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BSI 21/30431007 DC:2021 Edition

BSI 21/30431007 DC:2021 Edition

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BS EN 60287-1-2. Electric cables. Calculation of the current rating – Part 1. Current rating equations (100 % load factor) and calculations of losses. Section 2. Sheath eddy current loss factors for two circuits in flat formation

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PDF Pages PDF Title
1 30431007
3 20_1951e_CD
20/1951/CD
COMMITTEE DRAFT (CD)
Project number:
IEC 60287-1-2 ED2
Date of circulation:
Closing date for comments:
2021-02-05
2021-04-30
Supersedes documents:
20/1945/RR
IEC TC 20 : Electric cables
Secretariat:
Secretary:
Germany
Mr Walter Winkelbauer
Of interest to the following committees:
Proposed horizontal standard:
Other TC/SCs are requested to indicate their interest, if any, in this CD to the secretary.
Functions concerned:
EMC
Environment
Quality assurance
Safety
This document is still under study and subject to change. It should not be used for reference purposes.
Recipients of this document are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to provide supporting documentation.
Title:
Electric cables – Calculation of the current rating – Part 1: Current rating equations (100 % load factor) and calculations of losses – Section 2: Sheath eddy current loss factors for two circuits in flat formation
Note from TC/SC officers:
HORIZONTAL_STD
FUNCTION_EMC
FUNCTION_ENV
FUNCTION_QUA
FUNCTION_SAFETY
4 CONTENTS
FOREWORD 3
1 Scope 5
2 Normative references 5
3 Terms and definitions 6
4 Symbols 6
5 Description of method 7
5.1 General 7
5.2 Outline of method 7
5.3 Criteria for use of formulae and coefficients 8
6 Formulae for sheath loss factors for high-resistance sheaths in a single circuit, (0s 8
7 Calculation of the coefficientsCH, CN and CJ 9
7.1 Allocation of coefficients to each cable, time sequence and phase identification 9
7.2 Calculation of coefficients CH (1, 2 and 3), table 1 10
7.3 Calculation of coefficients CN (1, 2, 3, 4, 5 and 6), table 2 11
7.4 Calculation of coefficients CJ (1, 2, 3, 4, 5 and 6), tables 3 to 11 11
7.5 Calculation of coefficients Gs and gs 13
8 Notes on transposition of cables 13
9 Worked examples of calculation of eddy current losses 14
9.1 Introduction 14
9.2 Example 1 14
9.3 Example 2 15
Figure 1 – Cable configuration 7
Table 1 – CH coefficients 19
Table 2 – CN coefficients 20
Table 3 – CJ coefficients 21
Table 4 – CJ coefficients 22
Table 5 – CJ coefficients 23
Table 6 – CJ coefficients 24
Table 7 – CJ coefficients 25
Table 8 – CJ coefficients 26
Table 9 – CJ coefficients 27
Table 10 – CJ coefficients 28
Table 11 – CJ coefficients 29
5 INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRIC CABLES –
CALCULATION OF THE CURRENT RATING –
Part 1: Current rating equations
(100% load factor) and calculation of loses –
Section 2: Sheath eddy current loss factors
for two circuits in flat formation
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work. International, governmental and non-governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications. Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60287-1-2 has been prepared by subcommittee 20A: High-voltage cables, of IEC technical committee 20: Electric cables.
This third edition cancels and replaces the second edition published in 1993. This edition constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous edition:
a) Change and update of list of symbols;
6 The text of this International Standard is based on the following documents:
FDIS
Report on voting
XX/XX/FDIS
XX/XX/RVD
Full information on the voting for the approval of this International Standard can be found in the report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this document will remain unchanged until the stability date indicated on the IEC website under “http://webstore.iec.ch” in the data related to the specific document. At this date, the document will be
 reconfirmed,
 withdrawn,
 replaced by a revised edition, or
 amended.
The National Committees are requested to note that for this document the stability date is 20XX..
this text is included for the information of the national committees and will be deleted at the publication stage.
7 ELECTRIC CABLES – CALCULATION OF THE CURRENT RATING –
Part 1: Current rating equations (100% load factor) and calculation of loses – Section 2: Sheath eddy current loss factors for two circuits in flat formation
1 Scope
This section of IEC 60287-1 provides a method for calculating the eddy current losses in the metallic sheaths of single-core cables arranged as a three-phase double circuit in flat formation. The sheaths are bonded at one point or are cross-bonded so that there are no significant sheath circulating currents. Where metallic sheaths are bonded at both ends there are significant circulating currents which result in a lower current-carrying capacity. A method of calculating circulating current losses for double circuits is provided in IEC 60287-1-3.
The method provides coefficients which are applied as corrections to the loss factors for the sheaths of one isolated three-phase circuit. These corrections are negligible for cables
where the parameter m is less than about 0,1 (m = (/107 Rs), which corresponds to a sheath longitudinal resistance higher than 314 ((/m at 50 Hz.
Consequently, the method should be used for most sizes of aluminium-sheathed cables, but is not required for lead-sheathed cables unless they are unusually large.
The coefficients are provided in tabular form and have been computed from fundamental formulae for sheath losses, the evaluation of which calls for expertise in computer programming which might not be readily available in general commercial situations. The development of simplified formulae for some of the tabulated coefficients is under consideration.
