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Thermal analysis of underground cable crossings at various crossing angles

Conference Paper · November 2014

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Lazaros Exizidis Vasilis Chatziathanasiou

European Network of Transmission System Operators for Electricity (ENTSO-E) Aristotle University of Thessaloniki
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Thermal analysis of underground cable crossings at
various crossing angles
L. Exizidis 1 *, V.Chatziathanasiou1 and B. Hennuy2

1
Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki
54124 Thessaloniki, Greece
2
Department of Electricity, Grids and End-Use, Laborelec GDF SUEZ
Rodestraat 125, 1630 Linkebeek, Belgium

*
lazaros.exizidis@umons.ac.be

according to IEC-IEEE, suggesting a possibly better

Abstract— When an underground power cable crosses other
cables or external heat sources there is obviously an impact on methodology. In [3] an improved formula for the assessment
the cable’s initial temperature. The rise on the cable’s of the external thermal resistance of three buried single-core
temperature depends highly on the angle of the crossing and, in cables is proposed. V.T. Morgan in [4] studied a group of
particular, the closest to 0o the angle is (parallel cables), the buried power cables in thermally non-uniform soil of defined
higher the temperature rise becomes. In this work, the shape and calculated the external thermal resistances of the
temperature of two 3-phase cables that are installed parallel, cables while H. Brakelmann and G. Anders in [5] made a
perpendicular and oblique to each other is examined with a 3D study investigating cases where cables cross regions with
simulation study using a Finite Element Methods Software. The unfavourable thermal conditions. In the majority of the cases
presented method can be used for different crossing angles and
the unfavourable thermal environment is very short leading to
multiphase cables in the same way as it is used for the three
common cases. The findings of this work are useful for industrial the effect of the crossing being ignored, but in the latter paper
installations, as it provides information about the temperature the authors presented an analytical solution for the
increase of cable crossings under various crossing angles leading computation of the derating factors in such a case. Lastly, a
to a better derating factor and defining the distance after which very interesting and fundamental work was presented by the
the effect of the crossing eliminates. It is calculated that as the same authors in [6] and [7], where the effect of cable
angle approaches to 90o, the temperature at the central point of crossings under different angles was investigated. An
the crossing reduces importantly and the effect of the crossing analytical solution for the computation of the derating factors
eliminates faster. has been developed by the authors, followed by an illustrative
Index Terms— Cable crossings, Finite Element Methods, example.
thermal behaviour, underground power cables Although there is a considerable number of papers focused
on the thermal effects of cable crossings, most of them
I. INTRODUCTION perform an analytical study and approach. Software packages
Underground power cables that are installed adjacently to that use FEM were introduced quite recently for power cable
other power cables are subject to higher temperatures than the installations, adding important knowledge to the existing
expected ones, due to the thermal contribution of the other studies. In 2012, Z. Y. Huang et al. presented in [8] a study
cables of the array. In such cases the crossing angle can be investigating the thermal ratings in HV cable crossings using
considered as zero, which makes the calculation of 3D finite element analysis. The effect of a realistic cable
temperature easier while staying in the safe side in terms of crossing case was investigated and the results of the FEM
overheating, given that the temperature cannot exceed the analysis were compared to the ones of the conventional study
calculated one for parallel cables [1]. However it will be using the IEC standards, with the first one giving more
proved that the temperature rise for particular crossing angles detailed and accurate results. In another recent study in [9],
like 45o and 90o is considerably lower than for parallel cables, the authors carry out a 3D FEM analysis of a distribution
which can lead to an increase on the current carrying capacity ductbank that crosses a transmission one. The derating impact
of the cable and a reduction on the installation costs. For cable is then investigated based on the results of the FEM analysis.
arrays with 3-phase cables the calculation of temperature is This work investigates the thermal behaviour of two 3-
even more complicated as there is also the effect of the other phase power cables that cross each other, and evaluates the
two phases. effect of the crossing angle on their temperature, based on a
Cable crossings have been the topic of various research FEM-based simulation that overpasses the complex
papers in the past. In [1], an algorithm for the numerical mathematical formulas and provides more accurate results [8].
calculation of the derating factor for cable crossings is It also aims to deliver information about the elimination of
presented, taking into consideration the longitudinal heat flow the crossing effect as we move the investigated point away
in the cable’s metallic screen. In [2], Vollaro et al. made a from the crossing centre and it suggests a useful tool that can
comparison between the IEC-IEEE standards and the results be used for the computation of temperature of, other than
of a numerical analysis concerning the heat losses from arrays parallel, cable crossings.
of pipes or power cables buried in homogeneous soil. The
results of their study were different from the ones obtained
 II. SIMULATION OF CABLE CROSSINGS AT VARIOUS CROSSING TABLE 1: THERMAL PROPERTIES OF THE CABLE
ANGLES Properties Density, ρ Heat Thermal
For the purpose of this work two simplified versions of (kg/m3) Capacity, Conductivity, k
commercial 3-phase, MV cables were used. The cables were Cp (W/m.K)
installed underground at different depths crossing each other (J/kg.K)
at a specific angle. Conductor 2700 902 237
In Fig. 1, one can find the single-phase properties of the Insulation/Jacket 930 500 1/3.5
Concentric Wires 8940 385 401
simulated cables. The radius of the aluminium conductor is
Soil 1300 800 1
9.26 mm, the thickness of the XLPE insulation 4.74 mm, the
thickness of the concentric copper wires is 2.096 mm and the
thickness of the polyethylene jacket, 2.954 mm. In Fig. 2 the “Open boundaries” were applied at the edges of the cables
installation array for two parallel 3-phase cables is presented and the soil, in order to achieve an unaffected from the
for illustration reasons. The upper cable (Cable 1) is buried at boundaries thermal solution. Finally, the current of the cable
a depth of 0.8m and the deeper cable (Cable 2) 0.2m deeper. was constant with a value of I=400Amp and was applied by
The soil was assumed to have a k=1W/m.K thermal setting the conductor to be a heat source based on the thermal
conductivity which is a common value and the ambient losses calculated by the current and the conductor’s resistance.
temperature of the air was considered to be 10oC. The burying The thermal losses of the conductor, Wcond, and the
depth as well as the air and soil properties are kept the same accompanied calculations are based on the IEC60287
for all three different cases, with the only difference being the standards [10] as given by (1)-(4):
crossing angle of the two cables. The thermal properties of
the simulation are presented at table 1. 𝑊𝑐𝑜𝑛𝑑 = 𝐼 2 𝑅 (1)
𝑅′ = 𝑅0 (1 + 𝑎20 (𝑇 − 20)) (2)
𝑅 = 𝑅′ (1 + 𝑌𝑠 + 𝑌𝑝 ) (3)
𝐿
𝑅0 = 𝑝 ∗ (4)
𝐴

