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Numerical modeling of the thermal behavior of XLPE Power Cable

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Electro-Thermo-Mechanical Simulation of Eddy Current Braking Systems in EMS for SOLIDWORKS
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Crosslinked Polyethylene (XLPE) is extensively used as an electrical insulating material in Power cables for underground distribution and subsea transmission. It is gradually replacing the typical low-density Polyethylene in such applications, because of its excellent insulation characteristics (high dielectric strength, low dielectric permittivity and loss factor) and its great mechanical and thermal stabilities. XLPE come to be used on a large-scale voltage transmission for more than 200kV.

Nevertheless, XLPE life-time is limited when subjected to various stresses during its service period (Electrical, thermal, mechanical, etc..), which may change its chemical composition and physical morphology. It will be unable to meet its function after a certain time and even lead to failure.

Particularly, cable insulations suffer from thermal stresses which are proportionally related to the amount of loading current passing through it. The temperature rise, mainly due to Joule losses in the conductor, causes irreversible changes in dielectric parameters of the cable (dielectric loss tangent and dielectric permittivity) which are closely related with the physical and structural changes of the XLPE insulation.

Thus, to avoid thermal overstressing, the ampacity of the current carrying conductor is limited by the maximum operating temperature of the cable core. So, it is quite important to predict the temperature rise exactly while designing the cable.

In this study, the thermal behavior of an XLPE single power cable is investigated using a FEM simulation with EMS tool. The figure below illustrates the standard configuration of the XLPE power cable. It is consisting of two essential parts: the conductor and the isolator. Besides that, it is equipped with a few other components: Semiconductor layers which keep the electric field homogenous in the cable, Metallic layer which is considered as the ground conductor and an external insulating PVC layer which covering the cable and protects it.

Standard configuration of XLPE power cable [1].
Figure 1 - Standard configuration of XLPE power cable [1].

Problem description

Using the frequency domain AC module coupled to Thermal, heat transfer analysis is carried on across the XLPE Power Cable. The power losses calculated in the electromagnetic field analysis are used as the input data of the thermal analysis to predict the temperature rise in different cable layers.

In this simulation, the studied 3D model cable is simplified to contain only four different regions, shown in Figure 2, and constituted by: Copper internal conductor surrounded by the XLPE thick layer, a Polyethylene (PE) second thin layer and an external PVC protection.

a)-Cross-sectional schematic illustration and b)-3D design of the studied model

Figure 2 - a)-Cross-sectional schematic illustration and b)-3D design of the studied model.                 
Table 1 - Cable dimensions
Component Dimensions
Conductor diameter 23 mm
XLPE outer diameter 64.6 mm
PE outer diameter 73.6 mm
PVC outer diameter 113.6 mm
Cable Length 1 m

The table below define the corresponding material properties mentioned above.

Table - Material properties

Material Density
(begin mathsize 14px style K g divided by m cubed end style)
Magnetic permeability Electrical conductivity
Thermal conductivity
Specific heat capacity
Copper (Cu) 8900 0.99 6 E+07 385 390
XLPE 920 1 0 0.28 2174
PE 952 1 0 0.28 1796
PVC 1290 1 0 1 1600

Boundary conditions:

1-Electromagnetic input:

The copper inductor is defined as solid coil, supporting a current input range of 300-1600 A peak and a frequency of 50Hz.

2-Thermal input: 

A ground temperature of 305K (32°C) is applied to the external PVC layer of the cable.
Thermal convection is applied on the air body surrounding the model at ambient temperature of 305°K with a heat transfer coefficient set to 10 W/m².K. 


The cross-sectional view of the meshed model is shown in the figure 3. A fine mesh control is applied to the heated parts for more accurate temperature results especially for the conductor.
Cross-sectional view of the meshed power cable.
Figure 3 - Cross-sectional view of the meshed power cable.


To evaluate the thermal behavior of the XLPE power cable under loading currents passing through it, a succession of simulations was executed for a range of current inputs of 300A, 640A, 1200A and 1600A, in order to calculate the maximum operating temperature.
The magnetic flux density through the cross-sectional view of the cable is shown in figure 4. It attained a maximum value of 6.15E-3 Tesla for 300A input.

Cross-sectional view of the flux density distribution across the XLPE cable
Figure 4 - Cross-sectional view of the flux density distribution across the XLPE cable

The temperature reaches a maximum value of 306.3K for 300A current input, which confirms the Reference [1] results for the 2D model. The thermal distribution is presented in the figure below.

Temperature distribution for 300A 
Figure 5 - Temperature distribution for 300A.

For the different tested current inputs, the maximum operating temperatures, obtained from EMS simulation, are presented in 2D plot variation across the cable radius. Since it represents the source of heat, the temperature keeps its maximum across the conductor surface and it comes-down to the ground temperature across the insulation layers.

Plot of the temperature variation versus current inputs across the cable radius.

Figure 6 - Plot of the temperature variation versus current inputs across the cable radius.

A comparison between Reference [1] thermal results for the 2D model of the power cable and the EMS ones for the 3D cable model shows a good coincidence between them.

Table 3 - Comparative table between EMS and Reference [1] temperature results:
Results 300A 640A 1200A 1600A
3D model-EMS 306.3K 310.9K 325.75K 341.23K
2D model-Reference [1] 306.03K 309.89K 321.9K 335K


The active stresses that occur in the conventional XLPE cable insulation, including essentially thermal effects, vary with time and leads to failure and limit to the effective service life of the power cables. It is generally preceded by a degradation phase due to the resulting physical and chemical changes in the cable properties, which may last for several years.

Through this FEM simulation, an investigation of the thermal behavior of a 3-D model of a single-core XLPE armored cable. It allowed to predict the maximum operating temperatures under different current loading. Maximum rates of temperature are limited to the central conductor which is due to the low thermal conductivities of the insulation layers.


[1]. Boukezzi, L., Y. Saadi, and A. Boubakeur. "The radial distribution of temperature in XLPE cable: An analysis with the Finite Volume Numerical Method (FVM)." Electrical Insulation and Dielectric Phenomena (CEIDP), 2010 Annual Report Conference on. IEEE, 2010.