Losses for cables in a single circuit will be covered in IEC 60287-1-1.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
8 3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
 IEC Electropedia: available at http://www.electropedia.org/
 ISO Online browsing platform: available at http://www.iso.org/obp
4 Symbols
CA0, CB0, CC0, CD0 coefficients used to interpolate for CH and CJ
CH1, CH2, CH3 coefficients which correct for sheath resistance, the values obtained relate to cables 1, 2 or 3 in a single circuit
CN1, CN2, CN3, CN4, CN5, CN6 coefficients which introduce the mutual influences between circuits and are therefore dependent on the relative phase sequences of cables 1 to 3 and 4 to 6
CJ1, CJ2, CJ3, CJ4, CJ5, CJ6 coefficients which depend on the cable positions 1 to 3 and 4 to 6 in each circuit
CM0, CZ0 coefficients used for calculation of coefficients CH;
Ds external diameter of the metal sheath (mm)
Dit the diameter of the imaginary cylinder which just touches the inside surface of the troughs of a corrugated sheath (mm)
Doc the diameter of the imaginary coaxial cylinder which just touches the crests of a corrugated sheath (mm)
Gs coefficient which accounts for losses due to eddy currents across the thickness of the sheath due to the current in the conductor
R c alternating current resistance of the conductor at its maximum operating temperature (Ω/m)
R s resistance of the sheath (Ω/m)
CS, CT,CU,CV coefficients used to interpolate for J
CY coefficient used for calculation of coefficients CJ;
c1 is the distance between centres of cables in adjoining circuits (mm)
d mean diameter of sheath or screen (mm)
f system frequency (Hz)
gs coefficient which accounts for losses due to eddy currents across the thickness of the sheath, due to currents in adjacent cables
m /
s distance between centres of cables in the same circuit (mm)
ts thickness of the sheath (mm)
y1 is equal to s/c1
z is equal to
Cß1 coefficient used for calculation of coefficients Gs and gs
(0s sheath loss factor for a high-resistance sheath in a single circuit
9 (1s’’ is the sheath loss factor for a low-resistance sheath in a single circuit
(1d’’ sheath loss factor for a low-resistance sheath in a double circuit
(s electrical resistivity of sheath material at operating temperature ((.m)
( angular frequency of system (2πf) (l/s)
5 Description of method
5.1 General
The method proceeds in a way similar to that used for single circuits in IEC 60287-1-1. There, formulae for loss factors applicable to sheaths having a longitudinal resistance such that m is less than 0,1 (Rs = 314 ((/m at 50 Hz) are given, together with empirical formulae to calculate the correction coefficient for lower resistance sheaths.
However, for double circuits, accurate empirical formulae covering the complete range of coefficients would need to contain so many terms that their use would show little or no advantage over the use of precise, tabulated coefficients with interpolation, as necessary. This latter course has the advantage that the accuracy of the loss factors can be closely equal to that of the original calculations and is better than 1 %.
The development of empirical formulae for a limited range of coefficients is under consideration.
In order to explain the method, it is described here in a way appropriate to manual evaluation of the arithmetic. However, because of the appreciable effort required to provide loss factors for six cables, it is to be expected that calculations will usually be effected by means of a computer. Under these circumstances, the decision to use interpolation (as necessary) between tabulated values is fully justified.
However, in many cases, values of the relevant parameters will be such that interpolation is unnecessary or may be accomplished with sufficient accuracy by inspection.
Corrections to cover the effect of eddy currents circulating within the thickness of a sheath are derived with the use of the same formulae as those used in IEC 60287-1-1.
5.2 Outline of method
The loss factor for the sheath of a given cable in a double-circuit flat formation (see figure 1) is evaluated as follows:
(1)
The tasks performed by coefficients CN and CJ are not directly related to any physical function but have been selected to simplify the tabulation. The nomenclature is arbitrary.
Values of CH, CN and CJ are obtained from tables 1 to 11 and are chosen according to the following parameters together with the position of the cable and the phase sequence of the currents in the conductors.
(2)
10 (3)
(4)
where
c1 is the distance between centres of cables in adjoining circuits (see figure 1) (mm).
Figure 1 – Cable configuration
NOTE The factors for a single circuit having low-resistance sheaths can be obtained by using the coefficients CH (1, 2 and 3) only, as follows:
(5)
5.3 Criteria for use of formulae and coefficients
For sheaths for which the value of m is less than 0,1, which includes most lead-sheathed cables, it may be assumed that the coefficients CH, CN, CJ and gs are unity and Gs is zero. In such circumstances, (0s may be used for twin circuits without correction.
When the value of m is equal to 0,1 or greater, which is generally the case for all but the smaller aluminium-sheathed cables, values for CH, CN, CJ and gs shall be calculated. The coefficient Gs is important only when the value of m is 1,0 or higher.
6 Formulae for sheath loss factors for high-resistance sheaths in a single circuit, (0s
The sheath loss factor (0s is given by
(6)
For three single-core cables in flat formation, the coefficient CC is given by:
Cable
Coefficient CC0
Centre cable
6
Outer cables
1,5
11 7 Calculation of the coefficients CH, CN and CJ
7.1 Allocation of coefficients to each cable, time sequence and phase identification
It is important to note the way in which the coefficients CH, CN and CJ are dependent on the time sequence of the currents and the physical position of the conductors.
The cables shall be numbered according to figure 1.
The coefficients CH (1, 2 and 3), table 1, are allocated on a basis of time sequence associated with the positions of the cables, so that the following single-circuit arrangements have the same time sequence:
Cable number 1 2 3
Sequence R S T
Or S T R
Or T R S
With coefficients CH1 CH2 CH3
In the above example, cable 1 is always the outer conductor on a leading phase and takes coefficient CH1. Cable 3 is the outer conductor on a lagging phase and takes coefficient CH3.
It will be seen that, for these cases, the phase identification implied by the symbols R, S and T* is not important, it is only the time sequence which is of significance.
In double circuits, if either circuit has a reversed sequence, the values of CH must be allocated to the cables in the reverse order. The allocation of coefficient CH is dependent on the time sequence within each circuit.
In a double-circuit configuration, the phase identification implied by the symbols is significant to the extent that the phase identification in relation to cable position in one circuit must be either the same as, in the forward sequence, or a mirror image of, in the reverse sequence, that in the other.
Two sets of coefficients CN (1, 2, 3, 4, and 6) are given in table 2 corresponding to the forward and reverse sequences. If the cable positions are labelled sequentially and the phase identification rules are adhered to, the coefficients are allocated on the same basis as coefficient CH. Note that the values for cables 4, 5 and 6 in the reversed sequence are a reflection of the values for cables 1, 2 and 3.
The number of input parameters involved for the coefficients CJ (1, 2, 3, 4, 5 and 6) makes it desirable to use several tables. Tables 3 to 8 are for each cable for the forward sequence installation. For the reverse sequence, tables 9 to 11 are provided and the coefficients for cables 1 to 3 are also used for cables 6 to 4, in that order. The allocation is on the same lines as those for coefficient CN.
