  We investigate the stability properties of a multi-converter power system
model, defined on a high-order manifold. For this, we identify its symmetry
(i.e., rotational invariance) generated by a static angle shift and rotation of
AC signals. We characterize the steady state set, primarily determined by the
steady state angles and DC power input. Based on eigenvalue conditions of its
Jacobian matrix, we show asymptotic stability of the multi-converter system in
a neighborhood of the synchronous steady state set by applying the center
manifold theory. We guarantee the eigenvalue conditions via an explicit
approach. Finally, we demonstrate our results based on a numerical example
involving a network of identical DC/AC converter systems.
