Matrix Perturbation Theory of Inter-Area Oscillations

TL;DR

This paper develops a matrix perturbation theory to understand the origin of inter-area oscillations in large interconnected power systems, revealing how these modes emerge from the network Laplacian's zero-modes even in complex, real-world grids.

Contribution

It introduces a novel matrix perturbation framework that explains the emergence of inter-area oscillations beyond traditional assumptions, applicable to real power grid configurations.

Findings

Inter-area oscillations originate from zero-modes of the network Laplacian.

Weak hybridization of these modes explains their persistence in complex grids.

Theory validated on a two-area system and the European power grid model.

Abstract

Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may jeopardize the overall system stability with the emergence of so-called inter-area oscillations, which are coherent oscillations involving groups of rotating machines separated by large distances up to thousands of kilometers. These often weakly damped modes may have harmful consequences for grid operation, yet despite decades of investigations, the mechanisms that generate them are still poorly understood, and the existing theories are based on assumptions that are not satisfied in real power grids where such modes are observed. Here we construct a matrix perturbation theory of large interconnected power systems that clarifies the origin and the conditions for the emergence of inter-area oscillations. We show that coherent inter-area oscillations emerge from the zero-modes of a multi-area network Laplacian matrix, which hybridize only weakly with other modes, even under significant capacity of the inter-area tie-lines, i.e. even when the standard assumption of area partitioning is not satisfied. The general theory is illustrated on a two-area system, and numerically applied to the well-connected PanTaGruEl model of the synchronous grid of continental Europe.