Supplementary material to the paper

Dynamic Effects Increasing Network Vulnerability to Cascading Failures

By Ingve Simonsen, Lubos Buzna, Karsten Peters, Stefan Bornholdt, and Dirk Helbing




1.  Similarities of our model with realistic electrical simulation models

In this section we present the line flows obtained by our model and compare them with some available results obtained by very detailed and realistic AC-simulators of electrical grid. The compared simulation models share the same scenario, i.e. initially one line is removed from the network, and the figure shows the flow on a remaining line in the system.





Figure 1: The top figure shows the simulation of electrical currents in a power line with the EUROSTAG tool. The initial failure was caused by a disconnected power line [1]. The bottom figure shows similar link flows reproduced by our model.



Figure 2: The top figure shows the simulation power of currents in a power line with the model of Sadikovic [2]. The bottom figure shows similar link flows reproduced by our model.


1.  Example of a real cascading event in electrical power grids

To support our model, we give the example of a cascading blackout which very quickly spread across the European electrical grid on November 4th, 2006 [3]. The initial situation before the blackout is shown in Figure 3. Four power lines were switched off for maintenance and line 2 was switched off for the transfer of a ship by Meyer-Werft what triggered the cascade of events.

Figure 3: The situation of the power grid in Northern Germany shortly before the incident. Lines 1 4 were switched off for maintenance, while line 5 was temporarily switched off for a ship transfer [3].

After switching off the power line for transfer of a huge ship, a massive cascade of disconnecting lines spread in the European power grid. Figure 4 shows fast sequence of disconnected power lines. The incident affected the large parts of Europe. The affected areas are depicted in Figure 5.

Figure 4: Shortly after the line was switched off for the ship transfer, the overall situation in the power grid resulted in a cascade of disconnecting lines. The time information left of the figure demonstrates, how fast the cascade propagated in this case.

Figure 5: The incident on November 4th, 2006 resulted in failures across large parts of the continental European electricity grid [4].




1. .

2.  R. Sadikovic: Use of FACT devices for power flow control and damping of oscillations in power systems, (PhD thesis, ETH Zurich), 2006.

3.  Report on the system incident of November 4th, 2006. E.ON Netz.GmbH (

4.  E. Liuf: Critical Infrastructure protection, R&D view, EU project IRRIIS - Internal document available upon the request.