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各位電纜同仁好：

雖然我們可以通過(guò)實(shí)驗(yàn)儀器測(cè)試出導(dǎo)體的直流電阻，然后在用下面的公式，很輕易地從理論上計(jì)算出導(dǎo)體的交流電阻，但誰(shuí)可以用自己設(shè)計(jì)的實(shí)驗(yàn)來(lái)驗(yàn)證這個(gè)公式的正確性呢？

Ra.c=Rd.c(1+Ys+Yp)

——其中Ra.c是導(dǎo)體的交流電阻，Rd.c是導(dǎo)體的直流電阻，Ys是集膚效應(yīng)因子，Yp是鄰近效應(yīng)因子。

現(xiàn)在就有一幫外國(guó)的電纜專家做了這樣的事情，并把他們做的方法和結(jié)果寫了出來(lái)。

他們的工作組成員是：

Eric DORISON (FRANCE);

Laurant MOREAU (FRANCE);

Udo FROMM (GERMANY);

Vince BARRY (UNITED KINGDOM);

Christian REMY (ITALY);

Jose Manuel MENDEZ (SPAIN);

Asakiyo UEDA (JAPAN);

Graeme BARNEWELL (AUSTRILIA);

Mike SHUVALOV (RUSSIA)

他們發(fā)表的資料名叫《LARGE CROSS-SECTIONS AND COMPOSITE SCREENS DESIGN》，里面有詳細(xì)的實(shí)驗(yàn)設(shè)計(jì)方法及計(jì)算公式，已經(jīng)他們的實(shí)驗(yàn)結(jié)果。

CONTENTS
 
 
GENERAL
1
  Background................................................4
2  Terms of reference...............................................4
3  Brochure Content......................................4
 
 
PART 1 - LARGE CROSS SECTIONS CONDUCTORS.
4
  Introduction................................................................5
5  General considerations..................................................................6
5.1  Skin effect and proximity effect...................................................6
5.2  Skin effect in solid conductors......................................................6
5.3  Proximity effect between solid conductors..................................................7
5.4  Skin effect and proximity effect in stranded conductors...........................7
5.5  Losses in a wire influenced by a magnetic field..............................................8
5.5.1  General expression of the electromagnetic field...............................8
5.5.2  Fields and current density within the cylinder.............................9
5.5.3  Losses calculation............................10
5.5.4  Influencing current.........................................11
5.5.5  Multiple influences : using superposition principle.................................12
5.6  Segmental conductors......................................................13
5.7  Coefficients for cores using aluminium wires......................................14
5.7.1  General.......................................................................14
5.7.2  Solid conductor....................................................14
5.7.3  Segmental conductor.....................................................16
5.7.4  Segmental conductor with peripheral strands.....................................18
5.8  I.E.C. present statements.......................................19
6  Calculation Methods for segmental cores...............................21
6.1  Several possible ways......................................21
6.2  No exact solution............................................................23
6.3  A pragmatic approach..................................23
7  Derivation of practical formula for skin effect....................................24
7.1  Background.....................................................24
7.2  Skin effect in the segments.....................................................24
7.3  Proximity effect between segments.......................................25
7.4  Sugiyama!ˉs approach........................................25
7.4.1  Introduction.....................................................25
7.4.2  Basic assumptions...........................................26
7.4.3  Principles...............................................................26
7.4.4  Proximity effect : eddy currents............................................................27
7.4.5  Proximity effects : circulating currents................................29
7.4.6  Final expression...................................................30
7.5  Comparing calculation methods...........................................31
7.5.1  General..............................................31
7.5.2  Skin effect within segments and losses due to eddy currents  in the wires...................................31
7.5.3  Proximity effects between segments............................................34
7.5.4  Proximity effects between segments, using superposition.........................34
7.5.5  Looking for validation........................................36
7.6  Practical formula....................................37
7.7  Comparison with classical formula....................................38
8  Derivation of practical formula for proximity effects..............................41
8.1  Background..................................................41
8.2  Calculations...........................................41
8.2.1  General..............................................41
8.2.2  Losses generated within the strands.............................................42
8.2.3  Losses due to circulating current between the strands.................43
/87
2

