Pub-22 Copper for Busbars

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Pub 22 - Copper for Busbars

Prefaces

Design Considerations1.

Copper for Busbar Purposes2.

Current-carrying Capacity of Busbars3.

Alternating Current Effects in Busbars4.

Effect of Busbar Arrangements on Rating5.

Short-Circuit Effects6.

Jointing of Copper Busbars7.

Mechanical Strength Requirements8.

Busbar Impedance9.

Appendices10.

Bibliography11.

Publication 22, June 1996Reprinted January 2001 with some amendments

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Prefaces

Preface to 1984 Edition

This C.D.A. publication has long been accepted as the standard reference work on busbar design. Thisrevised and updated edition incorporates recent progress in the technology of busbar design as reflected innew standards and engineering practices.

All data and formulae have been metricated and the method of presentation facilitates the use of calculatorsor computers. The many variables to be considered are clearly explained and special attention has beengiven to determining the most economic loadings in order to maximise current carrying capacity for minimuminstallation costs and running losses. There is, therefore, a useful comparison of the electrical andmechanical properties of high conductivity copper and aluminium. Extra attention has been given torecommended jointing techniques, both by bolting and welding.

Improvements have also been made to the section dealing with skin effects. The information on impedancehas been expanded so that power factor variations can now be further predicted. The tables of ratings andproperties have been expanded as have the examples of typical calculations. The references have beenupdated to include recent publications.

CDA wishes to acknowledge the considerable help given in the revision of this text by Mr G M Boothman,Chief Engineer, Busbar Unit, Balfour Beatty Power Construction Ltd and by Mr W Jefferies, ChiefMetallurgist, Thomas Bolton & Sons Ltd. also for many helpful comments made on the text by Mr K G Cary(Simplex - G.E. Ltd), Mr A Jackson (GAMBICA), Mr J C Power (British Electric Repairs Ltd), Mr EG Wright (Ottermill Switchgear Ltd) and members of the British Non-Ferrous Metals Federation HighConductivity Copper Group.

Preface to 1996 Edition

This edition includes the new BS EN copper alloy designations and corrections to errors which appeared inthe earlier version.

BUSBAR DESIGN DATA DISC

In order to assist in the design of effective busbar systems, CDA has made available an interactive softwareprogram that allows optimum busbar size to be calculated, taking into account configuration, workingtemperature and overall lifetime cost.

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1. Design Considerations

Introduction

Types of Busbar

Choice of Busbar Material

Introduction

The word busbar, derived from the Latin word omnibus ('for all'), gives the idea of a universal system ofconveyance. In the electrical sense, the term bus is used to describe a junction of circuits, usually in the formof a small number of inputs and many outputs. 'Busbar' describes the form the bus system usually takes, abar or bars of conducting material.

In any electrical circuit some electrical energy is lost as heat which, if not kept within safe limits, may impairthe performance of the system. This energy loss, which also represents a financial loss over a period oftime, is proportional to the effective resistance of the conductor and the square of the current flowingthrough it. A low resistance therefore means a low loss; a factor of increasing importance as the magnitudeof the current increases.

The capacities of modern-day electrical plant and machinery are such that the power handled by their controlsystems gives rise to very large forces. Busbars, like all the other equipment in the system, have to be ableto withstand these forces without damage. It is essential that the materials used in their construction shouldhave the best possible mechanical properties and are designed to operate within the temperature limits laiddown in BS 159, BS EN 60439-1:1994, or other national or international standards.

A conductor material should therefore have the following properties if it is to be produced efficiently and havelow running costs from the point of view of energy consumption and maintenance:

a) Low electrical and thermal resistance

b) High mechanical strength in tension, compression and shear

c) High resistance to fatigue failure

d) Low electrical resistance of surface films

e) Ease of fabrication

f) High resistance to corrosion

g) Competitive first cost and high eventual recovery value

This combination of properties is met best by copper. Aluminium is the main alternative material, but acomparison of the properties of the two metals shows that in nearly all respects copper is the superiormaterial.

Types of Busbar

Busbars can be sub-divided into the following categories, with individual busbar systems in many casesbeing constructed from several different types:

a) Air insulated with open phase conductors

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b) Air insulated with segregating barriers between conductors of differentphases.

c) Totally enclosed but having the construction as those for (a) and (b)

d) Air insulated where each phase is fully isolated from its adjacent phase(s) byan earthed enclosure. These are usually called 'Isolated Phase Busbars'.

e) Force-cooled busbar systems constructed as (a) to (d) but using air, water,etc. as the cooling medium under forced conditions (fan, pump, etc.).

f) Gas insulated busbars. These are usually constructed as type (e) but use agas other than air such as SF6, (sulphur hexafluoride).

g) Totally enclosed busbars using compound or oil as the insulation medium.

The type of busbar system selected for a specific duty is determined by requirements of voltage, current,frequency, electrical safety, reliability, short-circuit currents and environmental considerations. Table 1outlines how these factors apply to the design of busbars in electricity generation and industrial processes.

Table 1 Comparison of typical design requirements for power generation and industrial processsystems

Feature Generation Industrial Processes

1 Voltage drop Normally not important Important

2 Temperature rise Usually near to maximum allowable.Capitalisation becoming important.

In many cases low due tooptimisation of first cost and runningcosts.

3 Current range Zero to 40 k A a .c . with frequencies of zero to400 Hz.

Zero to 200 kA a.c. and d.c.

4 Jointing and connections Usually bolted but high current applications areoften fully welded. Joint preparation veryimportant

Usually bolted. Joint preparation veryimportant.

5 Cross-sectional area Usually minimum. Somewhat larger ifoptimisation is required.

Usually larger than minimumrequired due to optimisation andvoltage drop considerations.

6 Kelvin's Law Not applied. Other forms of optimisation areoften used.

Applies. Also other forms ofoptimisation and capitalisation used

7 Construction Up to 36 k V. Individually engineered using basicdesigns and concepts.

Usually low voltage. Individuallyengineered. Standard products forlow current/voltage applications.

8 Enclosures Totally enclosed with or without ventilation. Usually open. Enclosed or protectedby screens when using standardproducts.

9 Fault capacity Usually large. Designed to meet systemrequirement.

Usually similar to running current.Standard products to suit systemshort circuit.

10 Phase arrangement Normally 3 phase flat though sometimes trefoil. Normally flat but transposition usedto improve current distribution onlarge systems

11 Load factor Usually high. Normally 1.0. Usually high but many have widelyvarying loads.

12 Cost Low when compared with associated plant. Major consideration in many cases.Particularly whenoptimisation/capitalisation is used.


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13 Effects of failure Very serious. High energies dissipated intofault.

Limited by low voltage and busbarsize.

14 Copper type High conductivity. High conductivity.

15 Copper shape Usually rectangular. Tubular used for high current force-cooled. Usually large cross section rectangular. Tubular used for somelow current high voltage applications and high current force-cooled.

Choice of Busbar Material

At the present time the only two commercially available materials suitable for conductor purposes arecopper and aluminium. The table below gives a comparison of some of their properties. It can be seen thatfor conductivity and strength, high conductivity copper is superior to aluminium. The only disadvantage ofcopper is its density; for a given current and temperature rise, an aluminium conductor would be lighter, eventhough its cross-section would be larger. In enclosed systems however, space considerations are of greaterimportance than weight. Even in open-air systems the weight of the busbars, which are supported atintervals, is not necessarily the decisive factor.

Table 2 Typical relative properties of copper and aluminium

Copper(CW004A) Aluminium (1350) Units

Electrical conductivity(annealed)

101 61 % IACS

Electrical resistivity(annealed)

1.72 2.83 mW cm

Temperature coefficient ofresistance(annealed)

0.0039 0.004 /° C

Thermal conductivity at 20°C 397 230 W/mK

Coefficient of expansion 17 x 10–6 23 x 10–6 /° C

Tensile strength (annealed) 200 – 250 50 – 60 N/mm2

Tensile strength (half–hard) 260 – 300 85 – 100 N/mm2

0.2% proof stress (annealed) 50 – 55 20 – 30 N/mm2

0.2% proof stress (half–hard) 170 – 200 60 – 65 N/mm2

Elastic modulus 116 – 130 70 kN/mm2

Specific heat 385 900 J/kg K

Density 8.91 2.70 g/cm3

Melting point 1083 660 °C

The electromagnetic stresses set up in the bar are usually more severe than the stress introduced by itsweight. In particular, heavy current-carrying equipment necessitates the use of large size conductors, andspace considerations may be important. It should be realised that the use of copper at higher operatingtemperatures than would be permissible for aluminium allows smaller and lighter copper sections to be usedthan would be required at lower temperatures.

The ability of copper to absorb the heavy electromagnetic and thermal stresses generated by overloadconditions also gives a considerable factor of safety. Other factors, such as the cost of frequent supportsfor the relatively limp aluminium, and the greater cost of insulation of the larger surface area, must beconsidered when evaluating the materials.


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From published creep data, it can be seen that high conductivity aluminium exhibits evidence of significantcreep at ambient temperature if heavily stressed. At the same stress, a similar rate of creep is only shownby high conductivity copper at a temperature of 150°C, which is above the usual operating temperature ofbusbars.

Table 3 Comparison of creep and fatigue properties of high conductivity copper and aluminium

a) Creep properties

Material Testing Temp. °C Min. Creep Rate % per1000 h

Stress N/mm2

Al (1080) annealed 20 0.022 26 *

HC Cu annealed 150 0.022 26 *

Cu-0.086% Ag 50% c.w. 130 0.004 138

Cu-0.086% Ag 50% c.w. 225 0.029 96.

5

* Interpolated from fig.3

b) Fatigue properties

Material Fatigue strength N/mm2 No. of cycles x 106

HC Al annealed 20 50

half-hard (H8) 45 50

HC Copper annealed 62 300

half-hard 115 300

If much higher stresses or temperatures are to be allowed for, copper containing small amounts (about0.1%) of silver can be used successfully. The creep resistance and softening resistance of copper-silveralloys increase with increasing silver content.

In the conditions in which high conductivity aluminium and copper are used, either annealed (or as-welded) orhalf-hard, the fatigue strength of copper is approximately double that of aluminium. This gives a usefulreserve of strength against failure initiated by mechanical or thermal cycling.

The greater hardness of copper compared with aluminium gives it better resistance to mechanical damageboth during erection and in service. It is also less likely to develop problems in clamped joints due to coldmetal flow under the prolonged application of a high contact pressure. Its higher modulus of elasticity gives itgreater beam stiffness compared with an aluminium conductor of the same dimensions. The temperaturevariations encountered under service conditions require a certain amount of flexibility to be allowed for in thedesign. The lower coefficient of linear expansion of copper reduces the degree of flexibility required.

Because copper is less prone to the formation of high resistance surface oxide films than aluminium, goodquality mechanical joints are easier to produce in copper conductors. Welded joints are also readily made.Switch contacts and similar parts are nearly always produced from copper or a copper alloy. The use ofcopper for the busbars to which these parts are connected therefore avoids contacts between dissimilarmetals and the inherent jointing and corrosion problems associated with them.

The higher melting point and thermal conductivity of copper reduce the possibility of damage resulting fromhot spots or accidental flashovers in service. If arcing occurs, copper busbars are less likely to support thearc than aluminium. Table 4 shows that copper can self-extinguish arcs across smaller separations, and at


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higher busbar currents. This self-extinguishing behaviour is related to the much larger heat input required tovaporise copper than aluminium.

Table 4 Self-extinguishing arcs in copper and aluminium busbars

Copper Aluminium

Minimum busbar spacing, mm 50 100

Maximum current per busbar, A 4500 3220

Copper liberates considerably less heat during oxidation than aluminium and is therefore much less likely tosustain combustion in the case of accidental ignition by an arc. The large amounts of heat liberated by theoxidation of aluminium in this event are sufficient to vaporise more metal than was originally oxidised. Thisvaporised aluminium can itself rapidly oxidise, thus sustaining the reaction. The excess heat generated in thisway heats nearby materials, including the busbar itself, the air and any supporting fixtures. As the busbarand air temperatures rise, the rates of the vaporisation and oxidation increase, so accelerating the wholeprocess. As the air temperature is increased, the air expands and propels hot oxide particles. The busbarmay reach its melting point, further increasing the rate of oxidation and providing hot liquid to be propelled,while other materials such as wood panels may be raised to their ignition temperatures. These dangers areobviated by the use of copper busbars.

Finally, copper is an economical conductor material. It gives long and reliable service at minimummaintenance costs, and when an installation is eventually replaced the copper will have a high recoveryvalue. Because of its many advantages, copper is still used worldwide as an electrical conductor materialdespite attempts at substitution.


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2.Copper for Busbar Purposes

Types of High Conductivity Copper available

Properties of Wrought HC Copper

In most countries, coppers of different types for specific applications have been given separate identities. Inthe United Kingdom this takes the form of an alloy designation number which is used in all British Standardsrelevant to copper and its alloys. Copper for electrical purposes is covered by the following British Standards:

BS 1432 : 1987 (strip with drawn or rolled edges)

BS 1433 : 1970 (Rod and bar)

BS 1434 : 1985 (Commutator bars)

BS 1977 : 1976 (High conductivity tubes)

BS 4109 : 1970 (wire for general electrical purposes and for insulated and flexible cords)

BS 4608 : 1970 (Rolled sheet, strip and foil)

(Copies of these are obtainable from the BSI Sales Office. 398 Chiswick High Road, London WS4 4AL.)

To bring the UK in line with current European requirements BS EN standards are being introduced. TheEuropean Standards relevant to electrical applications are expected to supersede the British Standards in duecourse.

The current standards most relevant to busbar applications are BS 1432, BS 1433 and BS 1977 which specifythat the end products shall be manufactured from copper complying with the following requirements:

Cu-ETP Electrolytic tough pitch high conductivity copper CW004A (formerly C101)Cu-FRHC Fire-refined tough pitch high conductivity copper CW005A (formerly C102)Cu-OF Oxygen-free high conductivity copper CW008A (formerly C103)

European Standards EN1976 and EN1978 have replaced BS 6017:1981. Table 5 shows the Europeanmaterial designations along with International Standards Organisation (ISO) and old British Standarddesignations.

Table 5 EN, BS and ISO designations for refinery shapes and wrought coppers

Designation

Description ISO cast and wrought European Designation Former UK Designations

Electrolytic tough pitchhigh-conductivity copper

Cu-ETP CW004A C101

Fire- refined tough pitchhigh-conductivity copper

Cu-FRHC CW005A C102

Oxygen-free high-conductivitycopper

Cu-OF CW008A C103

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Copper to be used for electrical purposes is of high purity because impurities in copper, together with thechanges in micro-structure produced by working, materially affect the mechanical and electrical properties.The degree to which the electrical conductivity is affected by an impurity depends largely on the elementpresent. For example, the presence of only 0.04% phosphorus reduces the conductivity of high conductivitycopper to around 80% IACS. (The approximate effect on conductivity of various impurity elements is shown inFigure 1). The level of total impurities, including oxygen, should therefore be less than 0.1% and copper of thistype is known as high conductivity (HC) copper.

Microscopic and analytical controls are applied to ensure a consistent product and in the annealed conditionconductivities over 100% IACS are usual. This figure corresponds to the standard resistivity of 0.017241mWm set some years ago by the International Electrotechnical Commission.

Figure 1 - Approximate effect of impurity elements on the electrical resistivity of copper

Types of High Conductivity Copper available

Tough pitch copper,CW004A and CW005A (C101 and C102 )

Coppers of this type, produced by fire-refining or remelting of electrolytic cathode, contain a small, deliberateaddition of oxygen which scavenges impurities from the metal. It is present in the form of fine, well-distributedcuprous oxide particles only visible by microscopic examination of a polished section of the metal. Typicaloxygen contents of these coppers fall in the range 0.02-0.05%. Between these limits the presence of theoxygen in this form has only a slight effect on the mechanical and electrical properties of the copper. It can,however, give rise to porosity and intergranular cracks or fissures if the copper is heated in a reducingatmosphere, as can happen during welding or brazing. This is a result of the reaction of the cuprous oxideparticles with hydrogen and is known as 'hydrogen embrittlement'. Provided a reducing atmosphere isavoided, good welds and brazes can be readily achieved. (See Jointing of Copper Busbars.)

Oxygen-free high-conductivity copper, CW008A (C103)

In view of the above remarks, if welding and brazing operations under reducing conditions are unavoidable, it


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is necessary to use a different (and more expensive) grade of high conductivity copper which is speciallyproduced for this purpose. This type of copper, known as 'oxygen-free high conductivity copper', is normallyproduced by melting and casting under a protective atmosphere. To obtain the high conductivity required it isnecessary to select the best raw materials. The result is a high purity product containing 99.95% copper. Thisenables a conductivity of 100% IACS to be specified even in the absence of the scavenging oxygen.

