On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability

TL;DR

This paper investigates the stability of power networks modeled by Telegrapher's equations, establishing their relation to powerflow solutions and introducing a stable numerical scheme for their analysis.

Contribution

It demonstrates the equivalence between Telegrapher's equations solutions and powerflow solutions and develops a second-order accurate, Lyapunov stable numerical scheme.

Findings

Equivalence of periodic solutions and powerflow solutions.

Development of a second-order accurate numerical scheme.

Proof of Lyapunov stability of the numerical method.

Abstract

In this contribution we analyze the exponential stability of power networks modeled with the Telegrapher's equations as a system of balance laws on the edges. We show the equivalence of periodic solutions of these Telegrapher's equations and solutions to the well-established powerflow equations. In addition we provide a second-order accurate numerical scheme to integrate the powerflow equations and show (up to the boundary conditions) Lyapunov stability of the scheme.