Abstract
Transmission line failures in power systems propagate non-locally, making the control of the resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes the patterns of line failure propagation and localization in terms of network graph structure. It provides a novel perspective on distribution factors that precisely captures Kirchhoff's Law in terms of topological structures. Our results show that the distribution of specific collections of subtrees of the transmission network plays a critical role on the patterns of power redistribution, and motivates the block decomposition of the transmission network as a structure to understand long-distance propagation of disturbances. In Part I of this paper, we present the case when the post-contingency network remains connected after an initial set of lines are disconnected simultaneously. In Part II, we present the case when an outage separates the network into multiple islands.
Highlights
C ASCADING failures in power systems propagate nonlocally, making their analysis and mitigation difficult
We focus on transmission line failures and take a different approach that leverages the spectral representation of transmission network topology to establish several structural properties
We show how specific topological structures naturally emerge in the analysis of several important and well-studied quantities in power system contingency analysis, such as the generation shift sensitivity factors and the line outage redistribution factors
Summary
C ASCADING failures in power systems propagate nonlocally, making their analysis and mitigation difficult. GUO et al.: LINE FAILURE LOCALIZATION OF POWER NETWORKS PART I: NON-CUT OUTAGES lack of structural properties is a key challenge in the modeling, control, and mitigation of cascading failures in power systems. Contributions of this paper: We establish a mathematical theory that characterizes line failure localization properties of power systems This theory makes crucial use of the weighted Laplacian matrix of a transmission network and its spectral properties. We establish a new set of graphical representations of generation shift sensitivity factors and line outage distribution factors in contingency analysis This novel graph-theoretical viewpoint enables us to derive precise algebraic properties of power redistribution using purely graphical argument, and shows that disturbances propagate through “subtrees” in a power network. This technique can be synergistically applied, or sometimes replace, controlled islanding (see e.g. [31]–[39]) as a corrective action, in which an inter-connected power system will be partitioned into multiple blocks after a contingency that are connected by either bridges or cut vertices. By not separating the system into multiple islands, more loads can potentially be supported in the emergency state, more reliably, until restoration
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