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Prefaces 1. Design Considerations 2. Copper for Busbar Purposes 3. Current-carrying Capacity of Busbars 4. Alternating Current Effects in Busbars 5. Effect of Busbar Arrangements on Rating 6. Short-Circuit Effects 7. Jointing of Copper Busbars 8. Mechanical Strength Requirements 9. Busbar Impedance 10. Appendices Bibliography COPPER DEVELOPMENT ASSOCATION Publication 22, June 1996 Reprinted January 2001 with some amendments
Preface to 1984 Edition This C.D.A. publication has long been accepted as the standard reference work on busbar design. This revised and updated edition incorporates recent progress in the technology of busbar design as reflected in new standards and engineering practices. All data and formulae have been metricated and the method of presentation facilitates the use of calculators or computers. The many variables to be considered are clearly explained and special attention has been given to determining the most economic loadings in order to maximise current carrying capacity for minimum installation costs and running losses. There is, therefore, a useful comparison of the electrical and mechanical properties of high conductivity copper and aluminium. Extra attention has been given to recommended jointing techniques, both by bolting and welding. Improvements have also been made to the section dealing with skin effects. The information on impedance has been expanded so that power factor variations can now be further predicted. The tables of ratings and properties have been expanded as have the examples of typical calculations. The references have been updated 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, Chief Metallurgist, 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 E G Wright (Ottermill Switchgear Ltd) and members of the British Non-Ferrous Metals Federation High Conductivity Copper Group. Preface to 1996 Edition
1. Design Considerations
Introduction Types of Busbar Choice of Busbar Material
The word busbar, derived from the Latin word omnibus ('for all'), gives the idea of a universal system of conveyance. In the electrical sense, the term bus is used to describe a junction of circuits, usually in the form of a small number of inputs and many outputs. 'Busbar' describes the form the bus system usually takes, a bar or bars of conducting material. In any electrical circuit some electrical energy is lost as heat which, if not kept within safe limits, may impair the performance of the system. This energy loss, which also represents a financial loss over a period of time, is proportional to the effective resistance of the conductor and the square of the current flowing through it. A low resistance therefore means a low loss; a factor of increasing importance as the magnitude of the current increases. The capacities of modern-day electrical plant and machinery are such that the power handled by their control systems gives rise to very large forces. Busbars, like all the other equipment in the system, have to be able to withstand these forces without damage. It is essential that the materials used in their construction should have the best possible mechanical properties and are designed to operate within the temperature limits laid down 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 have low 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 a comparison of the properties of the two metals shows that in nearly all respects copper is the superior material.
Types of Busbar
Busbars can be sub-divided into the following categories, with individual busbar systems in many cases being constructed from several different types: a) Air insulated with open phase conductors
b) Air insulated with segregating barriers between conductors of different phases. 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) by an 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 a gas 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 1 outlines 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 process systems
Feature 1 2 Voltage drop Temperature rise Generation Normally not important Usually near to maximum allowable. Capitalisation becoming important. Zero to 40 k A a .c . with frequencies of zero to 400 Hz. Usually bolted but high current applications are often fully welded. Joint preparation very important Usually minimum. Somewhat larger if optimisation is required. Industrial Processes Important In many cases low due to optimisation of first cost and running costs. Zero to 200 kA a.c. and d.c.
Current range
Jointing and connections
Usually bolted. Joint preparation very important.
Cross-sectional area
Usually larger than minimum required due to optimisation and voltage drop considerations. Applies. Also other forms of optimisation and capitalisation used Usually low voltage. Individually engineered. Standard products for low current/voltage applications. Usually open. Enclosed or protected by screens when using standard products. Usually similar to running current. Standard products to suit system short circuit. Normally flat but transposition used to improve current distribution on large systems Usually high but many have widely varying loads.
Kelvin's Law
Not applied. Other forms of optimisation are often used. Up to 36 k V. Individually engineered using basic designs and concepts.
Totally enclosed with or without ventilation.
Fault capacity
Usually large. Designed to meet system requirement.
Phase arrangement
Normally 3 phase flat though sometimes trefoil.
Load factor
Usually high. Normally 1.0.
Low when compared with associated plant.
Major consideration in many cases. Particularly when optimisation/capitalisation is used. Limited by low voltage and busbar size. High conductivity.
Effects of failure
Very serious. High energies dissipated into fault. High conductivity.
Copper type
15 Copper shape Usually rectangular. Tubular used for high current force-cooled. Usually large cross section rectangular. Tubular used for some low 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 are copper and aluminium. The table below gives a comparison of some of their properties. It can be seen that for conductivity and strength, high conductivity copper is superior to aluminium. The only disadvantage of copper is its density; for a given current and temperature rise, an aluminium conductor would be lighter, even though its cross-section would be larger. In enclosed systems however, space considerations are of greater importance than weight. Even in open-air systems the weight of the busbars, which are supported at intervals, is not necessarily the decisive factor. Table 2 Typical relative properties of copper and aluminium
Copper(CW004A) Electrical conductivity (annealed) Electrical resistivity (annealed) Temperature coefficient of resistance(annealed) Thermal conductivity at 20°C Coefficient of expansion Tensile strength (annealed) Tensile strength (half–hard) 0.2% proof stress (annealed) 0.2% proof stress (half–hard) Elastic modulus Specific heat Density Melting point 101 Aluminium (1350) 61 Units % IACS
1.72 0.0039
2.83 0.004
µΩ cm /° C
397 17 x 10–6 200 – 250 260 – 300 50 – 55 170 – 200 116 – 130 385 8.91 1083
230 23 x 10–6 50 – 60 85 – 100 20 – 30 60 – 65 70 900 2.70 660
W/mK /° C N/mm2 N/mm2 N/mm2 N/mm2 kN/mm2 J/kg K g/cm3 °C
The electromagnetic stresses set up in the bar are usually more severe than the stress introduced by its weight. In particular, heavy current-carrying equipment necessitates the use of large size conductors, and space considerations may be important. It should be realised that the use of
copper at higher operating temperatures than would be permissible for aluminium allows smaller and lighter copper sections to be used than would be required at lower temperatures. The ability of copper to absorb the heavy electromagnetic and thermal stresses generated by overload conditions also gives a considerable factor of safety. Other factors, such as the cost of frequent supports for the relatively limp aluminium, and the greater cost of insulation of the larger surface area, must be considered when evaluating the materials. From published creep data, it can be seen that high conductivity aluminium exhibits evidence of significant creep at ambient temperature if heavily stressed. At the same stress, a similar rate of creep is only shown by high conductivity copper at a temperature of 150°C, which is above the usual operating temperature of busbars. Table 3 Comparison of creep and fatigue properties of high conductivity copper and aluminium a) Creep properties
Material Testing Temp. °C Min. Creep Rate % per 1000 h 0.022 0.022 0.004 0.029 Stress N/mm2
Al (1080) annealed HC Cu annealed Cu-0.086% Ag 50% c.w. Cu-0.086% Ag 50% c.w.
20 150 130 225
26 * 26 * 138 96.
