Comparisons of purely topological model, betweenness based model and direct current power flow model to analyze power grid vulnerability

Abstract

This paper selects three frequently used power grid models, including a purely topological model (PTM), a betweennness based model (BBM), and a direct current power flow model (DCPFM), to describe three different dynamical processes on a power grid under both single and multiple component failures. Each of the dynamical processes is then characterized by both a topology-based and a flow-based vulnerability metrics to compare the three models with each other from the vulnerability perspective. Taking as an example, the IEEE 300 power grid with line capacity set proportional to a tolerance parameter tp, the results show non-linear phenomenon: under single node failures, there exists a critical value of tp = 1.36, above which the three models all produce identical topology-based vulnerability results and more than 85% nodes have identical flow-based vulnerability from any two models; under multiple node failures that each node fails with an identical failure probability fp, there exists a critical fp = 0.56, above which the three models produce almost identical topology-based vulnerability results at any tp ≥ 1, but producing identical flow-based vulnerability results only occurs at fp = 1. In addition, the topology-based vulnerability results can provide a good approximation for the flow-based vulnerability under large fp, and the priority of PTM and BBM to better approach the DCPFM for vulnerability analysis mainly depends on the value of fp. Similar results are also found for other failure types, other system operation parameters, and other power grids. © 2013 AIP Publishing LLC.