Output Impedance Diffusion into Lossy Power Lines

Coping with lossy distribution lines has been an obstacle in control and stability of power networks. Often, imposing an inductive output impedance to the sources has been considered as a means to justify the commonly adopted assumption of purely inductive lines, which in turn facilitates the construction of energy-based Lyapunov functions. In this paper, we propose a measure to evaluate the inductivity of the resulting grid, and investigate the extent to which the output impedance can affect the behavior of the distribution lines seen from the voltage source outputs. We show analytically that the more connected the network is, the more the output impedance diffuses into the network.