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各位電纜同仁好:
雖然我們可以通過實驗儀器測試出導(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算出導(dǎo)體的交流電阻,但誰可以用自己設(shè)計的實驗來驗證這個公式的正確性呢?
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。
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)的實驗設(shè)計方法及計算公式,已經(jīng)他們的實驗結(jié)果。
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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
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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
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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
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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.
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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.
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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.
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學(xué)習(xí)了~
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很不錯的東東
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能不能不要金幣啊,下不不來啊,我很需要英文這篇文獻(xiàn)
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kz在嗎,能不能把設(shè)置成免費下載啊
急用
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終于下到了,50金幣啊