Partial synchronization in the second-order Kuramoto model: An auxiliary system method

2021 ◽  
Vol 31 (11) ◽  
pp. 113113
Author(s):  
Nikita V. Barabash ◽  
Vladimir N. Belykh ◽  
Grigory V. Osipov ◽  
Igor V. Belykh
Keyword(s):  
Second Order ◽  
Kuramoto Model ◽  
Auxiliary System ◽  
Partial Synchronization ◽  
System Method ◽  
Auxiliary System Method

scholarly journals Generalized Outer Synchronization between Complex Networks with Unknown Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Di Ning ◽  
Xiaoqun Wu ◽  
Jun-an Lu ◽  
Hui Feng
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Sufficient Criterion ◽  
Unknown Parameters ◽  
Outer Synchronization ◽  
Functional Relations ◽  
System Method ◽  
Barbalat’S Lemma ◽  
Auxiliary System Method ◽  
Theoretical Results

As is well known, complex networks are ubiquitous in the real world. One network always behaves differently from but still coexists in balance with others. This phenomenon of harmonious coexistence between different networks can be termed as “generalized outer synchronization (GOS).” This paper investigates GOS between two different complex dynamical networks with unknown parameters according to two different methods. When the exact functional relations between the two networks are previously known, a sufficient criterion for GOS is derived based on Barbalat's lemma. If the functional relations are not known, the auxiliary-system method is employed and a sufficient criterion for GOS is derived. Numerical simulations are further provided to demonstrate the feasibility and effectiveness of the theoretical results.

Power System Transient Stability Analysis via Second-Order Non-Uniform Kuramoto Model

2014 ◽  
Vol 960-961 ◽  
pp. 1054-1057
Author(s):  
Liu Yang ◽  
Yu Feng Guo ◽  
Ning Chen ◽  
Min Hui Qian ◽  
Xiao Ping Xue ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Power System ◽  
Transient Stability ◽  
Stable Equilibrium ◽  
Stability Margin ◽  
Second Order ◽  
Kuramoto Model ◽  
Trapping Region ◽  
Novel Approach ◽  
Transient Stability Analysis

Based on frequency synchronization theory of the second-order non-uniform Kuramoto model, a novel approach for power system transient stability analysis is put forward by establishing the correspondence between the classic power system model and the second-order non-uniform Kuramoto model. This method relates network parameters with the region of attraction of the disturbed system’s stable equilibrium and thus the transient stability information of the disturbed system can be obtained by comparing the initial configuration with trapping region of the stable equilibrium of the disturbance-canceling system. The application of our approach to single machine infinite bus system shows that this method features a fast computation speed. It can determine the transient stability of the system when a certain perturbation acts on as well as offer the stability margin of the disturbed system, which is of great importance for practical use.

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