This work was developed during my bachelor's project at the Potsdam Institute for Climate Impact Research. It addresses the question of how the stability of synchronous states in networks of coupled oscillators is affected by the presence of delays in the dynamics of the oscillators. We derive necessary and sufficient stability conditions for a wide class of inertial oscillator dynamics with a constant processing delay and arbitrary network structures.

The study was motivated by the potential need to control processing delays in future renewable power grids, where electronic power inverters need to measure and react to changes in supply and demand to stabilize the grid frequency.

Related publications

• R. Börner et al., Delay master stability of inertial oscillator networks. Phys. Rev. Research 2, 023409 (2020).

Read more in my bachlor's thesis on this topic.

Further resources

Some code to calculate the delay master stability function is available on Github.