* Interpolated from fig.3 b) Fatigue properties
Material HC Al annealed half-hard (H8) HC Copper annealed half-hard Fatigue strength N/mm2 20 45 62 115 No. of cycles x 106 50 50 300 300
If much higher stresses or temperatures are to be allowed for, copper containing small amounts (about 0.1%) of silver can be used successfully. The creep resistance and softening resistance of copper-silver alloys increase with increasing silver content. In the conditions in which high conductivity aluminium and copper are used, either annealed (or as-welded) or half-hard, the fatigue strength of copper is approximately double that of aluminium. This gives a useful reserve of strength against failure initiated by mechanical or thermal cycling. The greater hardness of copper compared with aluminium gives it better resistance to mechanical damage both during erection and in service. It is also less likely to develop problems in clamped joints due to cold metal flow under the prolonged application of a high contact pressure. Its higher
modulus of elasticity gives it greater beam stiffness compared with an aluminium conductor of the same dimensions. The temperature variations encountered under service conditions require a certain amount of flexibility to be allowed for in the design. 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, good quality 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 of copper for the busbars to which these parts are connected therefore avoids contacts between dissimilar metals 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 from hot spots or accidental flashovers in service. If arcing occurs, copper busbars are less likely to support the arc than aluminium. Table 4 shows that copper can self-extinguish arcs across smaller separations, and at higher busbar currents. This self-extinguishing behaviour is related to the much larger heat input required to vaporise copper than aluminium. Table 4 Self-extinguishing arcs in copper and aluminium busbars
Copper Minimum busbar spacing, mm Maximum current per busbar, A 50 4500 Aluminium 100 3220
Copper liberates considerably less heat during oxidation than aluminium and is therefore much less likely to sustain combustion in the case of accidental ignition by an arc. The large amounts of heat liberated by the oxidation of aluminium in this event are sufficient to vaporise more metal than was originally oxidised. This vaporised aluminium can itself rapidly oxidise, thus sustaining the reaction. The excess heat generated in this way heats nearby materials, including the busbar itself, the air and any supporting fixtures. As the busbar and air temperatures rise, the rates of the vaporisation and oxidation increase, so accelerating the whole process. As the air temperature is increased, the air expands and propels hot oxide particles. The busbar may 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 are obviated by the use of copper busbars. Finally, copper is an economical conductor material. It gives long and reliable service at minimum maintenance costs, and when an installation is eventually replaced the copper will have a high recovery value. Because of its many advantages, copper is still used worldwide as an electrical conductor material despite attempts at substitution.
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. In the United Kingdom this takes the form of an alloy designation number which is used in all British Standards relevant 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. The European Standards relevant to electrical applications are expected to supersede the British Standards in due course. The current standards most relevant to busbar applications are BS 1432, BS 1433 and BS 1977 which specify that 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 European material designations along with International Standards Organisation (ISO) and old British Standard designations. Table 5 EN, BS and ISO designations for refinery shapes and wrought coppers
Designation Description Electrolytic tough pitch highconductivity copper Fire- refined tough pitch highconductivity copper Oxygen-free high-conductivity copper ISO cast and wrought Cu-ETP European Designation CW004A Former UK Designations C101
Copper to be used for electrical purposes is of high purity because impurities in copper, together with the changes 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 element present. For example, the presence of only 0.04% phosphorus reduces the conductivity of high conductivity copper to around 80% IACS. (The approximate effect on conductivity of various impurity elements is shown in Figure 1). The level of total impurities, including oxygen, should therefore be less than 0.1% and copper of this type is known as high conductivity (HC) copper. Microscopic and analytical controls are applied to ensure a consistent product and in the annealed condition conductivities over 100% IACS are usual. This figure corresponds to the standard resistivity of 0.017241 µΩm 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, deliberate addition of oxygen which scavenges impurities from the metal. It is present in the form of fine, well-distributed cuprous oxide particles only visible by microscopic examination of a polished section of the metal. Typical oxygen contents of these coppers fall in the range 0.020.05%. Between these limits the presence of the oxygen 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 reducing atmosphere, as can happen during welding or brazing. This is a result of the reaction of the cuprous oxide particles with
hydrogen and is known as 'hydrogen embrittlement'. Provided a reducing atmosphere is avoided, 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 is necessary to use a different (and more expensive) grade of high conductivity copper which is specially produced for this purpose. This type of copper, known as 'oxygen-free high conductivity copper', is normally produced by melting and casting under a protective atmosphere. To obtain the high conductivity required it is necessary to select the best raw materials. The result is a high purity product containing 99.95% copper. This enables 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 modern casting technology is leading to a decline in wirebar production. The cast shape is hotworked by rolling or extrusion to produce a form suitable for further processing by cold work into its final wrought form, either by rolling 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 and disperses the cuprous oxide to give a uniform distribution of oxide particles throughout a new network of fine grains. In the case of oxygen-free HC copper, the hot working operation breaks up the coarse grains into a new network of fine grains.
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 the bar 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 as maximum ambient temperatures. BS 159 stipulates a maximum temperature rise of 50°C above a 24 hour mean ambient temperature of up to 35°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, provided that silver-plated (or acceptable alternative) bolted terminations are used. If not, a temperature rise of 30°C is allowed. These upper temperature limits have been chosen because at higher maximum operating temperatures the rate of surface oxidation in air of conductor materials increases rapidly and may give rise in the long term to excessive local heating at joints and contacts. This temperature limit is much more important for aluminium than copper because it oxidises very much more readily than copper. In practise these limitations on temperature rise may be relaxed for copper busbars if suitable insulation materials are used. A nominal rise of 60°C or more above an ambient of 40°C is allowed by BS EN 60439-1:1994 provided that suitable precautions are taken. BS EN 604391:1994 (equivalent to IEC 439) states that the temperature rise of busbars and conductors is limited by the mechanical strength of the busbar material, the effect on adjacent equipment, the permissible temperature rise of insulating materials in contact with the bars, and the effect on apparatus 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 given to the capitalised cost of the heat generated by the effective ohmic resistance and current (I2R) which leads to an optimised design using Kelvin's Law of Maximum Economy. This law states that 'the cost of lost energy plus that of interest and amortisation on initial cost of the busbars (less allowance for scrap) should not be allowed to exceed a minimum value'. Where the interest, amortisation and scrap values are not known, an alternative 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 a current density of 2 A/mm2 (1250 A/in2) in still air. This method should only be used to estimate a likely size of busbar, the final size being chosen after consideration has been given to the calculation methods and experimental 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 balance between the rate at which heat is produced in the bar, and the rate at which heat is lost from the bar. 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 busbar system. Conduction can only be used where a known amount of heat can flow into a heat sink outside the busbar system or where adjacent parts of the system have differing cooling capacities. The proportion of heat loss by convection and radiation is dependent on the conductor size with the portion attributable to convection 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 its temperature rise. This value is usually calculated for still air conditions but can be increased greatly if forced air cooling is permissible. Where outdoor busbar systems are concerned calculations should always be treated 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 θ = 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:
It can be seen when diagrams (a) and (b) are compared and assuming a similar cross-sectional area the heat loss from arrangement (b) is much larger, provided the gap between the laminations is not less than the thickness 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 of the temperatures of the body and its surroundings, and is proportional to the relative emissivity between the body and its surroundings.
The following table lists typical absolute emissivities ε for copper busbars in various conditions. Changes in emissivity give rise to changes in current ratings, as shown in Table 7.
Bright metal 0.1 Partially oxidised 0.30 Heavily oxidised 0.70 Dull non-metallic paint 0.9
Table 7 Percentage increase in current rating when ε is increased from 0.1 to 0.9 - threephase arrangement
Phase centres, mm No. of bars in parallel 1 2 3 4 5 150 23 15 10 9 6 200 23 16 11 9 7 250 25 18 14 12 9
The figures given in Table 7 are approximate values applicable to 80 to 160 mm wide busbars for a 105°C operating temperature and 40°C ambient. The relative emissivity is calculated as follows:
where e = relative emissivity ε1 = absolute emissivity of body 1 ε2 = absolute emissivity of body 2 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., ambient temperature of the surroundings) Radiation is considered to travel in straight lines and leave the body at right angles to its surface. The diagrams 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 I2R watts, where I is the current flowing in the conductor and R its resistance per unit length. The value for the resistance can in the case of d.c. busbar systems be calculated directly from the resistivity of the copper or copper alloy. Where an a.c. busbar system is concerned, the resistance is increased due to the tendency of the current to flow in the outer surface of the conductor. The ratio between the a.c. value of resistance and its 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, Ω/mm S = skin effect ratio also
where Rf = effective a.c. resistance of conductor, Ω (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 round copper busbars carrying a direct current. The equations assume a naturally bright copper finish where emissivity is 0.1 and where ratings can be improved substantially by coating with a matt black or similar surface. The equations are also approximately true for a.c. current provided that the skin effect and proximity ratios stay close to 1.0, as is true for many low current applications. Methods of calculation for other configurations and conditions can be found in subsequent sections. (a) Flat bars on edge:
(1 where I = current, A A = cross-sectional area, mm2 p = perimeter of conductor, mm θ = temperature difference between conductor and the ambient air, °C α = resistance temperature coefficient of copper at the ambient temperature, per °C ρ = resistivity of copper at the ambient temperature, µΩ 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 copper at 20°C is 1.724 µΩcm, 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 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 following formula can be used to find the corresponding new temperature rise or current:
(8 where I1 = current 1, A I2 = current 2, A θ1 = temperature rise for current 1, °C θ2 = temperature rise for current 2, °C T1 = working temperature for current 1, °C T2 = working temperature for current 2, °C α20 = 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 when re-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 a single bar times the number of bars used. This is due to the obstruction to convection and radiation losses from the inner conductors. To facilitate the making of interleaved joints, the spacing between laminated bars is often made equal to the bar thickness. For 6.3 mm thick bars up to 150 mm wide, mounted on edge with 6.3 mm spacings between laminations, the isolated bar d.c. rating may be multiplied by the following factors to obtain the total rating.