  Conclusion.....................................................44
8.3
9  Measurement techniques.....................................45
9.1  General.........................................................45
9.2  Electric Methods.....................................45
9.2.1  Introduction............................................45
9.2.2  Measurement of conductor ac resistance using the sheath as the return conductor......................46
9.2.3  Measurement of ac resistance using an ac bridge with a current transformer...............................46
9.2.4  Methods that could be used to give greater accuracy in measurement.........................................48
9.3  The Thermal Measurement Method...........................................50
10  Recommendations...............................................52
 
PART 2 - SHORT-CIRCUIT PERFORMANCES OF COMPOSITE SCREENS
11
  Introduction....................................53
12  Calculation method.......................................53
13  Investigating test data..........................................................53
14  Recommendations.............................................................54
 
 
PART 3 - EDDY CURRENT LOSSES IN COMPOSITE SCREENS.
  Introduction............................................................55
15
16  losses in cable screen wires....................................55
17  Circulating currents in a bundle of wires due to a magnetic field.................................56
17.1  General..........................56
17.2  Wires are assumed to be laid straight.........................................57
17.3  Wires are wound.....................................58
18  Calculation of losses in cable screen wires............................59
18.1  Eddy current losses due to the magnetic fields acting on every wire.............................59
18.2  Losses due to longitudinal currents.....................61
18.2.1  General.......................................61
18.2.2  Calculations using circuit theory.........................................61
18.3  Losses in the foil and screening effect of the foil..........................................64
18.4  Calculation results..........................................65
18.5  Stranding effect...................................................................66
18.6  Inter-wire medium and counter-helix........................................................66
19  Recommendations.....................................................66
 
REFERENCES
 
APPENDIX 1 : FROM MAXWELL!ˉS EQUATINS TO EDDY CURRENTS IN A WIRE.
1
  Maxwell!ˉs quations................................................70
2  Fields expressions.........................................72
3  Boundary conditions.................................................72
4  fields and current density within the cylinder.....................................74
 
APPENDIX 2 : SUGIYAMA!ˉS CALCULATION OFSKIN EFFECT IN SEGMENTAL CORES
1
  General.......................................................75
2  Equivalent conductance............................................75
3  Skin effect in the strands of a segment alone......................................76
4  Final expression for skin effecct in segmental cores...............................77
4.1  Introduction................................................77
4.2  Dealing with Hc..............................................77
4.3  Dealing with Hs................................................78
4.4  Consolidation........................................................79
4.5  Simplifications........................................................79
4.6  Working formulae..................................80
 
APPENDIX 3 : LOSSES IN A BUNDLE OF SCREEN WIRES
1.
  Taking into account inter-wire conductivity......................................81
2.  Losses induced by the counter helix.............................................84

GENERAL




1 BACKGROUND.

Some areas in cable engineering which appear to be more and more frequently referred to, still remain
uncovered by International Standards or CIGRE Recommendations.

There is an increasing demand for large conductor cross section XLPE cables for bulk power transmission.
But there is no agreed method to define the value of the a.c. resistance to take into account when calculating the
current-carrying capacity of such cables, whereas it is a critical parameter.

Metallic screens for extruded cables are more and more designed in some countries as a combination of
aluminium or copper wires and metallic sheath or tape acting as water barrier.
No method is available yet to calculate the short-circuit current performance of these composite screens and to
calculate the eddy current losses associated with these cable constructions.

CIGRE Working Group B1-03 was set up in September 2001 to address these matters.


2 TERMS OF REFERENCE.

The Working Group was required to elaborate some recommendations for calculation and/or measurement of :
a.c. resistance of large conductor cross-section cables,
short-circuit performance of composite screens,
losses assessment of composite screens,

for HV/EHV extruded power cables.


3 BROCHURE CONTENT

The technical brochure is split into 3 parts, corresponding to the fields stated in the terms of reference :

The first part deals with a.c. resistance of large conductor cross-section cables.
The second one gives directions for calculating composite screens short-circuit performances.
And the third part gives recommendations on the way to take into account losses in composite screens when
performing cable current-carrying capacity calculations.

