Frequency Synchronization of a High-Order Multiconverter System

We investigate the frequency stability of a high-order multi-converter system. For this, we identify its symmetry (i.e., rotational invariance) generated by a static angle shift and rotation of ac signals. We characterize the synchronous 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 frequency synchronous steady-state set by applying the center manifold theory. We guarantee the Jacobian's eigenvalue condition via an explicit approach that requires sufficient damping on the dc and ac side. Finally, we demonstrate our results based on a numerical example involving a network of dc/ac converters.