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# Behavior of Electrical cables at High-frequencies

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## Shielded Electric Cable at High-frequencies

In the field of electric power transmission, transient phenomena can lead to over voltages or over currents along the lines or cables. These phenomena are rarely considered from the design stage. Transient phenomena can cause overvoltage or over current and affect the integrity of the cable and may lead to malfunction. A second well-known phenomenon on the transmission lines is the appearance of an overvoltage at the end of the line if the latter is unloaded. For an underground cable whose intrinsic capacity is much greater this phenomenon appears for Distances. Thus, at high-frequency, Power cables, found in power distribution systems and motor drives, need to be modeled with special precaution, as many frequency-dependent features including skin and proximity effect, dielectric losses, and delay need to be appropriately included.

## SOLIDWORKS model of a two wire Shielded Electric Cable

The SOLIDWORKS model of a two wire shielded electric cable consists of two conductors, internal and external PVC and a shielding layer, as shown in Figure 1.

Figure 1 - 3D model of the electric cable

## EMS Simulation of a two wire shielded electric cable at high frequencies

In EMS, the two wire shielded electric cable is analyzed using AC Magnetic study to calculate the inductances, resistances and the distribution of the eddy currents at 500 KHz.

## Material

The simulated model is composed of two conductors, internal and external PVC and a shielding layer. The properties of the materials are summarized in Table 1.

Table 1 - Materials used in the EMS simulation

 Component Material Relative permeability Electrical Conductivity (S/m) The two conductors and the shielding layer Copper 0.99991 4.6e+007 Internal PVC, External PVC Fiberglass 1 0 Air region Air 1 0

## Coils

In this simulation, the two conductors are modeled as solid coils.
The two currents, of 1 Ampere RMS magnitude each one, are imposed by the wires at 500 kHz in an opposite direction.

## Meshing

Meshing is a very crucial step in the design analysis. EMS estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The quality of mesh plays a key role in the accuracy of the results.

Mesh control refers to specifying different element sizes at different regions in the model. A smaller element size in a region improves the accuracy of results in that region.

Figure 2 is the meshed model after using Mesh Controls shown in Table 2.

Table 2 - Mesh control

 Name Mesh size Components /Bodies Mesh control 1 0.01mm The two conductors Mesh control 2 0.5 mm The Air region

Figure 2 - Meshed model

## Inductance result

In AC Magnetic study, EMS computes inductances, resistances, flux linkage, leakage inductance, eddy current, induced voltage, energy and losses.
The computed self inductance in one conductor, compared to the reference [1] is shown in Table 3.

Table 3 - Self inductance result by EMS compared to Reference [1]

 Parameter EMS Reference [1] Self Inductance 0.264 n H 0.260 n H

## 3D fields generated by EMS

The distribution of the eddy currents in this cable, when the two currents are imposed by the wires at 500 kHz in an opposite direction, is shown in Figure 3 and Figure 4. The Skin and proximity effects are well presented.

Figure 3 - Current density distribution (Front View)

Figure 4 - Current density distribution (Dimetric View)

## Conclusion

This example shows that using EMS, electric cables are easily simulated at high frequency and the skin and proximity effects are studied.

## References

[1] Duc Quang NGUYEN, “ Développement d’un outil d’investigation pour le diagnostic des phénomènes hautes fréquences dans des câbles électriques ‘’, Doctorat Paris Tech THÈSE pour obtenir le grade de docteur délivré par l’École Nationale Supérieure d'Arts et Métiers Spécialité “ Génie électrique ”, le 19 novembre 2013.

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