BSI 21/30431003 DC:2021 Edition

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BS IEC 60287-1-1. Electric cables. Calculation of the current rating – Part 1-1. Current rating equations (100 % load factor) and calculation of losses. General

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3	20_1950e_CD 20/1950/CD COMMITTEE DRAFT (CD) Project number: IEC 60287-1-1 ED3 Date of circulation: Closing date for comments: 2021-02-05 2021-04-30 Supersedes documents: 20/1944/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 1-1: Current rating equations (100 % load factor) and calculation of losses – General Note from TC/SC officers: HORIZONTAL_STD FUNCTION_EMC FUNCTION_ENV FUNCTION_QUA FUNCTION_SAFETY
4	CONTENTS CONTENTS 2 FOREWORD 3 INTRODUCTION 5 1 General 6 1.1 Scope 6 1.2 Normative references 6 1.3 Symbols 7 1.4 Permissible current rating of cables 11 2 Calculation of losses 14 2.1 AC resistance of conductor 14 2.2 Dielectric losses (applicable to a.c. cables only) 18 2.3 Loss factor for sheath and screen (applicable to power frequency a.c. cables only) 18 2.4 Loss factor for armour, reinforcement and steel pipes (applicable to power frequency a.c. cables only) 28 Annex A (informative) Correction factor for increased lengths of individual cores within multicore cables 37 Table 1 – Electrical resistivities and temperature coefficients of metals used 33 Table 2 – Skin and proximity effects – Experimental values for the coefficients ks and kp 34 Table 3 – Values of relative permittivity and loss factors for the insulation of high-voltage and medium-voltage cables at power frequency 35 Table 4 – Absorption coefficient of solar radiation for cable surfaces 36
5	INTERNATIONAL ELECTROTECHNICAL COMMISSION____________ ELECTRIC CABLES – CALCULATION OF THE CURRENT RATING – Part 1-1: Current rating equations (100 % load factor) and calculation of losses – General 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. This edition x.y of IEC 60287-1-1 uses a set of symbols that has been harmonized over all chapters of the standards IEC 60287 and IEC 60853. Technical changes concern corrections by considering the unit lengths of cable instead of conductor. This publication has been prepared for user convenience.
6	International Standard IEC 60287-1-1 has been prepared by IEC technical committee 20: Electric cables. This publication has been drafted in accordance with the ISO/IEC Directives, Part 2. A list of all parts of the IEC 60287 series, published under the general title: Electric cables – Calculation of the current rating, can be found on the IEC website. The committee has decided that the contents of the base publication and its amendment will remain unchanged until the stability date indicated on the IEC web site under “http://webstore.iec.ch” in the data related to the specific publication. At this date, the publication will be  reconfirmed,  withdrawn,  replaced by a revised edition, or  amended.
7	INTRODUCTION This Part 1-1 contains formulae for the quantities RC, Wd, 1 and 2. It contains methods for calculating the permissible current rating of cables from details of the permissible temperature rise, conductor resistance, losses and thermal resistivities. Formulae for the calculation of losses are also given. The formulae in this standard contain quantities which vary with cable design and materials used. The values given in the tables are either internationally agreed, for example, electrical resistivities and resistance temperature coefficients, or are those which are generally accepted in practice, for example, thermal resistivities and permittivities of materials. In this latter category, some of the values given are not characteristic of the quality of new cables but are considered to apply to cables after a long period of use. In order that uniform and comparable results may be obtained, the current ratings should be calculated with the values given in this standard. However, where it is known with certainty that other values are more appropriate to the materials and design, then these may be used, and the corresponding current rating declared in addition, provided that the different values are quoted. Quantities related to the operating conditions of cables are liable to vary considerably from one country to another. For instance, with respect to the ambient temperature and soil thermal resistivity, the values are governed in various countries by different considerations. Superficial comparisons between the values used in the various countries may lead to erroneous conclusions if they are not based on common criteria: for example, there may be different expectations for the life of the cables, and in some countries design is based on maximum values of soil thermal resistivity, whereas in others average values are used. Particularly, in the case of soil thermal resistivity, it is well known that this quantity is very sensitive to soil moisture content and may vary significantly with time, depending on the soil type, the topographical and meteorological conditions, and the cable loading. The following procedure for choosing the values for the various parameters should, therefore, be adopted. Numerical values should preferably be based on results of suitable measurements. Often such results are already included in national specifications as recommended values, so that the calculation may be based on these values generally used in the country in question; a survey of such values is given in Part 3-1. A suggested list of the information required to select the appropriate type of cable is given in Part 3-1.
