A study of synchronisation in the classical phase-oscillator model of an electrical power grid

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.