PART 1 - LARGE CROSS SECTIONS CONDUCTORS.
 
 
 
 
 
4   INTRODUCTION.
 
It is well known that the current rating of cables for a.c. transmission strongly depends on the a.c. resistance of
the conductor.
 
The current-carrying capacity of large cross section stranded conductors can be seriously reduced by skin and
proximity effects, i.e. electromagnetic effects which produce an uneven distribution of current over the
conductor cross section and hence effectively increase its resistance.
To reduce the magnitude of these effects, segmental conductors were developed.
 
The IEC 60 287-1-1 standard [1] provides formulae to determine the a.c. resistance from the d.c. resistance.
 
These formulae were obtained by solving Maxwell!ˉs equation in solid round conductors, and using
approximations of Bessel!ˉs functions.
It was experimentally established that they are also suitable for stranded conductors, with some minor
amendments.
 
They were, next, extended to segmental conductors, introducing empirical coefficients from measurements
performed on 1600 mm2 - 4 segments oil-filled cables.
 
According to measurements performed on many conductors, this extension to segmental conductors is more
questionable, especially for XLPE cables and when insulated wires are used.
 
It is worth noting that :
 * the effective value of the a.c. resistance of cores with bare copper strands may be higher than the IEC
recommended value, which may lead to undersize the cable, and, so,  may be hazardous.
* the cable cost increase due to the use of insulated wires is not balanced with the permissible increase in cable
current-carrying capacity.
 
In this brochure, a general formula is proposed for calculating the a.c. resistance of segmental large cross-
sections.
 
But, due to the complexity of an accurate computation, measurement of the a.c. resistance has to be
recommended.
 
Measurement methods are reviewed, stressing upon new solutions.

5  GENERAL CONSIDERATIONS.
 
5.1  Skin effect and proximity effect.
 
Skin effect is the name given to the tendency for current to flow predominantly in the periphery of a conductor
due to the internal magnetic field in the conductor.
 
Proximity effect is the tendency for current to flow along one side of a conductor due to interaction of the
magnetic fields of the current in the conductor considered and the currents in adjacent conductors.
 
The a.c. resistance of a solid circular conductor is given by :
 
RRyy'()1
sp
 (1)
where :
   R!ˉ is the d.c. resistance,   y
 is the skin effect factor and y  is the proximity effect factor
s p
 
Skin effect in solid round circular conductors and proximity effects between solid round circular conductors
were deeply investigated, specially by A.H.M. Arnold [2 - 3 - 4 - 5], and formulae were worked out [6] for ys
and yp, through tedious calculations to approximate the Bessel!ˉs functions involved in the solution of Maxwell!ˉ
equations.
 
5.2  Skin effect in solid conductors.
 
The skin effect factor ys for an isolated solid circular conductor is given by :
 
'.'. xberxbeixbeixberx
1.xy  (2)
 
s2'2'2 xbeixber
where:
fx .2 
 
R'.
 
 
R!ˉ being the d.c. resistance.
|ì being the magnetic permeability and f the frequency.
 
ber(x), bei(x) and their derivatives ber!ˉ(x) and bei!ˉ(x) are tabulated Bessefunctions (e.g. see reference [7]).
 
The derivation of this formula is given in !ì 5..  
 
 
The following approximate formulae [6] have been obtained for ys :
 
4
x
)2(8.20 a
xyx
s
4
8.0192 x
)2(20563.00177.0136.08.38.2 bxxxyx
 
s
)2(733.0354.08.3 cxxyx
s
 
6/87

 
 
The maximum error is less than 0.6 %, and is negligible.
The above formulae (2a) and (2c), for small and large values of x respectively are taken from Arnold!ˉs work,
while formula (2b) has been derived to fit the values of y at intermediate values of x, and at the same time not to
allow an appreciable discontinuity in the calculated values of y at x=2.8 and x=3.8.
 
5.3  Proximity effect between solid conductors.
 
Derivation of  formulae for proximity effects, even in the simple case of solid conductors, is anything but
straightforward.
 
