# Optimization in Power Systems

The transmission grid is an infrastructure for the bulk transfer of electrical energy from generation facilities to loads. For its economic utilization, an optimal allocation of generation resources needs to be identified that serves the load and complies with the physical model as well as system constraints. This operational task is known as the optimal power flow (OPF) problem. Due to the underlying physical laws, it constitutes a nonconvex optimization problem that is hard to solve for conventional transmission grids.

Although the OPF problem was introduced as far back as the 1960s, it is still subject of ongoing research due to its challenging mathematical structure. To circumvent its mathematical difficulty, typically simplified system models are employed, e.g., the widely used linearization called “DC power flow”. Therewith, computational tractability is traded for a model mismatch, which requires more conservative system constraints and leads to a suboptimal utilization.

In our research, we utilize mathematical concepts like convex relaxation and emerging technologies like high-voltage direct current transmission to develop novel system architectures. The aim is to combine the implementation of engineering objectives, e.g., capacity expansion, with an improvement in the mathematical structure of OPF. Therewith, necessary infrastructure reinforcements additionally enhance grid utilization and operation - and pave the way to efficient future transmission grids.