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• W2912602146 abstract "The phenomenon of multistability, in which systems have multiple stable operating points, is central to power grid operations like optimal power flow and transient stability. Transitions between stable states may create undesirable circulating flows and lead to inefficiencies and blackouts. Unfortunately, it is not yet fully understood how many stable states exist, how to characterize them, and how to compute them efficiently. A deeper understanding of multistability, including its dependence upon network structures and power transmission, may lead to more reliable and efficient power flows in future grids. This paper provides a rigorous and comprehensive framework for studying the multistability of active power flows in lossless grids. This problem is equivalent to both the equilibrium analysis of the coupled swing equations and the synchronization problem for Kuramoto oscillators. The proposed framework is based on a novel of the $n$-torus into winding cells, defined by Kirchhoff's angle law for undirected graphs. The winding partition possesses several useful properties, including notably that each winding cell contains at most one equilibrium power flow solution. This paper also proposes a complete algorithm to compute these equilibrium points using a novel contraction mapping. Finally, we apply our results to numerically study multistability in several tests cases and estimate power capacity and congestion." @default.
• W2912602146 created "2019-02-21" @default.
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• W2912602146 date "2019-01-31" @default.
• W2912602146 modified "2023-09-27" @default.
• W2912602146 title "Multistable Synchronous Power Flows: From Geometry to Analysis and Computation" @default.
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• W2912602146 hasPublicationYear "2019" @default.
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