On the continuation-path uniqueness of homotopy enhanced power flow method for general distribution networks with distributed generators

The integration of renewable energies requests smart power grids to be capable of supporting various power flow patterns, and thus urgently needs the development of smart and robust power flow solvers. However, there are several great challenges, as the problem of power flow divergence and the issue of multi-solution. Homotopy methodology is commonly utilized to deal with these issues. This paper proposes a set of sufficiently conditions for the uniqueness of power flow solution, by showing the uniqueness of continuation path in a homotopy method, which can serve as the condition for controlling when to apply the costly global-searching techniques for finding multiple power flow solutions. Theoretical results are illustrated by simulations on the IEEE 1123-bus distribution network with distributed generation.