8	ELECTRIC CABLES – CALCULATION OF THE CURRENT RATING – Part 1-1: Current rating equations (100 % load factor) and calculation of losses – General 1 General 1.1 Scope This part of IEC 60287 is applicable to the conditions of steady-state operation of cables at all alternating voltages, and direct voltages up to 5 kV, buried directly in the ground, in ducts, troughs or in steel pipes, both with and without partial drying-out of the soil, as well as cables in air. The term “steady state” is intended to mean a continuous constant current (100 % load factor) just sufficient to produce asymptotically the maximum conductor temperature, the surrounding ambient conditions being assumed constant. This part provides formulae for current ratings and losses. The formulae given are essentially literal and designedly leave open the selection of certain important parameters. These may be divided into three groups: – parameters related to construction of a cable (for example, thermal resistivity of insulating material) for which representative values have been selected based on published work; – parameters related to the surrounding conditions, which may vary widely, the selection of which depends on the country in which the cables are used or are to be used; – parameters which result from an agreement between manufacturer and user and which involve a margin for security of service (for example, maximum conductor temperature). 1.2 Normative references The following referenced documents are indispensable for the application 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. IEC 60027-3, Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units IEC 60028:1925, International standard of resistance for copper IEC 60141 (all parts), Tests on oil-filled and gas-pressure cables and their accessories IEC 60228, Conductors of insulated cables IEC 60502-1, Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36 kV) – Part 1: Cables for rated voltages of 1 kV (Um = 1,2 kV) and 3 kV (Um = 3,6 kV)
9	IEC 60502-2, Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36 kV) – Part 2: Cables for rated voltages from 6 kV (Um = 7,2 kV) up to 30 kV (Um = 36 kV) IEC 60889, Hard-drawn aluminium wire for overhead line conductors 1.3 Symbols The symbols used in this standard and the quantities which they represent are given in the following list. cross-sectional area of the armour mm² B1 /m B2 C capacitance per core F/m CLL length correction factor for considering laying up of cores D external diameter of cable m Di diameter over insulation mm D diameter over the individual core of a multicore cable Ds external diameter of metal sheath mm Doc the diameter of the imaginary coaxial cylinder which just touches the crests of a corrugated sheath mm Dit the diameter of the imaginary cylinder which just touches the inside surface of the troughs of a corrugated sheath mm CF coefficient defined in 2.3.5 Ee intensity of solar radiation W/m² H magnetizing force (see 2.4.2) A/m Hs inductance of sheath H/m H1 H2 H/m H3 I current in one conductor (r.m.s. value) A IS current in sheath (r.m.s. value) A is the axial cable length over which the cores make one full helical turn (m) CM1 CN CP /m CQ RC alternating current resistance of conductor at its maximum operating temperature per unit length of the cable /m RA a.c. resistance of armour at its maximum operating temperature per unit length of the cable /m a.c. resistance of armour at 20 °C per unit length of the cable /m Re equivalent a.c. resistance of sheath and armour in parallel /m Rs a.c. resistance of cable sheath or screen at their maximum operating temperature per unit length of the cable /m
10	a.c. resistance of cable sheath or screen at 20 °C per unit length of the cable /m R d.c. resistance of conductor at maximum operating temperature per unit length of the cable /m Ro d.c. resistance of conductor at 20 °C per unit length of the cable /m T1 thermal resistance per core between conductor and sheath per unit length of the cable K·m/W T2 thermal resistance between sheath and armour per unit length of the cable K·m/W T3 thermal resistance of external serving per unit length of the cable K·m/W T4 thermal resistance of surrounding medium (ratio of cable surface temperature rise above ambient to the losses per unit length) K·m/W
11	T#4 external thermal resistance in free air, adjusted for solar radiation K·m/W Uo voltage between conductor and screen or sheath V WA losses in armour per unit length of the cable W/m Wc losses in conductor per unit length of the cable W/m Wd dielectric losses per unit length of the cable per phase W/m Ws losses dissipated in sheath per unit length of the cable W/m W(s+A) total losses in sheath and armour per unit length of the cable W/m X reactance of sheath (two-core cables and three-core cables in trefoil) per unit length of the cable /m X1 reactance of sheath (cables in flat formation) /m Xm mutual reactance between the sheath of one cable and the conductors of the other two when cables are in flat information /m a shortest minor length in a cross-bonded electrical section having unequal minor lengths c distance between the axes of conductors and the axis of the cable for three-core cables (= 0,55 r1 + 0,29 t for sector-shaped conductors) mm d mean diameter of sheath or screen mm d mean diameter of sheath and reinforcement mm d2 mean diameter of reinforcement mm dA mean diameter of armour mm dc external diameter of conductor mm dc external diameter of equivalent round solid conductor having the same central duct as a hollow conductor mm dd internal diameter of pipe mm df diameter of a steel wire mm di internal diameter of hollow conductor mm dM major diameter of screen or sheath of an oval conductor mm dm minor diameter of screen or sheath of an oval conductor mm dx diameter of an equivalent circular conductor having the same cross-sectional area and degree of compactness as the shaped one mm f system frequency Hz Cgs coefficient used in 2.3.6.1 kf factor used in the calculation of hysteresis losses in armour or reinforcement (see 2.4.2.4) kp factor used in calculating xp (proximity effect) ks factor used in calculating xs (skin effect) l* length of a cable section (general symbol, see 2.3 and 2.3.4) m ln natural logarithm (logarithm to base e, see IEC 60027-3) m 10–7 n number of conductors in a cable n1 number of steel wires in a cable (see 2.4.2) p length of lay of a steel wire along a cable (see 2.4.2) pCp qCq r1 circumscribing radius of two- or three-sector shaped conductors mm
12	s axial separation of conductors mm s1 axial separation of two adjacent cables in a horizontal group of three, not touching mm s2 axial spacing between adjacent cables in trefoil formation; for cables in flat formation s2 is the geometric mean of the three spacings mm t0 insulation thickness between conductors mm t3 thickness of the serving mm ts thickness of the sheath mm v ratio of the thermal resistivities of dry and moist soils (v = d/w) xp argument of a Bessel function used to calculate proximity effect xs argument of a Bessel function used to calculate skin effect yp proximity effect factor ys skin effect factor 20 temperature coefficient of electrical resistivity at 20 °C, per kelvin I/K 1 coefficient used in 2.3.6.1  angle between axis of armour wires and axis of cable (see 2.4.2)  angular time delay (see 2.4.2) 1 2  equivalent thickness of armour or reinforcement mm tan loss factor of insulation  relative permittivity of insulation  maximum operating temperature of conductor °C a ambient temperature °C ar maximum operating temperature of armour °C sc maximum operating temperature of cable screen or sheath °C x critical temperature of soil; this is the temperature of the boundary between dry and moist zones °C  permissible temperature rise of conductor above ambient temperature K x critical temperature rise of soil; this is the temperature rise of the boundary between dry and moist zones above the ambient temperature of the soil K 0 coefficient used in 2.3.6.1 1, 2 ratio of the total losses in metallic sheaths and armour respectively to the total conductor losses (or losses in one sheath or armour to the losses in one conductor) ratio of the losses in one sheath caused by circulating currents in the sheath to the losses in one conductor ratio of the losses in one sheath caused by eddy currents to the losses in one conductor loss factor for the middle cable loss factor for the outer cable with the greater losses loss factor for the outer cable with the least losses  relative magnetic permeability of armour material
13	e longitudinal relative permeability t transverse relative permeability  conductor resistivity at 20 °C ·m d thermal resistivity of dry soil K.m/W w thermal resistivity of moist soil K.m/W s sheath resistivity at 20 °C ·m  absorption coefficient of solar radiation for the cable surface  angular frequency of system (2f) 1.4 Permissible current rating of cables When the permissible current rating is being calculated under conditions of partial drying out of the soil, it is also necessary to calculate a rating for conditions where drying out of the soil does not occur. The lower of the two ratings shall be used. 1.4.1 Buried cables where drying out of the soil does not occur or cables in air 1.4.1.1 AC cables The permissible current rating of an a.c. cable can be derived from the expression for the temperature rise above ambient temperature: where I is the current flowing in one conductor (A);  is the conductor temperature rise above the ambient temperature (K); NOTE The ambient temperature is the temperature of the surrounding medium under normal conditions, at a situation in which cables are installed, or are to be installed, including the effect of any local source of heat, but not the increase of temperature in the immediate neighbourhood of the cables due to heat arising therefrom. RC is the alternating current resistance per unit length of the cable at maximum operating temperature (/m); Wd is the dielectric loss per unit length of the cable for the insulation surrounding the conductor (W/m); T1 is the thermal resistance per unit length of the cable between one conductor and the sheath (K.m/W); T2 is the thermal resistance per unit length of the cable of the bedding between sheath and armour (K.m/W); T3 is the thermal resistance per unit length of the cable of the external serving of the cable (K.m/W); T4 is the thermal resistance per unit length between the cable surface and the surrounding medium, as derived from 2.2 of Part 2 (K.m/W); n is the number of load-carrying conductors in the cable (conductors of equal size and carrying the same load); 1 is the ratio of losses in the metal sheath to total losses in all conductors in that cable; 2 is the ratio of losses in the armouring to total losses in all conductors in that cable.
