Synchronization of a Kuramoto-like model for power grids with frustration

Xiaoxue Zhao; Zhuchun Li; Xiaoxue Zhao; Zhuchun Li

doi:10.3934/nhm.2020030

Networks and Heterogeneous Media

2020, Volume 15, Issue 3: 543-553. doi: 10.3934/nhm.2020030

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Synchronization of a Kuramoto-like model for power grids with frustration

Xiaoxue Zhao ^{1
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Zhuchun Li ^{2
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1.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received: 01 July 2019 Revised: 01 September 2019 Published: 09 September 2020
92D25, 34D06

We discuss the complete synchronization for a Kuramoto-like model for power grids with frustration. For identical oscillators without frustration, it will converge to complete phase and frequency synchronization exponentially fast if the initial phases are distributed in a half circle. For nonidentical oscillators with frustration, we present a framework leading to complete frequency synchronization where the initial phase configurations are located inside the half of a circle. Our estimates are based on the monotonicity arguments of extremal phase and frequency.
- Synchronization,
- Kuramoto-like model,
- frustration,
- power grids
Citation: Xiaoxue Zhao, Zhuchun Li. Synchronization of a Kuramoto-like model for power grids with frustration[J]. Networks and Heterogeneous Media, 2020, 15(3): 543-553. doi: 10.3934/nhm.2020030

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Abstract

We discuss the complete synchronization for a Kuramoto-like model for power grids with frustration. For identical oscillators without frustration, it will converge to complete phase and frequency synchronization exponentially fast if the initial phases are distributed in a half circle. For nonidentical oscillators with frustration, we present a framework leading to complete frequency synchronization where the initial phase configurations are located inside the half of a circle. Our estimates are based on the monotonicity arguments of extremal phase and frequency.

References

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