The drastic change of electric power supply in the up-coming decades provides an extraordinary challenge for the operation of future power grids. Traditionally, electrical energy was almost exclusively provided by relatively few large
power plants, but modern grids are transformed to decentralized structures. Robust synchronization (frequency locking) of power plants and consumers centrally underlies the stable operation of electric power grids. Therefore, it is important to understand the conditions enabling self-organized synchronization in oscillator networks that serve as coarse-scale models for power grids. Despite
current attempts to control large-scale networks, even their uncontrolled collective dynamics is not fully understood. To reveal essential aspects of the oscillatory dynamics of power grids and their nonlinear dynamics, consider coarse-scale
oscillator models of power grids. They are derived from the physics of synchronous generators (power plants) and motors (consumers). In such a model, the phase of generators/motors are described by the swing equations (see PDF).
Project description. In this project, you would investigate conditions for the dynamic stability of complete and spatially non-uniform synchronization modes in models of real-world power grid topologies.
Goals. The following questions could be addressed:
1. Effect of transmission delays.
2. Existence and stability of attractors with partial (spatially non-uniform) synchronization, such as chimera states , in real-world power grid topologies.
3. Effect of power failure in nodes on synchronization capability of the power grid.
4. How do fluctuations (perturbations) dynamically spread from one node to another in a complex network?
Numerical simulation, dynamical systems theory, network/graph theory, bifurcation theory, (concepts of representation theory*).