Effects of hot and cold working on structures

In the as-cast form, HC copper is available in wirebar and billet form, although the advancement of moderncasting technology is leading to a decline in wirebar production. The cast shape is hot-worked by rolling orextrusion to produce a form suitable for further processing by cold work into its final wrought form, either byrolling or drawing through dies.

In the case of tough-pitch HC copper, the as-cast structure is coarse-grained with oxygen present as copper-cuprous oxide eutectic in the grain boundaries. The hot working operation breaks up the coarse grains anddisperses the cuprous oxide to give a uniform distribution of oxide particles throughout a new network of finegrains. In the case of oxygen-free HC copper, the hot working operation breaks up the coarse grains into anew network of fine grains.


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Properties of Wrought HC Copper

Mechanical

Electrical

Mechanical properties

The room temperature physical and mechanical properties of the high conductivity coppers in the annealed condition do not differ significantlyfrom one another.

Tensile strength

Proof stress

Hardness

Resistance to softening

Creep resistance

Fatigue resistance

Bending and forming

Tensile strength

In the as-cast condition, high conductivity copper has a tensile strength of 150-170 N/mm2. The changes in structure brought about by hotworking raise the tensile strength to the order of 200-220 N/mm2. Upon further working the resulting mechanical properties of a particular formare influenced by the amount of cold work given to the material which has the effect of raising its tensile strength, proof stress and hardnessbut reducing its elongation. The effect on the mechanical properties of cold work (reduction in area) by rolling is shown in Figure 2.

The maximum tensile strength obtainable in practice depends on the shape and cross-sectional area of the conductor. The larger the cross-sectional area of a conductor the lower its tensile strength, since the amount of cold work that can be applied is limited by the reduction inarea which can be achieved.

For the usual sizes of busbar conductors in the hard condition, tensile strengths from 250 N/mm2 up to 340 N/mm2 can be obtained dependingon the cross-sectional area.

Proof stress

The 'proof stress' required to produce a definite amount of permanent deformation in the metal is a valuable guide to its physical properties.Proof stress is defined as the stress at which a non-proportional elongation equal to a specified percentage (usually 0.2) of the original gaugelength occurs.

As with the tensile strength, the proof stress varies with the amount of cold work put into the material (see Figure 2).

Figure 2 - Effect of cold rolling on mechanical properties and hardness of high conductivity

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Hardness

British Standards applicable to busbar conductors do not specify hardness measurement as part of the testing requirements. It can howeverbe more quickly and easily carried out than a tensile test and is convenient therefore as a guide to the strength of a conductor. The resultshave to be used with discretion for two reasons:

a) Unlike ferrous materials the relationship between hardness and tensile strength is not constant (see Figure 2).

b) A hardness test is usually only a measurement of the outer skin of the material tested. If the conductor is oflarge cross-sectional area and has received a minimum amount of cold work the skin will be harder than theunderlying metal. Consequently, variations in hardness may be obtained dependent on where the measurement ismade in relation to its cross-section.

As a guide, typical hardness figures of the temper range of conductors supplied are:

Annealed (O) 60 HV max

Half-hard (½H) 70-95 HV

Hard (H) 90 HV min.

Resistance to softening

It is well known that the exposure of cold worked copper to elevated temperatures results in softening and mechanical properties typical ofthose of annealed material. Softening is time and temperature dependent and it is difficult to estimate precisely the time at which it starts andfinishes. It is usual therefore to consider the time to 'half-softening', i.e., the time taken for the hardness to fall by 50% of the original increasein hardness caused by cold reduction.

In the case of HC copper this softening occurs at temperatures above 150°C. It has been established experimentally that such copper wouldoperate successfully at a temperature of 105°C for periods of 20-25 years, and that it could withstand short circuit conditions as high as250°C for a few seconds without any adverse effect.

If hard drawn conductors are required to retain strength under operating conditions higher than normal, the addition of small amounts of silverat the melting and casting stage produces alloys with improved resistance to softening. The addition of 0.06% silver raises the softeningtemperature by approximately 100°C without any significant effect on its conductivity, at the same time appreciably increasing its creepresistance.


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Creep resistance

Figure 3 - Typical creep properties of commercially pure copper and aluminium

Creep, another time and temperature dependent property, is the non-recoverable plastic deformation of a metal under a prolonged stress.The ability of a metal to resist creep is of prime importance to design engineers.

The creep resistance of oxygen-free HC copper is better than that of tough pitch HC copper. This is due to the very small amounts ofimpurities which remain in solid solution in oxygen-free copper, but which are absorbed in the oxide particles in tough pitch copper. Sometypical observations are shown in Figure 3. Tough pitch copper creeps relatively rapidly under low stress at 220°C. The addition of silver toboth oxygen-free and tough pitch coppers results in a significant increase in creep resistance.

Fatigue resistance

Fatigue is the mechanism leading to fracture under repeated or fluctuating stresses. Fatigue fractures are progressive, beginning as minutecracks which grow under the action of the stress. As the crack propagates the load bearing area is reduced and failure occurs by ductilefracture before the crack develops across the full area.

Conditions for such failures can be set up in a busbar system rigidly clamped for support and then subjected to vibrating conditions. Supportsystems are discussed in detail in Section 8.

Bending and forming

The high conductivity coppers are ductile and in the correct temper will withstand severe bending and forming operations. As a general guideto bending, copper in the half-hard or hard temper will bend satisfactorily round formers of the following radii:

Table 6 HC copper minimum bend radius

Thickness Minimum bend radiusUp to 10 mm 1t11-25 mm 1.5t26-50 mm 2t

where t = bar thickness

Material of thicknesses greater than 50 mm is not normally bent; however, it is possible to do so by localised annealing prior to bending.


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Electrical properties

International Annealed Copper Standard

Effect of cold work on conductivity

Effect of temperature on conductivity

Copper in electrical contacts

International Annealed Copper Standard

The electrical properties of HC copper were standardised in 1913 by the International ElectrotechnicalCommission which defined the International Annealed Copper Standard (IACS) in terms of the followingproperties at 20°C:

Volume conductivity sv = 58 MS/m

Density d = 8890 kg/m3

Temperature coefficient of resistance a = 0.00393/°C

It follows from the first two of these two values that:

Volume resistivity rv = 1/ sv = 1.7241 mWcm

Mass conductivity sm = sv /d = 6524 Sm2/kg

Mass resistivity rm = 1/ sm = 153.28 mWkg/m2

These values correspond to 100% IACS. However, the lower oxygen and impurity levels of modern HCcoppers have led to higher typical values of density and conductivity, 101.5% of the IACS value being typicalof the conductivity of modern HC copper in the annealed condition.

Effect of cold work on conductivity

The conductivity of copper is decreased by cold working and may be 2 to 3% less in the hard drawncondition than when annealed. Thus standards for hard drawn HC copper products should stipulate aminimum conductivity requirement of 97% IACS compared with 100% IACS for annealed products.

An approximate relationship between tensile strength of cold worked copper and its increase in electricalresistivity is:

P = T/160

Where P = % increase in electrical resistivity of coldworked copper over its resistivity when annealed.

T = tensile strength, N/mm2

Effect of temperature on conductivity

As temperature increases, the conductivity of all metallic materials decreases with the correspondingincrease in resistivity, according to the formula:

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where rT1 = resistivity at temperature T1, mWcm

rT2 = resistivity at temperature T2, mWcm

bT1T2 = the temperature coefficient of resistivity forthe temperature range T1 to T2, per°C

The value of b itself changes with temperature, but for small temperature ranges, the value of b and T1 isusually taken as a constant over the range. Its value at any temperature above -200°C is taken as

where T is expressed in degrees Celsius.

Hence the value of

b20 = 0.003947 per °C.

Resistance is related to resistivity by

where R = resistance, (mW)

b = volume resistivity, (mWcm)

l = length of conductor, (cm)

A = cross-sectional area of conductor, (cm2)

It follows that the resistance of a metallic conductor also rises with temperature. Thermal changes ofresistance can be calculated in a similar way to thermal changes of resistivity, but a different coefficient, a, isused.

Hence

where RT1 = resistance at temperature T1, W

RT2 = resistance at temperature T2, W

aT1T2 = temperature coefficient of resistance for thetemperature range T1 to T2, per °C

Like b, a itself changes with temperature but for small temperature ranges its value at T1 can be taken asconstant over the range. Its value at any temperature T (°C) above -200°C is taken as


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Copper in electrical contacts

Copper and copper alloys have properties which make them ideal for many types of contacts from lightelectronics applications to very heavy duties. The ranges of compositions and properties of the coppers,copper alloys and copper-based sintered materials, and the duties for which they are suitable are describedin the CDA booklet Copper in Electrical Contacts (Available on CD-ROM 'Megabytes on Copper II').

Available forms

HC copper conductors are obtainable in bar, strip, rod or tube form. For busbar applications, the mostcommon forms supplied are bar, rod or tube and these are normally supplied in the hard condition. In thiscondition they offer greater stiffness, strength and hardness and have a better surface finish. Because of thepractical difficulty of straightening uncoiled hard material it is normally supplied in straight lengths, coiledmaterial being limited to the smaller sizes.

The maximum length of material available with the advent of continuous casting methods is dependent on asupplier's plant capabilities rather than the piece weight of a billet or wirebar. The following notes can beused as a guide to what is available at the present time:

Drawn bars and rods

HC tubes

Special sections

Dimensional tolerances and preferred sizes

Drawn bars and rods

For the reason given above these are drawn straight in the final stages of manufacture. The maximum lengthattainable is therefore limited by the length of the drawbenches on which they are produced. For sizes up to100 mm x 25 mm, lengths up to 9 m, and for 200 mm x 37.5 mm lengths up to 5 m can be obtained. Rodsup to 50 mm dia. can be supplied in lengths up to 9 m. Larger diameters are available but because of thelimited reductions to which they can be subjected with normal commercial equipment hardness variationsacross the section will be obtained.

Because of the difficulty in producing long lengths free from surface blemishes and the handling problemsencountered as the bar or rod weight increases with size and lengths, it is normal practice for lengthssupplied to be around 3 - 4 m.

HC tubes

Seamless, high conductivity copper tubes, complying with the requirements of BS 1977 can be supplied in arange of sizes covering outside diameters of 1 mm up to 610 mm in wall thicknesses of 0.3 mm to 27 mm.Clearly, all combinations of wall thickness and outside diameter are not available, because it is not possibleto produce the extremes of thickness in tubes at the extremes of the outside diameter range.

The maximum lengths available depend upon the tube dimensions specified. As a general rule, tubes in thesize range 108 mm o.d. to 610 mm o.d. are supplied in 6 m lengths. Sizes smaller than 108 mm o.d. can beproduced up to 10 m long.

It is usual practice to supply tubes in the as-drawn condition, M, or alternatively, in the annealed condition,O. However, other tempers can be supplied by arrangement.

Mandrel or bar drawing of tube is virtually obsolete and all the sizes indicated above are manufactured byplug drawing processes. Thus, bore and outer surface finishes are good and dimensional tolerances can be


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maintained over the whole length.

Special sections

These generally take the form of hard drawn angle or channel sections produced by extrusion and drawing.Larger sizes can be fabricated from large sheets or plate by shearing and bending.

Dimensional tolerances and preferred sizes

BS 159 for busbars requires the dimensions of flat and round bars to be within the tolerances in BS 1432,BS 1433 and BS 1977.

If necessary, material can be supplied to closer tolerances than those quoted in the respective BritishStandards. Obviously these involve a higher initial cost, but this may be offset by the savings accrued fromreduced or eliminated machining operations normally carried out to ensure a good contact surface and fit.

The benefit to users of a range of preferred sizes is obvious and designers using copper should be aware ofthis desirable and growing trend. BS 1432 and BS 1433 list the recommended sizes.


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3. Current-carrying Capacity of Busbars

Design Requirements

Calculation of Current-carrying Capacity

Methods of Heat Loss

Heat Generated by a Conductor

Approximate dc Current Ratings for Flat and Round bars

Design Requirements

The current-carrying capacity of a busbar is usually determined by the maximum temperature at which thebar is permitted to operate, as defined by national and international standards such as British Standard BS 159, American Standard ANSI C37.20, etc. These standards give maximum temperature rises as well asmaximum ambient temperatures.

BS 159 stipulates a maximum temperature rise of 50°C above a 24 hour mean ambient temperature of up to35°C, and a peak ambient temperature of 40°C.

ANSI C37.20 alternatively permits a temperature rise of 65°C above a maximum ambient of 40°C, providedthat silver-plated (or acceptable alternative) bolted terminations are used. If not, a temperature rise of 30°Cis allowed.

These upper temperature limits have been chosen because at higher maximum operating temperatures therate of surface oxidation in air of conductor materials increases rapidly and may give rise in the long term toexcessive local heating at joints and contacts. This temperature limit is much more important for aluminiumthan copper because it oxidises very much more readily than copper. In practise these limitations ontemperature rise may be relaxed for copper busbars if suitable insulation materials are used. A nominal riseof 60°C or more above an ambient of 40°C is allowed by BS EN 60439-1:1994 provided that suitableprecautions are taken. BS EN 60439-1:1994 (equivalent to IEC 439) states that the temperature rise ofbusbars and conductors is limited by the mechanical strength of the busbar material, the effect on adjacentequipment, the permissible temperature rise of insulating materials in contact with the bars, and the effect onapparatus connected to the busbars.

The rating of a busbar must also take account of the mechanical stresses set up due to expansion, short-circuit currents and associated inter-phase forces. In some busbar systems consideration must also be givento the capitalised cost of the heat generated by the effective ohmic resistance and current (I2R) which leadsto an optimised design using Kelvin's Law of Maximum Economy. This law states that 'the cost of lost energyplus that of interest and amortisation on initial cost of the busbars (less allowance for scrap) should not beallowed to exceed a minimum value'. Where the interest, amortisation and scrap values are not known, analternative method is to minimise the total manufacturing costs plus the cost of lost energy.

Calculation of Current-carrying Capacity

A very approximate method of estimating the current carrying capacity of a copper busbar is to assume acurrent density of 2 A/mm2 (1250 A/in2) in still air. This method should only be used to estimate a likely sizeof busbar, the final size being chosen after consideration has been given to the calculation methods andexperimental results given in the following sections.

Methods of Heat Loss

The current that will give rise to a particular equilibrium temperature rise in the conductor depends on the

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balance between the rate at which heat is produced in the bar, and the rate at which heat is lost from thebar. The heat generated in a busbar can only be dissipated in the following ways:

(a) Convection

(b) Radiation

(c) Conduction

In most cases convection and radiation heat losses determine the current-carrying capacity of a busbarsystem. Conduction can only be used where a known amount of heat can flow into a heat sink outside thebusbar system or where adjacent parts of the system have differing cooling capacities. The proportion ofheat loss by convection and radiation is dependent on the conductor size with the portion attributable toconvection being increased for a small conductor and decreased for larger conductors.

Convection

The heat dissipated per unit area by convection depends on the shape and size of the conductor and itstemperature rise. This value is usually calculated for still air conditions but can be increased greatly if forcedair cooling is permissible. Where outdoor busbar systems are concerned calculations should always betreated as in still air unless specific information is given to the contrary.

The following formulae can be used to estimate the convection heat loss from a body in W/m2:

where q = temperature rise, °C

L = height or width of bar, mm

d = diameter of tube, mm

The diagrams below indicate which formulae should be used for various conductor geometries:


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It can be seen when diagrams (a) and (b) are compared and assuming a similar cross-sectional area theheat loss from arrangement (b) is much larger, provided the gap between the laminations is not less than thethickness of each bar.

Convection heat loss: forced air cooling

If the air velocity over the busbar surface is less than 0.5 m/s the above formulae for Wv, Wh and Wc apply.For higher air velocities the following may be used:

where Wa = heat lost per unit length from bar, W/m

v = air velocity, m/s

A = surface area per unit length of bar, m2/m

Radiation

The rate at which heat is radiated from a body is proportional to the difference between the fourth power ofthe temperatures of the body and its surroundings, and is proportional to the relative emissivity between thebody and its surroundings.

The following table lists typical absolute emissivities e for copper busbars in various conditions. Changes inemissivity give rise to changes in current ratings, as shown in Table 7.

Bright metal 0.1


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Partially oxidised 0.30

Heavily oxidised 0.70

Dull non-metallic paint 0.9

Table 7 Percentage increase in current rating when e is increased from 0.1 to 0.9 - three-phasearrangement

Phase centres, mm

No. of bars in parallel 150 200 250

1 23 23 25

2 15 16 18

3 10 11 14

4 9 9 12

5 6 7 9

The figures given in Table 7 are approximate values applicable to 80 to 160 mm wide busbars for a 105°Coperating temperature and 40°C ambient. The relative emissivity is calculated as follows:

where e = relative emissivity

e1 = absolute emissivity of body 1

e2 = absolute emissivity of body 2


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The rate of heat loss by radiation from a body (W/m2) is given by:

where e = relative emissivity

T1 = absolute temperature of body 1, K

T2 = absolute temperature of body 2, K (i.e., ambienttemperature of the surroundings)

Radiation is considered to travel in straight lines and leave the body at right angles to its surface. Thediagrams above define the effective surface areas for radiation from conductors of common shapes.

