Optimizing Synchronization Stability of the Kuramoto Model in Complex Networks and Power Grids

TL;DR

This paper presents a method to optimize synchronization stability in the Kuramoto model and power grids by minimizing the dominant Lyapunov exponent, leading to improved stability through efficient algorithms and network adjustments.

Contribution

It introduces a novel optimization approach using cut-set space approximation and quasi-Newton methods to enhance synchronization stability in complex networks and power grids.

Findings

Optimized systems show improved synchronization stability.

Method applicable to systems with or without inertia.

Adjusting link coupling strengths enhances stability.

Abstract

Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the dominant Lyapunov exponent. With the help of the recently proposed cut-set space approximation of the steady states, we greatly simplify the objective function, and further derive its gradient and Hessian with respect to natural frequencies, which leads to an efficient algorithm with the quasi-Newton's method. The optimized systems are demonstrated to achieve better synchronization stability for the Kuramoto model with or without inertia in certain regimes. Hence our method is applicable in improving the stability of power grids. It is also viable to adjust the coupling strength of each link to improve the stability of the system. Various operational constraints can also be easily integrated into our scope by employing the interior point method in convex optimization. The properties of the optimized networks are also discussed.