Ultimate boundedness and regions of attraction of frequency droop controlled microgrids with secondary control loops

In this paper we study theoretical properties of the frequency control problem in inverter-based microgrids with primary and decentralised/distributed secondary control loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of attraction is guaranteed under a condition on the power mismatch between demand and generation at each inverter bus. An estimate of the region of attraction is obtained from which an ultimate bound set for the state trajectories can be determined by recursive iterations of a nonlinear mapping. The derived results provide a certificate of the overall stability and performance of the controlled microgrid.