  Symmetries are widespread in physical, technological, biological, and social
systems and networks, including power grids. The swing equation is a classic
model for the dynamics of powergrid networks. The main goal of this paper is to
explain how network symmetries affect the swing equation transient and steady
state dynamics. We introduce a modal decomposition that allows us to study
transient effects, such as the presence of overshoots in the system response.
This modal decomposition provides insight into the peak flows within the
network lines and allows a rigorous characterization of the effects of
symmetries in the network topology on the dynamics. Our work applies to both
cases of homogeneous and heterogeneous parameters. Further, the model is used
to show how small perturbations propagate in networks with symmetries. Finally,
we present an application of our approach to a large power grid network that
displays symmetries.

Systems and Control;Systems and Control;Adaptation and Self-Organizing Systems