Maximum Tolerance to Load Uncertainty of a Multiple-Model-Based Topology Detector

A problem to find the maximum tolerance to load uncertainty of a multiple-model-based detector designed for a set of nominal loads is formulated and solved. The detector contains one design model for each anticipated circuit topology. Each model is used to determine a topology-specific detection threshold, selected to define the smallness of measurement residuals only if they are from the matched model-circuit pair. To quantity the detector's tolerance to load uncertainty, an iterative algorithm is developed for computing the largest ellipsoid representing the most severe load current uncertainty tolerable without detection errors. Each iteration starts from a sufficiently large ellipsoid in an uncertain parameter space centered at nominal load current vector, solves a convex optimization problem to identify the worst-case load uncertainty, verifies against the set of detection thresholds, then reduces the volume of the uncertainty ellipsoid until all violations of thresholds are resolved. The worst tolerable load uncertainty is computed for the IEEE 9-bus test system with respect to one normal circuit and 6 open-circuit thresholds defined by 2-norms of measurement residuals. The thresholds are determined through simulations. The thresholds are shown (by simulations) to be robust for load perturbations within the predicted uncertainty ellipsoid. Application to large scale networks is enabled by our recently developed concept and method of network partition.