Synchronization Conditions for a Third-order Kuramoto Network

This paper presents synchronization conditions for a third-order Kuramoto network, which is inspired by a transient model of the electric power network. In this model, the amplitude dynamics of oscillators are introduced into a conventional second-order Kuramoto network. By using an energy function method, we propose sufficient conditions on the initial configurations of a Kuramoto network to determine the stability of phases and amplitudes of oscillators. Then, we show that these conditions ensure the synchronization in frequencies and phases of oscillators. Furthermore, an algorithm is designed to calculate an ultimate bound for the phase differences of oscillators at synchronized state, which evaluates overall network synchronization performance.