  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.
