Abstract: Lyapunov-based stability proofs and passivity-based control (PBC) frameworks guaranteeing asymptotic voltage and frequency convergence in zero-rotational-inertia islanded microgrids.
By defining a global energy-storage function combining magnetic flux linkages, DC link capacitor electrostatics, and virtual rotor kinetic states, we demonstrate that the time derivative of V is strictly negative semi-definite, ensuring robust phase synchronization under arbitrary large load steps.