Optimization and Stabilization of Hierarchical Electrical Networks

Triggered by the increasing number of renewable energy sources, the German electricity grid is undergoing a fundamental change from mono to bidirectional power flow. This paradigm shift confronts grid operators with new problems but also new opportunities. In this chapter we point out some of these problems arising on different layers of the grid hierarchy and sketch mathematical methods to handle them. While the transmission system operator’s main concern is stability and security of the system in case of contingencies, the distribution system operator aims to exploit inherent flexibilities. We identify possible interconnections among the layers to make the flexibility from the distribution grid available within the whole network. Our presented approaches include: the distributed control of energy storage devices on a residential level; transient stability analysis via a new set-based approach; a new clustering-based model-order reduction technique; and a modeling framework for the power flow problem on the transmission level which incorporates new grid technologies.