A reference frame-based microgrid primary control for ensuring global convergence to a periodic orbit

Power systems with a high penetration of renewable generation are vulnerable to frequency oscillation and voltage instability. Traditionally, the stability of power systems is considered either in terms of local stability or as an angle oscillator synchronization problem with the simplifying assumption that the dynamics of the amplitudes are on much shorter time scales. Without this assumption, however, the steady state being studied is essentially a limit cycle with the convergence of its orbit in question. In this paper, we present a method to analyze the orbital stability of a microgrid and propose a voltage controller for the inverter-interfaced renewable generators. The main hurdle to the problem lies in the constant terms in the rotating internal reference frames of each generator. We extend the shifted passivity of port-Hamiltonian systems to the analysis of limit cycles and prove that, if the system is shifted passive without considering these constant terms, then the periodic orbit is globally attractive. To the best of our knowledge, this is the first global stability result for non-nominal steady states of the microgrid in the full state space, which provides new insights into the synchronization phenomenon where the dissipativity of the system ensures convergence. The proposed controller is verified with a test microgrid, demonstrating its stability and transient smoothness compared to the standard droop control.