Power flow dynamics in electricity grids can be described by equations resembling a Kuramoto model of non-linearly coupled oscillators with inertia. The coupling of the oscillators or nodes in a power grid generally exhibits pronounced heterogeneities due to varying features of transmission lines, generators, and loads. In studies aiming at uncovering mechanisms related to failures or malfunction of power systems, these grid heterogeneities are often neglected. However, over-simplification can lead to different results away from reality. We investigate the influence of heterogeneities in power grids on stable grid functioning and show their impact on estimating grid stability. Our conclusions are drawn by comparing the stability of an Institute of Electrical and Electronics Engineers test grid with a homogenized version of this grid.
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If one would be interested only in the grid return times (see below), an alternative way to obtain smoothly varying times is to consider the energy of coupled harmonic oscillators, which characterizes the system in the neighborhood of the fixed point, see Eq. (7). If the phase space trajectory enters the nearest neighborhood, this energy decreases monotonically with time .