No. of laminations Multiplying factor
No. of laminations 2 3 4 5 6 8 10
Multiplying factor 1.8 2.5 3.2 3.9 4.4 5.5 6.5
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 flux created by an alternating current interacts with the conductor, generating a back e.m.f. which tends to reduce the current in the conductor. The centre portions of the conductor are affected by the greatest number of lines of force, the number of line linkages decreasing as the edges are approached. The electromotive force produced in 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 parts of the conductor in which the opposing e.m.f. is a minimum; that is, into the skin of a circular conductor or the edges of a flat strip, producing what is known as 'skin' or 'edge' effect. The resulting non-uniform current density has 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 S = skin effect ratio The magnitude and importance of the effect increases with the frequency, and the size, shape and thickness of conductor, 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 lower than expected a.c. resistance at elevated temperatures. This effect is more marked for a copper conductor than an aluminium conductor of equal cross-sectional area because of its lower resistivity. The difference is particularly 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 and others (Bulletin of the Bureau of Standards, 1912):
where S = Skin effect ratio
d = diameter of rod, mm f = frequency, Hz ρ = resistivity, µΩ cm µ = permeability of copper (=1) For HC copper at 20°C, ρ = 1.724 µΩ 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 and x where x = 1.207 x 10–2 √(Af) (Note: For values of x less than 2. use inset scale for Rf/Ro)
Copper tubes
Skin effect in tubular copper conductors is a function of the thickness of the wall of the tube and the ratio of that thickness to the tube diameter, and for a given cross sectional area it can be reduced by increasing the tube diameter 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 (Figure 5), it can be seen that to obtain low skin effect ratio values it is desirable to ensure, where possible, low values of t/d and √(f/r). For a given cross-sectional area the skin effect ratio for a thin copper tube is appreciably lower than that for any other form of conductor. Copper tubes, therefore, have a maximum efficiency as conductors of alternating 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 is clearly shown in Figure 5.
Figure 5 Resistance of HC copper tubes, 100 mm outside diameter, d.c. and 50 Hz a.c.
Figure 6 Skin effect for rods and tubes
Flat copper bars The skin effect in flat copper bars is a function of its thickness and width. With the larger sizes of conductor, for a given cross-sectional area of copper, the skin effect in a thin bar or strip is usually less than in a circular copper rod but greater than in a thin tube. It is dependent on the ratio of the width to the thickness of the bar and increases as the thickness of the bar increases. A thin copper strip, therefore, is more efficient than a thick one 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
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
Proximity Effect
n the foregoing consideration of skin effect it has been assumed that the conductor is isolated and at such a distance from the return conductor that the effect of the current in it can be neglected. When conductors are close together, particularly in low voltage equipment, a further distortion of current density results from the interaction 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 flux of 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 one another and tend to force one another apart. This results in a decrease of flux
linkages around the adjacent parts of the conductors and an increase in the more remote parts, which leads to a concentration of current in the adjacent parts where the opposing e.m.f. is a minimum. If the currents in the conductors are in the same direction 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 better distribution of current as in the case of strip conductors arranged with their flat sides towards one another. If the conductors are arranged edgewise to one another the proximity effect increases. In most cases the proximity effect also tends to increase the stresses set up under short-circuit conditions and this may therefore have to be taken into account. The currents in various parts of a conductor subjected to skin and proximity effects may vary considerably in phase, and the resulting circulating current give rise to additional losses which can be minimised only by the choice 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 the spacing and arrangement of the conductors. The graphs in Figure 14 (Section 6) can be used to obtain values of proximity effect for various conductor configurations at 50 or 60 Hz. Methods of calculation for other frequencies are available (Dwight 1946). The unbalancing of current due to the proximity effect can be reduced by spacing the conductors of different phases as far apart as possible and sometimes by modifying their shape in accordance with the spacing adopted. In the case of laminated bars a reduction may be obtained by transposing the 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 one inside the other as is used for isolated phase busbar systems. The magnetic field round busbar conductors may be considerably modified and the current distortion increased by the presence of magnetic materials and only metals such as copper or copper alloys should be used for parts 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 inductance which exist between different 'elements' of current-carrying conductors. The necessary condition for avoidance of both these effects (and hence for minimum loss) is that the shapes of each of the conductors in a single-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 where space is limited and where inductive voltage drop due to busbar reactance must be reduced to a minimum. In the case of heavy current single-phase busbars and where space is slightly less restricted, the single channel arrangement 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 current resistance may be calculated using the earlier sections. It is often necessary to know the depth of penetration of the current into a conductor, that is the depth at which the current density has been reduced to 1/e, or 0.368 of its value at the conductor surface. This can be calculated using the following formula when its resistivity and the frequency are known. depth of penetration
where d = depth of penetration, mm ρ = resistivity of copper, µΩ cm f = frequency, Hz
5. Effect of Busbar Arrangements on Rating
Laminated copper bars Channel and angle bars
Inter-leaving of conductors
Comparison of conductor arrangements
Transposition of conductors Enclosed copper conductors Hollow square arrangement Tubular bars Concentric 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 factors being: 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 the natural movements of air currents. c) An approximately uniform current density in all parts of the conductors. This is normally obtained by having as much copper as possible equidistant from the magnetic 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, as well as copper extrusions of various cross-sections. Figure 9 Busbar arrangements
Laminated copper bars
To obtain the best and most efficient rating for rectangular strip copper conductors they should be mounted whenever 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 the most 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 the expected relative ratings are given in Table 8 below for a 50 Hz system. The ratings for single bars can be estimated 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 test measurements.
For all normal light and medium current purposes an arrangement such as that in Figure 9a is entirely satisfactory, but for a.c. currents in excess of 3000 A where large numbers of laminations would be required it 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. 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 each lamination, the outer laminations carrying approximately four times the current in those at the centre. The two 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 their numerical sum may be greater than their vectorial sum, which is equal to the line current. These circulating currents give rise to additional losses and lower efficiency of the system. It should also be noted that the curve 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 following sections, 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, inductive volt drop may become a serious problem with laminated bars arranged as in Figure 9a. The voltage drop for any given size of conductor is proportional to the current and the length of the bars, and increases as the separation between conductors of different phases increases. In the case of laminated bars the inductive volt drop can be reduced by splitting up the bars into an equivalent number of smaller circuits in parallel, with the conductors of different phases interleaved as shown in Figure 9b. This reduces the average spacing between 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 effects may be counteracted by transposing laminations or groups of laminations at intervals. Tappings and other connections make transposition difficult, but it can be worthwhile where long sections of bars are free from tappings. 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 copper should be equidistant from the magnetic centre of a bar, as in the case of a tubular conductor. This can reduce the skin effect to little greater than unity whereas values of 2 or more are possible with other 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 square formation as shown in Figure 9c, though the current arrangement is still not as good as in a tubular conductor. The heat dissipation is also not as good as the same number of bars arranged side by side as in Figure 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 square arrangement, but it does have the advantage that the heat dissipation is much improved. This arrangement can have a current-carrying capacity of up to twice that for bars mounted side by side, or alternatively the total 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 of material is located at a uniform distance from the magnetic centre of the conductor. The skin effect reduces as the diameter increases for a constant wall thickness, with values close to unity possible when the ratio of outside 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 crosssectional area, but when the proximity effects are taken into account the one-piece tube ensures that the whole tube attains 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 air or liquid cooling where heat can be removed from the internal surface of the tubes. Current ratings of several times the natural air cooled value are possible using forced cooling with the largest increases when liquid cooling is employed. A tubular bar also occupies less space than the more usual copper laminated bar and has a further advantage that its strength and rigidity are greater and uniform in all deflection planes. These advantages are, however, somewhat reduced by the difficulty of making joints and connections which are more difficult than those for laminated bars. These problems have now been reduced by the introduction of copper welding and exothermic copper forming methods. Copper tubes are particularly suitable for high current applications, such as arc furnaces, where forced liquid cooling can be used to great advantage. The tube can also be used in isolated phase busbar systems due to the ease with which it can be supported by insulators.
