Group-Testing on Hypergraphs with Variable-Cost Tests: A Power Systems Case Study

Abstract: Assessing risk of cascading failure in an electrical grid requires identifying many small "defective" subsets of the N elements in a power system, such that the simultaneous failure of all elements in a defective set triggers a large cascading blackout. Most supersets of defective sets will also initiate cascades. This property was leveraged by Random Chemistry (RC), a state-of-the-art algorithm for efficiently finding minimal defective sets. While not previously acknowledged as such, RC is a group-testing algorithm, in that it tests pools of candidate solutions. RC then reduces the size of defective pools until a minimal defective set is found. Using a synthetic model of the Western United States power grid, we show that run times are minimized with a much smaller initial pool size than previously recommended, nearly doubling the speed of RC. We compare RC to a proposed new alternative group-testing algorithm (SIGHT). Both algorithms have their advantages; while SIGHT is shown to require fewer total tests than RC, RC requires fewer tests of defective sets. Thus, the relative speed of each algorithm depends on the relative cost of defective vs. non defective tests, a factor not previously considered in the group-testing literature. In the power systems application, tests of defective sets are much more computationally costly, so RC is faster. However, with only a single control parameter (compared to many in RC), SIGHT is easier to optimize, and in applications where the cost ratio of defective:non-defective tests is low enough, SIGHT will be faster than RC.