Where R΄ is the resistance at maximum temperature, R0 and

α20 are the resistance and the temperature coefficient at 20oC,
T is the operating temperature, p is the thermal resistivity, A
and L are the area and the length of the conductor and R is the
resistance of the conductor taking into account the proximity
and skin effect factors, Yp and Ys, as given by (5)-(8):
𝑋𝑠4
𝑌𝑠 = (5)
(192+0.8𝑋𝑠4 )
𝑋𝑝4 𝑑 𝑑 2 1.18
𝑌𝑝 = ( 𝑐 )2 [0.312 ( 𝑐 ) + 𝑋4
] (6)
(192+0.8𝑋𝑝4 ) 𝑠 𝑠 𝑝
+0.27
(192+0.8𝑋4
𝑝)

8𝜋𝑓
𝑋𝑠 = √ 10−7 𝑘𝑠 (7)
Figure 1: Properties of the single-phase cable 𝑅′
8𝜋𝑓
𝑋𝑝 = √ 10−7 𝑘𝑝 (8)
𝑅′
Xs and Xp are the arguments of the Bessel function, according
to [10].
A. Parallel cables
As it was mentioned at the introduction section, cables that
are buried parallel to each other show the highest possible
temperature rise compared to cable crossings at any other
angle. The geometry of the cable array that is examined at the
present subsection is presented in Fig. 2 and 3. The two
power cables are buried parallel and their characteristics are
the ones presented at the introduction of section II.

