Chris DeMarco Participated at the 2013 DIMACS Workshop: http://dimacs.rutgers.edu/Workshops/Cascading/program.html
Title and Abstract: Lyapunov Functions to Characterize Cascading Failure Vulnerability in Dynamic Power Grid Models
Christopher L. DeMarco and Honghao Zheng,
University of Wisconsin-Madison
In an electric power network experiencing a transient following some initial disturbance, relay actions interrupting transmission lines or disconnecting generators may create further transient over-current in other lines or over-frequency in other generators. Relay actions that disconnect equipment in response to such overloads may induce cascading equipment disconnection, and possibly system wide outage. Full time domain simulations to credibly examine the wide range of possible switching actions that can lead to cascading failure events under transient conditions is extremely costly. To address these problems, this work extends prior results on bi-stable models of transmission line over-current relays, to now also include generator disconnection under the action of over/under-frequency relays. By incorporating such relay action in a smooth dynamic model, the problem becomes amenable to analytic stability analysis, with new insights and computational efficiencies to be gained. In particular, partially degraded network configurations appear as multiple equilibria in this augmented transient stability model, and vulnerability to transition to a degraded configuration may be quantified via a closed form “energy-like” Lyapunov function. This work develops the model, and demonstrates the construction of the associated Lyapunov function, confirming this function to be locally positive definite about stable equilibria and non-increasing along system trajectories (including trajectories that capture the relay action). This work is intended as a first step to demonstrate the promise for Lyapunov methods to contribute to cascading failure analysis. As one application, we suggest that short duration simulation be augmented with a computationally inexpensive Lyapunov function threshold test, to yield a sufficient condition for a post-disturbance state to be “captured” in the potential well about a partially degraded stable equilibrium, thereby ensuring no further line or generator outages can occur along the remaining portion of the trajectory.