Heat Generated by a Conductor

The rate at which heat is generated per unit length of a conductor carrying a direct current is the product I2Rwatts, where I is the current flowing in the conductor and R its resistance per unit length. The value for theresistance can in the case of d.c. busbar systems be calculated directly from the resistivity of the copper orcopper alloy. Where an a.c. busbar system is concerned, the resistance is increased due to the tendency ofthe current to flow in the outer surface of the conductor. The ratio between the a.c. value of resistance andits corresponding d.c. value is called the skin effect ratio (see Section 4). This value is unity for a d.c.system but increases with the frequency and the physical size of the conductor for an a.c. current.

Rate of Heat generated in a Conductor,

W/mm = I2 RoS

where I = current in conductor, A

Ro = d.c. resistance per unit length, W/mm

S = skin effect ratio

also

where Rf = effective a.c. resistance of conductor, W (see above)

Approximate dc Current Ratings for Flat and Round bars

The following equations can be used to obtain the approximate d.c. current rating for single flat and roundcopper busbars carrying a direct current. The equations assume a naturally bright copper finish whereemissivity is 0.1 and where ratings can be improved substantially by coating with a matt black or similarsurface. The equations are also approximately true for a.c. current provided that the skin effect andproximity ratios stay close to 1.0, as is true for many low current applications. Methods of calculation forother configurations and conditions can be found in subsequent sections.

(a) Flat bars on edge:


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(1

where I = current, A

A = cross-sectional area, mm2

p = perimeter of conductor, mm

q = temperature difference between conductor and the ambient air, °C

a = resistance temperature coefficient of copper at the ambient temperature, per °C

r = resistivity of copper at the ambient temperature, mW cm

(b) Hollow round bars:

(2

(c) Solid round bars:

(3

If the temperature rise of the conductor is 50°C above an ambient of 40°C and the resistivity of the copperat 20°C is 1.724 mWcm, then the above formulae become:

(i) Flat bars:

(4

(ii) Hollow round bars:

(5

(iii) Solid round bars:

(6

For high conductivity copper tubes where diameter and mass per unit length (see Table 14) are known,

(7


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where m = mass per unit length of tube, kg/m

d = outside diameter of tube, mm

Re-rating for different current or temperature rise conditions

Where a busbar system is to be used under new current or temperature rise conditions, the followingformula can be used to find the corresponding new temperature rise or current:

(8

where

I1 = current 1, A

I2 = current 2, A

q1 = temperature rise for current 1, °C

q2 = temperature rise for current 2, °C

T1 = working temperature for current 1, °C

T2 = working temperature for current 2, °C

a20 = temperature coefficient of resistance at 20°C ( = 0.00393)

If the working temperature of the busbar system is the same in each case (i.e., T1 = T2), for example whenre-rating for a change in ambient temperature in a hotter climate, this formula becomes

Laminated bars

When a number of conductors are used in parallel, the total current capacity is less than the rating for asingle bar times the number of bars used. This is due to the obstruction to convection and radiation lossesfrom the inner conductors. To facilitate the making of interleaved joints, the spacing between laminated barsis often made equal to the bar thickness. For 6.3 mm thick bars up to 150 mm wide, mounted on edge with6.3 mm spacings between laminations, the isolated bar d.c. rating may be multiplied by the following factorsto obtain the total rating.

No. of laminations Multiplying factor

No. oflaminations

Multiplyingfactor

2 1.8

3 2.5


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4 3.2

5 3.9

6 4.4

8 5.5

10 6.5


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4. Alternating Current Effects in Busbars

Skin Effect

Proximity Effect

Condition for Minimum Loss

Penetration Depth

Skin Effect

The apparent resistance of a conductor is always higher for a.c. than for d.c. The alternating magnetic fluxcreated by an alternating current interacts with the conductor, generating a back e.m.f. which tends to reducethe current in the conductor. The centre portions of the conductor are affected by the greatest number of lines offorce, the number of line linkages decreasing as the edges are approached. The electromotive force producedin this way by self-inductance varies both in magnitude and phase through the cross-section of the conductor,being larger in the centre and smaller towards the outside. The current therefore tends to crowd into those partsof the conductor in which the opposing e.m.f. is a minimum; that is, into the skin of a circular conductor or theedges of a flat strip, producing what is known as 'skin' or 'edge' effect. The resulting non-uniform current densityhas the effect of increasing the apparent resistance of the conductor and gives rise to increased losses.

The ratio of the apparent d.c. and a.c. resistances is known as the skin effect ratio:

where Rf = a.c. resistance of conductor

Ro = d.c. resistance of conductor


The magnitude and importance of the effect increases with the frequency, and the size, shape and thickness ofconductor, but is independent of the magnitude of the current flowing.

It should be noted that as the conductor temperature increases the skin effect decreases giving rise to a lowerthan expected a.c. resistance at elevated temperatures. This effect is more marked for a copper conductor thanan aluminium conductor of equal cross-sectional area because of its lower resistivity. The difference isparticularly noticeable in large busbar sections.

Copper rods

The skin effect ratio of solid copper rods can be calculated from the formulae derived by Maxwell, Rayleigh andothers (Bulletin of the Bureau of Standards, 1912):

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where S = Skin effect ratio

d = diameter of rod, mm

f = frequency, Hz

r = resistivity, mW cm

m = permeability of copper (=1)

For HC copper at 20°C, r = 1.724 mW cm, hence

where A = cross-sectional area of the conductor, mm2

Figure 4 Skin effect in HC copper rods at 20°C. Relation between diameter and x, and between Rf/Ro andx where x = 1.207 x 10–2 Ö(Af)

(Note: For values of x less than 2. use inset scale for Rf/Ro)


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Copper tubes

Skin effect in tubular copper conductors is a function of the thickness of the wall of the tube and the ratio of thatthickness to the tube diameter, and for a given cross sectional area it can be reduced by increasing the tubediameter and reducing the wall thickness.

Figure 5, Figure 6, and Figure 7, which have been drawn from formulae derived by Dwight (1922) and Arnold(1936), can be used to find the value of skin effect for various conductor sections. In the case of tubes (Figure5), it can be seen that to obtain low skin effect ratio values it is desirable to ensure, where possible, low valuesof t/d and Ö(f/r). For a given cross-sectional area the skin effect ratio for a thin copper tube is appreciably lowerthan that for any other form of conductor. Copper tubes, therefore, have a maximum efficiency as conductors ofalternating currents, particularly those of high magnitude or high frequency.

The effect of wall thickness on skin effect for a 100 mm diameter tube carrying a 50Hz alternating current isclearly shown in Figure 5.

Figure 5 Resistance of HC copper tubes, 100 mm outside diameter, d.c. and 50 Hz a.c.


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Figure 6 Skin effect for rods and tubes


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Flat copper bars

The skin effect in flat copper bars is a function of its thickness and width. With the larger sizes of conductor, fora given cross-sectional area of copper, the skin effect in a thin bar or strip is usually less than in a circularcopper rod but greater than in a thin tube. It is dependent on the ratio of the width to the thickness of the barand increases as the thickness of the bar increases. A thin copper strip, therefore, is more efficient than a thickone as an alternating current conductor. Figure 7 can be used to find the skin effect value for flat bars.

Figure 7 Skin effect for rectangular conductors


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Square copper tubes

The skin effect ratio for square copper tubes can be obtained from Figure 8.

Figure 8 Skin effect ratio for hollow square conductors


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Proximity Effect

n the foregoing consideration of skin effect it has been assumed that the conductor is isolated and at such adistance from the return conductor that the effect of the current in it can be neglected. When conductors areclose together, particularly in low voltage equipment, a further distortion of current density results from theinteraction of the magnetic fields of other conductors.

In the same way as an e.m.f. may be induced in a conductor by its own magnetic flux, so may the magnetic fluxof one conductor produce an e.m.f. in any other conductor sufficiently near for the effect to be significant.

If two such conductors carry currents in opposite directions, their electro-magnetic fields are opposed to oneanother and tend to force one another apart. This results in a decrease of flux linkages around the adjacentparts of the conductors and an increase in the more remote parts, which leads to a concentration of current inthe adjacent parts where the opposing e.m.f. is a minimum. If the currents in the conductors are in the samedirection the action is reversed and they tend to crowd into the more remote parts of the conductors.

This effect, known as the 'proximity effect' (or 'shape effect'), tends usually to increase the apparent a.c.resistance. In some cases, however, proximity effect may tend to neutralise the skin effect and produce a betterdistribution of current as in the case of strip conductors arranged with their flat sides towards one another.


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If the conductors are arranged edgewise to one another the proximity effect increases. In most cases theproximity effect also tends to increase the stresses set up under short-circuit conditions and this may thereforehave to be taken into account.

The currents in various parts of a conductor subjected to skin and proximity effects may vary considerably inphase, and the resulting circulating current give rise to additional losses which can be minimised only by thechoice of suitable types of conductor and by their careful arrangement.

The magnitude of the proximity effect depends, amongst other things, on the frequency of the current and thespacing and arrangement of the conductors. The graphs in Figure 14 (Section 6) can be used to obtain values ofproximity effect for various conductor configurations at 50 or 60 Hz. Methods of calculation for other frequenciesare available (Dwight 1946). The unbalancing of current due to the proximity effect can be reduced by spacingthe conductors of different phases as far apart as possible and sometimes by modifying their shape inaccordance with the spacing adopted. In the case of laminated bars a reduction may be obtained by transposingthe laminations at frequent intervals or by employing current balancers using inductances.

Proximity effect may be completely overcome by adopting a concentric arrangement of conductors with oneinside the other as is used for isolated phase busbar systems.

The magnetic field round busbar conductors may be considerably modified and the current distortion increasedby the presence of magnetic materials and only metals such as copper or copper alloys should be used forparts likely to come within the magnetic field of the bars.

Condition for Minimum Loss

Both skin and proximity effects are due to circulating or 'eddy' currents caused by the differences of inductancewhich exist between different 'elements' of current-carrying conductors. The necessary condition for avoidanceof both these effects (and hence for minimum loss) is that the shapes of each of the conductors in asingle-phase system approximates to 'equi-inductance lines'. Arnold (1937) has shown that for close spacing,rectangular section conductors most closely approach this ideal. Such an arrangement is also convenient wherespace is limited and where inductive voltage drop due to busbar reactance must be reduced to a minimum. Inthe case of heavy current single-phase busbars and where space is slightly less restricted, the single channelarrangement gives the closest approximation to the equi-inductance condition, the channels of 'go' and 'return'conductors being arranged back-to-back, while for wider spacing a circular section is preferable.

Penetration Depth

In the case of special conductor arrangements, or where high frequencies are employed, the alternating currentresistance may be calculated using the earlier sections. It is often necessary to know the depth of penetration ofthe current into a conductor, that is the depth at which the current density has been reduced to 1/e, or 0.368 ofits value at the conductor surface. This can be calculated using the following formula when its resistivity and thefrequency are known.

depth of penetration

where d = depth of penetration, mm

r = resistivity of copper, mW cm

f = frequency, Hz


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5. Effect of Busbar Arrangements on Rating

Laminated copper bars

Inter-leaving of conductors

Transposition of conductors

Hollow square arrangement

Tubular bars

Concentric conductors

Channel and angle bars

Comparison of conductor arrangements

Enclosed copper conductors

Compound insulated conductors

Plastic insulated conductors

Isolated phase busbars

The efficiency of all types of heavy current busbars depends upon careful design, the most important factorsbeing:

a) The provision of a maximum surface area for the dissipation of heat.

b) An arrangement of bars which cause a minimum of interference with thenatural movements of air currents.

c) An approximately uniform current density in all parts of the conductors. This isnormally obtained by having as much copper as possible equidistant from themagnetic centre of the busbar.

d) Low skin effect and proximity effect for a.c. busbar systems.

To meet these requirements there are many different arrangements of copper busbars using laminations, aswell as copper extrusions of various cross-sections.

Figure 9 Busbar arrangements

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Laminated copper bars

To obtain the best and most efficient rating for rectangular strip copper conductors they should be mountedwhenever possible with their major cross-sectional axes vertical so giving maximum cooling surfaces.

Laminations of 6 or 6.3 mm thickness, of varying widths and with 6 or 6.3 mm spacings are probably themost common and are satisfactory in most a.c. low current cases and for all d.c. systems.

It is not possible to give any generally applicable factors for calculating the d.c. rating of laminated bars,since this depends upon the size and proportions of the laminations and on their arrangement. A guide to theexpected relative ratings are given in Table 8 below for a 50 Hz system. The ratings for single bars can beestimated using the methods given in Section 3 and Section 4.

Table 8 Multiplying factors for laminated bars

Table 13 (Appendix 2) gives a.c. ratings for various configurations of laminated bars based on testmeasurements.

For all normal light and medium current purposes an arrangement such as that in Figure 9a is entirelysatisfactory, but for a.c. currents in excess of 3000 A where large numbers of laminations would be requiredit is necessary to rearrange the laminations to give better utilisation of the copper bars.

The effect of using a large number of laminations mounted side by side is shown in Figure 10 for a.c.


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currents. The current distribution is independent of the total current magnitude.

Figure 10 Alternating current distribution in a bar with ten laminations

This curve shows that due to skin effect there is a considerable variation in the current carried by eachlamination, the outer laminations carrying approximately four times the current in those at the centre. Thetwo centre laminations together carry only about one-tenth of the total current.

The currents in the different laminations may also vary appreciably in phase, with the result that theirnumerical sum may be greater than their vectorial sum, which is equal to the line current. These circulatingcurrents give rise to additional losses and lower efficiency of the system. It should also be noted that thecurve is non-symmetrical due to the proximity effect of an adjacent phase.

For these reasons it is recommended that alternate arrangements, such as those discussed in the followingsections, are used for heavy current a.c. svstems.

Inter-leaving of conductors

Where long low-voltage a.c. bars are carrying heavy currents, particularly at a low power factor, inductivevolt drop may become a serious problem with laminated bars arranged as in Figure 9a. The voltage drop forany given size of conductor is proportional to the current and the length of the bars, and increases as theseparation between conductors of different phases increases. In the case of laminated bars the inductivevolt drop can be reduced by splitting up the bars into an equivalent number of smaller circuits in parallel, withthe conductors of different phases interleaved as shown in Figure 9b. This reduces the average spacingbetween conductors of different phases and so reduces the inductive volt drop.

Transposition of conductors

The unbalanced current distribution in a laminated bar carrying a.c. current due to skin and proximity effectsmay be counteracted by transposing laminations or groups of laminations at intervals. Tappings and otherconnections make transposition difficult, but it can be worthwhile where long sections of bars are free fromtappings. The arrangement is as shown in Figure 9e.

Hollow square arrangement

To obtain a maximum efficiency from the point of view of skin effect, as much as possible of the coppershould be equidistant from the magnetic centre of a bar, as in the case of a tubular conductor. This canreduce the skin effect to little greater than unity whereas values of 2 or more are possible with other


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arrangements having the same cross-sectional area.

With flat copper bars the nearest approach to a unity skin effect ratio is achieved using a hollow squareformation as shown in Figure 9c, though the current arrangement is still not as good as in a tubularconductor. The heat dissipation is also not as good as the same number of bars arranged side by side as inFigure 9b, due to the horizontally mounted bars at the top and bottom.

Modified hollow square

This arrangement (Figure 9d) does not have as good a value of skin effect ratio as the hollow squarearrangement, but it does have the advantage that the heat dissipation is much improved. This arrangementcan have a current-carrying capacity of up to twice that for bars mounted side by side, or alternatively thetotal cross-sectional area can be reduced for similar current-carrying capacities.

Tubular bars

A tubular copper conductor is the most efficient possible as regards skin effect, as the maximum amount ofmaterial is located at a uniform distance from the magnetic centre of the conductor. The skin effect reducesas the diameter increases for a constant wall thickness, with values close to unity possible when the ratio ofoutside diameter to wall thickness exceeds about 20.

The natural cooling is not as good as that for a laminated copper bar system of the same cross-sectionalarea, but when the proximity effects are taken into account the one-piece tube ensures that the whole tubeattains an even temperature - a condition rarely obtained with laminated bar systems.

Tubular copper conductors also lend themselves to alternative methods of cooling by, for example, forced airor liquid cooling where heat can be removed from the internal surface of the tubes. Current ratings of severaltimes the natural air cooled value are possible using forced cooling with the largest increases when liquidcooling is employed.

