Collective effects of link failures in linear flow networks
arXiv:1909.00774 · doi:10.1088/1367-2630/ab6793
Abstract
The smooth operation of supply networks is crucial for the proper functioning of many systems, ranging from biological organisms such as the human blood transport system or plant leaves to man-made systems such as power grids or gas pipelines. Whereas the failure of single transmission elements has been analysed thoroughly for power grids, the understanding of multiple failures is becoming more and more important to prevent large scale outages with an increasing penetration of renewable energy sources. In this publication, we examine the collective nature of the simultaneous failure of several transmission elements. In particular, we focus on the difference between single transmission element failures and the collective failure of several elements. We demonstrate that already for two concurrent failures, the simultaneous outage can lead to an inversion of the direction of flow as compared to the two individual failures and find situations where additional outages may be beneficial for the overall system. In addition to that, we introduce a quantifier that performs very well in predicting if two outages act strongly collectively or may be treated as individual failures mathematically. Finally, we extend on recent progress made on the understanding of single link failures demonstrating that multiple link failures may be treated as superpositions of multiple electrical dipoles for lattice-like networks with collective effects completely vanishing in the continuum limit. Our results demonstrate that the simultaneous failure of multiple lines may lead to unexpected effects that cannot be easily described using the theoretical framework for single link failures.
arXiv commentFirst two authors contributed equally, 16 pages, 8 figures
References in corpus (18)
- Modularity and community structure in networks
- Error and attack tolerance of complex networks
- Defining and identifying communities in networks
- A model for cascading failures in complex networks
- Cascade control and defense in complex networks
- PyPSA-Eur: An Open Optimisation Model of the European Transmission System
- Damage and fluctuations induce loops in optimal transport networks
- Small vulnerable sets determine large network cascades in power grids
- Dynamically induced cascading failures in power grids
- Critical links and nonlocal rerouting in complex supply networks
- Nonlocal effects and counter measures in cascading failures
- Nonlocal failures in complex supply networks by single link additions
- Dual theory of transmission line outages
- Delocalization of Phase Disturbances and the Stability of AC Electricity Grids
- Non-Local Impact of Link Failures in Linear Flow Networks
- Curing Braess' Paradox by Secondary Control in Power Grids
- Long-range Response in AC Electricity Grids
- Long-Range Response to Transmission Line Disturbances in DC Electricity Grids