Optimisation-Based Control in Electrical Grids and Epidemiology

This thesis is a result of my work within the KONSENS project funded by the Federal Ministry of Education and Research (BMBF, Germany). The main focus of the KONSENS consortium was the Consistent Optimization aNd Stabilisation of Electrical Networked Systems, which explains the name of the project. In the course of the COVID-19 pandemic, the members of the consortium used their expertise in mathematical modelling, (numerical) analysis, and optimal control to evaluate countermeasures and propose strategies to mitigate the spread of the disease. As a result, this thesis is divided into two parts:

Part I: Distributed Optimisation and Control of Microgrids,
Part II: Coordinating Countermeasures against the Spread of Infectious Diseases.

The key to tackle both seemingly different problems with basically similar methods lies in the generality of optimisation-based approaches. We formulate mathematical models describing dynamical systems - in Part I that is battery dynamics, whereas in Part II we model the spread of an infectious disease over time. Such models in combination with a, e.g. economic, objective lead to optimal control problems (OCPs). In both parts of this thesis, the OCPs have inherent uncertainties like the unknown future net consumption (Part I) and the general evolution of a pandemic (Part II). Those control problems are solved numerically in order to determine optimal strategies. Implementing the computed control strategy over the entire control horizon - referred to as open-loop control - neglects new data becoming available during the process. Model predictive control (MPC) on the other hand, only implements the first part of the computed control and solves an updated OCP in the consecutive time step. This is referred to as closed-loop control. MPC is a state-of-the-art tool to solve OCPs with state and input constraints in real time and is used in case studies throughout this thesis.