Journal
IEEE TRANSACTIONS ON POWER SYSTEMS
Volume 36, Issue 5, Pages 4140-4151Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TPWRS.2021.3066336
Keywords
Transmission line matrix methods; Power system protection; Power system faults; Matrix decomposition; Mathematical model; Laplace equations; Power transmission lines; Cascading failure; contingency analysis; laplacian matrix; spanning forests
Categories
Funding
- Resnick Fellowship
- Linde Institute Research Award
- NWO Rubicon [680.50.1529]
- NSF [CCF 1637598, ECCS 1619352, ECCS 1931662, CNS 1545096, CNS 1518941, CPS ECCS 1739355, CPS 154471]
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The propagation of transmission line failures in power systems is non-local, making it extremely difficult to control the resulting outages. The distribution of specific collections of subtrees in the transmission network plays a critical role in the patterns of power redistribution.
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.
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