  We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has natural links to classical stability theories of interconnected systems. We find stability conditions descending from a particular Lyapunov function involving an oblique projection onto the complement of the synchronous steady state set and enjoying insightful structural properties. Our sufficient and explicit stability conditions can be evaluated in a fully decentralized fashion, reflect a parametric dependence on the converter's steady-state variables, and can be one-to-one generalized to other types of systems exhibiting the same behavior, such as synchronous machines. Our conditions demand for sufficient reactive power support and resistive damping. These requirements are well aligned with practitioners' insights. 
Parametric local stability condition of a multi-converter system