Analogies to Power Flow — Towards Algorithms for the Power Flow and Maximum Power Flow Problem

Power flow formulations are commonly used to check if there is a feasible power flow for a given network topology including fixed demands and supplies. In this talk, we purely focus on the DC feasibility problem (known as power flow; in short PF) and the Maximum Power Flow (MPF). For tree topologies, we know that these flows behave similar to graph-theoretical flows. However, for general graphs power flows act differently. In contrast to graph-theoretical flows, power flows try to balance themselves. In this talk, we informally describe this property from an algorithmic point of view. In addition, using different mathematical formulations of the same problem, we got structural insights into the power flow problem. We currently investigate an algorithmic approach that might lead to a power flow algorithm. This algorithmic modeling helps us to find analogies to certain geometric problems. This increases the understanding of discrete (e.g., switching, TNEP) and continuous changes (e.g., FACTS) to the power grid topology. Using the graph-theoretical model, we give a translation to game theory, where the problem essentially represents a Prisoner's dilemma and shows why the Braess's Paradox occurs.