Time-Domain Generalization of Kron Reduction

Manish K. Singh, Sairaj V. Dhople, Florian Dörfler, Georgios B. Giannakis

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R/L$ </tex-math></inline-formula> ratios. In contrast, this letter considers the generalized setting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RL$ </tex-math></inline-formula> networks without such restriction and puts forth a provably exact time-domain version of Kron reduction. Exemplifying empirical tests on a ⅄ – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> network are provided to validate the analytical results.