Duality-driven optimization in energy management: Offline and online algorithms for resource allocation problems

The future stability and reliability of our current energy systems are threatened as shown by new scientific insights on the effect of these systems on our planet. A widely advocated solution to this problem is to switch to more sustainable and cleaner energy sources such as solar and wind power. Moreover, many innovations have been done that led to an increase in energy-efficiency of devices. Although these developments towards a reliable future energy system are seen as promising, they come with several disadvantages. One major disadvantage is the uncertainty of both energy supply and demand. Furthermore, due to the rapidly increasing electrification of heating and transport, there is also a rapid increase in the amount of electricity that needs to be transported throughout the electricity distribution network. The capacity of the current network, however, is not sufficiently large to accommodate this increase in transported electricity. To resolve these two issues and to avoid huge financial investments in the energy infrastructure, it is crucial to actively manage the energy flows within an energy system or device.
The aim of this thesis is to develop solution approaches and algorithms for energy management problems. The goal hereby is, on the one hand, that the developed approaches can be implemented in practice within reasonable time and with limited effort and, on the other hand, that they come with theoretical performance guarantees on, e.g., the execution time or solution accuracy. To solve the considered energy management problems, a so-called duality perspective is employed. The idea behind this perspective is, roughly, that the problem might become significantly easier to solve if first some of its restrictions are relaxed and only enforced in a later stadium.
The concrete contributions of this thesis are twofold. The first contribution is the extension of several existing energy management problems so that practical requirements and physical properties of the given system or device are incorporated while maintaining theoretical performance guarantees. The second contribution is a new framework for solving energy management problems where uncertainty is present in several of the problem parameters called “online duality-driven optimization”.