Active Fault Detection in Static Systems

We study auxiliary signal-based fault detection in static linear systems with quadratic constraints. Auxiliary signals are perturbations that make faults easier to detect, at the cost of some disruption to normal operation. In this article, we find minimally disruptive auxiliary signals that guarantee detection under set-based uncertainty. Our motivation is distance protection in inverter-dominated power systems, wherein small fault currents can go undetected by traditional schemes. We focus on static systems because distance protection is based on phasors. We formulate a general auxiliary signal design problem with constraints imposed by system operational requirements, and additive and multiplicative noise. We use a relaxation and duality to reformulate the problem as a semidefinite bilinear program. In the special case of additive uncertainty and no constraints, we obtain an analytical lower bound on the magnitude an auxiliary signal must have to guarantee detection. We solve the optimizations in an example based on distance protection, in which the auxiliary signal is negative sequence current.