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000872568 1001_ $$00000-0002-3620-9012$$aBalestra, Chiara$$b0
000872568 245__ $$aMultistability in lossy power grids and oscillator networks
000872568 260__ $$aWoodbury, NY$$bAmerican Institute of Physics$$c2019
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000872568 520__ $$aNetworks of phase oscillators are studied in various contexts, in particular in the modeling of the electric power grid. A functional grid corresponds to a stable steady state, such that any bifurcation can have catastrophic consequences up to a blackout. But also the existence of multiple steady states is undesirable, as it can lead to  transitions or circulatory flows. Despite the high practical importance there is still no general theory of the existence and uniqueness of steady states in such systems. Analytic results are mostly limited to grids without Ohmic losses. In this article, we introduce a method to systematically construct the solutions of the real power load-flow equations in the presence of Ohmic losses and explicitly compute them for tree and ring networks. We investigate different mechanisms leading to multistability and discuss the impact of Ohmic losses on the existence of solutions.
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000872568 7001_ $$0P:(DE-Juel1)176610$$aKaiser, Franz$$b1
000872568 7001_ $$0P:(DE-HGF)0$$aManik, Debsankha$$b2
000872568 7001_ $$0P:(DE-Juel1)162277$$aWitthaut, Dirk$$b3$$eCorresponding author
000872568 773__ $$0PERI:(DE-600)1472677-4$$a10.1063/1.5122739$$gVol. 29, no. 12, p. 123119 -$$n12$$p123119 -$$tChaos$$v29$$x1089-7682$$y2019
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