An Investigation into the Stabilization of Electrical Power Grids Using a Second Order Kuramoto Model

An Investigation into the Stabilization of Electrical Power Grids Using a Second Order Kuramoto Model

Luik, Ian (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Dubbeldam, Johan (mentor)
Blanter, Yaroslav (mentor)

Delft University of Technology

Applied Mathematics | Applied Physics

2020-06-26

In this thesis different mechanisms of stabilizing a power grid are tested. The grid dynamics are modelled by a second order extension of the Kuramoto coupled oscillator model, also known as the swing equation. First we prove basic properties of the model such as periodicity and existence and uniqueness. Then
we explore the properties of simple network topologies governed by the Kuramoto model. Finally we proceed to the testing of stabilization mechanisms. The stabilization mechanisms tested are (a) increasing the capacity of the power grid lines (b) implementing time delayed feedback mechanisms on the nodes and (c) decentralizing the power generation in the network. Moreover, we test whether examples of Braess’ paradox, which states that adding an edge in a network can locally improve flow but globally cause congestion, can be found in a small network. Increasing the capacity of the power grid lines and implementing time delayed feedback are shown to have a positive effect on the stability of the grid. For a specific grid (the German power grid) it is shown that replacing a large power generator by many smaller generators can indeed have a positive effect on the stability, but this result has mediocre statistical certainty (p-value of 0:16). No instances have been found where removing a line from the network has a positive effect (Braess’ paradox), however this is insufficient to conclude that no such instances exist.

http://resolver.tudelft.nl/uuid:d0d6c030-d945-43ea-b9a3-4b93a3568985

Student theses

bachelor thesis

© 2020 Ian Luik