cable impedance calculations - open electrical

Cable Impedance CalculationsFrom Open ElectricalThis article provides details on the calculation of cable impedances - dc resistance, ac resistance andinductive reactance.

Contents1 Cable Resistance

1.1 DC Resistance1.2 AC Resistance

2 Cable Reactance3 References

Cable ResistanceThe dc and ac resistance of cable conductors can be calculated based on IEC 60287-1 Clause 2.1.

DC ResistanceThe dc resistance of cable conductors is calculated as follows:

Where is the dc resistance at the conductor operating temperature ( / km)

is the resistivity of the conductor material at 20oC (.km).For copper conductors, = 1.7241 x 10-5

For aluminium conductors, = 2.8264 x 10-5

is the cross-sectional area of the conductor (mm2) is the temperature coefficient of the conductor material per K at 20oC.

For copper conductors, = 3.93 x 10-3

For aluminium conductors, = 4.03 x 10-3

is the conductor operating temperature (oC)

AC ResistanceThe ac resistance of cable conductors is the dc resistance corrected for skin and proximity effects.

Where is the ac resistance at the conductor operating temperature ( / km)

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is the dc resistance at the conductor operating temperature ( / km) is the skin effect factor (see below) is the proximity effect factor (see below)

The skin effect factor is calculated as follows:

Where

is the dc resistance at the conductor operating temperature ( / km) is the supply frequency (Hz) is a constant (see table below)

Note that the formula above is accurate provided that 2.8.

The proximity effect factor varies depending on the conductor geometry. For round conductors, the followingformulae apply.

For 2C and 2 x 1C cables:

For 3C and 3 x 1C cables:

Where

is the dc resistance at the conductor operating temperature ( / km) is the supply frequency (Hz) is the diameter of the conductor (mm)

is the distance between conductor axes (mm) is a constant (see table below)

Note that the formula above is accurate provided that 2.8.

For shaped conductors, the proximity effect factor is two-thirds the values calculated above, and with:

equal to the diameter of an equivalent circular conductor of equal cross-sectional area anddegree of compaction (mm)

where is the thickness of the insulation between conductors (mm)


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Type of Conductor Dried andImpregnated?Copper

Round, stranded Yes 1 0.8

Round, stranded No 1 1

Round, segmental - 0.435 0.37

Sector-shaped Yes 1 0.8

Sector-shaped No 1 1

AluminiumRound, stranded Either 1 1

Round, 4 segment Either 0.28 0.37



Cable ReactanceThe series inductive reactance of a cable can be approximated by the following equation:

Where is the conductor inductive reactance ( / km) is the supply frequency (Hz) is the axial spacing between conductors (mm) is the diameter of the conductor, or for shaped conductors, the diameter of an equivalent

circular conductor of equal cross-sectional area and degree of compaction (mm) is a constant factor pertaining to conductor formation (see below for typical values)

No. of wirestrands inconductor

K

3 0.0778

7 0.0642

19 0.0554

37 0.0528

>60 0.0514

1 (solid) 0.0500

For 3C and 3 x 1C cables, the axial spacing parameter depends on the geometry of the conductors:


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ReferencesIEC 60287-1-1, Electric cables Calculation of current rating Part 1: Current ratingequations (100% load factor) and calculation of losses Section 1: General(http://webstore.iec.ch/p-preview/info_iec60287-1-1%7Bed1.2%7Den_d.pdf) , 2006G.F. Moore, Electric Cables Handbook (http://www.amazon.com/gp/product/0632040750/ref=as_li_tf_tl?ie=UTF8&tag=openelect-20&linkCode=as2&camp=217145&creative=399349&creativeASIN=0632040750) , Third Edition, 1997, an excellent referencebook for cables

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This page was last modified on 4 October 2012, at 17:20.


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cable impedance calculations - open electrical

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