Kron reduction of nonlinear networks

Seminar by Arjan Van der Schaft

Start: 17/04/2024, 14:00 - 15:00
Location: B91.100

Speaker: Professor Arjan Van der Schaft, University of Groningen

Title: Kron reduction of nonlinear networks

Abstract: Kron reduction is concerned with the elimination of interior nodes of physical network systems. Simplest example is an electrical circuit only containing linear resistors, where part of the nodes are boundary nodes (terminals). Elimination of the interior nodes results in a reduced electrical circuit with newly defined resistors between the terminals. This reduced network is equivalent to the original one in the sense of having the same voltage-current behavior at the terminals. Furthermore, by Maxwell’s minimum heat theorem the reduced network exhibits the same dissipated power. The Kron reduced network is obtained by computing a Schur complement of the Laplacian (or Kirchhoff) matrix of the network, which again defines a Laplacian matrix. Special case of Kron reduction is the computation of the effective resistance, where only two terminals are selected.In this talk we will consider Kron reduction of nonlinear networks, such as electrical circuits consisting of nonlinear resistors/conductors. Under two technical assumptions it will be shown how Kron reduction can still be performed, resulting in an equivalent nonlinear network. Key tool will be a function intrinsically defined by the network, whose Hessian matrix is again a Laplacian matrix, with weights depending on the variables of the network. A second application concerns the Kron reduction of memristor networks.

Organized by: Rodolphe Sepulchre