:mo>\u2212<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:msubsup>\n                <mml:mo>,<\/mml:mo>\n                <mml:msubsup>\n                  <mml:mi>\u03b1<\/mml:mi>\n                  <mml:mi>i<\/mml:mi>\n                  <mml:mrow>\n                    <mml:mo>+<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:msubsup>\n                <mml:mo stretchy=\"false\">]<\/mml:mo>\n                <mml:mrow>\n                  <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">)<\/mml:mo>\n                <\/mml:mrow>\n                <mml:mo>,<\/mml:mo>\n              <\/mml:math>\n            <\/jats:disp-formula>\n            where\n            <jats:bold>LMP<\/jats:bold>\n            is the vector of LMPs at the\n            <jats:italic>n<\/jats:italic>\n            power grid nodes, and\n            <jats:bold>\u03b1<\/jats:bold>\n            <jats:sup>\u2212<\/jats:sup>\n            ,\n            <jats:inline-formula>\n              <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                <mml:msup>\n                  <mml:mi mathvariant=\"bold-italic\">\u03b1<\/mml:mi>\n                  <mml:mrow>\n                    <mml:mo>+<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:msup>\n                <mml:mo>\u2208<\/mml:mo>\n                <mml:msup>\n                  <mml:mrow>\n                    <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                  <\/mml:mrow>\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:msup>\n              <\/mml:math>\n            <\/jats:inline-formula>\n            are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply\u2013demand 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.\n          <\/jats:p>\n          <jats:p>This article is part of the theme issue \u2018The mathematics of energy systems\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2019.0438","type":"journal-article","created":{"date-parts":[[2021,6,7]],"date-time":"2021-06-07T07:14:56Z","timestamp":1623050096000},"page":"20190438","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Large fluctuations in locational marginal prices"],"prefix":"10.1098","volume":"379","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1404-6531","authenticated-orcid":true,"given":"T.","family":"Nesti","sequence":"first","affiliation":[{"name":"CWI, Amsterdam 1098 XG, Netherlands"},{"name":"TU\/e, Eindhoven 5612 AZ, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Moriarty","sequence":"additional","affiliation":[{"name":"Queen Mary University, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Zocca","sequence":"additional","affiliation":[{"name":"VU, Amsterdam 1081 HV, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Zwart","sequence":"additional","affiliation":[{"name":"CWI, Amsterdam 1098 XG, Netherlands"},{"name":"TU\/e, Eindhoven 5612 AZ, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2021,6,7]]},"reference":[{"key":"e_1_3_7_2_2","unstructured":"REN21. 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