  This article reviews different kinds of models for the electric power grid
that can be used to understand the modern power system, the smart grid. From
the physical network to abstract energy markets, we identify in the literature
different aspects that co-determine the spatio-temporal multilayer dynamics of
power system. We start our review by showing how the generation, transmission
and distribution characteristics of the traditional power grids are already
subject to complex behaviour appearing as a result of the the interplay between
dynamics of the nodes and topology, namely synchronisation and cascade effects.
When dealing with smart grids, the system complexity increases even more: on
top of the physical network of power lines and controllable sources of
electricity, the modernisation brings information networks, renewable
intermittent generation, market liberalisation, prosumers, among other aspects.
In this case, we forecast a dynamical co-evolution of the smart grid and other
kind of networked systems that cannot be understood isolated. This review
compiles recent results that model electric power grids as complex systems,
going beyond pure technological aspects. From this perspective, we then
indicate possible ways to incorporate the diverse co-evolving systems into the
smart grid model using, for example, network theory and multi-agent simulation.
