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

Xiaoxue Zhao; Zhuchun Li

doi:10.3934/nhm.2020030

Article Contents

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

This issue Previous Article Kinetic modelling of multiple interactions in socio-economic systems Next Article

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

Xiaoxue Zhao^1, and
Zhuchun Li^2, ,

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

^* Corresponding author: Zhuchun Li
^* Corresponding author: Zhuchun Li

Received: July 2019

Revised: September 2019

Early access: September 2020

Published: September 2020

This work was supported by NSF of China grant 11671109. The work of Z. Li was also supported in part by Heilongjiang Provincial Natural Science Foundation of China (grant LH2019A012)

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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.

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Mathematics Subject Classification: 92D25, 34D06.

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References

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