The following tables give examples of four common cases:
Forward sequence
Cable number 1 2 3 4 5 6
Sequence R S T R S T
Allocation CH CH1 CH2 CH3 CH1 CH2 CH3 table 1
12 Allocation CN CN1 CN2 CN3 CN4 CN5 CN6 table 2, forward
Allocation CJ CJ1 CJ2 CJ3 CJ4 CJ5 CJ6 tables 3 to 8, forward
Forward sequence
Cable number 1 2 3 4 5 6
Sequence T S R T S R
Allocation CH CH3 CH2 CH1 CH3 CH2 CH1 table 1
Allocation CN CN6 CN5 CN4 CN3 CN2 CN1 table 2, forward
Allocation CJ CJ6 CJ5 CJ4 CJ3 CJ2 CJ1 tables 3 to 8, forward
Reverse sequence
Cable number 1 2 3 4 5 6
Sequence R S T T S R
Allocation CH CH1 CH2 CH3 CH3 CH2 CH1 table 1
Allocation CN CN1 CN2 CN2 CN4 CN5 CN6 table 2, forward
Allocation CJ CJ1 CJ2 CJ3 CJ4 CJ5 CJ6 tables 9 to 11, forward
Reverse sequence
Cable number 1 2 3 4 5 6
Sequence T S R R S T
Allocation CH CH1 CH2 CH3 CH3 CH2 CH1 table 1
Allocation CN CN6 CN5 CN4 CN3 CN2 CN1 table 2, forward
Allocation CJ CJ6 CJ5 CJ4 CJ3 CJ2 CJ1 tables 9 to 11, forward
*The letters R, S, T are used here for convenience and are equivalent to other well-known sets of symbols to denote time sequence and phase identification, such as L1, L2, L3; a, b, c; R, Y, B; etc.
7.2 Calculation of coefficients CH (1, 2 and 3), table 1
Each coefficient CH is obtained from table 1 using the parameters m and z as well as the position of each cable (see 7.1).
When values of m and z involve interpolation between values in table 1, the following procedure may be used where interpolation by inspection is not desired.
From the relevant part of table 1, values for CH (a, b, c, d) are obtained as shown in the following diagram:
z0
z
z1
m0
CHa
CHc
m
CH
m1
CHb
CHd
where m0, m1, z0 and z1 are tabulated values smaller and larger than the values of m and z.
13 Tabulate:
m0…………………………….
m1……………………………. CM0 = (m1-m0)………………………………………………
z0…………………………….
z1……………………………. CZ0 = (z1-z0)…………………………………………………
CHa…………………………….
CHb…………………………….
CHc…………………………….
CHd…………………………….
Then:
CA = CHa = ……………………………………………………………
CB= (CHb – CHa)/CM0 = ……………………………………………………………
CC = (CHc – CHa)/CZ0 = ……………………………………………………………
CD = (CHd + CHa – CHc – CHb)/CM0.CZ0 = ……………………………………………………………
Add together:
CA = ……………………………………………………………
+CB·(m – m0) = ……………………………………………………………
+CC·(z – z0) = ……………………………………………………………
+CD·(m – m0)·(z – z0) = ……………………………………………………………
Coefficient CH=total = ……………………………………………………………
This process is to be repeated for each of the three cables in a circuit to obtain CH1, CH2 and CH3.
7.3 Calculation of coefficients CN (1, 2, 3, 4, 5 and 6), table 2
Values of coefficient CN are obtained from table 2, using parameter y for each cable. The table has values for the forward and reverse sequences. Note that in the latter case the coefficients for cables 4, 5 and 6 form a mirror image of those for cables 1 to 3.
Where interpolation is required, a linear one-dimensional interpolation is adequate.
7.4 Calculation of coefficients CJ (1, 2, 3, 4, 5 and 6), tables 3 to 11
Values of coefficient CJ for each cable are obtained from tables 3 to 11, according to the sequence of the currents and the parameters m, z and y1.
Tables 3 to 8 apply to the six cables when the currents in the conductors follow the forward sequence. But, in a reversed sequence, tables 9 to 11 apply to cables 1 to 3 and also to cables 6 to 4, in that order.
It may be that interpolation between all three input parameters is necessary and the following scheme for a three-dimensional interpolation may be used.
14 The tables for each cable are arranged in groups, one for each value of the parameter y1. Two groups can be chosen, one for a value of y1 smaller, and one for a value larger, than the input value. For each group, values of CJ (a to d) and CJ (e to f) are required (in a similar way to the interpolation for CH ), as shown in the following diagrams.
z0
z
z1
m0
CJa
CJc
m
*
m1
CJb
CJd
z0
z
z1
m0
CJe
CJg
m
*
m1
CJf
CJh
Group for y0 Group for y1
Interpolation between the values marked * gives the required value of J for each cable.
The arithmetic may be tabulated as follows:
y0…………………… z0……………………… m0………………………… CJa………………
m1………………………… CJb………………
z1……………………… m0………………………… CJc………………
m1………………………… CJd………………
y1…………………… z0……………………… m0………………………… CJe………………
m1………………………… CJf………………
z1……………………… m0………………………… CJg………………
m1………………………… CJh………………
CM0 = (m1 – m0)…………………. CZ0 = (z1 – z0)………………… CY = (y1 – y0)…………
m’ = (m – m0)……………………. z’ = (z – z0)…………….……… y’ = (y – y0).……………
Calculate:
CA = CJa =…………………………
CB = (CJb – CJa) / CM0 =…………………………
CC = (CJc – CJa) / CZ0 =…………………………
CD = (CJe – CJa) / CY =…………………………
CS = [(CJa + CJd) – (CJb + CJc)] / CM0 · CZ0 =…………………………
CT = [(CJa + CJg) – (CJc + CJe)] / CZ0 · CY =…………………………
CU = [(CJa + CJf) – (CJb + CJe)] / CM0 · CY =…………………………
CV = [(CJb + CJc + CJe + CJh) – (CJa + CJd + CJf + CJg)] / CM0 · CZ0 · CY =…………………………
15 Then add up the following:
CA =…………………..
CB · m’ =…………………..
CC · z’ =…………………..
CD · y’ =…………………..
CS · m’ · z’ =…………………..
CT · z’ · y’ =…………………..
CU · m’ · y’ =…………………..
CV · m’ · z’ · y’ =…………………..
CJ = total =…………………..
Values of CJ for each of the other five cables are found in the same way.
7.5 Calculation of coefficients Gs and gs
(3)
(4)
NOTE – For corrugated sheaths, the mean outside diameter shall be used in place of Ds.
