Important properties of smart grids are their ability to survive perturbations and to repair themselves to adapt to new situations. The first ability is associated to the vulnerability of the system whereas the second property is related to its flexibility. Smart grids are multilayered and hierarchical systems and the dynamic interactions between the layers and between the components have some influence on its vulnerability and flexibility. Thus, the long-term objective of this project is to investigate impacts of the topology of the electrical layer on its dynamic properties (rotor angle stability and controllability).
Stability of power grids can be roughly analyzed by combining the DC loadflow equations with the swing equations for the generators. This gives a version of Kuramoto’s model of networks of non-linear oscillators. Kuramoto oscillators offer a comprehensive mathematical framework to study the emergence of collective dynamics and self-synchronization and to investigate links between topological parameters and dynamic properties. This modelling framework has already been used to obtain some interesting theoretical results (e.g. synchronization condition or basin stability expressed in terms of network topology). But it suffers from approximations and the goal of the work is to extend the modelling framework to include reactive power, control loops, intermittent energy sources and long wave propagation in order to be able to treat more realistic transmission systems.
For that purpose, we will study in detail some synthetic small graphs and how their topological arrangement may reinforce their stability and controllability. We will then try to extend our analysis to larger networks containing such small graphs. A particular attention will be paid to the stability of these networks when intermittent energy sources are connected.
- Litterature review on Kuramoto’s model of network of non-linear oscillators and its application to power systems.
- Proposing an extended modelling approach for analysing in detail the dynamics of power grids.
- Assessing the emergence of stability of power systems when intermittent energy sources are present.
- A mathematical framework that will be able to capture short and long-range interactions in the power grid.
- Stability conditions in terms of grid topology and parameters.