Long Wavelength Coherency in Well Connected Electric Power Networks

TL;DR

This paper demonstrates that long wavelength inter-area oscillations in power networks are a generic phenomenon, insensitive to network connectivity strength, and can be understood through matrix perturbation and classical mathematical theories.

Contribution

It shows that inter-area oscillations occur broadly in power networks regardless of weak or strong connections, extending the understanding beyond traditional singular perturbation theory.

Findings

Inter-area oscillations are common in both weakly and strongly connected networks.

These modes have the lowest oscillation frequencies and are moderately sensitive to network connectivity.

The structure of these oscillations remains stable regardless of inter-area coupling strength.

Abstract

We investigate coherent oscillations in large scale transmission power grids, where large groups of generators respond in unison to a distant disturbance. Such long wavelength coherent phenomena are known as inter-area oscillations. Their existence in networks of weakly connected areas is well captured by singular perturbation theory. However, they are also observed in strongly connected networks without time-scale separation, where applying singular perturbation theory is not justified. We show that the occurrence of these oscillations is actually generic. Applying matrix perturbation theory, we show that, because these modes have the lowest oscillation frequencies of the system, they are only moderately sensitive to increased network connectivity between well chosen, initially weakly connected areas, and that their general structure remains the same, regardless of the strength of the inter-area coupling. This is qualitatively understood by bringing together the standard singular perturbation theory and Courant's nodal domain theorem.