Small-Signal Stability Condition of Inverter-Integrated Power Systems: Closed-Form Expression by Stationary Power Flow Variables

This paper shows that a necessary and sufficient condition for the small-signal stability of an inverter-integrated power system can be expressed in terms of semidefinite matrix inequalities determined only by the synchronous reactance of the components, the susceptance matrix of the transmission network, and the stationary values of the power flow distribution. To derive the stability condition, we consider a class of grid-forming inverters corresponding to a singular perturbation of the synchronous generator. The resulting matrix inequality condition, which has twice as many dimensions as the number of buses and is independent of the dynamics of the connected components, is expressed in terms of each component compensating in a decentralized manner for the loss of frequency synchronization caused by the reactive power consumption in the transmission network. A simple numerical example using a 3-bus power system model shows that a grid-forming inverter load improves power system synchronization, while a grid-following inverter load disrupts it.