Kron Reduction of Generalized Electrical Networks

Kron reduction is used to simplify the analysis of multi-machine power systems under certain steady state assumptions that underly the usage of phasors. In this paper we show how to perform Kron reduction for a class of electrical networks without steady state assumptions. The reduced models can thus be used to analyze the transient as well as the steady state behavior of these electrical networks.

💡 Research Summary

Kron reduction is a classical technique for simplifying large power‑system networks by eliminating internal buses while preserving the behavior of a selected set of observable buses. Traditionally, this method relies on the steady‑state assumption that the system operates with sinusoidal phasors at a constant frequency. Under this assumption the network can be represented by a complex admittance (Laplacian) matrix, and the reduction is performed by a Schur complement of the internal‑bus block. While effective for small‑signal stability and power‑flow studies, the conventional approach cannot faithfully capture transient phenomena such as fault currents, switching surges, or the fast dynamics introduced by power‑electronics‑based devices and renewable generation.

The paper “Kron Reduction of Generalized Electrical Networks” addresses this limitation by extending Kron reduction to a class of electrical networks that do not require any steady‑state hypothesis. The authors introduce a generalized electrical network model in which each branch is described by a differential operator (or, equivalently, a Laplace‑domain impedance function) rather than a fixed complex admittance. In time domain the network equations become a set of linear differential‑algebraic equations (DAEs):

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