Locating line and node disturbances in networks of diffusively coupled dynamical agents

Robin Delabays,Melvyn Tyloo,Laurent Pagnier

doi:10.1088/1367-2630/abf54b

Abstract

A wide variety of natural and human-made systems consist of a large set of dynamical units coupled into a complex structure. Breakdown of such systems can have a dramatic impact, as in the case of neurons in the brain or lines in an electric grid, to name but a few. Preventing such catastrophic events requires in particular to be able to detect and locate the source of disturbances as fast as possible. We propose a simple method to identify and locate disturbances in networks of coupled dynamical agents, relying only on time series measurements and on the knowledge of the (possibly Kron-reduced) network structure. The strength and the appeal of the present approach lies in its simplicity paired with the ability to precisely locate disturbances and even to differentiate between line and node disturbances. If we have access to measurement at only a subset of nodes, our method is still able to identify the location of the disturbance if the disturbed nodes are measured. If not, we manage to identify the region of the network where the disturbance occurs.

Highlights

Despite recent advances in network science [1, 2], the understanding of large, networked dynamical system is still incomplete, even though such systems can play a major role in our daily life
We propose a simple method to identify and locate disturbances in networks of coupled dynamical agents, relying only on time series measurements and on the knowledge of the network structure
We proposed an elegant method to identify and locate disturbances in networked dynamical systems

Summary

Introduction

Despite recent advances in network science [1, 2], the understanding of large, networked dynamical system is still incomplete, even though such systems can play a major role in our daily life. In the context of power grids, recent applications of results from network science and dynamical systems theory allowed the development of new techniques aiming at a fast assessment of the system’s state Such improvements are based on the measurement of some quantities such as voltage amplitudes, phases, and frequencies, which are nowadays widely accessible on a high time resolution thank, for instance, to phasor measurement units (PMUs). In these approaches, the authors assume that the system operator is aware of the attack, and their analysis follows the line failure, which means that dramatic events already happened In this manuscript, we propose to detect and locate disturbances whose impact on the system is not (yet) threatening its operation, without any a priori knowledge of the faults’ characteristics or approximate location.

Notations and framework

Locating a single disturbance

Multiple disturbances

Implementation and numerical validation

Findings

Conclusion