Time-Domain Generalization of Kron Reduction

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. In contrast, this letter considers the generalized setting of $RL$ networks without such restriction and puts forth a provably exact time-domain version of Kron reduction. Exemplifying empirical tests on a ⅄ – $\Delta $ network are provided to validate the analytical results.