# Non-Stationary Random Process for Large-Scale Failure and Recovery of Power Distribution

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This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.

KEYWORDS

Resilience, Non-Stationary Random Process, Power Distribution, Dynamic Queue, Transient Little’s Law, Real Data

Cite this paper

Wei, Y. , Ji, C. , Galvan, F. , Couvillon, S. , Orellana, G. and Momoh, J. 2016 Non-Stationary Random Process for Large-Scale Failure and Recovery of Power Distribution. Applied Mathematics, 7, 233-249. doi: 10.4236-am.2016.73022.

Author: Yun Wei1*, Chuanyi Ji1, Floyd Galvan2, Stephen Couvillon2, George Orellana2, James Momoh3

Source: http://www.scirp.org/