A tubular bar also occupies less space than the more usual copper laminated bar and has a furtheradvantage that its strength and rigidity are greater and uniform in all deflection planes. These advantagesare, however, somewhat reduced by the difficulty of making joints and connections which are more difficultthan those for laminated bars. These problems have now been reduced by the introduction of copperwelding and exothermic copper forming methods. Copper tubes are particularly suitable for high currentapplications, such as arc furnaces, where forced liquid cooling can be used to great advantage. The tubecan also be used in isolated phase busbar systems due to the ease with which it can be supported byinsulators.

Concentric conductors

This arrangement is not widely used due to difficulties of support but has the advantage of the optimumcombination of low reactance and eddy current losses and is well suited to furnace and weld setapplications. It should be noted that the isolated phase busbar systems are of this type with the current inthe external enclosure being almost equal to that in the conductor when the continuously bonded three-phaseenclosure system is used.

Channel and angle bars

Alternative arrangements to flat or tubular copper bars are the channel and angle bars which can haveadvantages. The most important of these shapes are shown in the diagrams below.

These are easily supported and give great rigidity and strength while the making of joints and connectionspresents no serious difficulty.

The permissible alternating current density in free air for a given temperature rise is usually greater in thecase of two angle-shaped conductors (diagram (a)) than in any other arrangement of conductor material.


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For low voltage heavy current single-phase bars with narrow phase centres, single copper channels with thewebs of the 'go' and 'return' conductors towards one another give an efficient arrangement. The channelsizes can be chosen to reduce the skin and proximity effects to a minimum, give maximum dissipation of heatand have considerable mechanical strength and rigidity. Where high voltage busbars are concerned thephase spacing has to be much larger to give adequate electrical clearances between adjacent phases withbest arrangement being with the channel webs furthest apart. For high-capacity generators which areconnected to transformers and allied equipment by segregated or non-segregated copper busbars, thedouble angle arrangement gives the best combination with the copper bar sizes still being readilymanufactured. The current ratings of these arrangements are given in Table 15 (Appendix 2). The ratingsgiven are the maximum current ratings which do not take the cost of losses into account and hence are notoptimised.

Comparison of conductor arrangements

The extent to which the a.c. current rating for a given temperature rise of a conductor containing a givencross-sectional area of copper depends on the cross-section shape. The approximate relative a.c. ratingsfor a typical cross-sectional area of 10 000 mm2 are shown in Figure 11. For cross-sectional areas greaterthan 10 000 mm2 the factors are greater than those shown, and are smaller for smaller cross-sections. Inthe case of double-channel busbars, the ratio of web-to-flange lengths and also the web thickness have aconsiderable effect on the current carrying capacity.

Figure 11 Comparative a.c. ratings of various conductor arrangements each having a crosssectional area of 10,000 mm2 of HC copper


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Enclosed copper conductors

In many cases busbars are surrounded by enclosures, normally metallic, which reduce the busbar heatdissipation due to reduction in cooling air flow and radiation losses and therefore give current ratings whichmay be considerably less than those for free air exposure. Ventilated enclosures, however, providemechanical protection and some cooling air flow with the least reduction in current rating.

The reduction in rating for a given temperature rise will vary considerably with the type and size of bar andenclosure. The greatest decrease in current rating occurs with bars which depend mainly on free aircirculation and less on uniform current distribution such as the modified hollow square arrangement (Figure9d). In these cases the rating may be reduced to between 60 and 65% when the conductors are enclosed innon-magnetic metal enclosures. In the case of tubular conductors or those of closely grouped flatlaminations, which are normally not so well cooled by air circulation, the ratings may be reduced to about75% of free air ratings for normal temperature rises.

Where the busbar system is enclosed in thick magnetic enclosures, such as in metal-clad switchgear, thereduction is approximately a further 15%. The effect of thin sheet-steel enclosures is somewhat less. Theseadditional reductions are due to the heat generated by the alternating magnetic fields through hysteresis andeddy current losses. Besides the derating caused by enclosure conditions, other limitations on maximumworking temperature are often present, such as when the outside of enclosures should not exceed a givensafety value. These deratings are affected by the electrical clearances involved and the degree of ventilationin the enclosure. The above figures and the curves shown in Figure 12 should only be taken as a rough guideto the required derating; an accurate figure can only be obtained by testing.

All parts such as conductor and switch fittings, enclosures and interphase barriers may be subject toappreciable temperature rise due to circulating and eddy current losses when close to the heavy currentbars and connections. These losses can be reduced to a minimum by making these parts from highconductivity non-magnetic material such as copper or copper alloy.

Figure 12 Comparison of approximate current ratings for busbars in different enclosures


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Compound insulated conductors

The current rating of copper immersed in oil or compound depend upon a number of factors which may varywidely with design, and can normally only be confirmed by carrying out temperature rise tests on thecomplete assembly.

The ratings of enclosed bars are nearly always much lower than the free air ratings. The temperature rise isdependent on the rate at which heat is conducted through the insulating media and dissipated from theoutside casing by radiation and convection. There is nearly always a closer phase spacing betweenconductors giving high proximity effects and higher heat losses in the magnetic outer casings and so givingrise to higher temperature rises.

Proximity effect is often more important for insulated bars than those in air. Laminated bars have feweradvantages when immersed in oil or compound and circular copper conductors either solid or hollow thoughare often preferred particularly for high-voltage gear and high current generators, transformers, etc., wheremore effective cooling such as water cooling can be employed to improve conductor material utilisation andhence reduce the overall size of plant.

Plastic insulated conductors

There is a widening use of plastic continuous insulation as the primary insulation for low current and voltagebusbars. This insulation is usually of the shrink-on P.V.C. type though wrap-on tape is sometimes used. Thismethod is used for voltages up to about 15 kV, though much higher levels can be attained when specialisedinsulation systems such as epoxy resin or similar based tapes and powders are employed. These systemsare particularly useful where high atomic radiation levels, or high temperatures (up to 130°C) areencountered, although account must be taken of the possibility of halogen gassing from P.V.C. insulations attemperatures around 100°C. Modified P.V.C. materials with improved high-temperature performance areavailable.


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Isolated phase busbars

solated phase busbars consist of a metallic enclosed conductor where each individual phase or pole issurrounded by a separately earthed sheath which is connected at its ends by a full short-circuit current ratedbar. The sheath is intended primarily to prevent interphase short-circuit currents developing. They have thefurther advantage that the high magnetic fields created by the conductor current are almost completelycancelled by an equal and opposite current induced in the enclosure or sheath with reductions of 95% orbetter in the external magnetic field being possible. An important result is that the likelihood of steelworkoverheating when adjacent to the busbar system is considerably reduced except where the sheath short-circuit bars are located. This current flowing in the enclosure makes the method of estimating theperformance of the busbar system much more complicated and can only be resolved by obtaining a heatbalance between conductor and enclosure using an interactive calculation method.

These busbars are used normally for operating voltages of between 11 kV and 36 kV though equipmentusing much lower voltages and higher voltages are increasingly changing to this system. Examples of suchequipment are exciter connections, switchgear interconnections, generator to transformer connections, highvoltage switchgear using SF6 (sulphur hexafluoride) gas insulation (this gas having an insulation level manytimes better than air). The current flowing in the conductor ranges from as little as 1000 A to in excess of 40kA. To obtain the higher currents forced cooling is used, the most commonly used cooling media being airand water though other cooling gases or liquids can be used. The use of these cooling systems usuallycreates much increased heat losses and so their use must be justified by benefits in other areas, e.g.,reduced civil costs, reduced physical size where space is at a premium or reduction in size to enable normalmanufacturing methods be used both for the basic busbar material and also the complete busbar system.

Another factor which influences the method chosen for forced cooling is the naturally cooled rating of thebusbar system and also its ability to sustain overload conditions. The busbars are usually manufactured insingle-phase units of transportable length and consist of a central conductor usually tubular of round, squareor channel cross-section, supported by porcelain or epoxy resin insulators. The insulators are located by theexternal metallic sheath through which they are normally removed for servicing.


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6. Short-Circuit Effects

Short-Circuit Heating of Bars

Electromagnetic Stresses

Corona Discharge

Short-Circuit Heating of Bars

Copper busbars are normally part of a larger generation or transmission system. The continuous rating of the main components such as generators, transformers, rectifiers, etc.,therefore determine the nominal current carried by the busbars but in most power systems a one to four second short-circuit current has to be accommodated. The value of thesecurrents is calculated from the inductive reactances of the power system components and gives rise to different maximum short-circuit currents in the various system sections.

These currents are very often ten to twenty times the continuous current rating and therefore the transitory heating effect must be taken into account. This effect can, in many cases,lead to dangerous overheating, particularly where small conductors are part of a large heavy current system, and must be considered when determining the conductor size. Tocalculate the temperature rise of the conductor during a short circuit it is assumed that all the heat generated is absorbed by the conductor with none lost by convection and radiationas for a continuous rated conductor. The temperature rise is dependent therefore only on the specific heat of the copper conductor material and its mass. The specific heat ofcopper varies with temperature, increasing as the temperature rises. At normal ambient temperatures it is about 385 J/kg K and at 300°C it is about 410 J/kg K.

Short-circuit heating characteristics are not easy to calculate accurately because of complex a.c. and d.c. current effects, but for most purposes the formulae below will normallygive sufficiently accurate results:

where t = maximum short-circuit time, s

A = conductor cross-section area, mm2

I = conductor current, kA

q = conductor temperature rise, K

If q = 300°C, then

The value of t obtained from the above equation should always be greater than the required short circuit withstand time which is usually 1 to 4 seconds.

The temperature rise per second due to a current I is given by the following approximate formula:

(I/A) should be less than 0.25 for reasonable accuracy.

The maximum short-circuit temperature is very often chosen to be 300°C for earth bar systems but the upper limit for the phases is normally lower and is dependent on themechanical properties required and surface finish of the copper material.

Heating time constant

The previous section considered very short time effects but in many cases it may be necessary to calculate the temperature rise of a conductor over an extended time, for examplethe time taken for a conductor to reach normal operating temperature when carrying its rated continuous current. Under these conditions the conductor is absorbing heat as itstemperature rises. It is also dissipating heat by convection and radiation, both of which increase with rising temperature difference between the conductor and the surroundings.When maximum operating temperature is reached then the heat loss by convection and radiation is constant and the heat absorbed by the conductor ceases.

The temperature rise after time t from the start of heating is given by the following formula where the change of resistance with temperature can be assumed to be negligible:

where q = temperature rise, °C

qmax = maximum temperature rise, °C

e = exponential constant (=2.718)

t = time, s

t = time constant, s

The time constant can be found using the following formula:

where w = rate of generation of heat at t=0, W

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m = mass, kg

c = specific heat, J/kg K

The time constant gives the time taken to reach 0.636 of the maximum temperature rise, qmax.

Electromagnetic Stresses

When a conductor carries a current it creates a magnetic field which interacts with any other magnetic field present to produce a force. When the currents flowing in two adjacentconductors are in the same direction the force is one of attraction, and when the currents are in opposite directions a repulsive force is produced.

In most busbar systems the current-carrying conductors are usually straight and parallel to one another. The force produced by the two conductors is proportional to the products oftheir currents. Normally in most busbar systems the forces are very small and can be neglected, but under short-circuit conditions, they become large and must be taken intoaccount together with the conductor material fibre stresses when designing the conductor insulator and its associated supports to ensure adequate safety factors.

The factors to be taken into account may be summarised as follows:

a) stresses due to direct lateral attractive and repulsive forces.

b) Vibrational stresses.

c) Longitudinal stresses resulting from lateral deflection.

d) Twisting moments due to lateral deflection.

In most cases the forces due to short-circuits are applied very suddenly. Direct currents give rise to unidirectional forces while alternating currents produce vibrational forces.

Maximum stresses

When a busbar system is running normally the interphase forces are normally very small with the static weight of the busbars being the dominant component. Under short-circuitconditions this is very often not the case as the current rises to a peak of some thirty times its normal value, falling after a few cycles to ten times its initial value. These hightransitory currents create large mechanical forces not only in the busbars themselves but also in their supporting system. This means that the support insulators and their associatedsteelwork must be designed to withstand these high loads as well as their normal structural requirements such as wind, ice, seismic and static loads.

The peak or fully asymmetrical short circuit current is dependent on the power factor (cos f) of the busbar system and its associated connected electrical plant. The value is obtainedby multiplying the r.m.s. symmetrical current by the appropriate factor given in Balanced three-phase short-circuit stresses.

If the power factor of the system is not known then a factor of 2.55 will normally be close to the actual system value especially where generation is concerned. Note that thetheoretical maximum for this factor is 2Ö2 or 2.828 where cos f = 0. These peak values reduce exponentially and after approximately 10 cycles the factor falls to 1.0, i.e., thesymmetrical r.m.s. short circuit current. The peak forces therefore normally occur in the first two cycles (0.04 s) as shown in Figure 13.

In the case of a completely asymmetrical current wave, the forces will be applied with a frequency equal to that of the supply frequency and with a double frequency as the wavebecomes symmetrical. Therefore in the case of a 50 Hz supply these forces have frequencies of 50 or 100 Hz.

The maximum stresses to which a bus structure is likely to be subjected would occur during a short-circuit on a single-phase busbar system in which the line short-circuit currents aredisplaced by 180°.

In a three-phase system a short-circuit between two phases is almost identical to the single-phase case and although the phase currents are normally displaced by 120°, undershort-circuit conditions the phase currents of the two phases are almost 180° out of phase. The effect of the third phase can be neglected.

In a balanced three-phase short-circuit, the resultant forces on any one of the three phases is less than in the single-phase case and is dependent on the relative physical positionsof the three phases.

In the case of a single-phase short-circuit, the forces produced are unidirectional and are therefore more severe than those due to a three-phase short-circuit, which alternate indirection.

The short-circuit forces have to be absorbed first by the conductor. The conductor therefore must have an adequate proof strength to carry these forces without permanentdistortion. Copper satisfies this requirement as it has high strength compared with other conductor materials (Table 2). Because of the high strength of copper, the insulators can bemore widely spaced than is possible with lower-strength materials.

Figure 13 Short-circuit current waveform

Single phase short circuit stresses

The electromagnetic force developed between two straight parallel conductors of circular cross-section each carrying the same current is calculated from the following formula:

where Fmax = force on conductor, N/m


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I = current in both phases, A

s = phase spacing, mm

The value of I is normally taken in the fully asymmetrical condition as 2.55 times the r.m.s. symmetrical value or 1.8 times the peak r.m.s. value of the short-circuit current asdiscussed above. It is possible, in certain circumstances, for the forces to be greater than this due to the effect of an impulse in the case of a very rigid conductor, or due toresonance in the case of bars liable to mechanical vibration. It is therefore usual to allow a safety factor of 2.5 in such cases.

Balanced three-phase short-circuit stresses

A three-phase system has its normal currents displaced by 120° and when a balanced three-phase short-circuit occurs the displacement is maintained. As with all balancedthree-phase currents, the instantaneous current in one phase is balanced by the currents in the other two phases. The directions of the currents are constantly changing and sotherefore are the forces. The maximum forces are dependent on the point in the cycle at which the fault or short-circuit occurs.

The maximum force appearing on any phase resulting from a fully offset asymmetrical peak current is given by

(9

The condition when the maximum force appears on the outside phases (Red or Blue) is given by

(10

The condition when the maximum force is on the centre phase (Yellow) is given by

(11

where Fmax = maximum force on conductor, N/m

I = peak asymmetrical current, A

s = conductor spacing, mm

The peak current I attained during the short-circuit varies with the power factor of the circuit:

Power factor I, x Irms (symmetrical)

0 2.828

0.07 2.55

0.2 2.2

0.25 2.1

0.3 2

0.5 1.7

0.7 1.5

1.0 1.414

Correction for end effect

It has been assumed so far that the conductors are of infinite length. This assumption does not generally lead to great errors in the calculated short-circuit forces. This is not true,however, at the ends of bars where there is a great change in flux compared with the uniform magnetic field over most of the long straight conductor. Where the conductor isrelatively short this effect can be considerable, the normal formulae giving overestimates for the forces. To overcome this problem the preceding formulae can be rewritten in thefollowing form:

where Ftot = total force on the conductor, N

L = length of conductor, m

c = constant from relevant previous formula

The following substitution may then be made:

The formula will then be of the form


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(12

If

is very large then

is almost equal to

and therefore the modified formula becomes almost identical with the standard formula. In many cases, the following formula is sufficiently accurate:

(13

where Ftot is again the total force along the conductor in Newtons.

Formulae 9 to 11 may be used where

is greater than 20. For values between 20 and 4, is greater than 20. For values between 20 and 4, equation 13 above should be used. For values less than 4, equation 12 should beused.