Concentric conductors
This arrangement is not widely used due to difficulties of support but has the advantage of the optimum combination of low reactance and eddy current losses and is well suited to furnace and weld set applications. It should be noted that the isolated phase busbar systems are of this type
with the current in the external enclosure being almost equal to that in the conductor when the continuously bonded three-phase enclosure system is used.
Channel and angle bars
Alternative arrangements to flat or tubular copper bars are the channel and angle bars which can have advantages. 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 connections presents no serious difficulty. The permissible alternating current density in free air for a given temperature rise is usually greater in the case of two angle-shaped conductors (diagram (a)) than in any other arrangement of conductor material.
For low voltage heavy current single-phase bars with narrow phase centres, single copper channels with the webs of the 'go' and 'return' conductors towards one another give an efficient arrangement. The channel sizes can be chosen to reduce the skin and proximity effects to a minimum, give maximum dissipation of heat and have considerable mechanical strength and rigidity. Where high voltage busbars are concerned the phase spacing has to be much larger to give adequate electrical clearances between adjacent phases with best arrangement being with the channel webs furthest apart. For high-capacity generators which are connected to transformers and allied equipment by segregated or non-segregated copper busbars, the double angle arrangement gives the best combination with the copper bar sizes still being readily manufactured. The current ratings of these arrangements are given in Table 15 (Appendix 2). The ratings given are the maximum current ratings which do not take the cost of losses into account and hence are not optimised.
Comparison of conductor arrangements
The extent to which the a.c. current rating for a given temperature rise of a conductor containing a given cross-sectional area of copper depends on the cross-section shape. The approximate relative a.c. ratings for a typical cross-sectional area of 10 000 mm2 are shown in Figure 11. For cross-sectional areas greater than 10 000 mm2 the factors are greater than those shown, and are smaller for smaller cross-sections. In the case of double-channel busbars, the ratio of web-toflange lengths and also the web thickness have a considerable effect on the current carrying capacity. Figure 11 Comparative a.c. ratings of various conductor arrangements each having a cross sectional area of 10,000 mm2 of HC copper
Enclosed copper conductors
In many cases busbars are surrounded by enclosures, normally metallic, which reduce the busbar heat dissipation due to reduction in cooling air flow and radiation losses and therefore give current ratings which may be considerably less than those for free air exposure. Ventilated enclosures, however, provide mechanical 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 and enclosure. The greatest decrease in current rating occurs with bars which depend mainly on free air circulation and less on uniform current distribution such as the modified hollow square arrangement (Figure 9d). In these cases the rating may be reduced to between 60 and 65% when the conductors are enclosed in non-magnetic metal enclosures. In the case of tubular conductors or those of closely grouped flat laminations, which are normally not so well cooled by air circulation, the ratings may be reduced to about 75% of free air ratings for normal temperature rises. Where the busbar system is enclosed in thick magnetic enclosures, such as in metal-clad switchgear, the reduction is approximately a further 15%. The effect of thin sheet-steel enclosures is somewhat less. These additional reductions are due to the heat generated by the alternating magnetic fields through hysteresis and eddy current losses. Besides the derating caused by enclosure conditions, other limitations on maximum working temperature are often present, such as when the outside of enclosures should not exceed a given safety value. These deratings are affected by the electrical clearances involved and the degree of ventilation in the enclosure. The above figures and the curves shown in Figure 12 should only be taken as a rough guide to 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 to appreciable temperature rise due to circulating and eddy current losses when close to the heavy current bars and connections. These losses can be reduced to a minimum by making these parts from high conductivity non-magnetic material such as copper or copper alloy. Figure 12 Comparison of approximate current ratings for busbars in different enclosures
Compound insulated conductors
The current rating of copper immersed in oil or compound depend upon a number of factors which may vary widely with design, and can normally only be confirmed by carrying out temperature rise tests on the complete assembly. The ratings of enclosed bars are nearly always much lower than the free air ratings. The temperature rise is dependent on the rate at which heat is conducted through the insulating media and dissipated from the outside casing by radiation and convection. There is nearly always a closer phase spacing between conductors giving high proximity effects and higher heat losses in the magnetic outer casings and so giving rise to higher temperature rises. Proximity effect is often more important for insulated bars than those in air. Laminated bars have fewer advantages when immersed in oil or compound and circular copper conductors either solid or hollow though are often preferred particularly for high-voltage gear and high current generators, transformers, etc., where more effective cooling such as water cooling can be employed to improve conductor material utilisation and hence 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 voltage busbars. This insulation is usually of the shrink-on P.V.C. type though wrap-on tape is sometimes used. This method is used for voltages up to about 15 kV, though much higher levels can be attained when specialised insulation systems such as epoxy resin or similar based tapes and powders are employed. These systems are particularly useful where high atomic radiation
levels, or high temperatures (up to 130°C) are encountered, although account must be taken of the possibility of halogen gassing from P.V.C. insulations at temperatures around 100°C. Modified P.V.C. materials with improved high-temperature performance are available.
Isolated phase busbars
solated phase busbars consist of a metallic enclosed conductor where each individual phase or pole is surrounded by a separately earthed sheath which is connected at its ends by a full shortcircuit current rated bar. The sheath is intended primarily to prevent interphase short-circuit currents developing. They have the further advantage that the high magnetic fields created by the conductor current are almost completely cancelled by an equal and opposite current induced in the enclosure or sheath with reductions of 95% or better in the external magnetic field being possible. An important result is that the likelihood of steelwork overheating 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 the performance of the busbar system much more complicated and can only be resolved by obtaining a heat balance 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 equipment using much lower voltages and higher voltages are increasingly changing to this system. Examples of such equipment are exciter connections, switchgear interconnections, generator to transformer connections, high voltage switchgear using SF6 (sulphur hexafluoride) gas insulation (this gas having an insulation level many times better than air). The current flowing in the conductor ranges from as little as 1000 A to in excess of 40 kA. To obtain the higher currents forced cooling is used, the most commonly used cooling media being air and water though other cooling gases or liquids can be used. The use of these cooling systems usually creates 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 normal manufacturing 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 the busbar system and also its ability to sustain overload conditions. The busbars are usually manufactured in single-phase units of transportable length and consist of a central conductor usually tubular of round, square or channel cross-section, supported by porcelain or epoxy resin insulators. The insulators are located by the external metallic sheath through which they are normally removed for servicing.
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 these currents 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. To calculate 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 radiation as 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 of copper 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 normally give sufficiently accurate results:
where t = maximum short-circuit time, s A = conductor cross-section area, mm2 I = conductor current, kA θ = conductor temperature rise, K If θ = 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 the mechanical 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 example the 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 its temperature 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 θ = temperature rise, °C θmax = maximum temperature rise, °C e = exponential constant (=2.718) t = time, s τ = time constant, s The time constant can be found using the following formula:
where w = rate of generation of heat at t=0, W
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, θ max.