Figure 2: Parallel installation of the 3-phase cables

For the following analysis the soil was represented by a

rectangular box with thermal properties as those described.
Furthermore the same boundary conditions were applied for Figure 3: Simulated geometry for parallel cables
all three cases (parallel, oblique and perpendicular crossing), Performing the simulation to the described installation, we
and in particular heat flux was chosen at the surface between present in Fig. 4 and 5 the temperature versus the distance
the soil and the external environment, with the heat transfer from the central point of 6m long cables, for each of the three
coefficient being h=25 W/m2K.
phases of each cable of the array. As it was expected, phases temperature is 8.3% higher with a slow decreasing rate, and
2 and 3 of cable 1, that are closer to cable 2, show a thus the crossing effect is slowly eliminating.
temperature higher than the phase that is closer to the soil’s
surface. For cable 2 the result is the opposite. This result was C. Perpendicular Crossing
expected because cables that are closer to other external heat The last considered case is the one with cables being
sources show an additional rise in their temperature caused perpendicular to each other. As before the only difference in
by the latter one. Furthermore, from the results of the the installation is that the two 3-phase cable arrays are
simulation we notice that the maximum appeared temperature crossing each other at an angle of 90o, as presented in Fig. 8.
was around 84oC, and it refers to the phases of cable 1 that The temperature of the three phases versus the distance from
are buried closer to cable 2. This temperature is 24oC higher the central crossing point for cable 1 is presented in Fig. 9.
compared to a single-buried cable, i.e. without the effect of Comparing the results with the parallel and the oblique case,
the crossing, which is presented at subsection II.D. one can see a reduction in the temperature of the upper cable
at the centre of the crossing of about 10.12% and 2.58%
respectively, while at a distance of 3m from the centre the
reduction becomes higher reaching 24.4% compared to the
parallel’s case results.

Figure 4: Temperature results for parallel array - Cable 1

Figure 6: Simulated geometry for oblique crossing

Figure 5: Temperature results for parallel array - Cable 2

B. Oblique crossing
Figure 7: Temperature results for oblique crossing – Cable 1
The second of the three simulated geometries refers to the
same array of two underground 3-phase cable systems, with
only difference that the crossing angle is now 45o, as Furthermore at a distance of 3m from the crossing centre, the
presented in Fig 6. In fig 7 one can see the temperature versus temperature is 5.8% higher compared to the single-buried cable,
the distance from the central point of the crossing, for each of and even though the effect of the crossing is not yet eliminated,
the three phases of cable 1. Regarding cable 1, the phase it eliminates faster and in a smaller distance from the crossing
closer to the surface of the soil presents lower temperature, as point, compared to the oblique crossing.
expected, but the results of this simulation show a maximum D. Comparison of the parallel, oblique and perpendicular
indicated temperature for the first cable of about 77.5 oC, installations with a single-buried cable installation
which compared to the parallel case is 7.74% lower at the
central point of crossing. Furthermore, in a distance of just A 3-phase cable of the above characteristics buried
3m from the centre the temperature becomes 65oC, almost underground under the same soil and surrounding conditions
22.6% lower as seen in Fig. 7. Considering that the same 3- is also simulated for comparison reasons. The single-buried
phase cable when buried alone shows a temperature of 60 oC, cable indicates a maximum temperature under constant load
one notices that 3m away from an oblique crossing the of 60oC. Comparing this result to the presented installations,
at the previous subsections, it is indicated that the temperature comparing to the case of a parallel crossing. Information
of the cables installed in an array can increase from 15.5oC to about the temperature rise for cable crossings at a different
24oC above the temperature of a single-buried cable, for a than 0o angle, can assist in the calculation of such installations.
perpendicular (best case) or a parallel (worst case) installation Furthermore, obtaining information about the distance after
correspondingly. It is also important to point out that even at which the crossing effect is eliminated can be proved
a distance of 3m away from the point that the crossing takes important for the operation of the system, as it gives a scope
place, the effect is still obvious and the temperature of the two for safer installations, possibly higher current carrying
cables is higher than the temperature of a single-buried cable. capacity and reduction of the installation costs, as the size of
However, regarding the perpendicular crossing the effect is the installed cables can be chosen based on the real angle of
eliminating faster being only 3.5oC above the single-buried the crossing and not considering the safe case (parallel cables).
cable’s temperature while for the oblique crossing it is 5oC, Such an analysis can also be useful for cases that the cables
indicating that as the crossing angle approaches 90o, the effect are crossing other external heat sources, e.g. in geometries
on the temperature rise decreases. The comparison of all three that it is difficult to establish a mathematical formula
cases, along with the case that there is no crossing, are regarding the thermal interactions that take place, given the
presented at table 2. geometry of the problem.

