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E7-18 10th International Conference on Insulated Power Cables E7-18
Jicable'19 - Paris - Versailles 23-27 June, 2019 1 / 5
Ampacity Calculation of Multi-System Cable Crossings at 40 MVA Frequency
Converter Station Mendrisio
Damian AEGERTER, Braavos GmbH, Stetten (Switzerland), damian.aegerter@cableizer.com
Stephan MEIER, Emetor AB, Västerås (Sweden), stephan.meier@cableizer.com
ABSTRACT
The planning of a new 40 MVA frequency converter station
and substation for the Swiss federal railway and the local
electric utility in Mendrisio, Switzerland, needed to consider
multiple cable crossings for up to twenty cable systems at
various voltage levels between 11 and 150 kV, including
five 15 kV systems with 16.7 Hz for the supply of the railway
system. In order to reach this goal, an iterative method was
developed to analytically calculate the derating factors for
all cables in case of multiple systems crossing multiple
other systems.
KEYWORDS
Ampacity, Cable Rating, Cable Crossing, Derating Factor.
INTRODUCTION
It is common to find multiple medium- and high-voltage
cables crossing each other in the vicinity of substations,
even ductbanks containing multiple systems crossing other
ductbanks. In these cases, the permissible current-carrying
capacity of the cables should be reduced to avoid
overheating. This is a three-dimensional problem because
the temperature rise decreases with the distance from the
crossing. The resulting longitudinal heat flux in the
conductor reduces the temperature rise at the crossing.
Therefore, calculating the mutual heating using formulae
valid for parallel routes would overestimate the influence of
the crossing cables.
The IEC standard 60287-3-3 "Calculation of Power Ratings
– Cables Crossing External Heat Sources" [1] provides a
general simplified method to estimate the reduction of the
current rating of a cable crossed by heat sources. The
standard states that by applying a superposition principle
the method can be generalized for several heat sources
crossing the rated cable horizontally, plus it contains an
iterative example calculation of a three-core cable crossing
three single core cables in a 90° angle. However, the
standard gives no advice on multiple systems crossing
multiple other systems.
Only one commercially available software tool was found
capable to compute the cable rating for cables crossing
external heat sources, but again for only two systems
crossing each other.
As finite element calculation was not feasible for the
planning at hand, an analytical method, based on IEC
60287-3-3, but extended for crossing of multiple systems,
was implemented and integrated into an existing cable
rating software [5].
IEC 60287-3-3 Method
Capabilities
The IEC 60287-3-3 describes a method for calculating the
continuous current rating factor for cables of all voltages
where crossings of external heat sources are involved. The
standard was published in 2007 and the method is based
on the description and illustrations given in [3]. The method
was presented in 1999 in two publications [2]. The method
is applicable to any type of cable and assumes that the
entire region surrounding the cable(s) has uniform thermal
characteristics and that, consequently, the principle of
superposition applies. The crossing heat source can be
located either above or below the rated cable(s) with the
crossing angle ranging from parallel to perpendicular.
The conductor temperature rise along the route of the rated
cable, caused by the influence of the crossing heat source,
may be calculated using Kennelly’s principle. The
temperature rise is maximum at the crossing point and
decreases with the distance z from it. As a consequence of
the varying temperature rise along the cable length, a
longitudinal heat flux is generated in the conductor, which
leads to a reduction in the conductor temperature rise at
the crossing, compared to the case when this longitudinal
flux is ignored.
The maximum permissible current in the cable to be rated,
taking into account the presence of a crossing heat source,
is obtained by multiplying the steady-state rating of the
cable, without the crossing heat source, by a derating factor
(DF) related to the influence of the heat source.
Limitations
The method has some limitations and is not applicable
without further considerations when
• crossing cables are touching
• cables are installed in ducts
• the soil is not uniform
• drying-out of soil is considered
• the rating is dynamic
Extended Method
After implementing cable rating calculations for two
crossing systems as described in IEC 60287-3-3, the
method was extended to multiple systems crossing multiple
other systems, as well as cables installed in unfilled ducts,
and backfilling.