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 adjacent conductors 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 of their 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 into account 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-circuit conditions 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 high transitory 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 associated steelwork 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 φ ) of the busbar system and its associated connected electrical plant. The value is obtained by 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 the theoretical maximum for this factor is 2√2 or 2.828 where cos φ = 0. These peak values reduce exponentially and after approximately 10 cycles the factor falls to 1.0, i.e., the symmetrical 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 wave becomes 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 are displaced 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°, under short-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 positions of 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 in direction. 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 permanent distortion. 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 be more 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 crosssection each carrying the same current is calculated from the following formula:
where Fmax = force on conductor, N/m 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 as discussed 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 to resonance 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 threephase short-circuit occurs the displacement is maintained. As with all balanced three-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 so therefore 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
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 0 0.07 0.2 0.25 0.3 0.5 0.7 1.0 I, x Irms (symmetrical) 2.828 2.55 2.2 2.1 2 1.7 1.5 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 is relatively 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 the following 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
(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 be used.
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 round conductors. 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 in Figure 14. 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 almost unity 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 of symbols).
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 in Section 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 adjacent conductors. 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, the applied 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 damage the 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 shortcircuit forces causing damage to the conductor, the following can he used to reduce or eliminate 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 shortcircuit 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-circuit current. 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 shortcircuit effect is increased. e) Decrease the conductor flexibility. This method will reduce the effects of vibration due to either a continuous current or a shortcircuit. 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 of different 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 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 considerable burning 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 be incorporated 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 be calculated from the formula:
where E = r.m.s. voltage to neutral, kV r = conductor radius, mm d = distance between conductor centres, mm δ = 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 a safety factor.
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 which must remain substantially constant throughout the life of the joint. Efficient joints in copper busbar conductors can be made very simply by bolting, clamping, riveting, soldering or welding, the first two being used extensively, though copper welding is now more generally available through improvements in welding technology. Welded joints in copper busbars have the advantage that the current carrying capacity is unimpaired, as the joint is effectively a continuous copper conductor. Bolted joints are compact, reliable and versatile but have the disadvantage that they necessitate the drilling or punching of holes through the conductors with the bolt holes causing some distortion of the lines of current flow. 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 joint and hence cooling area helps to give a cooler running joint and with a well-designed clamp, gives a very even contact pressure. The further added advantage is that of easy erection during installation. A disadvantage is the 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 or tightened 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 since heating 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 flow through 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 to skin 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 the nature of the two contact surfaces. No matter how well a contact surface is polished, the surface is really made up of a large number of peaks and troughs which are readily visible under a microscope. When two surfaces are brought together contact is only made at the peaks, which are subjected to much higher contact 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 has been shown that in a typical busbar joint surface the effective contact area is confined to the region in which the 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 the resistance of the joint. This effect must also occur when the current flows from peak to peak from surface to surface 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 on the ratio of the length of the overlap to the thickness of the bars and not on the width, provided that this dimension is the same for both bars. It has been shown both mathematically and experimentally that even in a perfectly made overlapping joint between two relatively thin flat conductors having a uniform contact resistance, the distribution of current over the contact area is not uniform. Practically all of the current flowing across the contact surfaces is concentrated towards the extremities of the joint and the current density 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 the overlap increases and that from a purely electrical point of view no advantage is to be gained by employing an unduly long overlap. The relation between the resistance due to streamline effect of an overlapping joint between two flat copper conductors and the ratio of the length of the overlap to the thickness is shown in Figure 15. It has also been found 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 the resistance 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 ρ = resistivity of the conductor, µΩ mm From the graph it can be seen then that the effect falls very rapidly for ratios up to two and then very much more slowly for values up to seven. This means that in most cases the streamline effect has very little effect as the overlap is of necessity much greater than seven.
Figure 15 Streamline effect in overlapping joints
Contact resistance The contact interface between the two faces of a busbar joint consists of a large number of separate point contacts, 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 operating at 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 the copper should be flat and clean but need not be polished. Machining is not usually required. Perfectly flat joint faces are not necessary since very good results can in most cases be
obtained merely by ensuring that the joint is tight and clean. This is particularly the case where extruded copper bars are used. Where cast copper bars are used, however, machining may be necessary if the joints are to obtain a sufficiently flat contact 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 ordinary temperatures when freely exposed to air, although aluminium oxidises much more rapidly, and its oxide has a much higher resistivity. The negative temperature coefficient of resistance of copper oxide means that the joint conductivity tends to increase with temperature. This does not, of course, mean that a joint can be made without cleaning just prior to jointing to ensure that the oxide layer is thin enough to be easily broken as the contact surface peaks deform when the contact pressure is applied. Preparation of surfaces Contact surfaces should be flattened by machining if necessary and thoroughly cleaned. A ground or sand-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 the contact faces should be covered with a thin layer of petroleum jelly immediately after cleaning the contact surfaces. The joint surfaces should then be bolted together, the excess petroleum jelly being pressed out as the 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 ambient temperature conditions, it may be advisable to use a high melting point jelly to prevent it from flowing out of the 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 that recent tests carried out to investigate the performance of bolted joints under cyclic heating with wide temperature 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 to continuous pressures and raised temperatures tend to flow. This has the effect of reducing the number of high 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 is normally 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 joint deterioration. It may therefore be recommended in cases where the joints operate at unusually high temperatures 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. It should be noted that both the electrical conductivity and the oxidation protective action decrease as the lead content of the solder increases. Lead also has the effect of reducing the surface hardness of the coating and a high lead content in the tinning material should be avoided as this can cause the plating to creep once the joint 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 is manufactured 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 expensive to apply and must be protected prior to the final jointing process as they are always very thin coatings and can therefore be easily damaged. There is also
some doubt as to the stability of these joints under prolonged high temperature cycling. Very high contact resistances can be developed some time after jointing. 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 than on the area of contact. If the total applied pressure remains constant and the contact area is varied, as is the case in a switch blade moving between spring loaded contacts, the total contact resistance remains practically constant. This can be expressed by an equation of the form:
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 efficiency joints high pressure is usually necessary. This has the advantage that the high pressure helps to prevent deterioration 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 copper conductors
Joint resistance falls rapidly with increasing pressure, but above a pressure of about 15 N/mm2 there is little further improvement. Certain precautions must be observed to ensure that the contact pressure is not unduly high, since it is important that the proof stress of the conductor material or its bolts and clamps is not exceeded.
As a bar heats up under load the contact pressure in a joint made with steel bolts tends to increase because of the difference in expansion coefficients between copper and the steel. It is therefore essential that the initial contact pressure is kept to a such a level that the contact pressure is not excessive when at operating temperature. If the elastic limit of the bar is exceeded the joint will have a reduced contact pressure when it returns 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 a substantially constant contact pressure under cold and hot working conditions. This type of joint deterioration is very much more likely to happen with soft materials, such as E1E aluminium, where the material elastic limit 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 the conductor comprising the joint and that of an equal length of straight conductor. The resistance of a joint, as already mentioned, is made up of two parts, one due to the distortion of lines of current flow and the other to contact resistance. The resistance due to the streamline effect at an overlap joint is given by:
where for a given joint a, b and l are the width, thickness and overlap length, these all being constant, and contact 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 a more even contact pressure. For the sake of symmetry the length of overlap is often made equal to the width of the bar, though with thick and narrow bars the overlap can be increased to improve the overall joint performance. Owing to the larger surface area from which heat may be dissipated, efficient joints between single copper conductors 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-conductors join at one joint and/or the conductors are normally running close to the specified maximum temperature rises.
