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

Xiaoxue Zhao, ,School of Mathematics, Harbin Institute of Technology, Harbin 150001, China, Zhuchun Li, ,School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China
2020 Networks and Heterogeneous Media  
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
more » ... based on the monotonicity arguments of extremal phase and frequency. 2020 Mathematics Subject Classification. 92D25, 34D06.
doi:10.3934/nhm.2020030 fatcat:uutwj7f6lfegpifreu52tvcmcq