Output Impedance Diffusion into Lossy Power Lines

TL;DR

This paper investigates how output impedances influence the inductivity of power networks, revealing that network connectivity and impedance tuning can control inductivity levels, with practical validation via Kron reduction.

Contribution

It introduces a measure for network inductivity affected by output impedances and demonstrates how to tune impedances to achieve desired inductivity levels based on network connectivity.

Findings

Network inductivity depends on algebraic connectivity.

Output impedance diffusion increases with network connectivity.

Tuning output impedances can control system inductivity.

Abstract

Output impedances are inherent elements of power sources in the electrical grids. In this paper, we give an answer to the following question: What is the effect of output impedances on the inductivity of the power network? To address this question, we propose a measure to evaluate the inductivity of a power grid, and we compute this measure for various types of output impedances. Following this computation, it turns out that network inductivity highly depends on the algebraic connectivity of the network. By exploiting the derived expressions of the proposed measure, one can tune the output impedances in order to enforce a desired level of inductivity on the power system. Furthermore, the results show that the more "connected" the network is, the more the output impedances diffuse into the network. Finally, using Kron reduction, we provide examples that demonstrate the utility and validity of the method.