8 Notes on transposition of cables
The general effect of transposition is to rotate either all of the conductors or all of the sheaths, or both, progressively from sub-section to sub-section. Such changes do not affect the sequence of the conductor currents and, provided that the transpositions in each circuit are effected in the same way with respect to the phase sequence (that is, the requirements for time sequence and sheath position given in 7.1 are observed in the same way for all sub-sections), transposition will not affect the application.
Transposition can take place either in the same direction or in the opposite direction to that of the phase sequence. The direction does not affect the eddy current losses, provided that for both circuits the direction at each transposition, relative to the phase sequence, is the same. It follows that, if the circuits have reversed conductor current sequences, the physical direction of transposition in one circuit will be opposite to that in the other.
Values of sheath eddy current losses are dependent only on position in the cable arrangement and, once calculated, apply to any sheath in a certain position, irrespective of the sub-section.
16 9 Worked examples of calculation of eddy current losses
9.1 Introduction
The cable dimensions used in the following examples are arbitrary and do not represent any particular type of cable.
In many cases there is no need for interpolation, or the parameters use parts of the tables where interpolation by inspection is adequate.
However, where the intervals in the tables are too large for interpolation by inspection or when calculation is made by computer, the interpolation routines are useful and are not difficult to use manually or to program on a computer.
9.2 Example 1
In this example, the installation parameters coincide with entries in the tables and no interpolation is needed.
Let:
the mean diameter of the sheath d = 90 mm
aluminium sheath thickness ts = 3,18 mm
sheath resistance Rs = 62,9 x 10-6 Ω/m
conductor resistance, Rc = 11,3 x 10-6 Ω/m
sheath resistivity, ρs = 2,8264 x 10-8 Ω·m
(see table I, IEC 60287 (1982).
distance between centres of cables within circuits s = 150 mm
between circuits c1 = 375 mm
then:
17 Corrections for thickness:
Assume conductors are connected in a reversed sequence.
Cable
1
2
3
4
5
6
Sequence
R
S
T
T
S
R
CC
1,5
6,0
1,5
1,5
6,0
1,5
λ0s
0,0270
0,1080
0,0270
0,0270
0,1080
0,0270
CH (m = 0,5 z = 0,3)
1,2200
1,0250
0,9190
0,9190
1,0250
1,2200
CN (y = 0,4)
1,0605
1,1066
1,2593
1,2593
1,1066
1,0605
CJ (m = 0,5 z = 0,3 y = 0,4)
1,0100
1,0000
0,9650
0,9650
1,0000
1,0100
gs
1,026
1,026
1,026
1,026
1,026
1,026
Gs
0,0017
0,0017
0,0017
0,0017
0,0017
0,0017
Rs/Rc
5,57
5,57
5,57
5,57
5,57
5,57
Substitute these quantities in equation (1)
λ’’1d
0,0211
0,710
0,182
0,182
0,710
0,0211
For cable 1, the arithmetic is:
λ’’1d = 5,57 [(0,0270 x 1,2200 x 1,0605 x 1,0100 x 1,026) + 0,0017] = 0,211
9.3 Example 2
In this example, the arbitrary parameters have been selected so that interpolation between tabulated values is required.
Let:
the mean diameter of the sheath d = 100 mm
aluminium sheath thickness ts = 2,6 mm
18 sheath resistance Rs = 35 x 10-6 Ω/m
conductor resistance, Rc = 9 x 10-6 Ω/m
sheath resistivity, ρs = 2,8264 x 10-8 Ω·m
(see table I, IEC 60287 (1982).
distance between centres of cableswithin circuits s = 150 mm
between circuits c1 = 400 mm
then:
Take cable number 1, and a forward sequence of currents:
a) interpolate for CH:
m = 0,897 z = 0,333
from the table of CH coefficients:
m0 = 0,500
m1 = 1,000 CM0 = (m1 – m0) = 0,500
z0 = 0,300
19 z1 = 0,350 CZ0 = (z1 – z0) = 0,050
(m – m0) = (0,897 – 0,500) = 0,397
(z – z0) = (0,333 – 0,300) = 0,033
CHa = 1,220
CHb = 1,347
CHc = 1,309
CHd = 1,503
CA= 1,220
CB = (1,347 – 1,220)/0,5 = 0,254
CC = (1,309 – 1,220)/0,005 = 1,780
CD = (1,503 + 1,220 – 1,309 – 1,347)/(0,5 x 0,05) = 2,680
Add together:
CA = 1,2200
CB · (m – m0) = 0,254 x 0,397= 0,1008
CC · (z – z0) = 1,780 x 0,033 = 0,0587
