The effect of transmission-line dynamics on a globally synchronizing controller for power inverters

In this work, we analyze a dispatchable virtual oscillator control (dVOC) strategy for grid-forming power inverters that ensures almost global synchronization of inverterbased AC power systems when the dynamics of the transmission network are neglected, i.e., if an algebraic model of the transmission lines is used. While this approximation is often justified for conventional power systems, the dynamics of the transmission lines can compromise the stability of an inverterbased power system. Therefore, in this article, we use tools from singular perturbation theory to construct a Lyapunov function candidate and explicit bounds on the controller gains that guarantee global convergence to the set of steady-states for the full power-system with transmission line dynamics. Moreover, we show that the only undesirable steady-state is unstable.