Proximity factor

Figure 14 - Proximity factor for rectangular copper conductor

The formulae in the previous section used for calculating short-circuit forces do not take into account the effect of conductors which are not round as they strictly only apply to roundconductors. To overcome this when considering rectangular conductors, a proximity factor K is introduced into the ordinary force formulae, its value being found using the curves inFigure 14.


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Except in cases where the conductors are very small or are spaced a considerable distance apart the corrected general formula for force per unit length becomes:

The value of

is first calculated then K is read from the curve for the appropriate

ratio.

From the curves it can be seen that the effect of conductor shape decreases rapidly with increasing spacing and is a maximum for strip conductors of small thickness. It is almostunity for square conductors and is unity for a circular conductor.

Alternatively, the proximity factor can be calculated using the following formula, from which the curves in Figure 14 were drawn (Dwight 1917). (See Figure 14 for explanation ofsymbols).

This formula gives the intermediate curves of Figure 14, for s>a, b>0, a>0

Vibrational stresses

Stresses will be induced in a conductor by natural or forced vibrations the amplitude of which determines the value of the stress, which can be calculated from the formulae given inSection 8.

The conductor should be designed to have a natural frequency which is not within 30% of the vibrations induced by the magnetic fields resulting from the currents flowing in adjacentconductors. This type of vibration normally occurs during continuous running and does not occur when short-circuit currents are flowing.

The stresses resulting from the short-circuit forces are calculated using the beam theory formulae for simply supported beams for a single cantilever to multispan arrangements, theapplied forces being derived from the previous sections. The resulting deflections enable the conductor stress to be calculated and so determine if it is likely to permanently damagethe conductor because it has exceeded the proof stress of the conductor material.

Methods of reducing conductor stresses

In cases where there is a likelihood of vibration at normal currents or when subjected to short-circuit forces causing damage to the conductor, the following can he used to reduce oreliminate the effect:

a) Reduce the span between insulator supports.

This method can be used to reduce the effects of both continuous vibration and that due to short-circuit forces.

b) Increase the span between insulator supports.

This method can only be used to reduce the effects of vibration resulting from a continuous current. It will increase the stresses due to a short-circuitcurrent.

c) Increase or decrease the flexibility of the conductor supports.

This method will reduce the effects of vibration due to continuous current but has very little effect on that due to short-circuit forces.

d) Increase the conductor flexibility.

This can only be used to reduce the effects of vibration due to a continuous current. The short-circuit effect is increased.

e) Decrease the conductor flexibility.

This method will reduce the effects of vibration due to either a continuous current or a short-circuit.

It will be noted that in carrying out the various suggestions above, changes can only be made within the overall design requirements of the busbar system.

Corona Discharge

With very high voltage air-insulated busbars, particularly of the type usually installed out of doors, it is necessary to ensure that with the spacing adopted between conductors ofdifferent phases, or between conductors and earth, the electromagnetic stress in the air surrounding the conductors is low enough not to cause a corona discharge. Corona


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discharge is to be avoided where possible as it creates ionised gas which can lead to a large reduction in the air insulation surrounding the conductor and so can cause flash-over.Should flash-over occur, this will in many cases lead to a short-circuit between either adjacent phases or poles or the nearest earth point or plane. This will cause considerableburning of the conductors and associated equipment together with mechanical damage. Corona discharge can also cause radio interference which may be unacceptable.

To avoid these conditions the busbar system should be free from sharp edges or small radii on the conductor system. If this is not possible then additional equipment will have to beincorporated in the design such as corona rings and stress relieving cones mounted in the areas of high electric stress. The smallest radii required for prevention of corona can becalculated from the formula:

where E = r.m.s. voltage to neutral, kV

r = conductor radius, mm

d = distance between conductor centres, mm

d = air density factor

m = conductor surface condition factor

The values for the factors m and d are as follows:

m = 1 for a polished conductor surface, 0.98 to 0.93 for roughened or weathered surfaces, and 0.87 to 0.80 for stranded conductors.

d = 1 at 1 bar barometric pressure and 25°C. At other pressures and temperatures the value is found as follows:

where b = barometric pressure, bar

T = temperature, °C

At locations above sea level the normal pressure is reduced by approximately 0.12 bar per 1000 m of altitude.

The voltage Ev at which the corona discharge normally becomes visible is somewhat higher than given by the above formula and can be determined as follows:

In bad weather conditions the discharge may appear at a voltage lower than that indicated by the formulae and it is therefore advisable to make an allowance of about 20% as asafety factor.


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7. Jointing of Copper Busbars

Busbar Jointing Methods

Joint Resistance

Bolting Arrangements

Clamps

Welded Joints

Busbar Jointing Methods

It is necessary that a conductor joint shall be mechanically strong and have a relatively low resistance whichmust remain substantially constant throughout the life of the joint.

Efficient joints in copper busbar conductors can be made very simply by bolting, clamping, riveting, solderingor welding, the first two being used extensively, though copper welding is now more generally availablethrough improvements in welding technology.

Welded joints in copper busbars have the advantage that the current carrying capacity is unimpaired, as thejoint is effectively a continuous copper conductor.

Bolted joints are compact, reliable and versatile but have the disadvantage that they necessitate the drillingor punching of holes through the conductors with the bolt holes causing some distortion of the lines of currentflow. This joint type also has a somewhat more uneven contact pressure than one using clamp plates.

Clamped joints are easy to make with the full cross-section being unimpaired. The extra mass at the jointand hence cooling area helps to give a cooler running joint and with a well-designed clamp, gives a very evencontact pressure. The further added advantage is that of easy erection during installation. A disadvantage isthe much higher costs of the clamps and associated fixings.

Riveted joints are efficient if well made, but have the disadvantage that they cannot easily be undone ortightened in service and that they are not so convenient to make from an installation point of view.

Soldered or brazed joints are rarely used for busbars unless they are reinforced with bolts or clamps sinceheating under short-circuit conditions can make them both mechanically and electrically unsound.

Joint Resistance

The resistance of a joint is affected mainly by two factors:

a) Streamline effect or spreading resistance Rs, the diversion of the current flowthrough a joint.

b) The contact resistance or interface resistance of the joint Rj.

The total joint resistance Rj = Rs + Ri.

The above is specifically for a d.c. current. Where a.c. currents are flowing, the changes in resistance due toskin and proximity effects in the joint zone must also be taken into account.

Before considering the effect of the above factors on the efficiency of a joint, it is important to realise thenature of the two contact surfaces. No matter how well a contact surface is polished, the surface is really

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made up of a large number of peaks and troughs which are readily visible under a microscope. When twosurfaces are brought together contact is only made at the peaks, which are subjected to much highercontact pressures than the average joint contact pressure, and hence deform during the jointing process.The actual contact area in the completed joint is much smaller than the total surface area of the joint. It hasbeen shown that in a typical busbar joint surface the effective contact area is confined to the region in whichthe pressure is applied, i.e., near the bolts in the case of a lapped joint.

Streamline effect

The distortion of the lines of current flow at an overlapping joint between two conductors affects theresistance of the joint. This effect must also occur when the current flows from peak to peak from surface tosurface though the overall effect is that through the joint.

In the case of an overlapping joint between two flat copper bars, the streamline effect is dependent only onthe ratio of the length of the overlap to the thickness of the bars and not on the width, provided that thisdimension is the same for both bars. It has been shown both mathematically and experimentally that even ina perfectly made overlapping joint between two relatively thin flat conductors having a uniform contactresistance, the distribution of current over the contact area is not uniform. Practically all of the currentflowing across the contact surfaces is concentrated towards the extremities of the joint and the currentdensity at the ends of the overlapping conductors may be many times that at the centre of the joint.

It is evident from the above that the efficiency of an overlapping joint does not increase as the length of theoverlap increases and that from a purely electrical point of view no advantage is to be gained by employingan unduly long overlap.

The relation between the resistance due to streamline effect of an overlapping joint between two flat copperconductors and the ratio of the length of the overlap to the thickness is shown in Figure 15. It has also beenfound that the distortion effect in a T-joint is about the same as a straight joint.

The resistance ratio e in Figure 15 is the ratio of the resistance of a joint due to streamline effect RS, to theresistance of an equal length of single conductor Rb, i.e.

where a = breadth of bar, mm

b = thickness of bar, mm

l = length of overlap, mm

r = resistivity of the conductor, mW mm

From the graph it can be seen then that the effect falls very rapidly for ratios up to two and then very muchmore slowly for values up to seven. This means that in most cases the streamline effect has very little effectas the overlap is of necessity much greater than seven.

Figure 15 Streamline effect in overlapping joints


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Contact resistance

The contact interface between the two faces of a busbar joint consists of a large number of separate pointcontacts, the area of which increases as more pressure is applied and the peaks are crushed.

There are two main factors which therefore affect the actual interface resistance of the surfaces.

a) The condition of the surfaces.

b) The total applied pressure.

The type of coating applied to the contact surfaces to prevent or delay the onset of oxidation when operatingat elevated temperatures or in a hostile environment is also important, particularly in the long term.

Condition of contact surfaces

The condition of the contact surfaces of a joint has an important bearing on its efficiency. The surfaces of thecopper should be flat and clean but need not be polished. Machining is not usually required. Perfectly flatjoint faces are not necessary since very good results can in most cases be obtained merely by ensuring thatthe joint is tight and clean. This is particularly the case where extruded copper bars are used. Where castcopper bars are used, however, machining may be necessary if the joints are to obtain a sufficiently flatcontact surface.

Oxides, sulphides and other surface contaminants have, of course, a higher resistance than the base metal.Copper, like all other common metals, readily develops a very thin surface oxide film even at ordinarytemperatures when freely exposed to air, although aluminium oxidises much more rapidly, and its oxide has a


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much higher resistivity.

The negative temperature coefficient of resistance of copper oxide means that the joint conductivity tends toincrease with temperature. This does not, of course, mean that a joint can be made without cleaning justprior to jointing to ensure that the oxide layer is thin enough to be easily broken as the contact surface peaksdeform when the contact pressure is applied.

Preparation of surfaces

Contact surfaces should be flattened by machining if necessary and thoroughly cleaned. A ground orsand-roughened surface is preferable to a smooth one.

It is important to prevent the re-oxidation of the joint in service and it is therefore recommended that thecontact faces should be covered with a thin layer of petroleum jelly immediately after cleaning the contactsurfaces. The joint surfaces should then be bolted together, the excess petroleum jelly being pressed out asthe contact pressure is applied. The remaining jelly will help to protect the joint from deterioration.

It should be noted that in cases where joints have to perform reliably in higher than normal ambienttemperature conditions, it may be advisable to use a high melting point jelly to prevent it from flowing out ofthe joint, leaving it liable to attack by oxidation and the environment.

The following sections describe the use of coatings on conductor contact surfaces. It should be noted thatrecent tests carried out to investigate the performance of bolted joints under cyclic heating with widetemperature variations indicate that joints without coatings give the most reliable long-term performance(Jackson 1982). The reason for this is that most coatings are of soft materials which when subjected tocontinuous pressures and raised temperatures tend to flow. This has the effect of reducing the number ofhigh pressure contact points formed when the joint is newly bolted together.

Tinning. The tinning of the contact surfaces of a bolted or clamped joint with pure tin or a lead-tin alloy isnormally unnecessary, although advantages can be gained in certain circumstances.

If the joint faces are very rough, tinning may result in some improvement in efficiency. In most cases,however, its chief virtue lies in the fact that it tends to prevent oxidation and hence subsequent jointdeterioration. It may therefore be recommended in cases where the joints operate at unusually hightemperatures or current densities or when subjected to corrosive atmospheres.

For the best results the surfaces should be tinned or re-tinned immediately prior to the final joint clamping. Itshould be noted that both the electrical conductivity and the oxidation protective action decrease as the leadcontent of the solder increases. Lead also has the effect of reducing the surface hardness of the coating anda high lead content in the tinning material should be avoided as this can cause the plating to creep once thejoint is bolted together resulting in premature failure due to overheating.

Silver or nickel plating. This type of plating is being used increasingly, particularly where equipment ismanufactured to American standards which require plated joints for high temperature operation. Nickel-plating provides a harder surface than silver and may therefore be preferable. These platings are expensiveto apply and must be protected prior to the final jointing process as they are always very thin coatings andcan therefore be easily damaged. There is also some doubt as to the stability of these joints underprolonged high temperature cycling. Very high contact resistances can be developed some time afterjointing. It is therefore suggested that natural metal joints are in most cases preferable.

Effect of pressure on contact resistance

It has been shown above that the contact resistance is dependent more on the total applied pressure thanon the area of contact. If the total applied pressure remains constant and the contact area is varied, as isthe case in a switch blade moving between spring loaded contacts, the total contact resistance remainspractically constant. This can be expressed by an equation of the form:


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where Ri = resistance of the contact

p = total contact pressure

n = exponent between 0.4 and 1

C = a constant

The greater the applied total pressure the lower will be the joint resistance and therefore for high efficiencyjoints high pressure is usually necessary. This has the advantage that the high pressure helps to preventdeterioration of the joint. Figure 16 shows the effect of pressure on joint resistance.

Figure 16 The effect of pressure on the contact resistance of a joint between two copperconductors

Joint resistance falls rapidly with increasing pressure, but above a pressure of about 15 N/mm2 there is littlefurther improvement. Certain precautions must be observed to ensure that the contact pressure is not undulyhigh, since it is important that the proof stress of the conductor material or its bolts and clamps is notexceeded.

As a bar heats up under load the contact pressure in a joint made with steel bolts tends to increase becauseof the difference in expansion coefficients between copper and the steel. It is therefore essential that theinitial contact pressure is kept to a such a level that the contact pressure is not excessive when at operatingtemperature. If the elastic limit of the bar is exceeded the joint will have a reduced contact pressure when itreturns to its cold state due to the joint materials having deformed or stretched.

To avoid this, it is helpful to use disc spring washers whose spring rating is chosen to maintain asubstantially constant contact pressure under cold and hot working conditions. This type of joint deteriorationis very much more likely to happen with soft materials, such as E1E aluminium, where the material elasticlimit is low compared with that of high conductivity copper.

Joint efficiency

The efficiency of a joint may be measured in terms of the ratio of the resistance of the portion of theconductor comprising the joint and that of an equal length of straight conductor.


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The resistance of a joint, as already mentioned, is made up of two parts, one due to the distortion of lines ofcurrent flow and the other to contact resistance. The resistance due to the streamline effect at an overlapjoint is given by:

where for a given joint a, b and l are the width, thickness and overlap length, these all being constant, andcontact resistance of the joint is:

where Y = contact resistance per unit area.

The total joint resistance is:

and the efficiency of the joint is:

The resistance of an equal length of straight conductor is given by:

The resistance ratio e is obtained from Figure 15.

In most cases it is inadvisable to use contact pressures of less than 7 N/mm2, 10 N/mm2 being preferred.The contact pressure chosen is influenced by the size and number of bolts or clamps, the latter giving amore even contact pressure. For the sake of symmetry the length of overlap is often made equal to thewidth of the bar, though with thick and narrow bars the overlap can be increased to improve the overall jointperformance.

Owing to the larger surface area from which heat may be dissipated, efficient joints between single copperconductors usually have a lower temperature rise than the conductors themselves. It is important, in general,to ensure that all joints have a reasonable margin of safety. This is particularly so where multi-conductorsjoin at one joint and/or the conductors are normally running close to the specified maximum temperaturerises.

Bolting Arrangements

In deciding the number, size and distribution of bolts required to produce the necessary contact pressure togive high joint efficiency, both electrical and mechanical considerations have to be taken into account. Themethods used to determine these requirements have been given in previous sections.


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A joint normally decreases in resistance with an increase in the size and number of bolts used. Bolt sizesusually vary from M6 to M20 with between four and six being used in each joint with a preference for fourbolts in narrow conductors and six in large conductors. The torque chosen for each bolt size is dependent onthe bolt material and the maximum operating temperature expected. Because of the strength of copper,deformation of the conductor under the pressure of the joint is not normally a consideration.

Table 9 shows typical bolting arrangements for various busbar sizes. The recommended torque settings areapplicable to high-tensile steel (8.8) or aluminium bronze (CW307G, formerly Cy104) fasteners withunlubricated threads of normal surface finish. In the case of stainless steel bolts, these torque settings maybe used, but the threads must be lubricated prior to use.

In addition to the proof or yield stress of the bolt material and the thread characteristics, the correcttightening torque depends on the differential expansion between the bolt and conductor materials.Galvanised steel bolts are normally used but brass or bronze bolts have been used because theircoefficients of expansion closely match the copper conductor and hence the contact pressure does not varywidely with operating temperature. Copper alloy bolts also have the advantage that the possibility ofdissimilar metal corrosion is avoided. Because these alloys do not have an easily discernible yield stress,however, care has to be taken not to exceed the correct tightening torque.

