# Three-core cables belted or screened

Modelling and calculation of the internal thermal resistance and ampacity of 3-core belted cables and screened cables with fillers.

Posted 2015-12-14
Categories: Theory

For two- and three-core belted cables, the conductors are separately insulated and then stranded together. The clearance between the phases is filled with a packing or filling of fibrous material in order to obtain a circular section. An overall circumferential belting layer is applied on top. A common sheath may be added and on top of the sheath for its protection comes an outer covering or jacket.

## Belted cables

2/3-core cables with round conductors 2/3-core cables with sector-shaped conductors

The calculation of thermal resistances of the internal components of cables for single-core cables is straightforward. The thermal resistance \$T_1\$ between one conductor and the sheath is calculated using the formula \$T_1 = ρ_i/2π · ln(1+2t_1/d_c)\$
where:
\$ρ_i\$ is the thermal resistivity of insulation [K.m/W]
\$d_c\$ is the diameter of conductor [mm]
\$t_1\$ is the thickness of insulation between conductor and sheath [mm]

The calculations of two- and three-core cables are more complicated and rigorous mathematical formulas cannot be determined, but mathematical expressions to fit the conditions have been derived. The general method employs geometric factor \$G_1\$ in place of the logarithmic term for single-core cables. All three-core cables require fillers to fill the space between insulated cores and the belt insulation or a sheath. For paper-insulated cables, the thermal resistivity of the filler material \$ρ_f\$ is equal to the thermal resistivity of the insulation material \$ρ_i\$ with values between 5 and 6 K.m/W. The fillers of extruded cables usually have higher thermal resistivity which is likely to be between 6 K.m/W and 13 K.m/W, depending on the filler material and its compaction. For example, a value of 10 K.m/W is suggested for fibrous polypropylene fillers. At the same time, the resistivity of the extruded insulation material is usually 3.5 K.m/W and as such lower than that of impregnated paper.

The formula to calculate the thermal resistance \$T_1\$ in the first edition of the IEC 60287-2-1 from 1994 did not incorporate the influence of inhomogeneous thermal resistivities. In 1998, a new formula was developed and published in a technical paper from G.J. Anders. This formula has been introduced in an amendment to the IEC and is still used for three-core belted cables with circular conductors in the new edition 2 from April 2015 (please refer to chapter 4.1.2.2.4).

## Screened cables

 In addition to the semiconducting screens around the insulation, the majority of modern 3-core cable constructions also have a metallic screen made of copper tapes or wires added around each core. The main purpose of this screen is to provide a uniform electric field inside the cable. Screening provides additional heat paths along the screening material of high thermal conductivity. A tape screen is always considered overlapping and therefore the screening effect takes place. For flat wires, screening is only used if there are sufficient wires for them to be considered touching. We consider a coverage of 90% of the circumference sufficient. For round wires, screening is not considered. For three-core cables with a touching metallic screen made of copper tapes or flat wires around each core the thermal resistance of the insulation is obtained in two steps. First, the cables are considered as belted cables for which \$t_1/t=0.5\$. Then the resulting \$T_1\$ is multiplied by the screening factor K.
In a paper by G. Anders from 1999, a more precise formula was developed. This formula has not been included in the IEC, but is used by Cableizer. This formula did not find its way into the new IEC because it is still rather cumbersome and the improvement is small since the correlation between IEC and FEM as calculated in the paper was already 0.989.

References:

18
10
9
10
2
9
11
2