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Multistability and anomalies in oscillator models of lossy power grids

Author

Listed:
  • Robin Delabays

    (Center for Control, Dynamical Systems, and Computation, UC Santa Barbara)

  • Saber Jafarpour

    (Center for Control, Dynamical Systems, and Computation, UC Santa Barbara
    School of Electrical and Computer Engineering, Georgia Institute of Technology)

  • Francesco Bullo

    (Center for Control, Dynamical Systems, and Computation, UC Santa Barbara)

Abstract

The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate a close correspondence between stable synchronous states in dissipatively coupled oscillators, and the winding partition of their state space, a geometric notion induced by the network topology. Leveraging this winding partition, we accompany this article with an algorithms to compute all synchronous solutions of complex networks of dissipatively coupled oscillators. These geometric and computational tools allow us to identify anomalous behaviors of lossy networked systems. Counterintuitively, we show that loop flows and dissipation can increase the system’s transfer capacity, and that dissipation can promote multistability. We apply our geometric framework to compute power flows on the IEEE RTS-96 test system, where we identify two high voltage solutions with distinct loop flows.

Suggested Citation

  • Robin Delabays & Saber Jafarpour & Francesco Bullo, 2022. "Multistability and anomalies in oscillator models of lossy power grids," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32931-8
    DOI: 10.1038/s41467-022-32931-8
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    References listed on IDEAS

    as
    1. John W. Simpson-Porco & Florian Dörfler & Francesco Bullo, 2016. "Voltage collapse in complex power grids," Nature Communications, Nature, vol. 7(1), pages 1-8, April.
    2. Frank Hellmann & Paul Schultz & Patrycja Jaros & Roman Levchenko & Tomasz Kapitaniak & Jürgen Kurths & Yuri Maistrenko, 2020. "Network-induced multistability through lossy coupling and exotic solitary states," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
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