BS 7769-1 2-1994 Electric cables - Calculation of the current rating - Current rating equations (100% load factor) and calculation of losses - Sheath eddy current loss factors for .pdf

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1、BRITISH STANDARD BS 7769-1.2: 1994 IEC 287-1-2: 1993 Electric cables Calculation of the current rating Part 1: Current rating equations (100%load factor) and calculation of losses Section 1.2: Sheath eddy current loss factors for two circuits in flat formationBS7769-1.2:1994 This British Standard, h

2、aving been prepared under the directionof the Cables and Insulation Standards Policy Committee was published underthe authority of the Standards Board and comesintoeffect on 15July1994 BSI 12-1999 The following BSI references relate to the work on this standard: Committee reference CIL/20 Draft for

3、comment 93/202174 DC ISBN 0 580 23211 5 Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Cables and Insulation Standards Policy Committee (CIL/-) to Technical Committee CIL/20, upon which the following bodies were represented: Association

4、 of Consulting Engineers Association of Manufacturers of Domestic Electrical Appliances BEAMA Electrical Cable and Conductor Accessory Manufacturers Association British Approvals Service for Cables British Cable Makers Confederation British Plastics Federation British Steel Industry Department of Tr

5、ade and Industry (Consumer Safety Unit, CA division) Electricity Association Engineering Equipment and Materials Users Association Institution of Electrical Engineers London Regional Transport The following bodies were also represented in the drafting of the standard, through subcommittees and panel

6、s: ERA Technology Ltd. Institution of Incorporated Executive Engineers London Underground Ltd. Amendments issued since publication Amd. No. Date CommentsBS 7769-1.2:1994 BSI 12-1999 i Contents Page Committees responsible Inside front cover National foreword ii 1 Scope 1 2 Normative references 1 3 Sy

7、mbols 1 4 Description of method 2 5 Formulae for sheath loss factors for high-resistance sheaths in a singlecircuit, 2 0 4 6 Calculation of the coefficients H, N and J 4 7 Notes on transposition of cables 8 8 Worked examples of calculation of eddy current losses 8 Figure 1 Cable configuration 3 Tabl

8、e 1 H coefficients 14 Table 2 N coefficients 14 Table 3 J coefficients 15 Table 4 J coefficients 16 Table 5 J coefficients 17 Table 6 J coefficients 18 Table 7 J coefficients 19 Table 8 J coefficients 20 Table 9 J coefficients 21 Table 10 J coefficients 22BS7769-1.2:1994 ii BSI 12-1999 National fore

9、word This Section of BS7769 has been prepared under the direction of the Cables and Insulation Standards Policy Committee. It is identical with IEC287-1-2:1993 Electric cables Calculation of the current rating Part 1: Current rating equations (100% load factor) and calculation of losses Section 2: S

10、heath eddy current loss factors for two circuits in flat formation, published by the International Electrotechnical Commission (IEC). IEC287 is being revised as a multi-section document under the title Electric cables calculation of the current rating. These will be published as dual-numbered Britis

11、h Standards as they become available. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Sum

12、mary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages1 to 22 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover.BS7769-1.2:

13、1994 BSI 12-1999 1 1 Scope This section of IEC287-1 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 signifi

14、cant 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 under consideration. The method provides coefficien

15、ts 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 = 6/10 7R s ), which corresponds to a sheath longitudinal resistance higher than31447/m at50Hz. Con

16、sequently 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 cal

17、ls 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 IEC287-1-1 (under considerati

18、on). 2 Normative references The following normative documents contain provisions which, through reference in this text, constitute provisions of this section of IEC287-1. At the time of publication, the editions indicated were valid. All normative documents are subject to revision, and parties to ag

19、reements based on this section of IEC287-1 are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. IEC 287:1982, Calculation of the continuous

20、current rating of cables (100 % load factor). IEC 287-1-1:199X, Electric cables Calculation of the current rating Part 1: Current rating equations (100 %load factor) and calculation of losses Section 1: (under consideration). 3 Symbols The symbols used in this section of IEC287-1and the quantities t

21、hey represent are given in the following list. Some of the symbols used in this section may be used to represent different quantities in other section of IEC287. A, B, C, D are coefficients used to interpolate for H andJ D s is the external diameter of the metal sheath (mm) D it is the diameter of t

22、he imaginary cylinder which just touches the inside surface of the troughs of a corrugated sheath (mm) D oc is the diameter of the imaginary coaxial cylinder which just touches the crests of a corrugated sheath(mm) G s is the coefficient which accounts for losses due to eddy currents across the thic

23、kness of the sheath due to the current in the conductor R is the alternating current resistance of the conductor at its maximum operating temperature (7/m) R s is the resistance of the sheath (7/m) S, T, U, V are the coefficients used to interpolate forJ c is the distance between centres of cables i

24、n adjoining circuits (see Figure 1) (mm) d is the mean diameter of the sheath (mm) f is the system frequency (Hz) g s is the coefficient which accounts for losses due to eddy currents across the thickness of the sheath, due to currents in adjacent cables m is equal to s is the distance between centr

