# Surface Magnetic Field and Phase Current Sensing of Steel Tape-Wrapped 3-Core MV Cables

## TL;DR

This paper presents a method to accurately measure the surface magnetic field and phase currents in steel tape-wrapped three-core medium voltage cables.

## Contribution

A new model and differential evolutionary algorithm are proposed to account for steel tape shielding effects in magnetic field measurements.

## Key findings

- The difference between analytical and numerical solutions is below 5%.
- The differential evolution algorithm accurately estimates three-phase currents with a maximum amplitude error of 4.83%.
- The algorithm measures phase angles with a maximum error of 8.01°.

## Abstract

The surface magnetic field of three-core cables is essential for estimating phase currents and locating the single-phase grounding faults. However, the double-layer steel tape-wrapped structure will shield the magnetic field, affecting the measurement of the surface magnetic field of the three-core cable. Disregarding the shielding effect of the steel tape during the measurement of the surface magnetic field of the cable leads to an erroneous phase current obtained from the inversion of the observed magnetic field. To measure the surface magnetic field and invert it to obtain three-phase currents accurately, a model to evaluate the shielding effect of the steel tape is proposed, and a differential evolutionary algorithm method is proposed to invert it to obtain the three-phase currents. The results indicate that the difference between the analytical and numerical solutions is below 5%. As the thickness of steel tape increases, the shielding coefficient also increases. The differential evolution algorithm can accurately estimate the three-phase currents. The differential evolutionary algorithm measured the current amplitude of phases A, B, and C to 354.62 A, 354.33 A, and 323.46 A, respectively. Additionally, the algorithm measured the current phase magnitudes to be −8.21°, −128.01°, and 111.87°. The maximum value of the amplitude error of the three-phase current is 4.83%, and the maximum value of the phase error is 8.01°.