  Voltage and frequency control in an islanded AC microgrid (ImGs) amount to
stabilizing an a priori unknown ImG equilibrium induced by loads and changes in
topology. This paper puts forth a unified control framework which, while
guaranteeing such stability, allows for modular ImGs interconnecting multiple
subsystems, that is, dynamic RLC lines, nonlinear constant impedance, current,
power (ZIP) and exponential (EXP) loads, and inverter-based distributed
generation units (DGUs) controlled with different types of primary controllers.
The underlying idea of the framework is based one equilibrium-independent
passivity (EIP) of the ImG subsystems, which enables stability certificates of
ImG equilibria without their explicit knowledge. In order to render DGUs EIP,
we propose a decentralized controller synthesis algorithm based on
port-Hamiltonian systems (PHSs). We also show that EIP, being the key to
stability, provides a general framework which can embrace other solutions
available in the literature. Furthermore, we provide a novel argument based on
LaSalle's theorem for proving asymptotic voltage and frequency stability.
Finally, we analyze the impact of actuator saturation on the stability results
by exploiting the inherent EIP properties of the PHS DGU model. Theoretical
findings are backed up by realistic simulations based on the CIGRE benchmark
for medium voltage networks.