Bolting Arrangements
In deciding the number, size and distribution of bolts required to produce the necessary contact pressure to give high joint efficiency, both electrical and mechanical considerations have to be taken into account. The methods used to determine these requirements have been given in previous sections. A joint normally decreases in resistance with an increase in the size and number of bolts used. Bolt sizes usually vary from M6 to M20 with between four and six being used in each joint with a preference for four bolts in narrow conductors and six in large conductors. The torque chosen for each bolt size is dependent on the 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 are applicable to high-tensile steel (8.8) or aluminium bronze (CW307G, formerly Cy104) fasteners with unlubricated threads of normal surface finish. In the case of stainless steel bolts, these torque settings may be 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 correct tightening 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 their coefficients of expansion closely match the copper conductor and hence the contact pressure does not vary widely with operating temperature. Copper alloy bolts also have the advantage that the possibility of dissimilar 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 hightensile steel where high magnetic fields are expected. Alternatively, a non-magnetic stainless steel may be used. In most cases however, high-tensile steel is used for its very high yield stress. Table 9 Typical busbar bolting arrangements (single face overlap)
Bar width mm Joint overlap mm Joint area mm2 Number of bolts * Metric bolt size (coarse thread) M6 M6 M8 Bolt torque Nm Hole size mm Washer diameter mm Washer thickness mm
16 20 25
32 40 60
512 800 1500
2 2 2
7.2 7.2 17
7 7 10
14 14 21
1.8 1.8 2.0
30 40 50 60 80 100 120 160 200
60 70 70 60 80 100 120 160 200
1800 2800 3500 3600 6400 10000 14400 25600 40000
2 2 2 4 4 5 5 6 8
17 28 45 28 45 45 45 91 91
10 11.5 14 11.5 14 15 15 20 20
21 24 28 24 28 28 28 28 28
2.0 2.2 2.7 2.2 2.7 2.7 2.7 2.7 2.7
* high-tensile steel or aluminium bronze (CW307G, formerly C104)
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 machining from 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 required contact pressure. They can therefore be made from steel in cast, forged or stamped form. Where a.c. currents in excess of 3000 A are concerned, the choice of material is between the low or non-magnetic steels or a brass or bronze. Steel clamps are generally unsuitable because of the hysteresis losses induced in them.
Welded Joints
The inert gas shielded arc processes, tungsten inert gas (TIG) and metal inert gas (MIG) are the preferred welding methods for high conductivity coppers and are capable of producing excellent busbar joints. The welding data given in Table 10 are provided as a guide to good practice, but the actual welding conditions that will give the best results for a particular joint must be determined from experience. Certain physical and metallurgical properties of copper must, however, be taken account of when welding. The high thermal diffusivity of copper - four or five times that of mild steel - opposes the formation of an adequate weld pool necessary for good fusion and deoxidation which can give rise to lack of fusion defects and porosity. The rapid 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 Table 10. As explained in Section 2, the tough pitch grades of copper, CW004A and CW005A (formerly C101 and C102), contain particles of cuprous oxide which are normally in a form which has a minimal effect on electrical and mechanical properties. Prolonged heating of the copper however, allows the oxide particles to diffuse to grain boundaries where they can seriously affect the properties. This diffusion effect is both time and temperature dependent and is minimised by performing the welding operation as quickly as possible and by restricting the overall heating of the component as far as possible consistent with adequate fusion and a satisfactory weld profile. This consideration obviously does not apply to oxygen-free coppers which do not contain 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 conductivity copper.
TIG Designation Grade Argon or Helium CW004A Electrolytic tough pitch high conductivity Fire-refined tough pitch high conductivity Oxygen-free high conductivity C7, C21 Nitrogen Not recommended Argon or Helium C7, C8, C21 Nitrogen Not recommended MIG
Not recommended
Not recommended
Not recommended
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 Thickness (mm) Preheat temperature* (°C) Electrode diameter (mm) Filler rod diameter (mm) Gas nozzle diameter (mm) 9.5 9.5-12 12-18 12-18 12-18 Weld current (A) Gas flow (l/min) Helium Weld current (A) Gas flow (l/min)
1.5 3 6 12 >12
None None up to 400 400-600 500-700
1.6-2.4 2.4-3.2 3.2-4.8 4.8 4.8
1.6 1.6 3.2 3.2-4.8 3.2-4.8
80-130 120-240 220-350 330-420 >400
4-6 4-6 6-8 8-10 8-10
70-90 180-220 200-240 260-280 280-320
6-10 6-10 10-15 10-15 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) Preheat temperature (°C) None up to 500 up to 500 up to 700 Welding current (A) 240-320 320-380 340-400 340-420 Arc voltage (V) Wire feed rate (m/min) 6.5-8.0 5.5-6.5 5.5-6.5 5.5-6.5 Gas flow rate (l/min) 10-15 10-15 12-17 14-20
6 12 18 24
25-28 26-30 28-32 28-32
up to 700
Thermal expansion should be allowed for during welding as this leads to the closing of root gaps as the temperature 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 not recommended for welding tough pitch coppers as the reducing atmosphere produced in the flame can react with the cuprous oxide particles to produce steam inside the metal. This gives rise to porosity and is known as '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.
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 becomes more onerous with increasing voltage and decreasing current due to respectively longer insulators and smaller conductors. The conductor itself should have sufficient material strength under all operational conditions. It must be able to support itself without undue deflection under normal working conditions, and not suffer permanent damage under abnormal conditions. The following section enables the mechanical strength requirement of a conductor 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
The maximum deflection of a beam carrying a uniformly distributed load and freely supported at each end is given by the formula:
where ∆ = 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 the above formula and it follows that if a freely supported beam is also supported at its midpoint then its maximum deflection is reduced to 0.025 of its former value. If both ends of a beam are rigidly fixed in a horizontal 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 centre spans may be assumed to be 0.2 times that given by the formula, while the deflection in the end spans is 0.415 times. The deflection in the end spans, therefore, may be assumed to be twice that in the centre spans, assuming equal span distances.
Moments of inertia In the above formula the moment of inertia I for the section of the beam has to be calculated about the neutral axis which runs parallel to the beam where the beam has zero tensile forces. In most cases this is the 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 each individual force is applied. Moments of inertia for a range of copper rods, bars, sections and tubes are given in 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 ∆ = deflection, mm As the deflection with fixed ends is 0.2 times the value with freely supported ends it follows that the natural frequency is increased by 2.275 times by end-fixing; fixing one end only increases the natural frequency by about 50%. Where equipment is to be mounted outside, natural frequencies of less than 2.75 Hz should be avoided 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 itself be taken into account but also the weight of a coating of ice which it may carry, together with the wind pressure on the ice loaded conductor. The maximum thickness of the ice and the maximum wind speed are normally specified by the purchaser of the busbars but where these are not specified they are usually available from national standards bodies 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 ice load 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 θ° to the vertical given by the formula
The vertical sag or deflection in the conductor span is given by
where ∆i is the sag in mm in a plane inclined at an angle θ to the vertical.