14	The permissible current rating is obtained from the above formula as follows: Where the cable is exposed to direct solar radiation, the formulae given in 2.2.1.2 of Part 2 shall be used. The current rating for a four-core low-voltage cable may be taken to be equal to the current rating of a three-core cable for the same voltage and conductor size having the same construction, provided that the cable is to be used in a three-phase system where the fourth conductor is either a neutral conductor or a protective conductor. When it is a neutral conductor, the current rating applies to a balanced load. 1.4.1.2 DC cables up to 5 kV The permissible current rating of a d.c. cable is obtained from the following simplification of the a.c. formula: where R is the direct current resistance per unit length of the cable at maximum operating temperature (/m). Where the cable is exposed to direct solar radiation, the formulae given in 2.2.1.2 of Part 2 shall be used. 1.4.2 Buried cables where partial drying-out of the soil occurs 1.4.2.1 AC cables The following method shall be applied to a single isolated cable or circuit only, laid at conventional depths. The method is based on a simple two-zone approximate physical model of the soil where the zone adjacent to the cable is dried out whilst the other zone retains the site’s thermal resistivity, the zone boundary being on isotherm 1). This method is considered to be appropriate for those applications in which soil behaviour is considered in simple terms only. NOTE Installations of more than one circuit as well as the necessary spacing between circuits are under consideration. Changes in external thermal resistance, consequent to the formation of a dry zone around a single isolated cable or circuit, shall be obtained from the following formula (compared with the formula of 1.4.1.1): where v is the ratio of the thermal resistivities of the dry and moist soil zones (v = d/w); RC is the a.c. resistance of the conductor at its maximum operating temperature per unit length of the cable (/m); MTBlankEqn MTBlankEqn
15	d is the thermal resistivity of the dry soil (K.m/W); w is the thermal resistivity of the moist soil (K.m/W); x is the critical temperature of the soil and temperature of the boundary between dry and moist zones (°C); a is the ambient temperature (°C); x is the critical temperature rise of the soil. This is the temperature rise of the boundary between the dry and moist zones above the ambient temperature of the soil (x – a) (K); NOTE T4 is calculated using the thermal resistivity of the moist soil (w) using 2.2.3.2 of Part 2. Mutual heating by modification of the temperature rise as in 2.2.3.1 of Part 2 cannot be applied. x and d shall be determined from a knowledge of the soil conditions. NOTE The choice of suitable soil parameters is under consideration. In the meantime, values may be agreed between manufacturer and purchaser. 1.4.2.2 DC cables up to 5 kV The permissible current rating of a d.c. cable is obtained from the following simplification of the a.c. formula: where R is the direct current resistance per unit length of the cable at maximum operating temperature (/m). 1.4.3 Buried cables where drying-out of the soil is to be avoided 1.4.3.1 AC cables Where it is desired that moisture migration be avoided by limiting the temperature rise of the cable surface to not more than x, the corresponding rating shall be obtained from: However, depending on the value of x this may result in a conductor temperature which exceeds the maximum permissible value. The current rating used shall be the lower of the two values obtained, either from the above equation or from 1.4.1.1. The conductor resistance RC shall be calculated for the appropriate conductor temperature, which may be less than the maximum permitted value. An estimate of the operating temperature shall be made and, if necessary, subsequently amended. NOTE For four-core low-voltage cables, see the final paragraph in 1.4.1.1.
16	1.4.3.2 DC cables up to 5 kV The permissible current rating of a d.c. cable shall be obtained from the following simplification of the a.c. formula: The conductor resistance R shall be modified as in 1.4.2.2. 1.4.4 Cables directly exposed to solar radiation Permissible current ratings Taking into account the effect of solar radiation on a cable, the permissible current rating is given by the formulae: 1.4.4.1 AC cables 1.4.4.2 DC cables up to 5 kV where  is the absorption coefficient of solar radiation for the cable surface (see Table 4); Ee is the intensity of solar radiation which should be taken as 103 W/m² for most latitudes; it is recommended that the local value should be obtained where possible; T is the external thermal resistance of the cable in free air, adjusted to take account of solar radiation (see part 2) (K·m/W); D is the external diameter of cable (m) for corrugated sheaths D = (Doc + 2t3)  10–3 (m); t3 is the thickness of the serving (mm). 2 Calculation of losses 2.1 AC resistance of conductor The a.c. resistance per unit length of the cable at its maximum operating temperature is given by the following formula, except in the case of pipe-type cables (see 2.1.5): where RC is the alternating current resistance of the conductor at maximum operating temperature per unit length of the cable (/m); R is the d.c. resistance of the conductor at maximum operating temperature per unit length of the cable (/m);
17	ys is the skin effect factor; yp is the proximity effect factor.
