Steady state characterization and frequency synchronization of a multi-converter power system on high-order manifolds

We investigate the stability properties of a multi-converter power system model, defined on high-order manifolds than the circle. For this, we identify its symmetry (i.e., rotational invariance) generated by a static angle shift and rotation of AC signals and define a suitable equivalence class for the quotient space. Based on its Jacobian matrix, we characterize the quotient non-degenerate, stable and unstable steady state sets, primarily determined by their steady state angles and DC power input. We show that local contraction is achieved on a well-defined region of the space, based on a differential Lyapunov framework and Finsler distance measure. We demonstrate our results based on a numerical example involving three identical DC/AC converter bunchmark