Because of their non-magnetic properties, copper alloys may also be preferred to mild or high-tensile steelwhere high magnetic fields are expected. Alternatively, a non-magnetic stainless steel may be used. In mostcases however, high-tensile steel is used for its very high yield stress.

Table 9 Typical busbar bolting arrangements (single face overlap)

Bar widthmm

Jointoverlapmm

Joint areamm2

Numberof bolts *

Metricbolt size(coarsethread)

BolttorqueNm

Hole sizemm

Washerdiametermm

Washerthicknessmm

16 32 512 2 M6 7.2 7 14 1.8

20 40 800 2 M6 7.2 7 14 1.8

25 60 1500 2 M8 17 10 21 2.0

30 60 1800 2 M8 17 10 21 2.0

40 70 2800 2 M10 28 11.5 24 2.2

50 70 3500 2 M12 45 14 28 2.7

60 60 3600 4 M10 28 11.5 24 2.2

80 80 6400 4 M12 45 14 28 2.7

100 100 10000 5 M12 45 15 28 2.7

120 120 14400 5 M12 45 15 28 2.7

160 160 25600 6 M16 91 20 28 2.7

200 200 40000 8 M16 91 20 28 2.7

* high-tensile steel or aluminium bronze (CW307G, formerly C104)

Clamps

The choice of clamp material and method of manufacture depends on the a.c. or d.c. current requirements,and on the number of clamps of a given size required. The manufacturing methods used include machiningfrom plate, sand or die casting, or stamping from plate. In the case of low current a.c. (less than 3000 A)and d.c. systems the clamps should be made from a high-strength material compatible with the requiredcontact pressure. They can therefore be made from steel in cast, forged or stamped form. Where a.c.


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currents in excess of 3000 A are concerned, the choice of material is between the low or non-magneticsteels or a brass or bronze. Steel clamps are generally unsuitable because of the hysteresis losses inducedin them.

Welded Joints

The inert gas shielded arc processes, tungsten inert gas (TIG) and metal inert gas (MIG) are the preferredwelding methods for high conductivity coppers and are capable of producing excellent busbar joints. Thewelding data given in Table 10 are provided as a guide to good practice, but the actual welding conditionsthat will give the best results for a particular joint must be determined from experience. Certain physical andmetallurgical properties of copper must, however, be taken account of when welding. The high thermaldiffusivity of copper - four or five times that of mild steel - opposes the formation of an adequate weld poolnecessary for good fusion and deoxidation which can give rise to lack of fusion defects and porosity. Therapid heat sink effect, which is particularly pronounced in thicker sections, must therefore be overcome.Preheating of the copper before welding is necessary for thickness above about 3 mm as indicated in Table10.

As explained in Section 2, the tough pitch grades of copper, CW004A and CW005A (formerly C101 andC102), contain particles of cuprous oxide which are normally in a form which has a minimal effect onelectrical and mechanical properties. Prolonged heating of the copper however, allows the oxide particles todiffuse to grain boundaries where they can seriously affect the properties. This diffusion effect is both timeand temperature dependent and is minimised by performing the welding operation as quickly as possible andby restricting the overall heating of the component as far as possible consistent with adequate fusion and asatisfactory weld profile. This consideration obviously does not apply to oxygen-free coppers which do notcontain the oxide particles.

Table 10 Welding data for HC copper

a) Recommended usage of BS 2901 filler alloys for TIG and MIG welding of high conductivitycopper.

Designation GradeTIG MIG

Argon or Helium Nitrogen Argon or Helium Nitrogen

CW004A Electrolytic toughpitch high conductivity

C7, C21 Notrecommended

C7, C8, C21 Not recommended

CW005A Fire-refined toughpitch high conductivity


C7, C8, C21 Not recommended

CW008A Oxygen-free highconductivity


C7, C21 Not recommended

b) Typical operating data for TIG butt welds in high conductivity copper.

(Direct current; electrode negative; argon and helium shielding)

Shielding gas

Argon Helium

Thickness(mm)

Preheattemperature*(°C)

Electrodediameter(mm)

Filler roddiameter(mm)

Gasnozzlediameter(mm)

Weldcurrent(A)

Gas flow(l/min)

Weldcurrent(A)

Gas flow(l/min)

1.5 None 1.6-2.4 1.6 9.5 80-130 4-6 70-90 6-10

3 None 2.4-3.2 1.6 9.5-12 120-240 4-6 180-220 6-10

6 up to 400 3.2-4.8 3.2 12-18 220-350 6-8 200-240 10-15


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12 400-600 4.8 3.2-4.8 12-18 330-420 8-10 260-280 10-15

>12 500-700 4.8 3.2-4.8 12-18 >400 8-10 280-320 12-20

* May be reduced significantly in helium shielding

c) Typical operating data for MIG butt welds in high conductivity copper.

(1.6 mm diameter filler wire; argon shielding)

Thickness (mm) Preheattemperature (°C)

Welding current(A)

Arc voltage (V) Wire feed rate(m/min)

Gas flow rate(l/min)

6 None 240-320 25-28 6.5-8.0 10-15

12 up to 500 320-380 26-30 5.5-6.5 10-15

18 up to 500 340-400 28-32 5.5-6.5 12-17

24 up to 700 340-420 28-32 5.5-6.5 14-20

>24 up to 700 340-460 28-32 5.5-6.5 14-20

Thermal expansion should be allowed for during welding as this leads to the closing of root gaps as thetemperature of the metal rises. The root gaps indicated in Table 11 should therefore be allowed.

Oxy-acetylene and oxy-propane welding methods can be used with oxygen-free copper but they are notrecommended for welding tough pitch coppers as the reducing atmosphere produced in the flame can reactwith the cuprous oxide particles to produce steam inside the metal. This gives rise to porosity and is knownas 'hydrogen embrittlement'.

Further details of the factors involved in the welding of copper can be found in the CDA publication No 98.

Table 11 Recommended edge preparations for TIG and MIG butt-welds.


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8. Mechanical Strength Requirements

All busbar systems have to be designed to withstand the mechanical forces to which they may be subjected,whether these be due to their own weight, wind and ice loads, or short-circuit forces. This force becomesmore onerous with increasing voltage and decreasing current due to respectively longer insulators andsmaller conductors.

The conductor itself should have sufficient material strength under all operational conditions. It must be ableto support itself without undue deflection under normal working conditions, and not suffer permanent damageunder abnormal conditions. The following section enables the mechanical strength requirement of aconductor to be calculated using the short-circuit forces obtained from the formulae given previously.

Deflection

Natural Frequency

Wind and Ice Loadings

Maximum Permissible Stress

Thermal Expansion

Deflection

The maximum deflection of a beam carrying a uniformly distributed load and freely supported at each end isgiven by the formula:

where D = maximum deflection, mm

w= weight per unit length of loaded beam, N/mm

L = beam length between supports, mm

E = modulus of elasticity (124 x 103N/mm2)

I = moment of inertia of beam section, mm

If one end of a beam is rigidly fixed in a horizontal position the deflection is 0.415 times that given by theabove formula and it follows that if a freely supported beam is also supported at its mid-point then itsmaximum deflection is reduced to 0.025 of its former value. If both ends of a beam are rigidly fixed in ahorizontal position the deflection is 0.2 times that given by the above formula.

Thus with a continuous beam freely supported at four or more points the maximum deflection in the centrespans may be assumed to be 0.2 times that given by the formula, while the deflection in the end spans is0.415 times. The deflection in the end spans, therefore, may be assumed to be twice that in the centrespans, assuming equal span distances.

Moments of inertia

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In the above formula the moment of inertia I for the section of the beam has to be calculated about theneutral axis which runs parallel to the beam where the beam has zero tensile forces. In most cases this isthe same axis of the centre of cross-section.

For a rectangular section of depth D and breadth B

For a circular section of diameter D

For a tubular section of internal diameter d and external diameter D

It should be noted that the value of I for a given cross-section is dependent on the direction in which eachindividual force is applied. Moments of inertia for a range of copper rods, bars, sections and tubes are givenin Tables 12 – 16 (Appendix 2).

Natural Frequency

The natural frequency of a beam simply supported at its end is

and for a beam with both ends fixed horizontally it is

where fn = natural frequency, Hz

D = deflection, mm

As the deflection with fixed ends is 0.2 times the value with freely supported ends it follows that the naturalfrequency is increased by 2.275 times by end-fixing; fixing one end only increases the natural frequency byabout 50%. Where equipment is to be mounted outside, natural frequencies of less than 2.75 Hz should beavoided to prevent vibration due to wind eddies.

Wind and Ice Loadings

In considering the loading of a conductor for outdoor service not only must the weight of the conductor itselfbe taken into account but also the weight of a coating of ice which it may carry, together with the windpressure on the ice loaded conductor.

The maximum thickness of the ice and the maximum wind speed are normally specified by the purchaser ofthe busbars but where these are not specified they are usually available from national standards bodies


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within the country where the equipment is to be installed.

The wind and ice loading can be calculated using the following formulae:

Wind loading:

Ww = p(D+2t) x 105

Ice loading:

where ww = wind loading, N/m

wi = ice loading, N/m

p = wind pressure, N/mm2

D = diameter, mm

t = ice thickness, mm

It is assumed that the wind load is at right angles to the vertical load of the conductor weight, and that its iceload and hence the resultant load on the conductor has to be added vertically. The resultant load is given by:

where R = resultant load, N/m

w = conductor weight per unit length, N/m

and where R acts at an angle q° to the vertical given by the formula

The vertical sag or deflection in the conductor span is given by

where Di is the sag in mm in a plane inclined at an angle q to the vertical.

Maximum Permissible Stress

The maximum permissible stress in a conductor is the resultant of its own natural weight (w) and theadditional forces of wind (ww) and ice (wi) loadings (see above) and the magnetic forces resulting from ashort circuit. It should be noted that the direction of a short-circuit force (Ws) depends on the position ofadjacent phases and the direction of the currents in them.

In a general case the following method should be used for calculating the resultant force and its direction:


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and

The maximum skin stress in the conductor can then be calculated using the following formula:

where f = maximum skin stress, N/mm2

M = maximum bending moment, N mm

Z = section modulus, mm3

For a single beam of length L (mm) uniformly loaded and freely supported at both ends or freely supportedat one end and fixed at the other,

where W = load, N/mm

L = span, mm

For a circular section of external diameter D or for a rectangular section of depth D,


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where I = moment of inertia, mm

D = diameter, mm

Then the maximum stress

The maximum permissible stress is dependent on the conductor material, temper, etc., but must not exceedthe material proof stress or permanent deformation will occur. For a conductor manufactured from harddrawn copper the value is approximately 245 N/mm2.

For a beam which is horizontally fixed at both ends the bending moment at the centre is reduced to one thirdand that at its ends to two-thirds of those for a simple supported beam.

Thermal Expansion

If the changes in length that occur in a conductor as it expands and contracts with temperature variations arenot allowed for, undue forces will be set up in the conductor support system or in the equipment to which thebusbar is connected.

The coefficient of linear expansion for copper may be taken as 17 x 10–6 /°C (for temperatures from ambientup to 200°C) compared with 23 x 10–6 /°C for aluminium. The lower value for copper is of great importancewhen allowing for thermal expansion under both normal and transitory conditions, as up to 25% lessexpansion need be accommodated for a particular length of busbar. If a length of copper bar were to bekept from expanding or contracting, a force of nearly 2 N per mm2 of cross-sectional area would bedeveloped for a temperature change of 1°C.

In most cases the supports expand far less due to much smaller temperature changes and lower thermalexpansion coefficients. It is therefore normal practice to allow for the full expansion using flexible conductorconnections at suitable points.

Types of expansion joints

In the case of short bars it is usually not necessary to make any special provision to accommodateexpansion. There will normally be one or two reasonably flexible bends capable of relieving any unduestresses which may be set up.

Figure 17 Types of expansion joints in copper conductors


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To relieve intermediate supports of stress, clamps which allow the conductor to move freely in thelongitudinal direction should be provided. These clamps must be designed and arranged with care to avoidthe danger of stresses building up at any point at which the bar may become wedged or prevented frommoving freely.

In the case of long straight runs it is advisable that expansion joints should be introduced. The joints may uselaminated thin copper strips or leaves and have the same total current rating as the busbar itself.

As an alternative to laminated flexible joints, copper braid may be used. This type of joint is usually moreexpensive to manufacture but has the advantage that it can accommodate expansion in more than onedirection (in most cases three directions) and also tends to eliminate vibration forces being passed from onepiece of equipment to another. It is important that the ferrule into which the copper braid is clamped is ofsufficient thickness to ensure consistent high conductivity after manufacture and during its service life. Wherehigh resistances develop in the joint after manufacture, overheating and ultimately braid failure due tooxidation of the braid material may result.


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9. Busbar Impedance

VoltDrop

Inductance Formulae

Capacitance Formulae

Geometric Mean Distance Formulae

The busbar reactance is not normally sufficiently large to affect the total reactance of a power system andhence is not included in the calculations when establishing the short-circuit currents and reactive volt dropswithin a power system. The exception to this is when considering certain heavy current industrial applicationssuch as furnaces, welding sets, or roll heating equipment for steel mills. In these cases the reactance maybe required to be known for control purposes, or to obtain busbar arrangements to give minimum orbalanced reactance. This may be important because of its effect on both volt drop and power factor, andhence on the generating plant kVA requirement per kW of load, or on the tariffs payable where the power ispurchased from outside.

The busbar impedance is made up of three components: resistance, inductance and capacitance. The valuesof these components are given an ohmic value which in the case of inductance and capacitance is dependenton the frequency of the system. They are defined as follows:

Resistance:

where Rf = resistance at frequency f (Hz), W

Ro = d.c. resistance


K = proximity ratio

Inductance:

where XL = inductive reactance, W

f = frequency, Hz

L = inductance, H

Capacitance:

where Xc = capacitive reactance, W

f = frequency, Hz

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C = capacitance, F

Impedance:

where X = XL - XC

The value of XC is usually very much smaller than XL, and XL is usually much larger than Rf. The value of X istaken to be positive with the sign of XL - XC to indicate whether the system has a positive or negative powerfactor.

Volt Drop

The volt drop in a busbar system is estimated as follows from the usual formula:

VB = I ZB

where VB = volt drop, V

I = current flowing in the conductor, A

ZB = busbar impedance, W

However, to find the magnitude of the load voltage VL available, the busbar volt drop VB must be subtractedvectorially from the supply voltage VS:

VS = supply voltage, V qL = angle of load, °

VB = busbar volt drop, V fB = angle of busbar, °

VL = load voltage, V RB = busbar resistance, W

I = current, A XB = busbar reactance, W


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The apparent volt drop in the busbar trunking, phase to neutral, is given by:

Multiply by Ö3 for phase to phase volt drop.

The above formula gives a very close approximation as long as the busbar system volt drop remains small incomparison to the system voltage.


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Inductance Formulae

The development of inductance formulae is mathematically complex and is the subject of many electricalengineering papers and books. To enable many of the normal busbar configuration inductances to becalculated for self and mutual inductances, the following formulae have been included.

It should be noted that self inductance LS is the inductance due to a single conductor, assuming that it iseffectively outside the flux range of all other conductors. Mutual inductance M is the inductance resultingfrom the flux from other conductors.

Rectangular strip

Circular section bars

Rectangular strip

Single Conductor

where

Ls = self inductance, mH

Ds = 0.2235 (a + b)

= g.m.d. (geometric mean distance from itself), cm

l = length of busbar, cm

Two Parallel Conductors

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where

M = Mutual inductance, mH

Dm = g.m.d between bars

Obtain Dm from figure 18 or formulae at end of this Section)

l = length of busbar, cm

Go-and-Return Conductors

The inductance L per conductor includes both self and mutual components and therefore becomes equal toLS - M, i.e.,


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where the conductor spacing is small compared with the conductor length, or

where b is small compared with d.

Circular section bars

Single Conductor

Two Parallel Conductors

Go-and-return conductors

As before,

L = Ls - M


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if the conductor spacing is small in comparison with its length and in comparison with d.


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Capacitance Formulae

The capacitance of an a.c. system can be of great importance when designing the protection equipment forthe busbars and associated electrical plant. Capacitances for several configurations of busbars are asfollows, where

permittivity E = E0Er

where

Er = relative permittivity of the material.