18	2.1.1 DC resistance of conductor The d.c. resistance per unit length of the cable at its maximum operating temperature  is given by: where Ro is the d.c. resistance of the conductor at 20 °C per unit length of the cable (/m); The value of Ro shall be derived directly from IEC 60228. Where the conductor size is outside the range covered by IEC 60228, the value of Ro may be chosen by agreement between manufacturer and purchaser. The conductor resistance should then be calculated using the values of resistivity given in Table 1 and considering the length of the conductor in the finished cable, see also Annex A. 20 is the constant mass temperature coefficient at 20 °C per kelvin (see Table 1 for standard values);  is the maximum operating temperature in degrees Celsius (this will be determined by the type of insulation to be used); see appropriate IEC specification or national standard. 2.1.2 Skin effect factor ys The skin effect factor ys is given by the following equations: For 0  xs 2,8 For 2,8  xs 3,8 For xs 3,8 where f is the supply frequency in Hertz. Values for ks are given in Table 2. In the absence of alternative formulae, it is recommended that the above formula should be used for sector and oval-shaped conductors. 2.1.3 Proximity effect factor yp for two-core cables and for two single-core cables The proximity effect factor is given by: where dc is the diameter of conductor (mm); s is the distance between conductor axes (mm).
19	Values for kp are given in Table 2. The above formula is accurate providing xp does not exceed 2,8, and therefore applies to the majority of practical cases. 2.1.4 Proximity effect factor yp for three-core cables and for three single-core cables 2.1.4.1 Circular conductor cables The proximity effect factor is given by: where dc is the diameter of conductor (mm); s is the distance between conductor axes (mm). NOTE For cables in flat formation, s is the spacing between adjacent phases. Where the spacing between adjacent phases is not equal, the distance will be taken as s = . Values for kp are given in Table 2. The above formula is accurate provided xp does not exceed 2,8, and therefore applies to the majority of practical cases. 2.1.4.2 Shaped conductor cables In the case of multicore cables with shaped conductors, the value of yp shall be two-thirds of the value calculated according to 2.1.4.1, with: dc = dx = diameter of an equivalent circular conductor of the same cross-sectional area, and degree of compaction (mm); s = (dx + t0) (mm), where t0 is the thickness of insulation between conductors (mm). Values for kp are given in Table 2. The above formula is accurate provided xp does not exceed 2,8, and therefore applies to the majority of practical cases. 2.1.5 Skin and proximity effects in pipe-type cables For pipe-type cables, the skin and proximity effects calculated according to 2.1.2, 2.1.3 and 2.1.4 shall be increased by a factor of 1,5. For these cables, ((/m)
20	2.2 Dielectric losses (applicable to a.c. cables only) The dielectric loss is voltage dependent and thus only becomes important at voltage levels related to the insulation material being used. Table 3 gives, for the insulation materials in common use, the value of U0 at which the dielectric loss should be taken into account where three-core screened or single-core cables are used. It is not necessary to calculate the dielectric loss for unscreened multicore or d.c. cables. The dielectric loss per unit length of cable in each phase is given by: (W/m) where  = 2f; C is the capacitance per unit length of a core (F/m); U0 is the voltage to earth (V); CLL is the length correction factor for considering laying up cores. A proposal for its calculation is given in Annex A. Values of tan , the loss factor of the insulation at power frequency and operating temperature, are given in Table 3. The capacitance for cylindrical screens around circular conductors is given by: (F/m) where is the electric constant ;  is the relative permittivity of the insulation; Di is the external diameter of the insulation (excluding screen) (mm); dc is the diameter of conductor, including screen, if any (mm). The same formula can be used for oval conductors if the geometric mean of the appropriate major and minor diameters is substituted for Di and dc. Values of  are given in Table 3. 2.3 Loss factor for sheath and screen (applicable to power frequency a.c. cables only) The power loss in the sheath or screen (1) consists of losses caused by circulating currents () and eddy currents (), thus: 1 = + The formulae given in this section express the loss in terms of the total power loss in the conductor(s) and for each particular case it is indicated which type of loss has to be considered. The formulae for single-core cables apply to single circuits only and the effects of earth return paths are neglected. Methods are given for both smooth-sided and corrugated sheaths.
