This book explains the power grid as a hierarchy made up of the transmission, distribution, and microgrid levels.

Interfaces among these levels are explored to show how flexibility in power demand associated with residential batteries can be communicated through the entire grid to facilitate optimal power flow computations within the transmission grid.

To realize this approach, the authors combine semi-definite optimal power flow with model-order reduction at the distribution level and with a new heuristic algorithm for stable power flow at the transmission level. To demonstrate its use, a numerical case study based on modified IEEE 9-bus and 33-bus systems for the transmission and distribution grid, respectively, is included.

This book shows how exploiting the flexibility on the residential level improves the performance of the power flow with the transmission grid.

Autorentext
The authors combine expertise from various fields such as mathematical optimization, automatic and optimization-based control, and model-order reduction as well as practical aspects from transmission and distribution grids. They jointly worked in the project KONSENS (Consistent Optimization and Stabilization of Electrical Network Systems) funded by the Federal Ministry of Education and Research in Germany. Among other things, the KONSENS consortium organized two minisymposia on the optimization of power grids at the 21st and the 22nd European Consortium for Mathematics in Industry (ECMI) Conference on Industrial and Applied Mathematics. The first one in 2018 "Mathematics as key factor to master the challenges of the energy transition" and the second in 2021 "Mathematical Innovations for Mastering the Energy Transition: a Holistic Perspective." During the project, the consortium published several journal and conference papers as well as book chapters on automation, stabilization, and optimization of future electrical grids. Additionally, the consortium applied similar methods to contribute to the understanding of the spread of COVID-19 and the impact of countermeasures.

Inhalt
Introduction.- Preliminary theory.- Providing flexibility via residential batteries.- Flexibility in the distribution grid.- Security and stability on the transmission grid.- Implementation in the distribution grid and the microgrids.- Numerical example.- Conclusion.