Transient Dynamics and Propagation of Voltage and Frequency Fluctuations in Transmission Grids

The  energy transition towards  increased  electric power production from renewable energy (RE) resources creates new challenges to ensure the  stability  of power grids. In conventional power grids voltage  fluctuations  can be controlled locally. Here, we explore whether the energy transition changes this situation. We  study systematically the  transients  of voltage amplitude,  phase and frequency deviations  due to  local contingencies in dependence on system inertia, heterogeneity and topology. The 3rd order dynamic power grid model is studied numerically and analytically and compared with  real grid simulations for the Nigerian (330 kV) power grid and other grid models, using DigSILENT PowerFactory software.  We provide a quantitative analysis of  the parametric dependence of the  velocity with which a disturbance propagates throughout the grid, and of the period of oscillations of the frequency and voltage transients. We find  beating patterns in the transients which we identify as footprints of the location of the fault bus. We confirm  that  voltage deviations remain local for  realistic ranges of parameters. However, we  find that this no longer holds true when the electrical power in the grid approaches its critical value. We furthermore consider time dependent second moments of  geodesic distance, weighted with frequency deviations and voltage deviations, respectively. We  confirm thereby  ballistic disturbance propagation  in homogeneous model grids. However, in real grid simulations, we observe  a linear time dependence of deviations indicating diffusive  propagation due to multiple scattering from the inhomogeneities in these power grids.