TABLE 2: TEMPERATURE COMPARISON AMONG THE DIFFERENT CASES

Crossin Highes Highest Temp. Temp.

g Angle t Temp. Increase Increase
Temp. 3m away from the from single
[oC] from the Parallel cable
crossing Installatio installation
point n [%] [%]
[oC]
No 60 60
crossing
0o 84 +40%
(Parallel
)
45o 77.5 65 -7.74% +29.16%
90o 75.5 63.5 -10.12% +25.8%
Figure 9: Temperature results for perpendicular crossing –Cable 1

IV. ACKNOWLEDGEMENTS
This research was co-funded by the EU Erasmus
Placements Program and Laborelec GDF SUEZ.

V. REFERENCES
[1] Anders G.J., Derating Factor for Cable Crossings With
Considerations of Longitudinal Heat Flow in Cable Screen, IEEE
Transactions on Power Delivery, Vol. 19, Issue 3, pp. 926-932 (2004).
[2] Vollaro RL, Fontana L, Quintino A, Vallati A., Improving evaluation
of the heat losses from arrays of pipes or electric cables buried in
homogeneous soil, Applied Thermal Engineering, Vol. 31, Issues 17-
18, pp. 3768-3773 (2011).
[3] Kovac N., Anders G.J., Poljak D., An Improved Formula for External
Thermal Resistance of Three Buried Single-Core Metal-Sheathed
Touching Cables in Flat Formation, IEEE Transactions on Power
Delivery, Vol. 24, Issue 1, pp. 3-11 (2009).
[4] Morgan V.T., Slaninka P., The external thermal resistance of power
cables in a group buried in a non-uniform soil, Electrical Power
Figure 8: Simulated geometry for perpendicular crossing Systems Research, Vol. 29, Issue 1, pp.35-42 (1994).
[5] Brakelmann H., Anders G.J., Ampacity Reduction Factors for Cables
Crossings - Thermally unfavorable Regions, IEEE Transactions on
III. CONCLUSION Power Delivery, Vol. 16, Issue 4, pp. 444-448 (2001).
In this paper a steady-state analysis of the thermal [6] Anders G.J., Brakelmann H., Cable crossings-derating considerations,
behaviour of two buried power cables that cross each other at Part I, Derivation of derating equations, IEEE Transactions on Power
Delivery, Vol. 14, Issue 3, pp. 709-714 (1999).
different angles was carried out. In particular, crossing angles [7] Anders G.J., Brakelmann H., Cable crossings-derating considerations,
of 0o, 45o and 90o were considered and the results were Part II, Example of derivation of derating curves, IEEE Transactions
compared in order to prove the importance of the angle on the on Power Delivery, Vol. 14, Issue 3, pp. 715-720 (1999).
resulting temperature. The study was made using a FEM [8] Huang Z.Y., Pilgrim J.A., Lewin P.L., An Investigation of thermal
Ratings for High Voltage Cable Crossings Through the Use of 3D
software and performing a 3D analysis. It was proved that a Finite Element Analysis, The Fifth UHVnet Colloquium, University
crossing angle of 90o can cause a temperature rise of about of Leicester, Leicester, UK, 18 - 19 Jan 2012. , 32.
2.6% less than the 45o and 10.12% less than a parallel [9] Chaaban M., Leduc J., Reduction in current carrying capacity due to
crossing while the effect of the crossing for this case reduces cables crossing, 8th International Conference on Insulated Power
Cables, jicable’11, Versailles, France, 19-23 June 2011.
importantly for distances above 3m approaching the [10] International Standard IEC 60287, Electric Cables – Calculation of
temperature of a single-buried power cable. Similarly, an the current rating, Edition 1.2 (2006)
angle of 45o results in a 7.74% lower temperature increase
 VI. BIOGRAPHIES
Lazaros Exizidis has studied Electrical and Computer
Engineering at the Aristotle University of Thessaloniki in
Greece. From the beginning of 2013 he is a PhD Candidate at
the University of Mons in Belgium, coping with the
uncertainty introduced by the high penetration of Renewable
Energy Sources to distribution grids, following a smart grid
approach.
Vasilis Chatziathanasiou has graduated from the
Department of Electrical and Computer Engineering of
Aristotle University of Thessaloniki in Greece, where he is
currently an Assistant Professor. His interests are in the area
of coupled electro-thermal problems in power transmission
systems.

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