Distribution System State and Impedance Estimation Augmented with Carson's Equations

The impedances of cables and lines used in (multi-conductor) distribution networks are usually unknown or approximated, and may lead to problematic results for any physics-based power system calculation, e.g., (optimal) power flow. Learning parameters from time series data is one of the few available options to obtain improved impedance models. This paper presents an approach that combines statistical learning concepts with the exploitation of domain knowledge, in the form of Carson's equations, through nonlinear mathematical optimization. The proposed approach derives impedance matrices for up-to-four-wire systems, using measurement data like those obtained from smart meters. Despite the lack of phasor measurements, the low signal-to-noise ratio of smart meter measurements, and the inherent existence of multiple equivalent solutions, our method produces good quality impedance models that are fit for power system calculations, significantly improving on our previous work both in terms of accuracy and computational time.