Time-domain Generalization of Kron Reduction

TL;DR

This paper extends Kron reduction to time-domain analysis for RL networks without R/L ratio restrictions, providing a provably exact method validated through empirical tests on a wye-delta network.

Contribution

It introduces a novel, exact time-domain generalization of Kron reduction applicable to RL networks without R/L ratio constraints.

Findings

Exact time-domain Kron reduction for RL networks.

Validation through empirical tests on a wye-delta network.

Broader applicability beyond sinusoidal steady state.

Abstract

Kron reduction is a network-reduction method that eliminates nodes with zero current injections from electrical networks operating in sinusoidal steady state. In the time domain, the state-of-the-art application of Kron reduction has been in networks with transmission lines that have constant R/L ratios. This paper considers RL networks without such restriction and puts forth a provably exact time-domain generalization of Kron reduction. Exemplifying empirical tests on a wye-delta network are provided to validate the analytical results.