Stability analysis for coupled synchronous generators with virtual friction

We investigate the stability of a microgrid composed of two identical synchronous generators, inductive lines and resistive loads, without using any model reduction for 'fast' variables. We derive sufficient conditions for local exponential stability, with a region of attraction that includes any initial state such that the states of the generators are sufficiently close to each other. This implies that if by some control technique we can bring the angular velocities close enough, regardless how far the system is from the equilibrium state, then the generators will synchronize. Such a control technique is the recently introduced virtual friction, that is easiest to apply on synchronverters, which behave like synchronous generators. Virtual friction necessitates fast communication lines between the synchronverters (typically over a long distance) so that they can communicate their instantaneous angular velocities to each other. The mathematical model described is the simplest possible model of a two-area network that may be affected by inter-area oscillations, that need to be damped.