CD · (m – m0) · (z – z0) = 2,68 x 0,397 x 0,033 = 0,0351
CH = 1,4146
b) interpolate for CN:
y = 0,375
from the table of N coefficients:
y0 = 0,3 y1 = 0,4
(y – y0) = 0,375 – 0,3 = 0,075
CNa = 0,9432 CNb = 0,9238
CN = 0,9432 + [(0,9238 – 0,9432) / (0,4 – 0,3)] x 0,075 = 0,929
c) interpolate for CJ:
m = 0,897 z = 0,333 y = 0,375
y0 = 0,200 z0 = 0,300 m0 = 0,500 CJa = 0,995
20 m1 = 1,000 CJb = 0,992
z1 = 0,400 CJc = 0,991
CJd = 0,984
y1 = 0,400 CJe = 0,991
CJf = 0,983
CJg = 0,982
CJh = 0,964
CM0 = 0,5 CZ0 = 0,1 CY = 0,2
m’ = 0,397 z’ = 0,033 y’ = 0,175
CA = 0,995
CB = (0,992 – 0,995) / 0,5 = -0,006
CC = (0,991 – 0,995) / 0,1 = -0,040
CD = (0,991 – 0,995) / 0,2 = -0,020
CQ = [(0,995 + 0,984) – (0,992 + 0,991)] / (0,5 x 0,1) = -0,080
CR = [(0,995 + 0,982) – (0,991 + 0,991)] / (0,1 x 0,2) = -0,250
CS = [(0,995 + 0,983) – (0,992 + 0,991)] / (0,5 x 0,2) = -0,050
CT = [(0,992 + 0,991 + 0,991 + 0,964) – (0,995 + 0,984 + 0,983 + 0,982)] / (0,5 x 0,1 x 0,2) = -0,600
Add together:
CA = 0,9950
CB·m’ = – 0,006 x 0,397 = –0,0024
CC·z’ = – 0,04 x 0,033 = –0,0013
CD·y’ = – 0,02 x 0,175 = –0,0035
CQ·m’·z’ = – 0,080 x 0,397 x 0,033 = –0,0011
CR·z’·y’ = – 0,25 x 0,033 x 0,175 = –0,0014
CS·m’·y’ = – 0,05 x 0,397 x 0,175 = –0,0035
CT·m’·z’·y’ = – 0,6 x 0,397 x 0,033 x 0,175 = –0,0014
CJ = 0,9804
21 Substitution in equation (1) gives:
λ1d’’ = 3,89 [(0,0743 x 1,4146 x 0,929 x 0,9804 x 1,018) + 0,0007] = 0,382
A summary of the sheath loss factors for all six cables, together with the corresponding factors for smaller values of the circuit separation c and for a single-circuit installation (corresponding to a very large circuit spacing) are as follows:
Spacing c1 mm
150
300
400
Single circuit
Cable nº
Sheath loss factors
1
0,346
0,373
0,382
0,419
2
0,955
1,100
1,151
1,262
3
0,274
0,250
0,256
0,276
4
0,402
0,336
0,356
0,419
5
0,943
1,094
1,142
1,262
6
0,230
0,251
0,258
0,276
22 Table 1 – CH coefficients
m
0,1
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
Cable 1
0,1
1,007
1,015
1,028
1,044
1,064
1,089
1,118
1,154
1,197
0,5
1,023
1,051
1,093
1,148
1,220
1,309
1,420
1,554
1,714
1,0
1,033
1,076
1,140
1,228
1,347
1,503
1,706
1,970
2,299
1,5
1,037
1,085
1,158
1,261
1,405
1,606
1,887
2,284
2,826
2,0
1,037
1,087
1,163
1,274
1,432
1,662
2,003
2,527
3,321
2,5
1,037
1,087
1,164
1,278
1,444
1,693
2,081
2,720
3,792
3,0
1,037
1,087
1,164
1,279
1,449
1,711
2,135
2,876
4,244
Cable 2
0,1
1,001
1,002
1,004
1,006
1,009
1,013
1,017
1,022
1,028
0,5
1,003
1,007
1,012
1,018
1,025
1,033
1,040
1,047
1,050
1,0
1,006
1,015
1,027
1,043
1,064
1,090
1,121
1,157
1,193
1,5
1,009
1,021
1,039
1,065
1,101
1,150
1,218
1,306
1,413
2,0
1,010
1,025
1,047
1,080
1,128
1,198
1,301
1,450
1,654
2,5
1,011
1,027
1,052
1,091
1,148
1,234
1,366
1,575
1,892
3,0
1,012
1,029
1,056
1,098
1,161
1,260
1,417
1,681
2,123
Cable 3
0,1
0,999
0,998
0,996
0,994
0,991
0,988
0,984
0,979
0,973
0,5
0,991
0,980
0,964
0,944
0,919
0,889
0,853
0,812
0,766
1,0
0,994
0,986
0,975
0,962
0,947
0,931
0,915
0,900
0,891
1,5
1,000
1,001
1,002
1,007
1,017
1,036
1,068
1,124
1,214
2,0
1,006
1,013
1,027
1,048
1,082
1,137
1,226
1,374
1,608
2,5
1,010
1,023
1,045
1,080
1,134
1,220
1,364
1,608
2,017
3,0
1,013
1,031
1,060
1,104
1,174
1,287
1,477
1,816
2,422
23 Table 2 – CN coefficients
Cable forward
y1=s/c1
1
2
3
4
5
6
0,1
0,9871
0,9861
0,9854
0,9849
0,9861
0,9875
0,2
0,9651
0,9588
0,9562
0,9554
0,9588
0,9656
0,3
0,9432
0,9286
0,9271
0,9259
0,9286
0,9438
0,4
0,9238
0,8990
0,9065
0,9049
0,8990
0,9243
0,5
0,9069
0,8714
0,8993
0,8974
0,8713
0,9075
0,6
0,8924
0,8461
0,9089
0,9067
0,8461
0,8929
0,7
0,8800
0,8232
0,9372
0,9351
0,8231
0,8804
0,8
0,8692
0,8024
0,9859
0,9842
0,8023
0,8696
0,9
0,8598
0,7836
1,0562
1,0552
0,7835
0,8601
1,0
0,8516
0,7665
1,1487
1,1490
0,7665
0,8517
Cable reverse
y1=s/c1
1
2
3
4
5
6
0,1
1,0110
1,0141
1,0185
1,0185
1,0141
1,0110
0,2
1,0286
1,0421
1,0696
1,0696
1,0421
1,0286
0,3
1,0456
1,0742
1,1504
1,1504
1,0742
1,0456
0,4
1,0605
1,1066
1,2593
1,2593
1,1066
1,0605
0,5
1,0736
1,1378
1,3953
1,3953
1,1378
