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

01/29/2021

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by   Eike Fokken, et al.

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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.