Passivity Conditions for Plug-and-Play Operation of Nonlinear Static AC Loads

Abstract: The complexity arising in AC microgrids from multiple interacting distributed generation units (DGUs) with intermittent supply behavior requires local voltage-source inverters (VSIs) to be controlled in a distributed or decentralized manner at primary level. In (Strehle et al., 2019), we use passivity theory to design decentralized, plug-and-play voltage and frequency controllers for such VSIs. However, the stability analysis of the closed-loop system requires a load-connected topology, in contrast to real grids where loads are arbitrarily located. In this paper, we expand our former approach by considering the more realistic and general case of nonlinear static AC loads (ZIP and exponential) at arbitrary locations within an AC microgrid. Investigating the monotonicity of differentiable mappings, we derive sufficient inequality conditions for the strict passivity of these nonlinear static AC loads. Together with our plug-and-play VSI controller, this allows us to use passivity arguments to infer asymptotic voltage and frequency stability for AC microgrids with arbitrary topologies. An illustrative simulation validating our theoretical findings concludes our work.