1,0736
0,6
1,0849
1,1673
1,5580
1,5580
1,1673
1,0849
0,7
1,0948
1,1948
1,7471
1,7471
1,1948
1,0948
0,8
1,1035
1,2204
1,9623
1,9623
1,2204
1,1035
0,9
1,1111
1,2441
2,2037
2,2037
1,2441
1,1111
1,0
1,1180
1,2662
2,4711
2,4711
1,2662
1,1180
24 Table 3 – CJ coefficients
Cable 1 / Forward z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
1,000
1,000
1,000
0,5
1,000
0,998
0,995
0,991
0,982
1,0
0,999
0,997
0,992
0,984
0,970
1,5
1,000
0,997
0,992
0,984
0,974
2,0
0,999
0,997
0,992
0,987
0,980
2,5
0,999
0,997
0,994
0,989
0,987
3,0
1,000
0,997
0,994
0,992
0,993
0,4
0,1
1,000
1,000
1,000
1,000
1,000
0,5
0,999
0,997
0,991
0,982
0,965
1,0
0,999
0,994
0,983
0,964
0,931
1,5
0,999
0,992
0,981
0,962
0,933
2,0
0,998
0,992
0,982
0,966
0,946
2,5
0,998
0,992
0,983
0,971
0,959
3,0
0,999
0,993
0,984
0,975
0,971
0,6
0,1
1,000
1,000
1,001
1,001
1,002
0,5
0,999
0,996
0,990
0,978
0,955
1,0
0,998
0,991
0,977
0,949
0,900
1,5
0,998
0,989
0,972
0,942
0,894
2,0
0,997
0,989
0,972
0,945
0,907
2,5
0,997
0,988
0,973
0,951
0,925
3,0
0,998
0,989
0,974
0,956
0,941
0,8
0,1
1,000
1,001
1,002
1,003
1,004
0,5
0,999
0,996
0,990
0,978
0,955
1,0
0,998
0,990
0,974
0,941
0,881
1,5
0,997
0,987
0,966
0,927
0,860
2,0
0,996
0,985
0,963
0,927
0,869
2,5
0,996
0,985
0,963
0,931
0,886
3,0
0,996
0,985
0,964
0,937
0,904
1,0
0,1
1,000
1,001
1,003
1,005
1,007
0,5
0,999
0,997
0,992
0,983
0,962
1,0
0,998
0,990
0,973
0,939
0,877
1,5
0,997
0,985
0,962
0,918
0,842
2,0
0,995
0,983
0,957
0,913
0,840
2,5
0,995
0,982
0,956
0,915
0,852
3,0
0,996
0,981
0,956
0,919
0,866
25 Table 4 – CJ coefficients
Cable 2 / Forward z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
1,000
1,001
1,001
0,5
1,000
1,000
1,000
1,000
1,000
1,0
1,000
1,000
1,001
1,001
1,002
1,5
1,000
1,000
1,001
1,003
1,006
2,0
1,000
1,001
1,002
1,005
1,011
2,5
1,000
1,001
1,002
1,007
1,014
3,0
1,000
1,001
1,003
1,008
1,018
0,4
0,1
1,000
1,001
1,001
1,002
1,003
0,5
1,000
1,000
1,000
1,000
1,000
1,0
1,000
1,000
1,000
1,002
1,003
1,5
1,000
1,000
1,002
1,007
1,014
2,0
1,000
1,000
1,003
1,011
1,026
2,5
1,000
1,000
1,004
1,015
1,036
3,0
1,000
1,000
1,005
1,017
1,043
0,6
0,1
1,000
1,001
1,002
1,003
1,006
0,5
0,999
0,999
0,999
0,999
0,998
1,0
0,999
0,998
0,998
0,999
1,000
1,5
0,999
0,998
0,999
1,005
1,016
2,0
0,999
0,998
1,001
1,012
1,034
2,5
0,999
0,998
1,002
1,018
1,049
3,0
0,999
0,998
1,003
1,022
1,062
0,8
0,1
1,000
1,001
1,002
1,004
1,008
0,5
0,999
0,999
0,998
0,996
0,995
1,0
0,999
0,996
0,993
0,992
0,991
1,5
0,998
0,995
0,993
0,998
1,007
2,0
0,998
0,995
0,994
1,006
1,029
2,5
0,998
0,995
0,996
1,013
1,049
3,0
0,998
0,994
0,997
1,017
1,065
1,0
0,1
1,000
1,001
1,003
1,006
1,010
0,5
0,999
0,997
0,995
0,993
0,993
1,0
0,998
0,992
0,987
0,982
0,978
1,5
0,997
0,990
0,984
0,984
0,988
2,0
0,996
0,989
0,984
0,991
1,006
2,5
0,996
0,989
0,985
0,997
1,027
3,0
0,996
0,988
0,986
1,002
1,044
26 Table 5 – CJ coefficients
Cable 3 / Forward z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,001
1,003
1,005
1,008
0,5
1,000
1,003
1,007
1,012
1,017
1,0
1,000
1,002
1,007
1,014
1,022
1,5
1,000
1,001
1,006
1,014
1,025
2,0
0,999
1,001
1,005
1,014
1,028
2,5
1,000
1,000
1,003
1,014
1,030
3,0
0,999
0,999
1,003
1,013
1,032
0,4
0,1
1,000
1,003
1,007
1,013
1,021
0,5
1,001
1,006
1,015
1,028
1,041
1,0
0,999
1,002
1,011
1,026
1,047
1,5
0,998
0,997
1,005
1,023
1,053
2,0
0,997
0,994
1,000
1,021
1,058
2,5
0,996
0,992
0,995
1,018
1,063
3,0
0,995
0,990
0,993
1,016
1,067
0,6
0,1
1,000
1,003
1,009
1,017
1,026
0,5
0,999
1,003
1,010
1,021
1,033
1,0
0,995
0,990
0,990
1,002
1,024
1,5
0,992
0,978
0,973
0,989
1,026
2,0
0,989
0,971
0,962
0,980
1,031
2,5
0,988
0,966
0,954
0,974
1,037
3,0
0,987
0,963
0,948
0,969
1,042
0,8
0,1
1,000
1,003
1,007
1,012
1,018
0,5
0,996
0,990
0,982
0,977
0,972
1,0
0,988
0,962
0,937
0,927
0,933
1,5
0,983
0,943
0,908
0,901
0,925
2,0
0,979
0,932
0,891
0,886
0,929
2,5
0,977
0,925
0,879
0,876
0,934
3,0
0,975
0,921
0,872
0,869
0,939
1,0
0,1
1,000
1,001
1,002
1,003
1,002
0,5
0,990
0,968
0,936
0,900
0,863
1,0
0,978
0,925
0,864
0,816
0,790
1,5
0,971
0,901
