  This paper examines small-signal stability of electrical networks composed
dominantly of three-phase grid-following inverters. We show that the mere
existence of a high-voltage power flow solution does not necessarily imply
small-signal stability; this motivates us to develop a framework for stability
analysis that systematically acknowledges inverter dynamics. We identify a
suitable time-scale decomposition for the inverter dynamics, and using singular
perturbation theory, obtain an analytic sufficient condition to verify
small-signal stability. Compared to the alternative of performing an eigenvalue
analysis of the full-order network dynamics, our analytic sufficient condition
reduces computational complexity and yields insights on the role of network
topology and constitution as well as inverter-filter and control parameters on
small-signal stability. Numerical simulations for a radial network validate the
approach and illustrate the efficiency of our analytic conditions for designing
and monitoring grid-tied inverter networks.
