A Generalized Linear Response Theory for Renewable Fluctuations in Microgrids


A central requirement in the operation of power grids is the stability of the grid frequency at 50 or 60Hz. In the language of theoretical physics this can be phrased as the question whether a networked system of inertial oscillators stays close to synchrony in the presence of disturbances or fluctuating energy infeed at the nodes.
In this talk a generalised linear response theory for network dynamical systems will presented. It is shown how external fluctuations with arbitrary power spectra couple to the eigenmodes of the dynamical system.
This theory is then applied to the study case of renewable power fluctuations in AC microgrids in order to calculate the variance of the frequency deviations from the nominal frequency. It is shown that in such midvoltage grids power flow losses on resistive lines play an important role in creating certain response patterns that mainly depent on the networks structure.
Particularly the slowest network mode reveals a strong asymmetry in the response dynamics that yields classes of nodes with enhanced vulnerability to external fluctuations (troublemaker nodes). It is shown that for microgrids with low inertia and a radial structure tat this particular mode is dominant and the vulnerability is strongly connected to the power flow in the grid.