Spreading of disturbances in realistic models of transmission grids in dependence on topology, inertia and heterogeneity

Abstract

The energy transition towards more renewable energy resources (RER) profoundly affects the frequency dynamics and stability of electrical power networks. Here, we investigate systematically the effect of reduced grid inertia, due to an increase in the magnitude of RER, its heterogeneous distribution and the grid topology on the propagation of disturbances in realistic power grid models. These studies are conducted with the DigSILENT PowerFactory software. By changing the power generation at one central bus in each grid at a specific time, we record the resulting frequency transients at all buses. Plotting the time of arrival (ToA) of the disturbance at each bus versus the distance from the disturbance, we analyse its propagation throughout the grid. While the ToAs are found to be distributed, we confirm a tendency that the ToA increases with geodesic distance linearly. Thereby, we can measure an average velocity of propagation by fitting the data with a ballistic equation. This velocity is found to decay with increasing inertia. Characterising each grid by its meshedness coefficient, we find that the distribution of the ToAs depends in more meshed grids less strongly on the grid inertia. In order to take into account the inhomogeneous distribution of inertia, we introduce an effective distance r_{mathrm{eff}}, which is weighted with a factor which strongly depends on local inertia. We find that this effective distance is more strongly correlated with the ToAs, for all grids. This is confirmed quantitatively by obtaining a larger Pearson correlation coefficient between ToA and r_{mathrm{eff}} than with r. Remarkably, a ballistic equation for the ToA with a velocity, as derived from the swing equation, provides a strict lower bound for all effective distances r_{mathrm{eff}} in all power grids. thereby yielding a reliable estimate for the smallest time a disturbance needs to propagate that distance as function of system parameters, in particular inertia. We thereby conclude that in the analysis of contingencies of power grids it may be advisable that system designers and operators use the effective distance r_{mathrm{eff}}, taking into account inhomogeneous distribution of inertia as introduced in Eq. (12), to locate a disturbance. Moreover, our results provide evidence for the importance of the network topology as quantified by the meshedness coefficient beta.