A Fast and Accurate Approximation Algorithm for Failure Frequency of Power Distribution Systems

This paper considers the problem of approximating the failure frequency of power distribution systems modeled as k-terminal reliability systems. In such systems, the nodes (i.e., buses), among which k nodes are terminals (i.e., generation and load buses), are connected via components (i.e., lines) that are subject to random failure and repair processes. Any time the surviving system fails to connect all terminals, a system failure occurs. Assuming that the up-times and down-times of each component follow statistically independent stationary random processes, and these processes are statistically independent across the components, the exact computation of failure frequency is known to be intractable (NP-hard). In this work, we propose a randomized algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of cutsets in the system, and has an arbitrarily small error probability. We illustrate the application of the proposed algorithm by simulating the distribution system of Micropolis, a virtual city designed to represent a typical small community in the United States. Our simulation results confirm that the proposed algorithm is faster and more accurate than the standard Monte Carlo simulation for approximating the failure frequency.