  We investigate local convergence of identical DC/AC converters interconnected
via identical resistive and inductive lines towards a synchronous equilibrium
manifold. We exploit the symmetry of the resulting vector field and develop a
Lyapunov-based framework, in which we measure the distance of the solutions of
the nonlinear power system model to the equilibrium manifold by analyzing the
evolution of their tangent vectors. We derive sufficient and fully
decentralized conditions to characterize the equilibria of interest, and
provide an estimate of their region of contraction. We provide ways to satisfy
these conditions and illustrate our results based on numerical simulations of a
two-converter benchmark.