Multiple Crossings
The IEC standard states that the DF can be generalized for
several heat sources crossing the rated cable by applying
a superposition principle. In order to make this
generalization, it is assumed that the point
z
= 0 is the
position where the temperature of the rated cable is at its
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Jicable'19 - Paris - Versailles 23-27 June, 2019 2 / 5
maximum. If the position of the hottest point cannot be
predetermined it may be necessary to perform the
calculation at several points to ensure that the hottest point
is found.
Since the IEC method requires knowledge of the hottest
point of the crossing, a weighting function of the losses for
both groups of cables was needed. Through multiple
iterative steps, the solver calculates the cable rating for
both groups and defines the derating for these groups.
For each system, the information of all crossing systems is
to be considered. The distance between the z-coordinate
of the rated system to the estimated hotspot is calculated
for each system. Using iterations over all systems, the
hotspot is eventually found.
The method considers an approximate weighted location
to be the hottest point in the x-coordinate of a system with
respect to a single crossing heat source.
=
()
[1]
number of cables in the system
cable n of the system
x-coordinate of cable n
distance between laying depth of cable n and crossing heat
source
Cables in Unfilled Ducts
In Switzerland, all power cables are laid in unfilled
polyethylene ducts. Therefore, crossing calculations must
comply with this condition.
The CIGRE Guide 640 [4] provides a recommendation on
how to allow for calculation of crossing cables installed in
unfilled ducts. The thermal resistance of the air space
between cable(s) and duct depends on the average air
temperature. The axial temperature gradient causes an
axial air flow in the air space leading to lower air
temperatures. The guide suggests to calculate the thermal
resistance of the air space without crossing to be on the
safe side. This suggestion was implemented
straightforward.
Addition of Backfill Material
Ducts are typically installed in concrete backfill which has
a lower thermal resistivity than soil.
The CIGRE Guide 640 [4] proposes to use an average soil
thermal resistivity but notes that this may introduce error
into the calculation, particularly where a wide range of
thermal resistivity values is encountered. The software
takes an average of the thermal resistivity of backfill and
soil, weighted by the distances for the calculation of the
temperature rises
∆θ
caused by the crossing systems. For
isolated ductbanks, the geometric factor of the external
thermal resistance of the backfill area is used.
Limitations
The implemented method has the following limitations:
• Crossing of multiple systems with different crossing
angles is not supported
• No consideration of soil drying-out caused by moisture
migration
• No dynamic ratings
IEC EXAMPLE CALCULATION
Description
The following example as presented in Fig. 1 is given in the
IEC standard 60287-3-3.
Fig. 1 Layout of IEC example calculation, [1]
The example is a 10 kV circuit of 300 mm2 Cu XLPE single-
core cables with a maximum permissible temperature of
90°C, laid in flat formation (with 0.072 m spacing) in 1.2 m
depth and a 400 mm2 Cu 132 kV three-core oil-filled cable
with a max. temperature of 85°C laid in 0.9 m depth. The
ambient temperature is 25°C, the soil resistivity is
0.8 K·m/W and the crossing angle is 90° (circuits are at
right angles). Furthermore, the standard provides the loss
factors, thermal resistances and losses in Table 1.
Table 1. Cable characteristics, [1]
Modelling and Calculation
As the method was integrated in [5] modelling of the cables
and arrangement as well as all testing took place using this
software.
Fig. 2 depicts the layout of the IEC example calculation as
a 2-dimensional preview. The crossing is indicated by
addition of the crossing angle next to the corresponding
system number.
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Jicable'19 - Paris - Versailles 23-27 June, 2019 3 / 5
Fig. 2 2-dimensional preview (Test 0, β=90°)
The software also provides a 3-dimensional preview of the
crossing situation as shown in Fig. 3. This is helpful when
considering multiple crossing systems.