25、es of cables in the same circuit (mm) 6 R s -10 7 BS7769-1.2:1994 2 BSI 12-1999 4 Description of method 4.1 General The method proceeds in a way similar to that used for single circuits in IEC287-1-1. There, formulae for loss factors applicable to sheaths having a longitudinal resistance such that m

26、 is less than 0,1 (R s= 314 47/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

27、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 than1%. The development of

28、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 exp

29、ected 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 o

30、r 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 IEC287-1-1. 4.2 Outline of method The loss factor for the sheath of a given cable

31、 in a double-circuit flat formation (seeFigure 1) is evaluated as follows: where t s is the thickness of the sheath (mm) y is equal to z is equal to “ 1 is the coefficient used in 6.5 2 0 is the sheath loss factor for a high-resistance sheath in a single circuit is the sheath loss factor for a low-r

32、esistance sheath in a single circuit is the sheath loss factor for a low-resistance sheath in a double circuit s s is the electrical resistivity of sheath material at operating temperature (7.m) 6 is the angular frequency of system (2;f) (l/s) (1) is the sheath loss factor for a low-resistance sheat

33、h in a double circuit; 2 0 is the sheath loss factor for a high-resistance sheath in a single circuit; H (1 to 3) are the coefficients which correct for sheath resistance, the values obtained relate to cables1, 2 or 3 in a single circuit; N (1 to 6) are the coefficients which introduce the mutual in

34、fluences between circuits and are therefore dependent on the relative phase sequences of cables 1 to 3 and 4 to 6; J (1 to 6) are the coefficients which depend on the cable positions 1 to 3 and 4 to 6 in each circuit; g s is the coefficient which accounts for losses due to eddy currents across the t

35、hickness of the sheath, due to currents in adjacent cables; G sis the coefficient which accounts for losses due to eddy currents across the thickness of the sheath, due to the current in the conductor. s c - d 2s - 2 1 2 1d 2 1dBS7769-1.2:1994 BSI 12-1999 3 The tasks performed by coefficients N and

36、J are not directly related to any physical function, but have been selected to simplify the tabulation. The nomenclature is arbitrary. Values of H, N and J are obtained fromTable 1 toTable 11 and are chosen according to the following parameters together with the position of the cable and the phase s

37、equence of the currents in the conductors. NOTEThe factors for a single circuit having low-resistance sheaths can be obtained by using the coefficients H (1, 2 and 3) only, as follows: 4.3 Criteria for use of formulae and coefficients For sheaths for which the value of m is less than 0,1, which incl

38、udes most lead-sheathed cables, it may be assumed that the coefficients H, N, J and g sare unity and G sis zero. In such circumstances, 2 0 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-

39、sheathed cables, values for H, N, J and g sshall be calculated. The coefficient G sis important only when the value of m is 1,0 or higher. where f is the system frequency (Hz); R s is the sheath resistance at operating temperature (7/m); where s is the distance between centres of cables in the same

40、circuit (mm); d is the mean diameter of a sheath (mm); where c is the distance between centres of cables in adjoining circuits (see Figure 1) (mm). Figure 1 Cable configuration z d 2 s - = y s c - =BS7769-1.2:1994 4 BSI 12-1999 5 Formulae for sheath loss factors for high-resistance sheaths in a sing

41、le circuit, 2 0 The sheath loss factor 2 0is given by For three single-core cables in flat formation, the coefficient C is given by: 6 Calculation of the coefficients H, N, and J 6.1 Allocation of coefficients to each cable, time sequence and phase identification It is important to note the way in w

42、hich the coefficients H, N and J 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 H (1, 2 and 3), Table 1, are allocated on a basis of time sequence associated with the positions of th

43、e cables, so that the following single-circuit arrangements have the same time sequence: In the above example, cable 1 is always the outer conductor on a leading phase and takes coefficient H 1 . Cable 3 is the outer conductor on a lagging phase and takes coefficient H 3 . It will be seen that, for

44、these cases, the phase identification implied by the symbols R, S and T 1) 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 H must be allocated to the cables in the reverse order. The allocation of c

45、oefficient H 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 se

46、quence, or a mirror image of, in the reverse sequence, that in the other. Two sets of coefficients N (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 co

47、efficients are allocated on the same basis as coefficient H. Note that the values for cables 4, 5 and6 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 J (1, 2, 3, 4, 5 and 6) makes it desirable to use several

48、 tables. Table 3 to Table 8 are for each cable for the forward sequence installation. For the reverse sequence, Table 9 to Table11 are provided and the coefficients for cables 1 to 3 are also used for cables6to4, in that order. The allocation is on the same lines as those for coefficient N. (2) Cabl

49、e Coefficient C Centre cable 6 Outer cables 1,5 Cable number 1 2 3 Sequence R S T or S T R or T R S with coefficients H 1 H 2 H 3 1) 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 L 1 , L 2 , L 3 ; a, b, c; R, Y, B; etc.BS7769-1.2:1994 BSI 12-1999 5 The following tables give examples of four common cases: 6.2 Calculation of coefficients H (1, 2 and 3), Table 1 Each coefficient H is obtai