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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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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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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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