Isolated twin line

Line above a conducting earth


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Twin line above a conducting earth


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Isolated three-phase line with transposition

Concentric cylinders


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Geometric Mean Distance Formulae

Rectangular Bars

Ref. Dwight 'Electrical Coils and Conduits' 1946, p. 143

Three Phase conductors


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Ref. Dwight ' Geometric Mean Distance for Rectangular Conductors' 1946

Figure 18 - Geometric Mean Distance - two rectangular bars (Apologies for quality of diagrams. Please contact CDA UK if you needbetter quality)

a) Short edges facing

b) Long edges facing


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Figure 18 - Geometric Mean Distance - two rectangular bars (Apologies for quality of diagrams. Please contact CDA UK if you need readable versions)

a) Short edges facing

Back

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Figure 18 - Geometric Mean Distance - two rectangular bars

(b) Long edges facing

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Back

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10. Appendices

Summary of Methods of Busbar Rating

Tables of Properties of HC Copper Conductors

Table 12. Current ratings, moments of inertia andsection moduli - strips and bars

Table 13. a.c. current ratings of laminated bars

Table 14. Current ratings, moments of inertia andsection moduli - tubes

Table 15. Current ratings, moments of inertia andsection moduli - sections

Table 16. Moments of inertia, section moduli andcurrent ratings - rods

Table 17. Comparison of flat bar d.c. currentratings for different ambient and workingtemperatures

Summary of Methods of Busbar Rating

The following examples summarise the rating methods detailed in section 3 and section 4 for typical cases.Unless otherwise stated, a temperature rise of 50°C above an ambient of 40°C and a frequency of 50 Hzhave been assumed. The ratings may be increased by blackening the busbar surfaces. (see Radiation)

Case I d.c., single rectangular-section bar on edge in still air

Case II d.c., single circular-section bar (solid or hollow) in stillair

Case III d.c., laminated bars in still air

Case IV a.c., single rectangular-section bar in still air

Case V a.c., single circular section bar, in still air

Case VI a.c., laminated bars, in still air

Case VII Enclosed busbars

Case VIII Economical use of busbar configurations

Case I d.c., single rectangular-section bar on edge in still air

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Apply formula 4 or read direct from Table 12, for standard sizes.

Example:

Copper bar l00 mm x 6.3 mm (A = 630 mm2, p= 212.6 mm)

I = 7.73 (630)0.5 (212.6)0.39 = 1570 A

(or read direct from Table 12).

Case II d.c., single circular-section bar (solid or hollow) in still air

Apply formula 6 or read direct from Table 16 for standard sizes.

Example:

50 mm diameter copper rod

I = 8.63 (1964)0.5 (157)0.36 = 2360 A

(or read direct from Table 16).

Case III d.c., laminated bars in still air


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a) Apply formula 4, or read direct from Table 12 for one bar.

b) Multiply by appropriate factor from section 3

Example:

4 copper bars 100 mm x 6.3 mm with 6.3 mm spacing.

I = 1570 A per bar.

Multiplying factor for 4 bars = 3.20.

Hence I = 3.2 x 1570 = 5020 A

Case IV a.c., single rectangular-section bar in still air

Divide d.c. rating by appropriate value of

as obtained from Figure 7

Example:

Copper bar 100 mm x 6.3 mm (a/b = 100/6.3 = 16)

d.c. rating = 1579 A (Case I).

Rf/Ro = 1.12 from Figure 7

Ö1.12= 1.058

Hence I = 1570/1.058 = 1480 A

Case V a.c., single circular section bar, in still air


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a) Divide d.c. rating by appropriate value of

as obtained from Figure 4 (solid rods or tubes).

Example:

50 mm diameter copper rod.

d.c. rating = 2360 A (Case II)

Hence Rf/Ro = 1.61, from Figure 4

Hence

Case VI a.c., laminated bars, in still air


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a) Determine rating of one bar as for Case IV.

b) Multiply by appropriate factor, Table 8

Example:

4 copper bars 100 mm x 6.3 mm with 6.3 mm spacing.

d.c. rating per bar = 1570 A (as Case I)

a.c. rating per bar = 1480 A (as Case IV).

Multiplying factor for 4 bars = 2.3

Hence I = 2.3 x 1480 = 3404A

Case VII Enclosed busbars

a) Multiply still air rating by appropriate constant (see Enclosed copperconductors) i.e.. by 0.6 to 0.65 for conductor configurations largely dependent onair circulation (e.g., modified hollow square arrangement, Figure 9c), or by 0.7for tubular conductors or closely grouped flat laminations.

b) Multiply by further 0.85 if enclosure of thick magnetic material.


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Example:

4 copper bars 100 mm x 6.3 mm arranged as in Figure 9c, to carry a.c.

d.c. rating, single bar = 1570 A (as in Case I).

a.c. rating, single bar = 1480 A (as in Case IV).

Multiplying factor for 4 laminations (Table 8) = 2.3

Multiplying factor for configuration of Figure 9c, (see Figure 11) = 1.28

Hence still air rating for this configuration = 1480 x 2.3 x 1.28 = 4360 A

Multiplying factor for non-magnetic enclosure (Enclosed copper conductors) = 0.60

Hence enclosed rating = 4360 x 0.6 = 2610 A

Multiplying factor for magnetic enclosure = 0.85

Hence rating in magnetic enclosure =2610 x0.85 = 2220 A

Case VIII Economical use of busbar configurations

Example:

Two channels, each 100 mm high x 45 mm flange width x 8.6 mm thick (A = 1430 mm2 per channel). a.c. 60Hz, 30°C rise on 40°C ambient in still air. From Table 15, rating based on 50°C rise on 40°C ambient. =5550 A

Use re-rating formula (equation 8) to obtain rating for 70°C working temperature and 40°C ambient.

Hence rating under conditions specified = 5550 x 0.756 = 4195 A

Equivalent 4-bar laminated configuration for same cross-sectional area = 118 mm x 6.3 mm per bar (A =743 mm2, p = 249 mm).

Hence d.c., rating per bar for 50°C rise on 40°C ambient. = 1300 A (from equation 4, and application ofappropriate conversion constant as above).

a/b = 118/6.3 = 18.7 (see Figure 7)

= 1.08 (from Figure 7 for 60 Hz).


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Hence a.c. rating per bar = 1300/1.08 = 1190 A

Multiplying factor for 4 laminations = 2.3 (Table 8)

Hence a.c. rating for 4 laminations = 1190 x 2.3 = 2760 A

Thus the double channel arrangement is able to carry more current than laminated bars, in the ratio 1.52:1for this cross-sectional area. This corresponds to the factor given in Figure 11. For larger cross-sectionalareas this factor would be still greater, for smaller sections the increase would be rather less than this, theexact value depends on the ratio of web to flange lengths of the channel used, and on the thickness of weband channel; a rather wide spacing between "go" and "return" conductors is also assumed in Table 15, inorder to approximate to the "equi-inductance line" condition (see Condition for minimum loss).


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Tables of Properties of HC Copper Conductors

Table 12. Current ratings, moments of inertia and section moduli - strips and bars

Approx. d.c.rating (1)

Approx. a.c.(2) rating

Moment of inertia, I Modulus of Section, Z

BusbarSize mm

X-Sectionalarea mm2

Weightkg/m

Approxd.c.resistance20°C mW/m

Stillair(3)A

Freeair(3)A

Stillair A

Freeair A

Edgewisemm4

Flatmm4

Edgewisemm3

Flatmm3

Busbar sizemm

10 x 1.60 16.0 0.143 1077 105 115 105 115 133.3 3.413 26.66 4.266 10 x 1.60

12.5 x 1.60 20.0 0.179 862 125 135 125 135 260.4 4.266 41.66 5.333 12.5 x 1.60

16 x 1.60 25.6 0.229 673 155 170 155 170 546.1 5.461 68.26 6.826 16 x 1.60

20 x 1.60 32.0 0.286 538 185 205 185 205 1066 6.826 106.6 8.533 20 x 1.60

25 x 1.60 40.0 0.357 431 225 250 225 250 2083 8.533 166.6 10.67 25 x 1.60

30 x 1.60 48.0 0.429 359 265 290 265 290 3600 10.24 240.0 12.80 30 x 1.60

10 x 2.00 20.0 0.179 862 115 130 115 130 166.6 6.666 33.32 6.666 10 x 2.00

12.5 x 2.00 25.0 0.223 689 140 155 140 155 325.5 8.333 52.08 8.333 12.5 x 2.00

16 x 2.00 32.0 0.286 538 175 190 175 190 682.6 10.66 85.33 10.66 16 x 2.00

20 x 2.00 40.0 0.357 431 210 230 210 230 1333 13.33 133.3 13.33 20 x 2.00

25 x 2.00 50.0 0.446 344 255 280 255 280 2604 16.66 208.3 16.66 25 x 2.00

30 x 2.00 60.0 0.536 287 295 330 295 330 4500 20.00 300 20.00 30 x 2.00

40 x 2.00 80.0 0.714 215 380 420 380 420 10660 26.66 533 26.66 40 x 2.00

10 x 2.50 25.0 0.223 689 130 145 130 145 208.3 13.02 41.66 10.42 10 x 2.50

12.5 x 2.50 31.25 0.279 557 160 175 160 175 406.9 16.27 65.60 13.02 12.5 x 2.50

16 x 2.50 40.0 0.357 431 195 215 195 215 853.3 20.83 106.70 16.66 16 x 2.50

20 x 2.50 50.0 0.446 344 235 260 235 260 1666 26.04 166.6 20.83 20 x 2.50

25 x 2.50 62.5 0.558 275 285 315 285 315 3255 32.55 260.4 26.04 25 x 2.50

30 x 2.50 75.0 0.670 229 330 370 330 370 5625 39.06 375.0 31.25 30 x 2.50

40 x 2.50 100 0.893 172 425 475 425 475 13330 52.08 666.5 41.66 40 x 2.50

50 x 2.50 125 1.115 137 520 575 520 575 26040 65.10 1041 52.08 50 x 2.50

60 x 2.50 150 1.339 114 605 675 605 675 45000 78.13 1500 62.50 60 x 2.50

10 x 2.75 31.5 0.281 547 150 170 150 170 262.5 26.05 52.5 16.54 10 x 2.75

12.5 x 2.75 39.4 0.352 437 180 200 180 200 512.7 32.56 82.03 20.67 12.5 x 2.75

16 x 2.75 50.4 0.450 342 220 245 220 245 1075 41.67 134.4 26.46 16 x 2.75

20 x 3.0 60.0 0.536 287 260 290 260 290 2000 45.00 200.0 30.00 20 x 3.0

25 x 3.0 75 0.670 229 315 350 314 350 3906 56.25 312.4 37.5 25 x 3.0

30 x 3.0 90 0.803 191 365 405 365 405 6750 67.50 450.0 45.0 30 x 3.0

40 x 3.0 120 1.071 143 470 520 470 520 16000 90.00 800.0 60.0 40 x 3.0

50 x 3.0 150 1.339 114 570 635 570 635 31250 112.50 1250 75.0 50 x 3.0

60 x 3.0 180 1.607 95.7 665 740 665 740 54000 135.00 1800 90.0 60 x 3.0

80 x 3.0 240 2.142 71.8 860 955 860 955 128 x 103 180.00 3200 120.0 80 x 3.0

10 x 4.0 40 0.357 431 175 195 175 195 333.3 53.33 66.66 26.67 10 x 4.0

12.5 x 4.0 50 0.446 344 210 230 210 230 651.0 66.67 104.2 33.34 12.5 x 4.0

16 x 4.0 64 0.571 269 255 285 255 285 1365 85.33 170.6 42.67 16 x 4.0

20 x 4.0 80 0.714 215 305 340 305 340 2666 106.7 266.6 53.35 20 x 4.0

25 x 4.0 100 0.893 172 365 410 365 410 5208 133.3 416.6 66.65 25 x 4.0

30 x 4.0 120 1.071 143 430 475 430 475 8999 1600 599.6 80.00 30 x 4.0

10.1 Tables of Properties of HC Copper Conductors file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

1 of 2 م 12:47 29/12/2009

40 x 4.0 160 1.428 107 545 610 540 605 21330 213.3 1066.5 106.7 40 x 4.0

50 x 4.0 200 1.785 86.2 665 740 660 735 41660 266.7 1666 133.4 50 x 4.0

60 x 4.0 240 2.142 71.8 775 860 770 855 72000 320.0 2400 160.0 60 x 4.0

80 x 4.0 320 2.856 53.8 995 1120 980 1105 170 x 10E3 426.7 4268 213.4 80 x 4.0

100 x 4.0 400 3.571 43.1 1210 1365 1185 1340 333 x 10E3 533.3 6666 266.7 100 x 4.0

10 x 5.0 50 0.446 344 200 225 200 225 416.7 104.2 83.34 41.68 10 x 5.0

12.5 x 5.0 62.5 0.558 275 240 265 240 265 813.4 130.2 130.1 52.08 12.5 x 5.0

16 x 5.0 80 0.714 215 290 325 290 325 1707 166.7 213.4 66.68 16 x 5.0

20 x 5.0 100 0.893 172 345 385 345 385 3333 208 333.3 83.20 20 x 5.0

25 x 5.0 125 1.116 137 415 465 415 465 6560 260.4 520.8 104.2 25 x 5.0

10.1 Tables of Properties of HC Copper Conductors file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

2 of 2 م 12:47 29/12/2009

Table 13. a.c. current ratings of laminated bars

Number and sizeof bars

Total Section Current for stated temperature rise above 20°C ambient

mm mm2 20°C 30°C 40°C 50°C

2 - 20 x 5 200 430 540 640 720

2 - 25 x 5 250 500 640 750 855

2 - 30 x 5 300 590 750 880 1000

3 - 30 x 5 450 800 1020 1200 1360

4 - 30 x 5 600 1030 1300 1530 1740

2 - 40 x 5 400 750 950 1120 1270

3 - 40 x 5 600 1030 1300 1530 1740

4 - 40 x 5 800 1260 1600 1890 2140

2 - 50 x 5 500 880 1120 1320 1500

3 - 50 x 5 750 1200 1520 1790 2030

4 - 50 x 5 1000 1500 1900 2240 2540

2 - 60 x 5 600 1030 1300 1530 1740

3 - 60 x 5 900 1380 1750 2060 2340

4 - 60 x 5 1200 1700 2150 2540 2880

2 - 80 x 5 800 1260 1600 1890 2140

3 - 80 x 5 1200 1700 2150 2540 2880

4 - 80 x 5 1600 2080 2630 3100 3520

2 - 100 x 5 1000 1460 1850 2180 2470

3 - 100 x 5 1500 1990 2520 2970 3370

4 - 100 x 5 2000 2420 3060 3610 4090

4 - 50 x 10 2000 2330 2950 3480 3950

4 - 60 x 10 2400 2580 3260 3850 4360

4 - 80 x 10 3200 2970 3760 4440 5030

3 - 100 x 10 3000 2880 3650 4300 4880

4 - 100 x 10 4000 3240 4100 4840 5480

Notes:

All values are bars arranged on edge and spacing equal to the bar thickness. All bars in free air and paintedblack.

10.2 Table 13. a.c. current ratings of laminated bars file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

1 of 2 م 12:47 29/12/2009

Values for 30°C rise based on test results, values for 20, 40 and 50°C rise based on 30°C rise values andassume temperature rise proportional to 1.75 power of I.

Courtesy of Ottermill Switchgear Ltd.

