Cascading Failures in Power Grids - Analysis and Algorithms

This paper focuses on cascading line failures in the transmission system of the power grid. Recent large-scale power outages demonstrated the limitations of percolation- and epid- emic-based tools in modeling cascades. Hence, we study cascades by using computational tools and a linearized power flow model. We first obtain results regarding the Moore-Penrose pseudo-inverse of the power grid admittance matrix. Based on these results, we study the impact of a single line failure on the flows on other lines. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We then study the cascade properties, considering metrics such as the distance between failures and the fraction of demand (load) satisfied after the cascade (yield). We use the pseudo-inverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the set of lines whose removal has the most significant impact (under various metrics) is NP-Hard and introduce a simple heuristic for the minimum yield problem. Overall, the results demonstrate that using the resistance distance and the pseudo-inverse of admittance matrix provides important insights and can support the development of efficient algorithms

Network hierarchy evolution and system vulnerability in power grids

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from a complex-systems point of view are given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. First, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Second, an antipyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex-systems point of view.Peer ReviewedPostprint (author's final draft

Spatial and performance optimality in power distribution networks

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Complex network theory has been widely used in vulnerability analysis of power networks, especially for power transmission ones. With the development of the smart grid concept, power distribution networks are becoming increasingly relevant. In this paper, we model power distribution systems as spatial networks. Topological and spatial properties of 14 European power distribution networks are analyzed, together with the relationship between geographical constraints and performance optimization, taking into account economic and vulnerability issues. Supported by empirical reliability data, our results suggest that power distribution networks are influenced by spatial constraints which clearly affect their overall performance.Peer ReviewedPostprint (author's final draft