On the frequency and damping of resonances in electrical networks: a discrete state-space approach using bounce diagrams

Abstract

The paper presents a novel method to compute resonances in a power system network using a discrete state-space approach based on bounce diagrams. The approach models the distributed parameter line as a lattice diagram, considering the reflection/transmission of traveling waves. This model is then represented as a discrete-time linear time-invariant system, enabling the computation of resonances in the network. Two applications are demonstrated: fault location and load placement to improve damping in black start scenario. The method is particularly useful to understand and control resonances in electric grids. Theoretical analysis and numerical examples illustrate the behavior of resonances as resistive loads are connected along the transmission line, providing insights for fault location and load allocation strategies.