22	For single-core cables with sheaths bonded at both ends of an electrical section, only the loss due to circulating currents in the sheaths need be considered (see 2.3.1, 2.3.2 and 2.3.3). An electrical section is defined as a portion of the route between points at which the sheaths or screens of all cables are solidly bonded. An allowance has usually also to be made for increased spacing at certain points on the route (see 2.3.4). For cables with Milliken conductors, the loss factor should be increased to take account of the loss due to eddy currents in the sheaths (see 2.3.5). For a cross-bonded installation, it is considered unrealistic to assume that minor sections are electrically identical and that the loss due to circulating currents in the sheaths is negligible. Recommendations are made in 2.3.6 for augmenting the losses in the sheaths to take account of this electrical unbalance. The electrical resistivities and temperature coefficients of lead and aluminium, for use in calculating the resistance of the sheath Rs are given in Table 1. The formulae given in this subclause use the resistance of the sheath or screen at its maximum operating temperature. The maximum operating temperature of the sheath or screen is given by: (°C) where is the maximum operating temperature of the cable screen or sheath (°C). Because the temperature of the sheath or screen is a function of the current, I, an iterative method is used for the calculation. The resistance of the sheath or screen at its maximum operating temperature is given by: (/m) where is the resistance of the cable sheath or screen at 20 °C per unit length of the cable (/m). 2.3.1 Two single-core cables, and three single-core cables (in trefoil formation), sheaths bonded at both ends of an electrical section For two single-core cables, and three single-core cables (in trefoil formation) with sheaths bonded at both ends, the loss factor is given by: where Rs is the resistance of sheath or screen per unit length of cable at its maximum operating temperature ((/m);
23	X is the reactance per unit length of sheath or screen per unit length of cable ((/m) = 2 ( 10–7 In ((/m); ( = 2 ( ( frequency (1/s); s is the distance between conductor axes in the electrical section being considered (mm); ds is the mean diameter of the sheath (mm); – for oval-shaped cores, ds is given by ; where dM and dm are the major and minor mean diameters respectively of the sheath – for corrugated sheaths, ds is given by ½ (Doc + Dit); = 0, i.e. eddy-current loss is ignored, except for cables having Milliken conductors when is calculated by the method given in 2.3.5. 2.3.2 Three single-core cables in flat formation, with regular transposition, sheaths bonded at both ends of an electrical section For three single-core cables in flat formation, with the middle cable equidistant from the outer cables, regular transposition of the cables and the sheaths bonded at every third transposition, the loss factor is given by: where X1 is the reactance per unit length of sheath ((/m) = = 0, i.e. eddy-current loss is ignored, except for cables having Milliken conductors whenis calculated by the method given in 2.3.5. 2.3.3 Three single-core cables in flat formation, without transposition, sheaths bonded at both ends of an electrical section For three single-core cables in flat formation, with the middle cable equidistant from the outer cables, without transposition and with the sheaths bonded at both ends of an electrical section, the loss factor for the cable which has the greatest loss (i.e. the outer cable carrying the lagging phase) is given by: For the other outer cable, the loss factor is given by:
24	For the middle cable, the loss factor is given by: In these formulae: CP = X + Xm CQ = X – where X is the reactance of sheath or screen per unit length of cable for two adjacent single-core cables (/m) = 2 ( 10–7 In ((/m); Xm is the mutual reactance per unit length of cable between the sheath of an outer cable and the conductors of the other two, when the cables are in flat formation (/m) = 2  10–7 ln (2) (/m); = 0, i.e. eddy-current loss is ignored, except for cables having Milliken conductors when is calculated by the method given in 2.3.5. Ratings for cables in air should be based on the first formula given above, i.e. the loss for the outer cable carrying the lagging phase. 2.3.4 Variation of spacing of single-core cables between sheath bonding points For single-core cable circuits with sheaths solidly bonded at both ends and possibly at intermediate points, the circulating currents and the consequent loss increase as the spacing increases, and it is advisable to use as close a spacing as possible. The optimum spacing is achieved by considering both losses and mutual heating between cables. It is not always possible to install cables with one value of spacing all along a route. The following recommendations relate to the calculation of sheath circulating current losses when it is not possible to install cables with a constant value of spacing over the length of one electrical section. A section is defined as a portion of the route between points at which sheaths of all cables are solidly bonded. The recommendations below give values for loss factors which apply to the whole of a section, but it should be noted that the appropriate values of conductor resistance and external thermal resistance must be calculated on the basis of the closest cable spacing at any place along the section. a) Where spacing along a section is not constant but the various values are known, the value for in 2.3.1, 2.3.2 and 2.3.3 shall be derived from: where are lengths with different spacings along an electrical section; are the reactances per unit length of cable, the relevant formulae being given in 2.3.1, 2.3.2 or 2.3.3 where appropriate values of spacings are used.
25	b) Where in any section the spacing between cables and its variation along the route are not known and cannot be anticipated, the losses in that section, calculated from the design spacing, shall be arbitrarily increased by 25%, this value having been found to be appropriate for lead-sheathed H.V. cables. A different increase may be used by agreement if it is considered that 25% is not appropriate to a particular installation. c) Where the section includes a spread-out end, the allowance in b) may not be sufficient and it is recommended that an estimate of the probable spacing be made and the loss calculated by the procedure given in a) above. NOTE This increase does not apply to installations with single-point bonding or cross-bonding (see 2.3.6). 2.3.5 Effect of Milliken conductors Where the conductors are subject to a reduced proximity effect, as with Milliken conductors, the sheath loss factor of 2.3.1, 2.3.2 and 2.3.3 cannot be ignored, but shall be obtained by multiplying the value of , obtained from 2.3.6 for the same cable configuration, by the factor CF given by the formula: where for cables in trefoil formation and Where the spacing along a section is not constant the value of shall be calculated as in 2.3.4 a). 2.3.6 Single-core cables, with sheaths bonded at a single point or cross-bonded 2.3.6.1 Eddy-current losses For single-core cables with sheaths bonded at a single point or cross-bonded the eddy-current loss factor is given by: where (s is the electrical resistivity of sheath material at operating temperature (see Table 1) ((.m); Ds is the external diameter of cable sheath (mm);
26	NOTE For corrugated sheaths, the mean outside diameter shall be used. ts is the thickness of sheath (mm); ( = 2(f; NOTE 1 For lead-sheathed cables, Cgscan be taken as unity and can be neglected. NOTE 2 For aluminium sheathed cables, both terms may need to be evaluated when sheath diameter is greater than about 70 mm or the sheath is thicker than usual. NOTE 3 For cables with a wire screen and an equalising tape, or foil screen over the wires, the eddy-current losses are considered negligible. Formulae for (0, (1 and (2 are given below: (in which: , for , (1 and (2 can be neglected) 1) Three single-core cables in trefoil formation: 2) Three single-core cables, flat formation: a) centre cable: b) outer cable leading phase: c) outer cable lagging phase:
