Synchronization and Stability in Dynamical Models of Power Supply Networks

Abstract

We are currently witnessing a change of electrical power supply from conventional power generation to power generation based on renewable energy sources such as wind and solar power. The main differences between these two ways of power generation are that power generation based on renewables produces typically less and more fluctuating power output. The changes in power production therefore pose a problem for the stability of power grids. In this thesis we analyze different effects of these changes for the stability of power grids. In the first part we introduce in detail the power grid model we are using. We analyze the model for the simplest possible system, a system consisting of one generator and one consumer. For this system an analytical analysis of the model is possible. We demonstrate that the model contains the most important features of real-world power grids and is such a useful tool for investigations of larger networks. The most important feature is that there exists both a stable and an unstable state and the dynamics depend on the initial conditions, i.e., the current state of the network. In the second part of the thesis we investigate the process of decentralization of power generation. This process is ongoing due to the replacement of conventional power sources with renewables. As renewable power sources are typically far away from consumers the replacements process ends up with a decentralized power grid. Our main results are that dynamical stability, i.e., stability against large scale power perturbations, is decreased for decentralized power grids compared with centralized ones. On the other hand, structural stability, i.e., stability against single transmission line failures, is increased for decentralized grids. In the last part we analyze structural stability in more detail. We develop a novel criterion to predict which transmission lines can induce large scale power outages if they fail and which not. We demonstrate that the load of a transmission line alone is not a good predictor for this behavior.