Reverse Kron reduction of Multi-phase Radial Network

TL;DR

This paper presents a method to exactly recover the full admittance matrix of a three-phase radial network from its Kron reduction by reversing the iterative process while preserving an invariance structure.

Contribution

It introduces a novel approach to invert the Kron reduction process for multi-phase radial networks, enabling precise admittance matrix recovery.

Findings

Successfully reverses Kron reduction to recover admittance matrices

Maintains invariance structure during iterative reversal process

Applicable to three-phase radial networks

Abstract

We consider the problem of identifying the admittance matrix of a three-phase radial network from voltage and current measurements at a subset of nodes. These measurements are used to estimate a virtual network represented by the Kron reduction (Schur complement) of the full admittance matrix. We focus on recovering exactly the full admittance matrix from its Kron reduction, i.e., computing the inverse of Schur complement. The key idea is to decompose Kron reduction into a sequence of iterations that maintains an invariance structure, and exploit this structure to reverse each step of the iterative Kron reduction.