27	2.3.6.2 Circulating current losses The circulating current loss is zero for installations where the sheaths are single-point bonded, and for installations where the sheaths are cross-bonded and each major section is divided into three electrically identical minor sections. Where a cross-bonded installation contains sections whose unbalance is not negligible, a residual voltage is produced which results in a circulating current loss in that section which must be taken into account. For installations where the actual lengths of the minor sections are known, the loss factor can be calculated by multiplying the circulating current loss factor for the cable configuration concerned, calculated as if it were bonded and earthed at both ends of each major section without cross-bonding by: Where in any major section, the two longer minor sections are Cp and Cq times the length of the shortest minor section (i.e. the minor section lengths are a, Cpa and Cqa, where the shortest section is a). This formula deals only with differences in the length of minor sections. Any variations in spacing must also be taken into account. Where lengths of the minor sections are not known, Cp should be set to 1 and Cq to 1,2, this gives a value of 0,004. 2.3.7 Two-core unarmoured cables with common sheath For a two-core unarmoured cable where the cores are contained in a common metallic sheath, is negligible and the loss factor is given by one of the following formulae: – for round or oval conductors: – for sector-shaped conductors: where  = 2f; f is the frequency (Hz); c is the distance between the axis of one conductor and the axis of the cable (mm); r1 is the radius of the circle circumscribing the two sector-shaped conductors (mm); d is the mean diameter of the sheath (mm);
28	– for oval-shaped cores, d is given by where dM and dm are the major and minor mean diameters respectively; – for corrugated sheaths, d is given by ½ (Doc + Dit). 2.3.8 Three-core unarmoured cables with common sheath For a three-core unarmoured cable where the cores are contained in a common metallic sheath, is negligible and the loss factor is, therefore, given by one of the following formulae: – for round or oval conductors, and where the sheath resistance is less than or equal to 100 /m: – for round or oval conductors, and where the sheath resistance Rs is greater than 100 /m: – for sector-shaped conductors, and Rs any value: where r1 is the radius of the circle circumscribing the three shaped conductors (mm); t is the thickness of insulation between conductors (mm); d is the mean diameter of the sheath (mm); – for oval-shaped cores, d is given by where dM and dm are the major and minor mean diameters respectively of the sheath or screen; – for corrugated sheaths, d is given by ½ (Doc + Dit). 2.3.9 Two-core and three-core cables with steel tape armour The addition of steel tape armour increases the eddy-current loss in the sheath. The values for given in 2.3.7 and 2.3.8 should be multiplied by the following factor if the cable has steel-tape armour: where dA is the mean diameter of armour (mm); ( is the relative permeability of the steel tape (usually taken as 300); (A is the equivalent thickness of armour = (mm);
29	where is the cross-sectional area of the armour (mm²). This correction is only known to be applicable to tapes 0,3 mm to 1,0 mm thick. 2.3.10 Cables with each core in a separate metallic sheath (SL type) and armoured For a three-core cable of which each core has a separate metallic sheath is zero and the loss factor for the sheaths is given by: where ((/m); s is the distance between conductor axes (mm). CLL is the length correction factor for considering laying up cores. A proposal for its calculation is given in Annex A. The loss factor for unarmoured cables with each core in a separate metallic sheath is obtained from 2.3.1. 2.3.11 Losses in screen and sheaths of pipe-type cables If each conductor of a pipe-type cable has a screen only over the insulation, for example a lead sheath or copper tape, the ratio of the screen loss to the conductor loss may be calculated by the formula given in 2.3.1 for the sheath of a single-core cable, provided that the formula is corrected for the additional loss caused by the presence of the steel pipe and considering the unit length of the cable when calculating the reactance . This modifies the formula to: If each core has a diaphragm sheath and non-magnetic reinforcement, the same formula is used, but the resistance Rs is replaced by the parallel combination of the resistance of the sheath and reinforcement. The diameter d is replaced by the value d: where d is the mean diameter of sheath and reinforcement (mm); d is the mean diameter of screen or sheath (mm); d2 is the mean diameter of reinforcement (mm). In the case of oval-shaped cores d and d2 is given by where dM and dm are the major and minor mean diameters respectively of the sheath or screen. NOTE See also 2.4.2.
30	2.4 Loss factor for armour, reinforcement and steel pipes (applicable to power frequency a.c. cables only) The formulae given in this subclause express the power loss occurring in metallic armour, reinforcement or steel pipes of a cable in terms of an increment 2 of the power loss in all conductors. Appropriate values of electrical resistivity and resistance temperature coefficients for the materials used for armour and reinforcement are given in Table 1. The formulae given in this subclause use the resistance of the armour at its maximum operating temperature. The maximum operating temperature of the armour is given by: (°C) where is the maximum operating temperature of armour (°C). Because the temperature of the armour is a function of the current, I, an iterative method is used for the calculation. The resistance of the armour per unit length of the cable at its maximum operating temperature is given by: (/m) where is the resistance of the armour per unit length of the cable at 20°C (/m). Where the equivalent resistance of sheath and armour in parallel is used, it is sufficiently accurate to assume that both components are at the operating temperature of the armour and to use an average value for the temperature coefficient of the materials. 2.4.1 Non-magnetic armour or reinforcement The general procedure is to combine the calculation of the loss in the reinforcement with that of the sheath. The formulae are given in 2.3 and the parallel combination of sheath and reinforcement resistance is used in place of the single sheath resistance Rs. The root mean square value of the sheath and reinforcement diameter replaces the mean sheath diameter d (see 2.3.11). This procedure applies to both single, twin and multicore cables. The value of the reinforcement resistance is dependent on the lay of the tapes as follows: a) If the tapes have a very long lay (longitudinal tapes), the resistance is based on a cylinder having the same mass of material per unit length of cable and also the same internal diameter as the tapes. b) If the tapes are wound at approximately 54° to the cable axis, the resistance is twice the value calculated according to item a) above. c) If the tapes are wound with a very short lay (circumferential tapes), the resistance is regarded as infinite, i.e. the loss can be neglected. d) If there are two or more layers of tapes in contact with each other, having a very short lay, the resistance is twice the value calculated according to item a) above. These considerations apply also to the cores of pipe-type cables dealt with in 2.3.11.