The browser-based plot module also allows to turn and
zoom the preview of your crossing situation.
Fig. 3 3-dimensional preview
The green surface is the earth surface level, the brown
surface represents the 2D-preview of the systems going
straight and the orange surface represents the rotated 2D-
preview of the systems crossing with the angle
.
Results
Crossing at 90°
The IEC standard states that four iterations were necessary
to get the derating factors of the two links when taking into
account mutual thermal effects. The resulting derating
factors in the standard were:
• System A, 300 mm2 XLPE 10 kV: 0.92
• System B, 400 mm2 132 kV oil-filled: 0.85
For the comparison with the standard, constant loss
factors, thermal resistances and losses as given in the IEC
standard were used as input for the Cableizer model. The
results from the implemented software were in good
agreement with the IEC standard.
During the verification a systematic error in the standard's
solution of this example was identified. The calculation of
the mutual thermal resistance between cable and heat
source
Tmh
was not correct for the right cable of system 1
(equal to system A). The error is small but is repeated with
each iteration and, therefore, systematic. This led to a false
value for the calculated temperature rise
∆θ
of the
conductor of the rated cable, due to the crossing heat
sources and, consequently, to a wrong DF.
Corrected results for the first five iterations are presented
in Table 2:
Sys
1st
2nd
3rd
4th
5th
DF
A
0.8852
0.9200
0.9128
0.9149
0.9144
0.91
B
0.8258
0.8656
0.8541
0.8565
0.8558
0.86
Table 2. Correct DF for IEC example calculation
Crossing at different angles between 0° and 90°
In a second step, the de-rating factors were calculated for
different crossing angles between 0 and 90° with constant
loss factors, thermal resistances and losses as given in the
IEC standard, refer to Fig. 4 (incl. systematic error).
Fig. 4 Derating factors as a function of crossing angle
The thermal resistances and losses for the two cables
calculated by the software Cableizer differ from the values
given in the IEC standard. The example in IEC 60287-3-3
was calculated based on the revisions of the IEC standards
valid in 2007 whereas our calculation was done according
to the latest editions of the IEC 60287. In addition, the
values are not constant but depend on temperature and
current, so the software recalculates the losses with each
iteration based on the new conditions. Additionally, the
values are calculated separately for each single-core cable.
Comparing Fig. 5 with Fig. 4 shows a slightly lower de-
rating of system A and a higher de-rating of system B.
Fig. 5 Derating factor (recalculated parameters)
The de-rated current
Ir
is calculated by multiplying the
current
Ic
of the isolated system with the DF. An increase in
the rating of 2% (about 11 A) for system A and 8% (about
40 A) for system B when crossing at 90° compared to both
being parallel to each other is found.
Note that because the arrangement is symmetric, the result
is the same for a crossing angle
between 0 and -90°.
However, this is not necessarily the case if there were
multiple systems because the position z where the
temperature is at its maximum will change.
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Jicable'19 - Paris - Versailles 23-27 June, 2019 4 / 5
The results at a crossing angle
of 0.1° are equal to the
calculation of the two systems being parallel to each other.
The results at a crossing angle
of 90° are presented as
case 0 in Table 3.
Sys
β
Ir [A]
=
DF
x
Ic [A]
A
90°
610.78
0.907042
673.3785
B
0°
535.70
0.871175
614.9158
Table 3. Results for case 0 (refer to Fig. 2)
METHOD VERIFICATION
Procedure
Verification of the implemented calculation method was
done through plausibility checks and parametric studies
based on numerous test cases with defined arrangements.
The same two types of cables were used for the studies.
The number of straight and crossing systems was
increased, their position was changed, cables were placed
in ducts, in backfill, and the crossing angle β was set to
different values.
Test Cases
A few simple test cases are presented in this chapter for
reference.
