Synchronization in adaptive Kuramoto oscillators for power grids with dynamic voltages

In this paper we are concerned with a coupled system of Kuramoto oscillators for power grids with dynamic voltages. Among various models describing the dynamics of synchronous generators, analytic results are available mainly for the second-order model with constant voltages which describes only the dynamics of rotor angles. It is known that two of the most important forms for power system stability are rotor angle stability and voltage stability. Schmietendorf et al (2014 Eur. Phys. J. 223 2577-2592) derived a model of adaptive Kuramoto oscillators for the power grids with dynamic voltages and carried out some numerical studies. In this model, the transient dynamics of voltages is incorporated and the voltage dynamics could be considered together with rotor angle dynamics. In this article, we will consider this model and derive some analytic results for the synchronization of phase angles and stabilization of voltages. We will find a region of attraction for a class of steady states which is explicitly expressed in the parameters of system.