Analysis of transient stability of coupled Kuramoto oscillators with asymmetric time delays and phase shifts

Author(s):  
Helang Xiong ◽  
Hua Zhang
1989 ◽  
Vol 2 (1-2) ◽  
pp. 9-18 ◽  
Author(s):  
Fernando Lopes da Silva ◽  
Jan Pieter Pijn ◽  
Peter Boeijinga

Author(s):  
Spase Petkoski ◽  
Viktor K. Jirsa

The timing of activity across brain regions can be described by its phases for oscillatory processes, and is of crucial importance for brain functioning. The structure of the brain constrains its dynamics through the delays due to propagation and the strengths of the white matter tracts. We use self-sustained delay-coupled, non-isochronous, nonlinearly damped and chaotic oscillators to study how spatio-temporal organization of the brain governs phase lags between the coherent activity of its regions. In silico results for the brain network model demonstrate a robust switching from in- to anti-phase synchronization by increasing the frequency, with a consistent lagging of the stronger connected regions. Relative phases are well predicted by an earlier analysis of Kuramoto oscillators, confirming the spatial heterogeneity of time delays as a crucial mechanism in shaping the functional brain architecture. Increased frequency and coupling are also shown to distort the oscillators by decreasing their amplitude, and stronger regions have lower, but more synchronized activity. These results indicate specific features in the phase relationships within the brain that need to hold for a wide range of local oscillatory dynamics, given that the time delays of the connectome are proportional to the lengths of the structural pathways. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.


2021 ◽  
Vol 104 (5) ◽  
Author(s):  
Erik Gustafson ◽  
Yingyue Zhu ◽  
Patrick Dreher ◽  
Norbert M. Linke ◽  
Yannick Meurice

2011 ◽  
Vol 13 (9) ◽  
pp. 093025 ◽  
Author(s):  
Shawn A Hilbert ◽  
Adam Caprez ◽  
Herman Batelaan

1999 ◽  
Vol 111 (24) ◽  
pp. 10934-10956 ◽  
Author(s):  
Allison W. Albrecht ◽  
John D. Hybl ◽  
Sarah M. Gallagher Faeder ◽  
David M. Jonas

Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2181
Author(s):  
Haris E. Psillakis ◽  
Antonio T. Alexandridis

In this paper, we present a nonlinear coordinated excitation and static var compensator (SVC) control for regulating the output voltage and improving the transient stability of a synchronous generator infinite bus (SGIB) power system. In the first stage, advanced nonlinear methods are applied to regulate the SVC susceptance in a manner that can potentially improve the overall transient performance and stability. However, as distant from the generator measurements are needed, time delays are expected in the control loop. This fact substantially complicates the whole design. Therefore, a novel design is proposed that uses backstepping methodologies and feedback linearization techniques suitably modified to take into account the delayed measurement feedback laws in order to implement both the excitation voltage and the SVC compensator input. A detailed and rigorous Lyapunov stability analysis reveals that if the time delays do not exceed some specific limits, then all closed-loop signals remain bounded and the frequency deviations are effectively regulated to approach zero. Applying this control scheme, output voltage changes occur after the large power angle deviations have been eliminated. The scheme is thus completed, in a second stage, by a soft-switching mechanism employed on a classical proportional integral (PI) PI voltage controller acting on the excitation loop when the frequency deviations tend to zero in order to smoothly recover the output voltage level at its nominal value. Detailed simulation studies verify the effectiveness of the proposed design approach.


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