31	2.4.2 Magnetic armour or reinforcement 2.4.2.1 Single-core lead-sheathed cables – steel wire armour, bonded to sheath at both ends The following method does not take into account the possible influence of the surrounding media, which may be appreciable in particular for cables laid under water. The method is intended for installations where spacing between cables is large (i.e. 10 m or more). It gives values for the sheath and armour losses that are usually higher than the actual ones, so that ratings are on the safe side. It should be noted that the hottest part of the cable route may be the on-shore section where both the losses and mutual heating may be high. Where the influence of the surrounding media can be ignored, e.g. in air, the method may be used for any spacing between cables. Calculation of the power loss in the lead sheath and armour of single-core cables with steel-wire armour with the sheath and armour bonded together at both ends is as follows: a) The equivalent resistance of sheath and armour in parallel is given by: ((/m) where Rs is the resistance of sheath per unit length of cable at its maximum operating temperature (/m); RA is the resistance a.c. resistance of armour per unit length of cable at its maximum operating temperature (/m). The a.c. resistance of armour wire varies from about 1,2 times the d.c. resistance of 2 mm diameter wires up to 1,4 times the d.c. resistance for 5 mm wires. The resistance does not critically affect the final result. b) The inductance of the elements of the circuit is calculated per phase, as follows: where Hs is the inductance due to the sheath per unit length of the cable (H/m) NOTE H3 is taken as zero for spaced wires. where H1, H2 and H3 are the components of the inductance due to the steel wires (H/m);
32	s2 is the axial spacing between adjacent cables in trefoil formation; for cables in flat formation s2 is the geometric mean of the three spacings (mm);CLL is the length correction factor for considering laying up cores. A proposal for its calculation is given in Annex A. dA is the mean diameter of armour (mm); df is the diameter of a steel wire (mm); p is the length of lay of a steel wire along the cable (mm); n1 is the number of steel wires;  is the angle between axis of armour wire and axis of cable;  is the angular time delay of the longitudinal magnetic flux in the steel wires behind the magnetizing force; e is the longitudinal relative permeability of steel wires; t is the transverse relative permeability of steel wires; For values of , e and t, see item d). Let B1 = (Hs + H1 + H3) (/m) B2 = H2 (/m). c) The total loss in sheath and armour W(s + A) per unit length of the cable is given by: (W/m) The loss in sheath and armour may be assumed to be approximately equal, so that: where Wc = I2 RC loss in conductor per unit length of the cable (W/m). d) Choice of magnetic properties , e and t. These quantities vary with the particular sample of steel and unless reference can be made to measurements on the steel wire to be used, some average values must be assumed. No appreciable error is involved if, for wires of diameters from 4 mm to 6 mm and tensile breaking strengths around 400 N/mm², the following values are assumed: e = 400 t = 10, when wires are in contact t = 1, where wires are separated  = 45° If a more precise calculation is required and the wire properties are known, then it is initially necessary to know an approximate value for the magnetizing force H in order to find the appropriate magnetic properties. (ampere turns/m) whereand are the vectorial values of conductor current and sheath current. For the initial choice of magnetic properties, it is usually satisfactory to assume that(+ = 0,6 I, and to repeat the calculations if it is subsequently established that the calculated value is significantly different.
33	2.4.2.2 Two-core cables – steel wire armour where RA is the a.c. resistance of armour at maximum armour temperature per unit length of the cable (/m); dA is the mean diameter of armour (mm); is the cross-sectional area of armour (mm²); r1 is the circumscribing radius over conductors (mm); t0 is the insulation thickness between conductors (mm). No correction has been made for non-uniform current distribution in the conductors because it is considered negligible for conductor sizes up to 400 mm². 2.4.2.3 Three-core cables – steel wire armour 2.4.2.3.1 Round conductor cable where RA is the a.c. resistance of armour at maximum armour temperature (/m); dA is the mean diameter of armour (mm); c is the distance between the axis of a conductor and the cable centre (mm). No correction has been made for non-uniform current distribution in the conductors because it is considered negligible for conductor sizes up to 400 mm². This equation is under consideration because it may overestimate the armour loss factor for some cable designs. 2.4.2.3.2 Sector conductor cables where r1 is the radius of the circle circumscribing the three shaped conductors (mm);  = 2f; f is the frequency of supply (Hz).
34	2.4.2.4 Three-core cables – steel tape armour or reinforcement The following formulae apply to tapes 0,3 mm to 1 mm thick. The hysteresis loss is given for a frequency of 50 Hz by: where s is the distance between conductor axes (mm); (A is the equivalent thickness of armour (mm) i.e. and is the armour cross-sectional area (mm²); dA is the mean diameter of armour (mm). The factor kf is given by: where ( is the relative permeability of the steel tape, usually taken as 300. For frequencies f other than 50 Hz, multiply the value of kf given by the above formula by the factor . The eddy-current loss is given for a frequency of 50 Hz by: and for any other frequency the value calculated from this formula must be multiplied by the factor . The total armour loss factor is given by the sum of both hysteresis and eddy-current losses, thus: NOTE Magnetic armour or reinforcement, if any, increase eddy-current losses in the sheaths. Reference should be made to 2.3.9. 2.4.2.5 SL type cables Where the armour is over a SL type cable, the screening effect of the sheath currents reduces the armour loss. The formula for (2 given in 2.4.2.3.1 or 2.4.2.3.2 shall be multiplied by the factor
35	where is obtained from 2.3.1. 2.4.3 Losses in steel pipes The loss in steel pipes is given by two empirical formulae, one for cables where the cores are bound in close trefoil formation and the other for cables where the cores are placed in a more open configuration (cradled) on the bottom of the pipe. Actual cores in service probably approximate to a configuration somewhere between the two. It is considered that the losses should be calculated for each configuration and a mean value used: NOTE These formulae have been empirically obtained in the United States of America and at present apply only to pipe sizes and steel types used in that country. where s is the axial spacing of adjacent conductors (mm); dd is the internal diameter of pipe (mm); RC is the a.c. resistance per unit length of the cable at maximum operating temperature (/m). The formulae given apply to a frequency of 60 Hz. For 50 Hz, each formula should be multiplied by 0,76. For pipe-type cables, where flat-wire armour is applied over all three cores after they are laid up, the losses are independent of the presence of the pipe. For such cables, the losses in the armour are to be calculated as for SL type cables (see 2.4.2.5 and the losses in the pipe are to be ignored). Table 1 – Electrical resistivities and temperature coefficients of metals used Material Resistivity (()ohm ( m at 20 °C Temperaturecoefficient ((20)per K at 20 °C a) Conductors Copper Aluminium 1,724 1 10–8 2,826 4 10–8 3,93 10–3 4,03 10–3 b) Sheaths and armour Lead or lead alloy Steel Bronze Stainless steel Aluminium 21,4 10–8 13,8 10–8 3,5 10–8 70 10–8 2,84 10–8 4,0 10–3 4,5 10–3 3,0 10–3 Negligible 4,03 10–3 NOTE Values for copper conductors are taken from IEC 60028.Value for aluminium conductors are taken from IEC 60889.
