Abstract:
In this work, we study synchronisation in power grids using a classical phase oscillator
model that can be thought of as a variant of the famous Kuramoto model for coupled
phase oscillators. In the recent literature, the connection between a Kuramoto-like
model and power grids has been made by Filatrella, Nielsen and Pedersen. Here,
we will show that this connection goes much further back, to the so-called Classical
Model of power grids that was introduced in 1951 by the work of Boast and Rector.
We also observe that in 2018, Arinushkin and Anishchenko developed a Kuramotolike
model for power grids in which, for the first time, there appear non-negligible
phase-lag parameters as a result of the Kron reduced approximation. Although a single
phase-lag (or frustration) parameter had been introduced much earlier in the so-called
Kuramoto-Sakaguchi model (from 1986), Arinushkin and Anishchenko were the first to
introduce multiple phase-lag parameters into a Kuromoto-like model for power grids.
Unfortunately, our attempts to replicate their results soon revealed that they used a
too-large, fixed time step for the numerical time integration of their equations, and that
this led them to make several erroneous conclusions about the grid which they modelled.
Therefore, in Chapter 3, we give a detailed critique of the 2018 paper by Arinushkin
and Anishchenko. Then, in a follow-up work by Arinushkin and Vadivasova, from
2021, we observe that use was made of nonlinear damping to control the synchronicity
of the Kron reduced grid. In this case, we were able to reproduce all the results
of Arinushkin and Vadivasova. We were able to develop a more efficient proportional
control scheme, based on the global order parameter. Our proposed control scheme and
its results were presented at the 2023 International Conference on Electrical, Computer,
and Energy Technologies (ICECET). The resulting conference proceeding is included
here, in slightly revised form, as Chapter 4. Finally, in Chapter 5, we provide a brief
summary of our main findings and some suggestions for future work.
