A passivity-based approach to voltage stabilization in DC microgrids with ZIP loads

We consider the application of passivity theory to the problem of voltage stabilization in DC microgrids, which are composed of distributed generation units, dynamic RLC lines, and nonlinear ZIP (constant impedance, constant current, and constant power) loads. To this aim, we leverage results on the compositional certification of stability for networks of locally passive systems. More specifically, we consider the decentralized multivariable PI controllers proposed in Tucci et al. (2018), and show that they passivate the generation units and the associated loads under certain conditions. To prove voltage stability in the closed-loop microgrid, we exploit properties of interconnection, passivity of individual components, and the LaSalle's invariance theorem. Moreover, we provide explicit inequalities on control gains to design local controllers. Control synthesis requires only the knowledge of local parameters of the generation units and is always feasible, allowing removal and addition of DGUs in a plug-n-play fashion. Theoretical results are backed up by simulations in PSCAD.