0,826
0,781
0,778
2,0
0,967
0,888
0,806
0,765
0,783
2,5
0,965
0,882
0,796
0,756
0,790
3,0
0,963
0,877
0,790
0,751
0,797
27 Table 6 – CJ coefficients
Cable 4 / Forward z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
0,999
0,998
0,997
0,5
0,999
0,995
0,989
0,979
0,963
1,0
0,998
0,993
0,982
0,967
0,946
1,5
0,999
0,992
0,983
0,970
0,956
2,0
0,998
0,993
0,984
0,976
0,968
2,5
0,998
0,993
0,986
0,981
0,979
3,0
0,999
0,994
0,988
0,985
0,988
0,4
0,1
1,000
0,999
0,997
0,994
0,990
0,5
0,997
0,984
0,962
0,929
0,881
1,0
0,994
0,973
0,936
0,884
0,819
1,5
0,993
0,969
0,933
0,888
0,841
2,0
0,992
0,970
0,937
0,903
0,876
2,5
0,992
0,971
0,942
0,919
0,906
3,0
0,993
0,972
0,947
0,930
0,929
0,6
0,1
1,000
0,998
0,995
0,991
0,987
0,5
0,994
0,972
0,934
0,879
0,807
1,0
0,987
0,946
0,878
0,782
0,671
1,5
0,985
0,937
0,863
0,772
0,685
2,0
0,983
0,935
0,864
0,790
0,732
2,5
0,983
0,935
0,870
0,811
0,775
3,0
0,984
0,936
0,875
0,828
0,809
0,8
0,1
1,000
0,999
0,998
0,999
1,003
0,5
0,992
0,966
0,924
0,869
0,809
1,0
0,982
0,926
0,836
0,716
0,596
1,5
0,977
0,907
0,801
0,675
0,566
2,0
0,974
0,900
0,793
0,681
0,595
2,5
0,973
0,897
0,795
0,697
0,630
3,0
0,973
0,897
0,799
0,713
0,662
1,0
0,1
1,000
1,003
1,011
1,026
1,053
0,5
0,993
0,974
0,949
0,929
0,947
1,0
0,980
0,924
0,839
0,743
0,698
1,5
0,972
0,896
0,784
0,664
0,602
2,0
0,968
0,882
0,764
0,647
0,585
2,5
0,965
0,875
0,758
0,650
0,591
3,0
0,964
0,873
0,757
0,657
0,602
28 Table 7 – CJ coefficients
Cable 5 / Forward z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
1,001
1,001
1,002
0,5
0,999
0,999
0,999
0,997
0,994
1,0
1,000
0,999
0,998
0,996
0,989
1,5
1,000
0,999
0,999
1,000
0,997
2,0
1,000
0,999
1,000
1,004
1,007
2,5
1,000
1,000
1,002
1,008
1,017
3,0
1,000
1,000
1,003
1,011
1,025
0,4
0,1
1,000
1,000
1,001
1,001
1,002
0,5
0,999
0,999
0,999
0,997
0,994
1,0
1,000
0,999
0,998
0,996
0,989
1,5
1,000
0,999
0,999
1,000
0,997
2,0
1,000
0,999
1,000
1,004
1,007
2,5
1,000
1,000
1,002
1,008
1,017
3,0
1,000
1,000
1,003
1,011
1,025
0,6
0,1
1,000
1,001
1,001
1,002
1,004
0,5
0,999
0,999
0,997
0,993
0,986
1,0
0,999
0,997
0,993
0,986
0,972
1,5
0,999
0,997
0,994
0,991
0,980
2,0
0,999
0,997
0,996
0,998
0,995
2,5
0,999
0,997
0,997
1,004
1,011
3,0
0,999
0,997
0,999
1,009
1,025
0,8
0,1
1,000
1,001
1,002
1,003
1,006
0,5
0,999
0,998
0,994
0,987
0,976
1,0
0,998
0,994
0,986
0,973
0,948
1,5
0,998
0,993
0,985
0,976
0,952
2,0
0,998
0,993
0,987
0,983
0,970
2,5
0,998
0,993
0,989
0,991
0,990
3,0
0,997
0,993
0,991
0,997
1,008
1,0
0,1
1,000
1,001
1,002
1,004
1,007
0,5
0,998
0,996
0,991
0,982
0,968
1,0
0,997
0,990
0,978
0,957
0,923
1,5
0,996
0,987
0,974
0,955
0,919
2,0
0,996
0,987
0,974
0,961
0,933
2,5
0,996
0,987
0,976
0,969
0,952
3,0
0,996
0,986
0,977
0,976
0,970
29 Table 8 – CJ coefficients
Cable 6 / Forward z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
1,001
1,002
1,004
0,5
1,000
1,001
1,002
1,005
1,007
1,0
1,000
1,001
1,002
1,005
1,010
1,5
1,000
1,000
1,002
1,006
1,013
2,0
0,999
1,000
1,002
1,007
1,016
2,5
1,000
1,000
1,001
1,007
1,019
3,0
0,999
1,000
1,001
1,007
1,020
0,4
0,1
1,000
1,001
1,002
1,004
1,007
0,5
1,000
1,001
1,003
1,006
1,009
1,0
0,999
1,000
1,002
1,006
1,012
1,5
1,000
0,999
1,001
1,007
1,020
2,0
0,999
0,998
1,000
1,008
1,028
2,5
0,999
0,997
0,998
1,009
1,034
3,0
0,999
0,997
0,998
1,009
1,039
0,6
0,1
1,000
1,001
1,002
1,005
1,008
0,5
0,999
1,000
1,000
1,002
1,004
1,0
0,999
0,997
0,996
0,998
1,003
1,5
0,998
0,995
0,994
0,999
1,013
2,0
0,998
0,994
0,992
1,001
1,026
2,5
0,998
0,993
0,991
1,002
1,036
3,0
0,997
0,993
0,991
1,003
1,045
0,8
0,1
1,000
1,000
1,002
1,004
1,007
0,5
0,999
0,998
0,996
0,994
0,993
1,0
0,998
0,993
0,988
0,985
0,984
1,5
0,997
0,990
0,984
0,985
0,995
2,0
0,996
0,989
0,982
0,986
1,010
2,5
0,996
0,988
0,981
0,988
1,024
3,0
0,996
0,987
0,980
0,989
1,036
1,0
0,1
1,000
1,000
1,001
1,003
1,005
0,5
0,998
0,995
0,990
0,984
0,978
1,0
0,997
0,988
0,977
0,967
0,958
1,5
0,996
0,985
0,972
0,964
0,964
2,0
0,995
0,983
0,969
0,965
0,978
2,5
0,995
0,982
0,968
0,967
0,993
3,0
0,995
0,981
0,967
0,968
1,006
