Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators

TL;DR

This paper links power network synchronization to a non-uniform Kuramoto oscillator model, providing algebraic conditions for transient stability and synchronization based on system parameters and initial states.

Contribution

It introduces a novel analysis connecting power system dynamics with non-uniform Kuramoto oscillators, extending existing synchronization methods to more complex models.

Findings

Derived algebraic conditions for synchronization and stability.

Extended Kuramoto synchronization criteria to non-uniform oscillators.

Improved upon existing tests for standard Kuramoto models.

Abstract

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model. Here, non-uniform Kuramoto oscillators are characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying system parameters and initial conditions.