论文标题
关于振荡器的kuramoto型模型的同步与耦合的振荡器模型
On the synchronization of the Kuramoto-type model of oscillators with lossy couplings
论文作者
论文摘要
我们考虑在具有损失耦合的库拉莫托型模型中耦合振荡器同步的问题。 Kuramoto模型已被用来洞悉通常是非线性并涉及大规模互连的功率网络的稳定性。这样的模型通常假设无损耦合和Lyapunov功能主要用于证明稳定性。但是，耦合电导会影响同步。因此，我们考虑了一个更先进的库拉莫托模型，该模型包括耦合电导，并以非均匀耦合权重和非整流耦合图为特征。 Lyapunov的分析一旦包括这种耦合电导和上述特性就变得不平凡，并且更常规的能量样的Lyapunov函数不适用或保守。已经针对此类模型进行了小信号分析，但是由于我们与多种线性化的稳定性分析是根据非线性模型的稳定性分析的。在本文中，我们使用中心歧管理论提供了正式的推导，即如果与耦合电导和感动率相关的平衡点上的特定条件，则所考虑的非线性系统的同步歧管是渐近稳定的。通过模拟证明了我们的分析。
We consider the problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large scale interconnections. Such models commonly assume lossless couplings and Lyapunov functions have predominantly been employed to prove stability. However, coupling conductances can impact synchronization. We therefore consider a more advanced Kuramoto model that includes coupling conductances, and is characterized by nonhomogeneous coupling weights and noncomplete coupling graphs. Lyapunov analysis once such coupling conductances and aforementioned properties are included becomes nontrivial and more conventional energy-like Lyapunov functions are not applicable or are conservative. Small-signal analysis has been performed for such models, but due to the fact that we have convergence to a manifold, stability analysis via a linearization is on its own inconclusive for the nonlinear model. In this paper, we provide a formal derivation using centre manifold theory that if a particular condition on the equilibrium point associated with the coupling conductances and susceptances holds, then the synchronization manifold for the nonlinear system considered is asymptotically stable. Our analysis is demonstrated with simulations.