Maximum Permissible Stress
The maximum permissible stress in a conductor is the resultant of its own natural weight (w) and the additional forces of wind (ww) and ice (wi) loadings (see above) and the magnetic forces resulting from a short circuit. It should be noted that the direction of a short-circuit force (Ws) depends on the position of adjacent 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:
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 supported at 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,
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 exceed the material proof stress or permanent deformation will occur. For a conductor manufactured from hard drawn 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 third and 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 are not allowed for, undue forces will be set up in the conductor support system or in the equipment to which the busbar is connected. The coefficient of linear expansion for copper may be taken as 17 x 10–6 /°C (for temperatures from ambient up to 200°C) compared with 23 x 10–6 /°C for aluminium. The lower value for copper is of great importance when allowing for thermal expansion under both normal and transitory conditions, as up to 25% less expansion need be accommodated for a particular length of busbar. If a length of copper bar were to be kept from expanding or contracting, a force of nearly 2 N per mm2 of cross-sectional area would be developed for a temperature change of 1°C. In most cases the supports expand far less due to much smaller temperature changes and lower thermal expansion coefficients. It is therefore normal practice to allow for the full expansion using flexible conductor connections at suitable points. Types of expansion joints
In the case of short bars it is usually not necessary to make any special provision to accommodate expansion. There will normally be one or two reasonably flexible bends capable of relieving any undue stresses which may be set up. Figure 17 Types of expansion joints in copper conductors
To relieve intermediate supports of stress, clamps which allow the conductor to move freely in the longitudinal direction should be provided. These clamps must be designed and arranged with care to avoid the danger of stresses building up at any point at which the bar may become wedged or prevented from moving freely. In the case of long straight runs it is advisable that expansion joints should be introduced. The joints may use laminated 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 more expensive to manufacture but has the advantage that it can accommodate expansion in more than one direction (in most cases three directions) and also tends to eliminate vibration forces being passed from one piece of equipment to another. It is important that the ferrule into which the copper braid is clamped is of sufficient thickness to ensure consistent high conductivity after manufacture and during its service life. Where high resistances develop in the joint after manufacture, overheating and ultimately braid failure due to oxidation of the braid material may result
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 and hence is not included in the calculations when establishing the short-circuit currents and reactive volt drops within a power system. The exception to this is when considering certain heavy current industrial applications such as furnaces, welding sets, or roll heating equipment for steel mills. In these cases the reactance may be required to be known for control purposes, or to obtain busbar arrangements to give minimum or balanced reactance. This may be important because of its effect on both volt drop and power factor, and hence on the generating plant kVA requirement per kW of load, or on the tariffs payable where the power is purchased from outside. The busbar impedance is made up of three components: resistance, inductance and capacitance. The values of these components are given an ohmic value which in the case of inductance and capacitance is dependent on the frequency of the system. They are defined as follows: Resistance:
where Rf = resistance at frequency f (Hz), Ω Ro = d.c. resistance S = skin effect ratio K = proximity ratio Inductance:
where XL = inductive reactance, Ω f = frequency, Hz L = inductance, H Capacitance:
where Xc = capacitive reactance, Ω
f = frequency, Hz 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 is taken to be positive with the sign of XL - XC to indicate whether the system has a positive or negative power factor.
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, Ω However, to find the magnitude of the load voltage VL available, the busbar volt drop VB must be subtracted vectorially from the supply voltage VS:
VS = supply voltage, V θL = angle of load, ° VB = busbar volt drop, V φ
= angle of busbar, °
VL = load voltage, V RB = busbar resistance, W I = current, A XB = busbar reactance, W
The apparent volt drop in the busbar trunking, phase to neutral, is given by:
Multiply by √3 for phase to phase volt drop. The above formula gives a very close approximation as long as the busbar system volt drop remains small in comparison to the system voltage.
10. Appendices
Summary of Methods of Busbar Rating Tables of Properties of HC Copper Conductors Table 12. Current ratings, moments of inertia and section moduli - strips and bars Table 13. a.c. current ratings of laminated bars Table 14. Current ratings, moments of inertia and section moduli - tubes Table 15. Current ratings, moments of inertia and section moduli - sections Table 16. Moments of inertia, section moduli and current ratings - rods Table 17. Comparison of flat bar d.c. current ratings for different ambient and working temperatures
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 Hz have 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 still air 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
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
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 √1.12= 1.058 Hence I = 1570/1.058 = 1480 A
Case V a.c., single circular section bar, in still air
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
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 copper conductors) i.e.. by 0.6 to 0.65 for conductor configurations largely dependent on air circulation (e.g., modified hollow square arrangement, Figure 9c), or by 0.7 for tubular conductors or closely grouped flat laminations. b) Multiply by further 0.85 if enclosure of thick magnetic material. 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. 60 Hz, 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 of appropriate conversion constant as above). a/b = 118/6.3 = 18.7 (see Figure 7) = 1.08 (from Figure 7 for 60 Hz). 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 1.52:1 for this cross-sectional area. This corresponds to the factor given in Figure 11. For larger cross-sectional areas this factor would be still greater, for smaller sections the increase would be rather less than this, the exact value depends on the ratio of web to flange lengths of the channel used, and on the thickness of web and channel; a rather wide spacing between "go" and "return" conductors is also assumed in Table 15, in order to approximate to the "equi-inductance line" condition (see Condition for minimum loss).
