Monotonicity Properties and Spectral Characterization of Power Redistribution in Cascading Failures
In this work, we apply spectral graph theory methods to study the monotonicity and structural properties of power redistribution in a cascading failure process. We demonstrate that in contrast to the lack of monotonicity in physical domain, there is a rich collection of monotonicity one can explore in the spectral domain, leading to a systematic way to define topological metrics that are monotonic. It is further shown that many useful quantities in cascading failure analysis can be unified into a spectral inner product, which itself is related to graphical properties of the transmission network. Such graphical interpretations precisely capture the Kirchhoff's law expressed in terms of graph structural properties and gauge the impact of a line when it is tripped.
Copyright is held by author/owner(s). This work has been supported by NSF grants through CCF 1637598, ECCS 1619352, CNS 1545096, ARPA-E grants through award DE-AR0000699 (NODES) and GRID DATA, DTRA grant through HDTRA 1-15-1-0003 and Skoltech grant through collaboration agreement 1075-MRA.