Colloquium Mathematics - J.W. Simpson Proco PhD - University of Waterloo

Titel: A Theory of Solvability for Lossless Power Flow Equations

Abstract:

This talk presents a theory of solvability for AC power flow equations in lossless networks. We formulate a new model of power flow, termed the fixed-point power flow (FPPF), which is parameterized by three graph matrices quantifying the internal coupling strength of the network. The FPPF leads to an explicit approximation of the high-voltage solution and a robust iterative method for its computation. For a subclass of acyclic networks, we derive necessary and sufficient parametric conditions for the existence of a power flow solution which is unique within a specified set, generalizing the classic textbook result for a two-node system. Finally, a roadmap is given for extending the results to networks with non-zero line resistances, along with some partial theoretical results in this direction.