Power grid efficiency and stability: effects of delay and time dependent power sources

In this thesis, we deal with the mechatronic control of the power grid efficiency and stability. The effects of delay, noise and time dependent power sources are taken into account. Three types of grid or topologies are considered: one machine and two generators, one machine and one generator, and finally an example of power grid present in Cameroon. After the schematic representation and the description of each topology, the mathematical models are written and appropriate theoretical and numerical methods are used to investigate their resilience and stability.
The following main results are obtained:
- asymmetry due to transmission lines capabilities increases the stability of the system,
- transmission time delay leads the system too quickly to an unstable state,
- when the system is subjected to a stochastic perturbation, its stability depends not only on the noise intensity, but also on the time delay and the value of the transmission lines capabilities,
- using a Proportional-Derivative (PD) control, the increase of the resilience of the system is found.
- time-delays associated to the feedback loop of the controller have a negative impact on the performance of the electricity networks,
- asymmetry due to energy demand of different consumers to power plant increases the stability of the system.