  This paper proposes a novel two-stage hybrid domain decomposition algorithm
to speed up the dynamic simulations and the analysis of power systems that can
be computationally demanding due to the high penetration of renewables. On the
first level of the decomposition, a Schwarz-based strategy is used to decouple
the original problem into various subsystems through boundary variable
relaxation, while on the second level, each decoupled subsystem is further
decomposed into subdomains that are solved independently using the
Schur-complement approach. Convergence is checked in both stages to ensure that
the parallelized implementation of the subsystems can produce identical results
to the original problem. The proposed approach is tested on an IEEE 9 bus
system in which one synchronous generator is replaced with a solar PV farm
through a grid-forming inverter (GFM) with an admittance control method to
evaluate its effectiveness and applicability for large-scale and
very-large-scale implementations. Since conventional dual-loop GFMs are not
stable when connecting to a stronger grid with a small grid inductance, a
virtual inductance method is adopted to increase the equivalent inductance
connecting the grid to enhance stability.
