Optimization in Power Systems

The electrical grid is an infrastructure for the 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 challenging to solve for large-scale 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 potentially leads to a suboptimal utilization.

In our research, we utilize mathematical concepts like convex relaxation and recent technologies like high-voltage direct current transmission to investigate the hypothesis that the structure of the OPF problem can inspire both beneficial approaches to system design and efficient OPF solution methods. To this end, we combine the implementation of engineering objectives, e.g., capacity expansion, with advantageous modifications of the mathematical structure of the OPF and study the arising benefits in OPF solution methods as well as the operation and utilization of the grid infrastructure.