Arnold worked out formulae for various cases, using complicated tabulated functions.
For instance, for 2 solid conductors carrying single-phase current :
 
2
d
c
.
xG
S
xy
p
2
d
c
.1
xA
S
 (3)
44
012.0042.0
xx
8.2:
xif
xGxAwith
4
20
0235.01
x
4
64
x
11
 
 
For 3 circular conductors carrying three-phase current, Neher and McGrath [8] have obtained the following
formula suitable for power frequency application :
 
22
4
x
dd
18.1
 (4)
 
cc
.312.0..
xy
p
44
SS
8.0192
x
x
27.0
4
8.0192
x
 
where d
 is the core diameter and S the axial spacing between conductors.
c
 
 
5.4  Skin effect and proximity effect in stranded conductors.
 
The basic contribution in this field once again comes from Arnold.
 
Skin effect.
 
The skin effect in a single-core cable is substantially the same as the skin effect in a solid round cylindrical
conductor having the same d.c. resistance per unit length.
 
 
Proximity effect.
 
The proximity effect may be calculated using formulae developed for solid round conductors provided that the
 , which is the ratio of the resistance of the path along the
resistance of the conductor is divided by a factor k
p
strands to the resistance of the path across the strands.
 
7/87

 
This factor depends on many parameters such as the surface condition of the strands, the lay of the strands, the
impregnation of the core and the tightness of the insulation on the core.

7.5  Comparing calculation methods
7.5.1  General
 
This paragraph presents a comparison of  the losses derived using Sugiyama!ˉs formula and other calculation
methods.
 
Particularly, circuit theory was applied to core structures with a ? true ? geometry; the current distribution in the
core is illustrated in following figures, for various configurations.
 
The purpose of these calculations was to check the important assumption in Sugiyama!ˉs approach, that sector
shaped segments may be considered as circular-shaped.
Of course, the actual distribution of the wires in a segment is not as fine as it may be in a simulated one, and the
cross-section of the wires is no more circular. So that the calculation results using circuit theory have also to be
carefully considered.
 
A 2000 mm2 Copper core was considered, with a current flowing in the core of 1000 A.
 
7.5.2  Skin effect within segments and losses due to eddy currents  in the wires.
 
Losses due to the current flow and skin effect within every segments  (W/m)

Segment  number                     SUGIYAMA     (IEC for circular shape)                          Circuit theory    

            4                                                          9.2                                                                              9.3    
            5                                                          9.0                                                                              9.1
            6                                                          8.8                                                                              8.9
            7                                                          8.8                                                                              8.9
 
Losses due to the skin effect within every segments  (mW/m)

Segment    number                       SUGIYAMA     (IEC for circular shape)

            4                                                         570
            5                                                         370
            6                                                         260
            7                                                         190
 

Losses inside every wires due to magnetic fields  (mW/m)

Segment            SUGIYAMA                  SUGIYAMA          From magnetic fields due to every wires  (*) 
 number               Cos  = 0.95                        Cos  = 1                                          Cos  = 1 
 
         4                         128                                   116                                                   120
         5                         105                                     95                                                     95
         6                           85                                     77                                                      78
         7                           71                                     64                                                      65
 
(*) Losses in a wire (radius a) located in a magnetic field H are given by :  

The magnetic field acting on a wire is the resultant of the magnetic fields due to the whole of other wires.
Elementary magnetic fields are derived from Ampere!ˉs teorem, assuming every wire carries the same current.

全英文啊

終于找到國(guó)內(nèi)的電纜廠家在2004年做到這樣的驗(yàn)證試驗(yàn)，但問(wèn)到試驗(yàn)者本人，說(shuō)誤差很大。我也仔細(xì)地對(duì)比了兩種的試驗(yàn)方法，確實(shí)不一樣，所以還是特別想自己做一遍，看自己的真實(shí)的實(shí)驗(yàn)結(jié)果會(huì)是怎么樣。

很正點(diǎn)

國(guó)外的測(cè)試方法一起分享！

學(xué)習(xí)了~

再添加幾個(gè)有關(guān)高壓交聯(lián)電纜和電纜附件的研究課題及標(biāo)準(zhǔn)

很不錯(cuò)的東東

真不錯(cuò)

很好的東西哦！

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