Propagation of Disturbances in AC Electricity Grids

Samyak Tamrakar,Stefan Kettemann,Michael Conrath

doi:10.1038/s41598-018-24685-5

Abstract

The energy transition towards high shares of renewable energy will affect the stability of electricity grids in many ways. Here, we aim to study its impact on propagation of disturbances by solving nonlinear swing equations describing coupled rotating masses of synchronous generators and motors on different grid topologies. We consider a tree, a square grid and as a real grid topology, the german transmission grid. We identify ranges of parameters with different transient dynamics: the disturbance decays exponentially in time, superimposed by oscillations with the fast decay rate of a single node, or with a smaller decay rate without oscillations. Most remarkably, as the grid inertia is lowered, nodes may become correlated, slowing down the propagation from ballistic to diffusive motion, decaying with a power law in time. Applying linear response theory we show that tree grids have a spectral gap leading to exponential relaxation as protected by topology and independent on grid size. Meshed grids are found to have a spectral gap which decreases with increasing grid size, leading to slow power law relaxation and collective diffusive propagation of disturbances. We conclude by discussing consequences if no measures are undertaken to preserve the grid inertia in the energy transition.

Highlights

In order to cover the increasing human energy demand by renewable energy resources and to ensure that this energy will be available wherever and whenever it is needed, more efficient energy transport and storage technologies need to be developed
Depending on the geographical distribution of power, power transmission capacity and grid topology we find that the disturbance may either decay exponentially in time with the decay rate of a single oscillator Γ0, or exponentially with a smaller decay rate Γ < Γ0, or, even more slowly, decaying with a power law in time
In order to study the transient behavior of AC grids perturbed by local disturbances, we solve the nonlinear swing equation (4) on the different grid topologies of Fig. 1 as function of the set of parameters (τ,ΠK, ΠP)

Summary

Introduction

In order to cover the increasing human energy demand by renewable energy resources and to ensure that this energy will be available wherever and whenever it is needed, more efficient energy transport and storage technologies need to be developed. The inverter-connected wind turbines and solar cells provide no inertia[1] This is in contrast to conventional generators, whose rotating masses hold inertia and thereby momentary power reserve available for the grid, which makes the grid resilient and prevents strong fluctuations of the grid frequency on time scales of several seconds[2,3]. The origin of disturbances can be fluctuations in generating power or sudden changes of transmission line capacitance We analyze these results, employing analytical results obtained from a linear response theory, mapping the swing equations on discrete linear wave equations for small perturbations[18]. Thereby, the stationary active power flow balance equations are obtained from Kirchhoff ’s laws as[20]

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Results

Conclusion