A set-theoretic framework to assess the impact of variable generation on the power flow

The increased penetration of renewable resources, such as wind and solar, into existing power systems introduces significant uncertainties in the generation side. We propose a method to assess whether power system static state variables, i.e., bus voltage magnitudes and angles, remain within acceptable ranges (with some confidence level), as dictated by system operational requirements, while the system is subject to variations in electricity generation arising from the uncertain nature of renewable resources. These variations are assumed to be unknown but constrained to lie (with some confidence level) within some bounded set. Through set operations, we propagate this set through the power flow model, and the result is another set that contains the possible values that (with some confidence level) the state variables (voltage magnitudes and angles) may take. The proposed method is applied to the IEEE 34-bus and 123-bus benchmark distribution systems.