A Structure-Preserving Model and Sufficient Condition for Frequency Synchronization of Lossless Droop Inverter-Based AC Networks

This paper presents a new method for analysis of frequency synchronization of lossless power networks whose sources are frequency-droop controlled inverters. Unlike most existing approaches, our method focuses on the interaction between inverters and the network to provide new physical insight into how those interactions create frequency synchronization. We introduce two structure-preserving models of such a network (one bus-oriented and one line-oriented), and show that frequency synchronization corresponds to convergence to an equilibrium of these models. We derive a necessary condition for existence of such equilibria, and determine a simple test for their local stability. Finally, we introduce a sufficient condition for frequency synchronization of such networks, and show that it consists of a set of local criteria which can each be determined from local measurements.