36	Table 2 – Skin and proximity effects –Experimental values for the coefficients ks and kp Type of conductor Conductor insulation system ks kp Copper Round, solid All 1 1 Round, stranded Fluidd/papere/PPLf 1 0,8 Round, stranded Extrudedg/Mineralh 1 1 Round, Millikenc Fluid/paper/PPL 0,435 0,37 Round, Milliken, insulated wiresb Extruded 0,35 0,20 Round, Milliken, bare uni-directional wiresb, Extruded 0,62 0,37 Round, Milliken, bare bi-directional wiresb, Extruded 0,80 0,37 Hollow, helical stranded All a 0,8 Sector-shaped Fluid/paper/PPL 1 0,8 Sector-shaped Extruded/Mineral 1 1 Aluminium Round, solid All 1 1 Round, stranded All 1 0,8 Round Milliken All 0,25 0,15 Hollow, helical stranded All a 0,8 a The following formula should be used for ks: where di is the inside diameter of the conductor (central duct) (mm); d’c is the outside diameter of the equivalent solid conductor having the same central duct (mm). b The coefficients for these designs can be influenced by the detail of the conductor design. Subject to agreement between the manufacturer and user measured values of ac resistance may be used. A common measurement method is under consideration. Cigre (TB272) discusses three measurement methods. c Milliken conductor: stranded conductor comprising an assembly of shaped stranded conductors, with each segment lightly insulated from each other. The individual strands may be either insulated (e.g. enamelled or oxidised) or bare. d Fluid insulation: insulation system consisting of lapped paper and an insulating fluid which is designed to maintain free movement of the fluid within the cable. e Paper insulation: lapped insulation consisting of paper impregnated with an insulating material. f PPL insulation: fluid filled cable where a polypropylene/paper laminate is used in place of lapped paper. g Extruded insulation: insulation consisting generally of one layer of a polymeric material and applied by an extrusion process. h Mineral insulation: insulation consisting of compressed mineral powder. Generally only used on specific types of LV cable. NOTE 1 The tabulated values of ks and kp for large stranded conductors have generally been derived from those given in Cigre Technical brochure Ref. N° 272, Large cross-sections and composite screens design. NOTE 2 The value of ks given for round, Milliken, insulated wires is a limiting value intended to cover all methods of insulating the wires including enamelling, oxidized wires or other methods. NOTE 3 The value of ks given for hollow helical stranded conductors is applicable to keystone conductors.
37	Table 3 – Values of relative permittivity and loss factors for the insulation of high-voltage and medium-voltage cables at power frequency 1 2 3 Type of cable ( tan (* Cables insulated with impregnated paper Solid type, fully-impregnated, pre-impregnated or mass-impregnated non-draining Oil-filled, self-containeda up to U0 = 36 kV up to U0 = 87 kV up to U0 = 160 kV up to U0 = 220 kV 4 3,63,63,53,5 0,01 0,003 50,003 30,003 00,002 8 Oil-pressure, pipe-typebExternal gas-pressurecInternal gas-pressured 3,73,63,4 0,004 50,004 00,004 5 Cable with other kinds of insulation Butyl rubber 4 0,050 EPRe up to and including 18/30 (36) kV cables greater than 18/30 (36) kV cables 33 0,0200,005 PVCe 8 0,1 PE (HD and LD) e 2,3 0,001 XLPEe up to and including 18/30 (36) kV cables (unfilled) greater than 18/30 (36) kV cables (unfilled) greater than 18/30 (36) kV cables (filled) 2,52,53,0 0,0040,0010,005 PPL equal to, or greater than 63/110 kV cables 2,8 0,001 4 * Safe values at maximum permissible temperature, applicable to the highest voltages normally specified for each type of cable. a See IEC 60141-1. b See IEC 60141-4. c See IEC 60141-3. d See IEC 60141-2. e See IEC 60502-1 and IEC 60502-2. NOTE The dielectric loss should be taken into account for values of U0 equal to or greater than the following: Type of cable U0 kV Cables insulated with impregnated paper Solid-type Oil-filled and gas-pressure Cables with other types of insulation Butyl rubberEPRPVCPE (HD and LD)XLPE (unfilled)XLPE (filled) 38 63,5 18 63,5 6 127 127 63,5
38	Table 4 – Absorption coefficient of solar radiation for cable surfaces Material ( Bitumen/jute servingPolychloroprenePVCPELead 0,80,80,60,40,6 ___________
39	Annex A (informative) Correction factor for increased lengths of individual cores within multicore cables In multicore cables the lengths of the individual cores are increased by their laying up compared to the length of the complete cable. For calculating physical properties like electrical resistance or capacitance relative to the length of the completed cable a correction factor may be applied on the results that have been calculated at the individual straight cores. In a three core cable this factor for taking into account this laying up could be evaluated as: where: is the diameter of the individual core (m) is the axial cable length over which the cores make one full helical turn (m) The factor 1,29 is used to take into account the position of the neutral axis of the helically wound core, since such axis does not generally correspond to the core center. The properties like electrical resistance or electrical capacitance of the cable can then be found as the electrical resistance or capacitance of an individual core multiplied by the lay length factor (1).

Additional information

Status	Definitive
Pages	39
Publication Date	2021-02-11
Standard Number	21/30431003 DC
Title	BS IEC 60287-1-1. Electric cables. Calculation of the current rating – Part 1-1. Current rating equations (100 % load factor) and calculation of losses. General
Identical National Standard Of	IEC 60287-1-1 Ed.3.0
Descriptors	Electric cable connectors, Electric cable systems, Electrical components, Electric conductors, Electric cables
Publisher	BSI
Committee	GEL/20/16
ICS Codes	29.060.01 - Electrical wires and cables in general

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