10.2 Table 13. a.c. current ratings of laminated bars file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

2 of 2 م 12:47 29/12/2009

Table 14. Current ratings, moments of inertia and section moduli - tubes

a. Metric sizes

Outsidediameter WallThick-ness Crosssectionalarea Approxweight Momentofinertiaofsection

Modulusofsection

Approxresistanceperm 20°C

Approx.d.c.currentrating(1)A

mm mm mm2 kg/m mm4 mm3 mW Indoor Outdoor

12 1.0 34.56 0.307 527.0 87.83 502 185 250

12 1.5 49.48 0.440 695.8 116.0 351 220 300

12 2.0 62.83 0.559 816.8 136.1 276 250 340

15 1.0 43.98 0.391 1083 144.4 394 225 300

15 1.5 63.62 0.566 1467 195.6 273 275 360

15 2.0 81.68 0.726 1766 235.5 212 310 400

18 1.0 53.40 0.475 1936 215.1 325 265 350

18 1.5 77.75 0.691 2668 296.4 223 320 420

18 2.0 100.5 0.894 3267 363.0 172 365 480

18 2.5 121.7 1.08 3751 416.8 143 405 530

22 1.0 65.98 0.587 3645 331.4 263 320 410

22 1.5 96.61 0.859 5102 463.8 179 385 500

22 2.0 125.7 1.12 6346 576.9 138 440 570

22 2.5 154.1 1.37 7399 672.7 112 490 630

22 3.0 179.1 1.59 8282 752.9 97.0 525 680

28 1.5 124.9 1.11 11000 785.5 139 480 620

28 2.0 163.4 1.45 13890 991.8 106.3 550 700

28 2.5 200.3 1.78 16440 1157 86.7 605 780

28 3.0 235.6 2.10 18670 1334 73.7 660 850

35 1.5 157.9 1.40 22190 1268 110 585 750

35 2.0 207.4 1.84 28330 1619 83.7 670 850

35 2.5 255.3 2.27 33900 1937 68.0 740 950

35 3.0 301.6 2.68 38940 2225 57.5 805 1030

54 1.5 247.4 2.20 85300 3160 70.2 855 1090

54 2.0 326.7 2.91 110600 4096 53.1 980 1250

54 2.5 404.5 3.60 134400 4978 42.9 1090 1390

54 3.0 480.7 4.27 156800 5808 36.1 1190 1520

76.1 2.0 465.6 4.14 319800 8404 37.3 1330 1690

76.1 2.5 578.1 5.14 392000 10300 30.0 1480 1880

76.1 3.0 689.0 6.13 461000 12110 25.2 1610 2050

76.1 3.5 798.3 7.10 527200 13850 21.7 1740 2210

108 2.5 828.6 7.37 1.153x106 21360 20.9 2010 2550

108 3.0 989.6 8.80 1.365x106 25280 17.5 2190 2790

10.3 Table 14. Current ratings, moments of inertia and section modu... file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

1 of 3 م 12:47 29/12/2009

108 3.5 1149 10.2 1.570x106 29080 15.1 2360 3010

133 3.0 1225 10.9 2.590x106 38940 14.1 2630 3350

133 3.5 1424 12.7 2.987x106 44920 12.1 2830 3610

159 3.0 1470 13.1 4.474x106 56280 11.8 3070 2910

159 3.5 1710 15.2 5.171x106 65040 10.1 3310 4420

b. Sizes based on Imperial dimensions

OutsideDiameter WallThick-ness Approx.sectionalarea Approxweight Momentofinertiax103

Modulusofsectionx103

Approx.resistanceperm 20°C

Approx. d.c.currentrating (1)A

mm mm mm2 kg/m mm4 mm3 mW Indoor Outdoor

12.5 1.22 43.9 0.387 0.738 0.115 400.2 205 285

12.5 2.65 83.9 0.744 1.14 0.178 210.0 285 390

19 1.22 68.4 0.610 2.75 0.286 257.0 300 400

19 2.65 136 0.218 4.74 0.494 129.0 420 560

19 5.1 223 1.984 6.20 0.646 78.73 540 715

25 1.22 92.9 0.819 6.84 0.534 189.2 390 505

25 1.63 118 1.063 8.69 0.679 148.7 440 570

25 2.04 149 1.325 10.3 0.808 118.1 490 640

25 2.65 189 1.684 12.5 0.976 92.95 555 720

25 4.07 272 2.431 16.2 1.26 64.52 665 865

25 6.36 380 3.38 19.3 1.51 45.93 785 1020

32 1.63 154 1.378 17.6 1.10 114.8 540 695

32 3.26 291 2.59 30.2 1.89 60.14 745 955

32 6.36 506 4.51 43.8 2.74 35.00 985 1260

38 1.63 186 1.65 31.3 1.63 94.37 635 838

38 3.26 356 3.178 54.9 2.86 49.43 880 1138

38 7.64 730 6.498 90.7 4.73 24.06 1260 1620

44 1.63 219 1.955 50.6 2.26 80.48 730 935

44 3.26 421 3.74 90.6 4.04 41.77 1020 1300

44 7.64 882 7.84 157 7.01 19.90 1470 1880

50 1.63 250 2.227 76.6 2.99 70.42 820 1050

50 2.04 312 2.775 93.4 3.65 56.42 915 1170

50 4.07 597 5.30 165 6.46 29.52 1270 1620

50 4.87 702 6.25 189 7.39 25.04 1380 1760

50 6.41 892 7.93 227 8.85 19.68 1560 1980

50 10.2 1300 11.5 287 11.2 13.56 1870 2390

64 2.04 392 3.48 187 5.85 44.83 1110 1420

64 4.07 759 6.89 339 10.6 23.18 1550 1980

64 10.2 1700 15.1 632 19.8 10.33 2310 2960


2 of 3 م 12:47 29/12/2009

75 1.63 380 3.40 267 6.95 46.26 1170 1500

75 2.04 472 4.21 328 8.55 37.29 1300 1670

75 2.65 610 5.43 417 10.9 28.87 1490 1900

75 4.07 912 8.13 606 15.8 19.25 1830 2320

75 4.89 1090 9.69 704 18.3 16.18 2000 2530

75 5.40 1200 10.78 761 19.8 14.65 2080 2660

75 10.2 2110 18.7 1190 30.9 8.311 2760 3530

89 2.65 716 6.37 672 15.0 24.60


3 of 3 م 12:47 29/12/2009

Table 15. Current ratings, moments of inertia and section moduli - sections

SINGLE CHANNEL TWO CHANNELS

Heighthmm Widthofflangefmm

Thicknesstmm AreaAmm Approx.weight*kg/m

Momentofinertiax105mm4

Modulusofsectionx105 mm3

Approx.d.c.resistanceat20°C Approxa.c.rating(A)

x-x y-y x-x y-y mW/m Test1

Calculated2

76.2 33.3 4.91 542 4.82 5.06 0.543 0.133 0.0226 31.8 2200 3000

76.2 33.3 5.49 690 6.15 6.30 0.673 0.165 0.0286 24.9 2500 3400

76.2 33.3 7.21 884 7.86 7.78 0.822 0.204 0.0358 19.5 2800 3800

102 44.5 5.08 890 7.92 14.5 1.60 0.286 0.0497 19.4 3200 4400

102 44.5 6.10 1050 9.35 16.9 1.86 0.333 0.0583 16.4 3500 4800

102 44.5 8.59 1430 12.7 22.3 2.42 0.439 0.0780 12.0 4000 5550

127 55.6 6.60 1450 12.9 36.4 4.05 0.573 0.102 11.9 4500 6150

127 55.6 8.61 1850 16.4 45.4 5.02 0.796 0.127 9.35 5000 6850

152 68.3 7.01 1850 16.8 68.9 7.30 0.901 0.147 9.15 5600 7700

152 68.3 9.75 2550 22.7 90.9 10.7 1.19 0.220 6.76 6300 8600

152 68.3 12.5 3180 28.3 111 12.9 1.45 0.270 5.41 6700 9200

178 81.0 8.26 2610 23.2 129 15.9 1.46 0.272 6.59 7000 9650

178 81.0 13.2 4010 35.7 191 23.7 2.18 0.417 4.29 7900 10850

203 81.0 11.9 4280 38.0 272 34.3 2.68 0.513 4.04 8900 12300

228 105 12.7 5140 45.7 413 51.7 3.61 0.688 3.35 10000 13750

89.9 63.5 x63.5

4.76 542 4.81 3.62 0.957 0.0806 0.0533 31.8 2750 3000

108 76.2 x76.2

4.76 671 5.95 6.41 1.71 0.119 0.0583 35.7 3300 3600

108 76.2 x76.2

6.35 910 8.08 8.08 1.92 0.150 0.0637 18.9 3650 4100

126 88.9 x88.9

6.35 1070 9.52 13.3 3.33 0.211 0.0957 16.1 4200 4500

144 102 x102

6.35 1230 10.9 17.5 5.00 0.243 0.128 14.1 4800 5200

162 114 x114

6.35 1390 12.3 29.1 7.33 0.359 0.167 12.4 5400 5850

162 114 x114

7.94 1650 14.7 35.5 9.20 0.439 0.208 10.4 6000 6550

180 127 x127

7.94 1850 16.4 49.2 12.4 0.549 0.251 9.32 6750 7400

216 152 x152

7.94 2260 20.1 86.5 21.6 0.803 0.370 7.61 8000 8700


1 of 2 م 12:47 29/12/2009

* Weights based on 8.89 g/cm3

1. 30°C rise on 40°C ambient

2. 50°C rise on 40°C ambientFor approximate values for ambients below or above 40°C decrease or increase rating by 0.25% per °C.Increase ratings by 20% if painted matt black.


2 of 2 م 12:47 29/12/2009

Table 16. Moments of inertia, section moduli and current ratings - rods

Diameter Sectionalarea

Weight Moment of inertiax 103

Section modulusx 103

Approx resistance per m

at 20°C

Approx. d.c. current capacity (1)

Approx. a.c.current rating (1)

mm mm2 g/m mm4 mm3 mW A A

6 28.27 251.9 0.0636 0.0212 609.7 130 130

8 50.27 447.9 0.2011 0.0503 343.0 195 195

10 78.54 699.8 0.4909 0.0982 219.5 265 265

12 113.1 1008 1.018 0.1696 152.4 340 340

15 176.7 1575 2.485 0.3313 97.56 460 460

18 254.5 2267 5.153 0.5726 67.75 590 590

22 380.1 3387 11.50 1.045 45.35 770 770

25 490.9 4374 19.17 1.534 35.12 920 910

28 615.8 5486 30.17 2.155 28.00 1070 1020

35 962.1 8572 73.66 4.209 17.92 1455 1275

42 1385 12344 152.7 7.274 12.44 1860 1550

50 1963 17495 306.8 12.27 8.780 2360 1850

56 2463 21945 482.8 17.24 7.000 2755 2040

63 3117 27775 773.3 24.55 5.531 3230 2270

68 3632 32358 1050 30.87 4.747 3585 2410

75 4418 39363 1553 41.42 3.902 4095 2630

1 50°C temperature rise and 40°C ambient

10.5 Table 16. Moments of inertia, section moduli and current rating... file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

1 of 1 م 12:47 29/12/2009

Table 17. Comparison of flat bar d.c. current ratings for different ambient and working temperatures

a. Ambient temp = 30°C

Calculated from formula 1, section 3

Temp. coeff. of resistance, a, at 30°C = 3.781 x 10–3

Temp. coeff. of resistivity, b, at 30°C = 3.794 x 10–3

Resistivity, r, at 30°C = 1.772mW.cm

Size Temp rise (°C)

mm 10 20 30 40 50 60

12.5 x 2.5 65 95 120 145 160 175

16 x 2.5 80 120 150 175 200 215

20 x 2.5 95 145 180 210 240 260

25 x 2.5 115 175 220 255 290 315

31.5 x 2.5 140 210 265 310 350 385

40 x 2.5 175 260 325 385 430 475

50 x 2.5 210 315 395 465 525 575

63 x 2.5 255 385 485 570 640 705

16 x 4 105 155 195 230 260 285

20 x 4 125 185 235 275 310 340

25 x 4 150 225 280 330 370 410

31.5 x 4 180 270 340 400 450 500

40 x 4 220 335 420 490 555 610

50 x 4 270 405 510 595 670 740

63 x 4 330 495 620 725 820 900

80 x 4 405 605 765 895 1010 1110

100 x 4 490 735 925 1085 1225 1350

25 x 6.3 195 290 365 425 480 530

31.5 x 6.3 235 350 440 515 580 640

40 x 6.3 285 425 535 630 710 780

50 x 6.3 345 515 650 760 855 940

63 x 6.3 420 625 790 925 1040 1145

80 x 6.3 515 770 970 1135 1280 1405

100 x 6.3 620 930 1175 1375 1550 1705

10.6 Table 17. Comparison of flat bar d.c. current ratings for differe... file:///C:/CATALOGS/IEC%20STANDARDS/Pub%2022%20Cop...

1 of 5 م 12:48 29/12/2009

125 x 63 755 1130 1425 1670 1885 2070

160 x 6.3 935 1405 1770 2070 2335 2570

50 x 10 445 665 835 980 1105 1215

63 x 10 535 805 1015 1190 1340 1475

80 x 10 655 985 1240 1455 1640 1800

100 x 10 795 1190 1500 1755 1980 2180

125 x 10 960 1440 1815 2125 2400 2640

160 x 10 1190 1785 2245 2635 2970 3265

200 x 10 1445 2165 2725 3195 3605 3965

250 x 10 1755 2635 3315 3885 4380 4820

100 x 16 1025 1535 1935 2270 2555 2815

125 x 16 1235 1855 2335 2735 3085 3395

160 x 16 1525 2290 2880 3375 3805 4185

200 x 16 1850 2770 3490 4090 4610 5070

250 x 16 2240 3360 4230 4955 5590 6150

315 x 16 2740 4105 5170 6060 6830 7515

b. Ambient temp = 40°C

Calculated from formula 1, Section 3



Resistivity, r, at 40°C = 1.833 mW.cm


mm 10 20 30 40 50 60

12.5 x 2.5 65 95 120 140 160 175

16 x 2.5 80 115 145 175 195 215

20 x 2.5 95 140 180 210 235 260

25 x 2.5 115 170 215 250 285 315

31.5 x 2.5 140 210 260 305 345 380

40 x 2.5 170 255 320 380 425 470

50 x 2.5 205 310 390 460 515 570

63 x 2.5 255 380 480 560 635 695

16 x 4 100 155 190 225 255 280


2 of 5 م 12:48 29/12/2009

20 x 4 120 185 230 270 305 335

25 x 4 145 220 280 325 365 405

31.5 x 4 180 270 335 395 445 490

40 x 4 220 330 415 485 545 600

50 x 4 265 395 500 585 660 730

63 x 4 325 485 610 715 810 890

80 x 4 400 595 750 880 995 1095

100 x 4 485 725 915 1070 1210 1330

25 x 6.3 190 285 360 420 475 525

31.5 x 6.3 230 345 435 510 575 630

40 x 6.3 280 420 530 620 700 770

50 x 6.3 340 505 640 750 845 930

63 x 6.3 410 615 775 910 1030 1130

80 x 6.3 505 755 955 1122 1260 1390

100 x 6.3 610 920 1155 1355 1530 1685

125 x 6.3 745 1115 1405 1645 1855 2045

160 x 6.3 920 1385 1740 2040 2305 2535

50 x 10 435 655 825 965 1090 1200

63 x 10 530 795 1000 1170 1320 1455

80 x 10 645 970 1220 1430 1615 1780

100 x 10 780 1170 1475 1730 1955 2150

125 x 10 945 1420 1790 2095 2365 2605

160 x 10 1170 1755 2215 2595 2930 3225

200 x 10 1420 2135 2685 3150 3555 3915

250 x 10 1730 2595 3265 3830 4320 4755

100 x 16 1010 1515 1905 2235 2520 2775

125 x 16 1220 1825 2300 2700 3045 3350

160 x 16 1500 2255 2840 3330 3755 4130

200 x 16 1820 2730 3435 4030 4545 5005

250 x 16 2205 3310 4165 4885 5510 6070

315 x 16 2695 4045 5095 5975 6740 7415

c. Ambient temp = 50°C

Calculated from formula 1, Section 3


3 of 5 م 12:48 29/12/2009



Resistivity, , at 50°C = 1.888 .cm


mm 10 20 30 40 50 60

12.5 x 2.5 65 95 120 140 155 175

16 x 2.5 75 115 145 170 195 210

20 x 2.5 95 140 175 205 230 255

25 x 2.5 110 170 210 250 280 310

31.5 x 2.5 135 205 260 305 340 375

40 x 2.5 170 250 320 375 420 465

50 x 2.5 205 305 385 455 510 565

63 x 2.5 250 375 470 555 625 690

16 x 4 100 150 190 220 250 275

20 x 4 120 180 230 265 300 330

25 x 4 145 215 275 320 365 400

31.5 x 4 175 265 335 390 440 485

40 x 4 215 325 410 480 540 595

50 x 4 260 390 495 580 655 720

63 x 4 320 480 605 705 800 880

80 x 4 390 590 740 870 980 1080

100 x 4 475 715 900 1060 1185 1315

25 x 6.3 185 280 355 415 470 515

31.5 x 6.3 225 340 430 500 565 625

40 x 6.3 275 415 520 610 690 760

50 x 6.3 335 500 630 740 835 920

63 x 6.3 405 610 765 900 1015 1120

80 x 6.3 500 745 940 1105 1245 1370

100 x 6.3 605 905 1140 1340 1510 1665

125 x 6.3 730 1100 1385 1625 1835 2020

160 x 6.3 910 1365 1720 2015 2275 2505

50 x 10 430 645 815 955 1075 1185

63 x 10 520 780 985 1155 1305 1435

80 x 10 635 955 1205 1415 1595 1755


4 of 5 م 12:48 29/12/2009

100 x 10 770 1155 1455 1710 1930 2125

125 x 10 935 1400 1765 2070 2335 2575

160 x 10 1155 1735 2185 2565 2890 3185

200 x 10 1400 2105 2650 3110 3510 3865

250 x 10 1705 2555 3220 3780 4265 4700

100 x 16 995 1495 1880 2210 2490 2745

125 x 16 1200 1800 2270 2665 3005 3310

160 x 16 1480 2220 2800 3285 3710 4085

200 x 16 1795 2690 3390 3980 4490 4945

250 x 16 2175 3265 4110 4825 5445 5995

315 x 16 2660 3990 5025 5900 6655 7330


5 of 5 م 12:48 29/12/2009

Documents

Pub-22 Copper for Busbars