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, it is explored whether this may be changed by the energy transition. It is well established that the increase of RE resources in power grids increases the amplitude of frequency deviations and the velocity with which these deviations spread throughout the power grid. However, its effect on voltage dynamics and propagation has not been systematically studied. Here, a systematic study is carried out of 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. 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 is provided. Beating patterns are found in the transients and are identified as footprints of the location of the fault bus, as caused by multiple reflections of propagating disturbances from the grid boundary. These may result in interarea oscillations. It is confirmed that voltage deviations remain local for realistic ranges of parameters, but that it can propagate by literally surfing on the frequency deviation wave. However, it is found that this no longer holds true when the electrical power in the grid approaches its critical value beyond which no stationary solution exists. Furthermore, time dependent second moments of the geodesic distance weighted with frequency deviations $S_{\delta \omega }(t)$ and voltage deviations $S_{\delta V}(t)$ , respectively are evaluated, confirming a ballistic disturbance propagation in homogeneous model grids. However, in real grid simulations, a linear time dependence of $S(t)$ is observed, indicating a diffusive propagation due to multiple scattering from the inhomogeneities in these power grids.