The Inverse Carson's Equations Problem: Definition, Implementation and Numerical Experiments

TL;DR

This paper introduces an inverse problem approach to recover detailed impedance matrices of low-voltage networks from sequence component data, addressing inaccuracies caused by unbalanced conditions in power flow studies.

Contribution

It formulates the inverse Carson's equations problem, providing a methodology to recover impedance data considering network properties and using nonlinear optimization.

Findings

Uniqueness of recovered impedance variables demonstrated

Likelihood of mismatch analyzed

Method applicable to overhead lines and cables

Abstract

In recent years, with the increase in renewable energy and storage penetration, power flow studies in low-voltage networks have become of interest in both industry and academia. Many studies use impedance represented by sequence components due to the lack of datasets with fully parameterized impedance matrices. This assumes that the network impedance is balanced, which is typically not the case in the low-voltage network and therefore risks the accuracy of the study. This paper proposes a methodology for the recovery of more detailed impedance data from sequence components as an inverse problem, i.e. the inverse Carson's equations problem, for both overhead lines and cables. We consider discrete properties like material and configuration of conductors common in the distribution network and investigate what data can be reliably recovered from only sequence components using nonlinear optimisation models. Presented results include uniqueness of recovered variables and the likelihood of mismatch.