Cableizer ®

Thermal resistance conductor—sheath

All three-core cables require fillers to fill the space between insulated cores and the belt insulation or a sheath. The fillers of extruded cables usually have higher thermal resistivities than the insulation, unlike paper-insulated cables. In a paper by G. Anders from 1998, a formula was developed to take into account the different thermal resistivities. This formula has been included in the new editions of the IEC standards.

For three-core cables with a touching metallic screen made of copper tapes each core the thermal resistance of the insulation is obtained in two steps:

  1. First, the cables are considered as belted cables for which $t_1/t$ = 0.5.
  2. Second, the resulting $T_1$ is multiplied by a factor $K$, called the screening factor.

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.

Type of screen/sheath of multi-core cables

For calculation of the cyclic and emergency current rating of cables acc. IEC 60853, the multi-core cable is replaced by an equivalent single-core construction dissipating the same total conductor losses. The space between the equivalent single-core conductor and the sheath is considered to be completely occupied by insulation. For oil-filled cables, this space is filled partly by the total volume of oil in the ducts and the remainder is oil-impregnated paper.

Symbol
$T_{1}$
Unit
K.m/W
Formulas
$\frac{\rho_{i}}{2\pi} \ln\left(1+\frac{2t_{1}}{d_{c}}\right)$single-core cables
$\frac{\rho_{i}}{2\pi} G_{1}$multi-core cables, general formula
$K_{1} \frac{\rho_{i}}{2\pi} G_{1}$three-core cables, screened, round conductors
$0.89T_{1}+K_{1} \left(\frac{\sqrt{3} \rho_{f}}{\rho_{i}}-0.12d_{c}+2.25\right) e^{0.13+\frac{t_{1}}{d_{c}}-7K_{1}}$three-core cables, screened, round conductors (Anders1999)
$\frac{\rho_{i}}{2\pi} G_{1}+0.031\left(\rho_{f}-\rho_{i}\right) e^{\frac{0.67t_{1}}{d_{c}}}$three-core cables, unscreened, round conductors
$0.385\rho_{i} \frac{2t_{ic}}{d_{c}+2t_{ic}}$three-core cables, oil-filled, round conductors, with metallized paper core screens & oil ducts between the cores
$0.35\rho_{i} \left(0.923-\frac{d_{c}}{d_{c}+2t_{ic}}\right)$three-core cables, oil-filled, round conductors, with metal tape core screens & oil ducts between the cores
$\frac{475}{{D_{sc}}^{1.74}} \left(\frac{0.5\left(\frac{D_{shb}+D_{sh}-2t_{sh}}{2}-2.16D_{sc}\right)}{D_{sc}}\right)^{0.62}+\frac{\rho_{i}}{2\pi} \ln\left(\frac{d_{c}-2t_{sc}}{d_{c}}\right)$three-core cables, oil-filled, round conductors, without fillers and oil ducts, having a copper woven fabric tape binding the cores together and a corrugated aluminium sheath
$1.07T_{1}$single-core cables, part-metallic sheathed, trefoil, up to 35 kV
$1.16T_{1}$single-core cables, part-metallic sheathed, trefoil, from 35 to 150 kV
$T_{ct}+T_{cs}+T_{ins}+T_{is}+T_{scb}$CIGRE TB 880 Guidance Point 15, cables with screen
$T_{ct}+T_{cs}+T_{ins}+T_{is}+T_{scb}+T_{scs}+T_{dsh}$CIGRE TB 880 Guidance Point 15, cables without screen
$\frac{1}{F_{lay,3c}} T_{1}$CIGRE TB 880 Guidance Point 44, three-core cables
$\frac{\rho_{i}}{2\pi} \ln\left(\frac{D_{ins}}{d_{c}}\right)$4-loop method
$\frac{\theta_{c}-\theta_{encl}}{W_{conv,ce}+W_{rad,ce}}$PAC/GIL
Related
$d_{c}$
External diameter conductor [mm]
$D_{ins}$
Diameter over insulation [mm]
$D_{sc}$
Diameter over screen [mm]
$D_{sh}$
Diameter over sheath [mm]
$D_{shb}$
Diameter below sheath [mm]
$F_{lay,3c}$
Effective length per unit lay length twisted conductors
$G_{1}$
Geometric factor $G_1$
$K_{1}$
Screening factor
$\pi$
Archimedes' constant $\pi$
$\rho_{f}$
Thermal resistivity filler [K.m/W]
$\rho_{i}$
Thermal resistivity insulation material [K.m/W]
$t_{1}$
Thickness conductor—sheath [mm]
$T_{cs}$
Thermal resistance conductor shield [K.m/W]
$T_{ct}$
Thermal resistance conductor tape [K.m/W]
$T_{dsh}$
Thermal resistance corrugation filling [K.m/W]
$t_{ic}$
Thickness core insulation [mm]
$T_{ins}$
Thermal resistance insulation [K.m/W]
$T_{is}$
Thermal resistance insulation screen [K.m/W]
$t_{sc}$
Thickness screen [mm]
$T_{scb}$
Thermal resistance screen bedding [K.m/W]
$T_{scs}$
Thermal resistance screen serving [K.m/W]
$t_{sh}$
Thickness sheath [mm]
$\theta_{c}$
Temperature conductor [°C]
$\theta_{encl}$
Temperature enclosure [°C]
$W_{conv,ce}$
Convective heat transfer conductor→enclosure [W/m]
$W_{rad,ce}$
Radiation heat transfer conductor→enclosure [W/m]
Used in
$d_{c,t}$
External diameter conductor, transient [mm]
$\Delta \theta_{dj}$
Temperature rise dielectric losses $\rightarrow$ cable surface [K]
$I_{c}$
Conductor current [A]
$Q_{B,i}$
Thermal capacitance B transient thermal circuit, insulation [J/(m.K)]
$Q_{B,s}$
Thermal capacitance B transient thermal circuit, screen/sheath [J/(m.K)]
$R_{c1}$
Thermal resistance part 1 [K.m/W]
$T_{A}$
Thermal resistance A transient thermal circuit [K.m/W]
$T_{B}$
Thermal resistance B transient thermal circuit [K.m/W]
$T_{d}$
Internal thermal resistance for dielectric losses [K.m/W]
$T_{eq}$
Thermal resistance, equivalent [K.m/W]
$T_{int}$
Internal thermal resistance for current losses [K.m/W]
$T_{r}$
Thermal resistance, total [K.m/W]
$T_{tot}$
Thermal resistance, transient [K.m/W]
$\theta_{ar}$
Temperature armour [°C]
$\theta_{c,z}$
Temperature conductor z [°C]
$\theta_{e}$
External temperature object [°C]
$\theta_{f}$
Temperature filler for multi-core cables type SS with sheath [°C]
$\theta_{s}$
Temperature screen/sheath [°C]
$\theta_{sc}$
Temperature screen [°C]
$\theta_{sh}$
Temperature sheath [°C]
$\theta_{sp}$
Temperature steel pipe [°C]