30 Table 9 – CJ coefficients
Cable 1 / Reverse
Cable 6 / Reverse
z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
1,000
1,001
1,001
0,5
1,000
1,002
1,005
1,011
1,018
1,0
1,001
1,004
1,009
1,017
1,033
1,5
1,001
1,004
1,009
1,018
1,031
2,0
1,000
1,004
1,009
1,016
1,024
2,5
1,001
1,004
1,008
1,013
1,018
3,0
1,001
1,003
1,007
1,011
1,014
0,4
0,1
1,000
1,000
1,000
1,001
1,002
0,5
1,001
1,004
1,010
1,022
1,041
1,0
1,002
1,008
1,019
1,040
1,076
1,5
1,002
1,008
1,021
1,042
1,074
2,0
1,002
1,008
1,020
1,038
1,058
2,5
1,002
1,008
1,019
1,032
1,047
3,0
1,002
1,008
1,017
1,027
1,037
0,6
0,1
1,000
1,000
1,001
1,001
1,002
0,5
1,002
1,006
1,014
1,029
1,057
1,0
1,003
1,010
1,027
1,058
1,113
1,5
1,004
1,012
1,030
1,063
1,112
2,0
1,003
1,012
1,029
1,056
1,089
2,5
1,003
1,012
1,028
1,049
1,072
3,0
1,004
1,012
1,026
1,042
1,056
0,8
0,1
1,000
1,001
1,001
1,002
1,003
0,5
1,002
1,007
1,017
1,036
1,072
1,0
1,004
1,013
1,034
1,073
1,144
1,5
1,005
1,015
1,038
1,079
1,141
2,0
1,004
1,015
1,037
1,072
1,113
2,5
1,004
1,015
1,035
1,063
1,088
3,0
1,005
1,015
1,033
1,054
1,071
1,0
0,1
1,000
1,000
1,001
1,001
1,003
0,5
1,002
1,007
1,019
1,041
1,083
1,0
1,004
1,014
1,038
1,084
1,168
1,5
1,004
1,017
1,043
1,091
1,163
2,0
1,004
1,017
1,042
1,082
1,130
2,5
1,004
1,017
1,040
1,072
1,100
3,0
1,004
1,017
1,038
1,063
1,080
31 Table 10 – CJ coefficients
Cable 2 / Reverse
Cable 5 / Reverse
z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
1,000
1,000
1,000
0,999
0,5
1,000
1,000
1,000
1,000
1,001
1,0
1,000
1,000
1,000
1,000
1,000
1,5
1,000
1,000
0,999
0,997
0,995
2,0
1,000
1,000
0,998
0,995
0,991
2,5
1,000
1,000
0,998
0,994
0,987
3,0
1,000
1,000
0,997
0,992
0,985
0,4
0,1
1,000
1,000
0,999
0,999
0,998
0,5
0,999
1,000
1,000
1,001
1,004
1,0
1,000
1,000
1,000
1,000
1,001
1,5
1,000
0,999
0,998
0,995
0,989
2,0
1,000
0,999
0,996
0,989
0,977
2,5
1,000
0,999
0,995
0,985
0,968
3,0
0,999
0,998
0,994
0,982
0,962
0,6
0,1
1,000
1,000
1,000
0,999
0,998
0,5
1,000
1,001
1,002
1,004
1,009
1,0
1,001
1,001
1,002
1,003
1,003
1,5
1,000
1,001
0,999
0,993
0,984
2,0
1,001
1,000
0,996
0,985
0,965
2,5
1,000
1,000
0,994
0,978
0,951
3,0
1,000
0,999
0,992
0,973
0,941
0,8
0,1
1,000
1,000
1,000
0,999
0,999
0,5
1,000
1,001
1,003
1,007
1,012
1,0
1,001
1,002
1,002
1,004
1,004
1,5
1,001
1,001
0,999
0,992
0,976
2,0
1,001
1,000
0,995
0,979
0,951
2,5
1,001
1,000
0,993
0,971
0,933
3,0
1,001
0,999
0,990
0,965
0,920
1,0
0,1
1,000
1,000
1,000
0,999
0,999
0,5
1,000
1,002
1,004
1,009
1,017
1,0
1,001
1,002
1,004
1,005
1,002
1,5
1,001
1,002
0,999
0,989
0,967
2,0
1,001
1,001
0,995
0,974
0,937
2,5
1,001
1,000
0,991
0,964
0,916
3,0
1,001
0,999
0,988
0,956
0,902
32 Table 11 – CJ coefficients
Cable 3 / Reverse
Cable 4 / Reverse
z = d/2s
y1=s/c1
m
0,1
0,2
0,3
0,4
0,5
0,2
0,1
1,000
0,998
0,996
0,992
0,989
0,5
0,999
0,995
0,990
0,982
0,975
1,0
0,998
0,994
0,987
0,977
0,966
1,5
0,999
0,994
0,987
0,974
0,961
2,0
0,998
0,994
0,986
0,973
0,956
2,5
0,999
0,994
0,986
0,972
0,953
3,0
0,999
0,995
0,987
0,972
0,951
0,4
0,1
1,000
0,995
0,987
0,977
0,964
0,5
0,997
0,985
0,965
0,940
0,913
1,0
0,996
0,979
0,951
0,916
0,881
1,5
0,996
0,977
0,946
0,905
0,862
2,0
0,995
0,977
0,944
0,898
0,850
2,5
0,996
0,977
0,943
0,894
0,841
3,0
0,996
0,977
0,943
0,893
0,836
0,6
0,1
1,000
0,992
0,978
0,959
0,936
0,5
0,994
0,970
0,933
0,886
0,838
1,0
0,991
0,956
0,902
0,836
0,775
1,5
0,990
0,951
0,889
0,812
0,740
2,0
0,989
0,949
0,883
0,799
0,720
2,5
0,989
0,948
0,879
0,792
0,707
3,0
0,989
0,948
0,879
0,788
0,698
0,8
0,1
1,000
0,989
0,970
0,945
0,914
0,5
0,991
0,957
0,902
0,835
0,765
1,0
0,985
0,932
0,850
0,755
0,669
1,5
0,983
0,921
0,827
0,717
0,622
2,0
0,982
0,917
0,816
0,698
0,596
2,5
0,982
0,915
0,811
0,688
0,581
3,0
0,981
0,914
0,808
0,681
0,570
1,0
0,1
1,000
0,987
0,966
0,937
0,902
0,5
0,988
0,944
0,873
0,788
0,698
1,0
0,979
0,907
0,800
0,678
0,571
1,5
0,975
0,891
0,766
0,628
0,517
2,0
0,973
0,884
0,750
0,604
0,490
2,5
0,973
0,881
0,742
0,591
0,474
3,0
0,972
0,879
0,738
0,583
0,463

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