AC RESISTANCE:

If a conductor is carrying high alternating currents, the distribution of current is not evenlydispersed throughout the cross section of the conductor. This is due to two independent effectsknown as skin effect and proximity effect.

SKIN EFFECT FACTOR(ys):

If the conductor is composed of one or more concentric circular elements, then the centre portionof the conductor will be enveloped by a greater magnetic flux than those on the outside.Consequently the self induced back-emf will be greater towards the centre of the conductor, thuscausing the current density to be less at the centre than the conductor surface. This extraconcentration at the surface is known as skin effect, and results in an increase in the effectiveresistance of the conductor.

ys = xs

4 / ( 192 + xs

4 )

wherexs

2= 8 . π . ƒ .10

-7 . ks / Rdct

f = Frequency (Hz)ks = Factor determined by conductor construction

1 for circular, stranded, compacted and sectored

Rdct =DC resistance at operating temperature t

PROXIMITY EFFECT FACTOR(yp):

The proximity effect also increases the effective resistance and is associated with the magneticfields of two conductors which are close together. If each carries a current in the same direction,the halves of the conductors in close proximity are cut by more magnetic flux than the remotehalves. Consequently the current distribution is not even throughout the cross-section, a greaterproportion being carried by the remote halves. If the currents are in opposite directions, the halvesin close proximity will carry the greater density of current.

1) For TWO CORE and TWO SINGLE CORE cables:

yp = xp 4 / ( 192 + 0.8 xp 4 ) ∗ (dc / S)2 ∗ 2.9

wherexp

2 = 8 . π . ƒ .10-7

. kp / Rdct

f = Frequency (Hz)

kp = Factor determined by conductor construction1 for circular, stranded, compacted and sectored0.8 if above conductors are dried and impregnated

dc = Diameter of conductor (mm)

AC Resistance, Skin& Proximity Effect

10.3.2.1

Diagrams of cables are illustrative only and are not necessarily to scale.

This brochure is distributed with the understanding that the authors and editors are not responsible for the results of any actions taken on the basis of information in this work , or any errors or omissions. Further,General Cable New Zealand Ltd is not engaged in rendering professional services. General Cable New Zealand Ltd expressly disclaims all and any liability to any person in respect of anything and of theconsequences of anything done or omitted to be done by any such person in reliance whether whole or partial of the whole or any of the contents of this publication. All rights reserved. No part of this work coveredby copyright may be reproduced or copied in any form or by any means without the written permission of General Cable New Zealand Ltd.

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Rdct =DC resistance at operating temperature t.

S = Spacing between conductor centres (mm)

2) For THREE CORE and THREE SINGLE CORE cables:

yp

= xp 4 / ( 192+0.8 xp 4) . (dc / S)2 . [0.312 . (dc / S)

2 +1.18 / { xp 4 / ( 192+0.8 xp 4) +0.27}]

where

xp2 = 8 . π . ƒ .10

-7. kp / Rdct

f = Frequency (Hz)

kp = Factor determined by conductor construction1 for circular, stranded, compacted and sectored0.8 if above conductors are dried and impregnated

dc = Diameter of conductor (mm)

Rdct =DC resistance at operating temperature t.

S = Spacing between conductor centres (mm)

For cables in flat formation, S = √(S1 ∗ S2), where S1, S2 are the distances between conductors.

THUS:AC RESISTANCE at temperature t :

Ract= Rdct

[1 + ys + yp]

NOTE: The formulae given apply to both copper and aluminium conductors. see IEC 60287 formore details.