  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.
