Power Grid Dynamics Simulation

Simulate local disturbances

Click on a node on the map to perturb its position and speed by these values.

Apply perturbance to all nodes


What do I see?

This is a simulation of the Scandinavian high-voltage power transmission network. The links are transmission lines, they change their width proportional to their usage. The nodes are sites of power producers or consumers.

The nodes produce or consume AC power and behave as so-called oscillators.

Think of them as fast-running clocks which exchange their current time via the links. In stable operation of the power grid, all clocks are required to run at the same global speed, i.e. no clock is overturning another one. Speed deviations are visualised in the changing size of the nodes.

When the clock speed is the same at all nodes, the time differences between them are constant. Each of the nodes is its own time zone, with some being in advance and some being behind of the others. After each clock cycle, the positions are identified. Nodes that are behind draw power from advanced nodes. This determines the direction of power transmission.


The normal operation at the global clock speed with constant time differences is called synchronisation. In Europe, the nodes are synchronised at a global speed of 50Hz, i.e. clock cycles per minute. The larger the “time difference” between two nodes, the more power is being transmitted between them.

At a base speed of 50hz the clocks appear to stand still. By reducing the base speed, you reduce the slow-motion effect until you observe the real-time simulation.

Each clock is subject to a certain amount of friction when it deviates from the global speed. By increasing the friction multiplier, the power grid becomes more stable.

Experiments with disturbances

You can manually perturb the clock position and speed of any node by clicking on it. The size of the perturbation can be selected with the sliders on the left.

Alternatively, you can observe predefined perturbations at special nodes

node in appendices Here, it should be comparably easy to desynchronise a small group of nodes from the rest. A disturbance in an appendix is typically confined there.

hub (a node with many neighbours) The more neighbours a node has, the more likely are large speed deviations after a disturbance.

detour node (a node parallel to a direct connection) Here, it should be difficult to destabilise the power grid.

dense sprout (an end node connected to node with many neighbours) Perturbing a dense sprout can cause an interesting effect: A single node running at its own speed while the remaining network is in synchronisation. It is an effect predominantly affecting dense sprouts.

Some advanced details

The nodes are actually net power producers or consumers, representing the power balance of the surrounding area. The dynamics are determined by rotating turbines in the power plants generating an AC voltage. Mathematically, they are treated as so-called oscillators.

We use the analogy of clocks for oscillators. Strictly speaking, this would be a clock with only one needle. Its position corresponds to the phase, while the speed is its frequency (revoluations per second, Hz). Phases are defined modulo 2π, i.e. the position is identified after each revolution just like on a real clock.

We simulate the self-organised synchronisation of the nodes. In reality, this is assisted by many controllors which also keep frequency deviation within strict limits. Large frequency deviations inevitably lead to black-outs. Hence, the very chaotic states in our simulation would correspond to a black-out in reality.
Learn more



Frank Hellmann
Paul Schultz

Additional design and adaptation by

IMAGINARY (imaginary.org)

The CoNDyNet project is sponsored by the Bundesministerium für Bildung und Forschung

Related CoNDyNet Publications

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    Nitzbon, Schultz, Heitzig, Kurths, Hellmann
    New Journal of Physics, 19(3), 033029, 2017
    DOI: 10.1088/1367-2630/aa6321
  • Potentials and limits to basin stability estimation
    Schultz, Menck, Heitzig, Kurths
    New Journal of Physics, 19(2), 023005, 2017
    DOI: 10.1088/1367-2630/aa5a7b
  • Survivability of Deterministic Dynamical Systems
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    Scientific Reports, 6, 29654, 2016
    DOI: 10.1038/srep29654
  • The impact of model detail on power grid resilience measures
    Auer, Kleis, Schultz, Kurths, Hellmann
    European Physical Journal-Special Topics, 225(3), 609-625, 2016
    DOI: 10.1140/epjst/e2015-50265-9
  • Detours around basin stability in power networks
    Schultz, Heitzig, Kurths
    New Journal of Physics, 16, 2014
    DOI: 10.1088/1367-2630/16/12/125001
  • How dead ends undermine power grid stability
    Menck, Heitzig, Kurths, Schellnhuber
    Nature Communications, 5, 2014
    DOI: 10.1038/ncomms4969
  • How basin stability complements the linear-stability paradigm
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    Nature Physics, 9(2), 2013
    DOI: 10.1038/nphys2516