An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

The Integration of Electricity from Renewable Energy Sources in the European Union Electricity Market – The case for “Smart Grids”

The power sector is to play a central role in a low carbon economy. In all the decarbonisation scenarios of the European Union renewable energy sources (RES) will be a crucial part of the solution. Current grids constitute however major bottlenecks for the future expansion of RES. Recognising the need for a modernisation of its grids, the European Union has called for the creation of a "smart supergrid" interconnecting European grids at the continental level and making them "intelligent" through the addition of information and communication technology (ICT). To implement its agenda the EU has taken a leading role in coordinating research efforts and creating a common legislative framework for the necessary modernisation of Europe’s grids. This paper intends to give both an overview and a critical appraisal of the measures taken so far by the European Union to "transform" the grids into the backbone of a decarbonised electricity system. It suggests that if competition is to play a significant role in the deployment of smart grids, the current regulatory paradigm will have to be fundamentally reassessed