A zonotope-based method for capturing the effect of variable generation on the power flow

This paper presents a set-theoretic method to capture the effects of uncertainty on the generation side of a power system; this uncertainty arises from the increasing penetration of renewable resources such as wind and solar into existing systems. Using this method, we can determine whether the system state variables are within acceptable ranges as dictated by operational requirements. We bound all possible values that the uncertain generation can take by a zonotope and propagate it through a linearized power flow model, resulting in another zonotope that captures all possible variations in the system static state variables. For verification, we test our proposed method on the IEEE 123-bus distribution system and the IEEE 145-bus, 50-machine transmission system.