Models for the modern power grid

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.     

Dynamic stability of externally pressurized elastic rings subjected to high rates of loading

Of interest here is the influence of loading rate on the stability of structures where inertia is taken into account, with particular attention to the comparison between static and dynamic buckling. This work shows the importance of studying stability via perturbations of the initial conditions, since a finite velocity governs the propagation of disturbances. The method of modal analysis that determines the fastest growing wavelength, currently used in the literature to analyze dynamic stability problems, is meaningful only for cases where the velocity of the perfect structure is significantly lower than the associated wave propagation speeds.