[
{
"id": "https://authors.library.caltech.edu/records/bns0y-j6t74",
"eprint_status": "archive",
"datestamp": "2024-02-13 20:24:07",
"lastmod": "2026-03-27 23:59:05",
"type": "conference_item",
"metadata_visibility": "show",
"creators": {
"items": [
{
"id": "Werner-Lucien",
"name": {
"family": "Werner",
"given": "Lucien"
}
},
{
"id": "Christianson-Nicolas",
"name": {
"family": "Christianson",
"given": "Nicolas"
},
"orcid": "0000-0001-8330-8964"
},
{
"id": "Zocca-Alessandro",
"name": {
"family": "Zocca",
"given": "Alessandro"
},
"orcid": "0000-0001-6585-4785"
},
{
"id": "Wierman-A",
"name": {
"family": "Wierman",
"given": "Adam"
},
"orcid": "0000-0002-5923-0199"
},
{
"id": "Low-S-H",
"name": {
"family": "Low",
"given": "Steven"
},
"orcid": "0000-0001-6476-3048"
}
]
},
"title": "Pricing Uncertainty in Stochastic Multi-Stage Electricity Markets",
"ispublished": "unpub",
"full_text_status": "public",
"note": "© 2023 IEEE.
\n\nThe authors thank Subhonmesh Bose (UIUC), Nathan Dahlin (UIUC), and Feng Zhao (ISO NE) for insightful conversations. The authors acknowledge support from NSF Graduate Research Fellowship (DGE-1745301), NSF grants CNS-2146814, CPS-2136197, CNS-2106403, NGSDI-2105648, ECCS 1931662, ECCS 1932611, and Caltech Resnick Sustainability Institute and S2I grants.
",
"abstract": "\n
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This work proposes a pricing mechanism for multi-stage electricity markets that does not explicitly depend on the choice of dispatch procedure or optimization method. Our approach is applicable to a wide range of methodologies for the economic dispatch of power systems under uncertainty, including multi-interval dispatch, multi-settlement markets, scenario-based dispatch, and chance-constrained dispatch policies. We prove that our pricing scheme provides both ex-ante and expost dispatch-following incentives by simultaneously supporting per-stage and ex-post competitive equilibria. In numerical experiments on a ramp-constrained test system, we demonstrate the benefits of scheduling under uncertainty and show how our price decomposes into components corresponding to energy, intertemporal coupling, and uncertainty.
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© 2023 IEEE.
\n\nThe work of B. Fang and C. Zhao was supported by Hong Kong Research Grants Council through grant GRF 14212822. The work of S. H. Low was supported by US NSF through grants ECCS 1931662, ECCS 1932611, and Caltech’s Resnick Sustainability Institute and S2I grants.
",
"abstract": "\n
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Solving power flow is perhaps the most fundamental calculation related to the steady state behavior of alternating-current (AC) power systems. The normally radial (tree) topology of a distribution network induces a spatially recursive structure in power flow equations, which enables a class of efficient solution methods called backward/forward sweep (BFS). In this paper, we revisit BFS from a new perspective, focusing on its convergence. Specifically, we describe a general formulation of BFS, interpret it as a special Gauss-Seidel algorithm, and then illustrate it in a single-phase power flow model. We prove a sufficient condition under which the BFS is a contraction mapping on a closed set of safe voltages and thus converges geometrically to a unique power flow solution. We verify the convergence condition, as well as the accuracy and computational efficiency of BFS, through numerical experiments in IEEE test systems.
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We thank the US NSF for its support through grants ECCS 1931662, ECCS 1932611, and Caltech’s Resnick Sustainability Institute and S2I grants.
\n\n© 2023 IEEE.
",
"abstract": "\n
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In this tutorial we present a simple approach to modeling unbalanced three-phase power flows. We allow general non-ideal models of voltage sources, ZIP loads as well as distribution lines and transformers. The basic idea is to explicitly separate a device/transformer model into an internal model, that depends on the characteristics of the single-phase devices or transformers, and a conversion rule, that depends on their configuration. This approach provides two benefits. First it facilitates the modeling of secondary distribution circuits where only the end devices are directly controllable, not the currents or powers at the secondary transformers. Second it allows us to exploit common structures across different device/transformer variants and derive their external models that are general and unified. We illustrate these benefits by extending a three-phase backward forward sweep method in the literature to allow secondary circuits and formulating a three-phase optimal power flow problem as a quadratically constrained quadratic program.
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