Dynamic stability of electric power grids: Tracking the interplay of the network structure, transmission losses, and voltage dynamics

Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stabilitycriteria focusing on the interplay of network structures and the local dynamics of synchronous machines. The results are based on an extensivelinear stability analysis of the third-order model for synchronous machines, comprising the classical power-swing equations and the voltagedynamics. The article addresses the impact of Ohmic losses, which are important in distribution and microgrids but often neglected inanalytical studies. We compute the shift of the stability boundaries to leading order, and thus provide a detailed qualitative picture of theimpact of Ohmic losses. A subsequent numerical study of the criteria is presented, without and with resistive terms, to test how tight thederived analytical results are