Stochastic Model for Power Grid Dynamics

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy...Comment: framework for a system-level analysis of the power grid from the viewpoint of complex network

Modelling interdependencies between the electricity and information infrastructures

The aim of this paper is to provide qualitative models characterizing interdependencies related failures of two critical infrastructures: the electricity infrastructure and the associated information infrastructure. The interdependencies of these two infrastructures are increasing due to a growing connection of the power grid networks to the global information infrastructure, as a consequence of market deregulation and opening. These interdependencies increase the risk of failures. We focus on cascading, escalating and common-cause failures, which correspond to the main causes of failures due to interdependencies. We address failures in the electricity infrastructure, in combination with accidental failures in the information infrastructure, then we show briefly how malicious attacks in the information infrastructure can be addressed

Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology

In a cascading power transmission outage, component outages propagate non-locally, after one component outages, the next failure may be very distant, both topologically and geographically. As a result, simple models of topological contagion do not accurately represent the propagation of cascades in power systems. However, cascading power outages do follow patterns, some of which are useful in understanding and reducing blackout risk. This paper describes a method by which the data from many cascading failure simulations can be transformed into a graph-based model of influences that provides actionable information about the many ways that cascades propagate in a particular system. The resulting "influence graph" model is Markovian, in that component outage probabilities depend only on the outages that occurred in the prior generation. To validate the model we compare the distribution of cascade sizes resulting from $n-2$ contingencies in a $2896$ branch test case to cascade sizes in the influence graph. The two distributions are remarkably similar. In addition, we derive an equation with which one can quickly identify modifications to the proposed system that will substantially reduce cascade propagation. With this equation one can quickly identify critical components that can be improved to substantially reduce the risk of large cascading blackouts.Comment: Accepted for publication at the IEEE Transactions on Power System