Fig. 6 Test 1
Fig. 7 Test 4
Sys
β
Ir [A]
=
DF
x
Ic [A]
A
90°
571.50
0.929042
615.1548
B
0°
465.65
0.757256
614.9158
C
90°
571.51
0.929040
615.1582
Table 4. Results for test 1 (refer to Fig. 6)
Sys
β
Ir [A]
=
DF
x
Ic [A]
A
90°
550.81
0.924715
595.6500
B
0°
479.64
0.780016
614.9158
C
90°
620.35
0.939665
660.1824
Table 5. Results for test 4 (refer to Fig. 7)
Fig. 8 Test 5
Fig. 9 Test 6
Sys
β
Ir [A]
=
DF
x
Ic [A]
A
90°
544.63
0.952751
571.6345
B
0°
374.01
0.608229
614.9158
C
90°
654.23
0.962138
679.9725
D
90°
575.12
0.952859
603.5753
Table 6. Results for test 5 (refer to Fig. 8)
Sys
β
Ir [A]
=
DF
x
Ic [A]
A
90°
505.16
0.883711
571.6345
B
0°
371.11
0.672314
551.9899
C
90°
617.07
0.907486
679.9725
D
90°
533.51
0.883913
603.5723
E
0°
447.34
0.810418
551.9899
Table 7. Results for test 6 (refer to Fig. 9)
SUBSTATION MENDRISIO
Planning Phase
The cable routing around the planned new substation
Mendrisio shows several critical locations (Fig. 10) with
respect to current rating.
As an example, location C/7 is a crossing of two duct banks
containing multiple medium voltage systems with two high
voltage systems below at an angle
of 45°.
Fig. 11 shows a two-dimensional preview of the situation
and Fig. 12 shows the same situation in a three-
dimensional preview.
Fig. 10 Situation Mendrisio with critical locations
Fig. 11 2D preview of the crossing C/7
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Jicable'19 - Paris - Versailles 23-27 June, 2019 5 / 5
The current load was defined and the calculation was done
to verify that all conductor temperatures are at or below the
maximum permissible temperature. Calculation was done
assuming the systems being parallel (
= 0°) and when
crossing (
= 45°) which resulted in lower temperatures as
expected because the resulting longitudinal heat flux in the
conductor reduces the temperature rise at the crossing.
The largest reduction was seen for the two crossing HV
systems with a reduction from 73.4° to 63.3° for the system
C (left) and 70.2°C to 56.7°C for the system I (right).
Conclusion
Many other calculations were done during the planning
phase of the substation until the beginning of 2018. Using
the newly developed method to calculate multiple systems
crossing multiple other systems allowed for an optimization
of the conductor cross-sections which helps reducing the
costs and ensures a safe and reliable operation.
Thereafter, tendering took place and the installation works
began in 2018. Commissioning of the new 40 MVA
frequency converter station and substation in Mendrisio,
Switzerland is expected in 2021.
REFERENCES
[1] IEC 60287-3-3, 2007, “Electric cables – Calculation of
the current rating – Part 3-3: Sections on operating
conditions – Cables crossing external heat sources”,
International Electrotechnical Commission, Geneva,
Switzerland
[2] G. Anders, H. Brakelmann, 1999, “Cable Crossings -
Derating Considerations Part I Derivation of Derating
Equations and II Example of Derivation of Derating
Equations”, IEEE Transactions on Power Delivery vol.
14, No. 3, 709-720.
[3] G. Anders, 2005, “Power Cables in Unfavorable
Thermal Environment”, Wiley-IEEE-Press, 121-164.
[4] Frank de Wild et al, 2015, “A Guide for Rating
Calculations of Insulated Cables”, CIGRE Working
Group B1.35, 100-101.
[5] Rating Software https://www.cableizer.com
GLOSSARY
DF: Derating factor
(1)
(2)
(3)
Fig. 12 3D preview of the crossing C/7 with view of xz-plane (1), yz-plane (2), xy-plane (3)
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