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) Busbar Size mm 10 x 1.60 12.5 x 1.60 16 x 1.60 20 x 1.60 25 x 1.60 30 x 1.60 10 x 2.00 12.5 x 2.00 16 x 2.00 20 x 2.00 25 x 2.00 30 x 2.00 40 x 2.00 10 x 2.50 12.5 x 2.50 16 x 2.50 20 x 2.50 25 x 2.50 30 x XSectional area mm2 16.0 Weight kg/m Approx d.c.resistanc e 20°C µΩ/m 1077 Still air (3)A 105 Free air (3)A 115 Approx. a.c. (2) rating Still air A Free air A 115 Moment of inertia, I Modulus of Section, Z Edgewis e mm3 26.66 Flat mm3 Busbar size mm
Edgewis e mm4
Flat mm4
10 x 1.60 12.5 x 1.60 16 x 1.60 20 x 1.60 25 x 1.60 30 x 1.60 10 x 2.00 12.5 x 2.00 16 x 2.00 20 x 2.00 25 x 2.00 30 x 2.00 40 x 2.00 10 x 2.50 12.5 x 2.50 16 x 2.50 20 x 2.50 25 x 2.50 30 x
2.50 40 x 2.50 50 x 2.50 60 x 2.50 10 x 2.75 12.5 x 2.75 16 x 2.75 20 x 3.0 25 x 3.0 30 x 3.0 40 x 3.0 50 x 3.0 60 x 3.0 80 x 3.0 10 x 4.0 12.5 x 4.0 16 x 4.0 20 x 4.0 25 x 4.0 30 x 4.0 40 x 4.0 50 x 4.0 60 x 4.0 100 0.893 172 425 475 425 475 13330 52.08 666.5 41.66
2.50 40 x 2.50 50 x 2.50 60 x 2.50 10 x 2.75 12.5 x 2.75 16 x 2.75 20 x 3.0
25 x 3.0
30 x 3.0
40 x 3.0
50 x 3.0
60 x 3.0
128 x 103
80 x 3.0
10 x 4.0
12.5 x 4.0 16 x 4.0
20 x 4.0
25 x 4.0
30 x 4.0
40 x 4.0
50 x 4.0
60 x 4.0
80 x 4.0 100 x 4.0 10 x 5.0 12.5 x 5.0 16 x 5.0 20 x 5.0 25 x 5.0 30 x 5.0 40 x 5.0 50 x 5.0 60 x 5.0 80 x 5.0 100 x 5.0 10 x 6.3 12.5 x 6.3 16 x 6.3 20 x 6.0 25 x 6.0 30 x 6.0 40 x 6.0 50 x 6.0 60 x 6.0 80 x
170 x 10E3 333 x 10E3 416.7
80 x 4.0
100 x 4.0 10 x 5.0
12.5 x 5.0 16 x 5.0
20 x 5.0
25 x 5.0
30 x 5.0
40 x 5.0
50 x 5.0
60 x 5.0
213 x 10E3 417 x 10E3 525
80 x 5.0
100 x 5.0 10 x 6.3
12.5 x 6.3 16 x 6.3
20 x 6.0
25 x 6.0
30 x 6.0
40 x 6.0
50 x 6.0
108 x 10E3 256
60 x 6.0
80 x 6.0
6.0 100 x 6.0 120 x 6.0 160 x 6.0 20 x 8.0 25 x 8.0 30 x 8.0 40 x 8.0 50 x 8.0 60 x 8.0 80 x 8.0 100 x 8.0 120 x 8.0 160 x 8.0 200 x 8.0 20 x 10 25 x 10 30 x 10 40 x 10 50 x 10 600 5.356 28.7 1490 1680 1480 1670
x10E3 500 x10E3 864 x10E3 2.05 x10E6 5333 1800 10000 600.0 100 x 6.0 120 x 6.0 160 x 6.0 20 x 8.0
25 x 8.0
30 x 8.0
40 x 8.0
50 x 8.0
144 x 10E3 341 x 10E3 667 x 10E3 1.15 x 10E6 2.73 x 10E6 5.33 x 10E6 6670 13020 22500 53330 104 x 10E3 180 x 10E3 427 x 10E3 833 x 10E3 144 x 10E3
60 x 8.0
80 x 8.0
100 x 8.0 120 x 8.0 160 x 8.0 200 x 8.0 20 x 10 25 x 10 30 x 10 40 x 10 50 x l0
200 250 300 400 500
1.785 2.232 2.678 3.571 4.464
86.2 68.9 57.4 43.1 34.4
525 625 720 910 1090
585 695 825 1030 1235
480 580 700 880 1060
535 645 795 995 1200
1667 2083 2500 3333 4167
667 1042 1500 2667 4168
333.4 416.6 500.0 666.6 833.4
60 x 10
60 x 10
80 x 10
80 x 10
100 x 10 120 x 10
100 x 10
120 x 10
160 x 10 200 x 10 250 x 10 25 x 12 30 x 12 40 x 12 50 x 12
341 x 10E3 6.67 x 10E6 13.0 x 10E6 15630 27000 64000 125 x 10E3 216 x 10E3 512 x 10E3 1.00 x 10E6 1.73 x 10E6 4.10 x 10E6 8.00 x 10E6 15.6 x 10E6 20830
160 x 10
200 x 10
104 x 103
250 x 10
300 360 480 600
2.678 3.214 4.285 5.356
57.4 47.8 35.9 28.7
700 805 1010 1210
710 820 1100 1330
640 750 950 1160
650 765 1030 1275
3599 4319 5759 7199
1250 1800 3200 5000
599.8 719.8 959.8 1199
25 x 12 30 x 12 40 x 12 50 x 12
60 x 12
60 x 12
80 x 12
80 x 12
100 x 12 120 x 12 160 x 12 200 x 12 250 x 12 25 x 16
100 x 12
120 x 12
160 x 12
200 x 12
125 x 103
250 x 12
16.7 x 103 24.0 x 103 42.7 x 103 66.7 x 103 96.0 x 103 171 x 103
25 x 16
30 x 16
30 x 16
40 x 16
40 x 16
50 x 16
167 x 10E3 288 x 10E3 683 x 10E3 1.33 x 10E6 2.30 x 10E6 5.46 x 10E6 10.7 x
50 x 16
60 x 16
60 x 16
80 x 16
80 x 16
100 x 16 120 x 16 160 x 16 200 x
267 x 103
100 x 16
384 x 103
120 x 16
683 x 103
160 x 16
1.07 x
200 x 16
16 250 x 16 300 x 16 4000 35.71 4.31 5520 6425 4500 5250
10E6 20.8 x 10E6 36.0 x 10E6 85330
106 1.67 x 106 2.40 x 106 10670 250 x 16
102 x 103
300 x 16
Notes: 1. Ratings apply for single bars on edge operating in a 40°C ambient temperature with 50°C temperature rise. For other ambient and working temperatures apply formula 8, section 3. 2. a.c. ratings are for frequencies up to 60 Hz. 3. 'Free air' conditions assume some air movement other than convection currents, and may be applicable for outside installations. 'Still' and 'free' air conditions both assume no enclosure.
Table 13. a.c. current ratings of laminated bars
Number and size of bars mm 2 - 20 x 5 2 - 25 x 5 2 - 30 x 5 3 - 30 x 5 4 - 30 x 5 2 - 40 x 5 3 - 40 x 5 4 - 40 x 5 2 - 50 x 5 3 - 50 x 5 4 - 50 x 5 2 - 60 x 5 3 - 60 x 5 4 - 60 x 5 2 - 80 x 5 3 - 80 x 5 4 - 80 x 5 2 - 100 x 5 3 - 100 x 5 4 - 100 x 5 4 - 50 x 10 4 - 60 x 10 Total Section Current for stated temperature rise above 20°C ambient
mm2 200 250 300 450 600 400 600 800 500 750 1000 600 900 1200 800 1200 1600 1000 1500 2000 2000 2400
4 - 80 x 10 3 - 100 x 10 4 - 100 x 10
3200 3000 4000
2970 2880 3240
3760 3650 4100
4440 4300 4840
5030 4880 5480
Notes: All values are bars arranged on edge and spacing equal to the bar thickness. All bars in free air and painted black. Values for 30°C rise based on test results, values for 20, 40 and 50°C rise based on 30°C rise values and assume temperature rise proportional to 1.75 power of I. Courtesy of Ottermill Switchgear Ltd.
Table 14. Current ratings, moments of inertia and section moduli - tubes a. Metric sizes
Outsidediameter WallThickness Crosssectionalarea Approxweight Moment ofinertia ofsection mm4 527.0 695.8 816.8 1083 1467 1766 1936 2668 3267 3751 3645 5102 6346 7399 8282 11000 13890 16440 18670 22190 Modulusof section Approxresistanceper m 20°C Approx. d.c.currentrating (1)A Indoor 185 220 250 225 275 310 265 320 365 405 320 385 440 490 525 480 550 605 660 585 Outdoor 250 300 340 300 360 400 350 420 480 530 410 500 570 630 680 620 700 780 850 750
mm 12 12 12 15 15 15 18 18 18 18 22 22 22 22 22 28 28 28 28 35
mm 1.0 1.5 2.0 1.0 1.5 2.0 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 1.5
mm2 34.56 49.48 62.83 43.98 63.62 81.68 53.40 77.75 100.5 121.7 65.98 96.61 125.7 154.1 179.1 124.9 163.4 200.3 235.6 157.9
kg/m 0.307 0.440 0.559 0.391 0.566 0.726 0.475 0.691 0.894 1.08 0.587 0.859 1.12 1.37 1.59 1.11 1.45 1.78 2.10 1.40
mm3 87.83 116.0 136.1 144.4 195.6 235.5 215.1 296.4 363.0 416.8 331.4 463.8 576.9 672.7 752.9 785.5 991.8 1157 1334 1268
µΩ 502 351 276 394 273 212 325 223 172 143 263 179 138 112 97.0 139 106.3 86.7 73.7 110
35 35 35 54 54 54 54 76.1 76.1 76.1 76.1 108 108 108 133 133 159 159
2.0 2.5 3.0 1.5 2.0 2.5 3.0 2.0 2.5 3.0 3.5 2.5 3.0 3.5 3.0 3.5 3.0 3.5
207.4 255.3 301.6 247.4 326.7 404.5 480.7 465.6 578.1 689.0 798.3 828.6 989.6 1149 1225 1424 1470 1710
1.84 2.27 2.68 2.20 2.91 3.60 4.27 4.14 5.14 6.13 7.10 7.37 8.80 10.2 10.9 12.7 13.1 15.2
28330 33900 38940 85300 110600 134400 156800 319800 392000 461000 527200 1.153x106 1.365x106 1.570x106 2.590x106 2.987x106 4.474x106 5.171x106
1619 1937 2225 3160 4096 4978 5808 8404 10300 12110 13850 21360 25280 29080 38940 44920 56280 65040
83.7 68.0 57.5 70.2 53.1 42.9 36.1 37.3 30.0 25.2 21.7 20.9 17.5 15.1 14.1 12.1 11.8 10.1
670 740 805 855 980 1090 1190 1330 1480 1610 1740 2010 2190 2360 2630 2830 3070 3310
850 950 1030 1090 1250 1390 1520 1690 1880 2050 2210 2550 2790 3010 3350 3610 2910 4420
b. Sizes based on Imperial dimensions
OutsideDiameter WallThickness Approx.sectionalarea Approxweight Momentof inertiax 103 mm4 0.738 1.14 2.75 4.74 6.20 6.84 8.69 10.3 Modulusof sectionx 103 mm3 0.115 0.178 0.286 0.494 0.646 0.534 0.679 0.808 Approx.resistanceper m 20°C Approx. d.c. currentrating (1)A
mm 12.5 12.5 19 19 19 25 25 25
mm 1.22 2.65 1.22 2.65 5.1 1.22 1.63 2.04
mm2 43.9 83.9 68.4 136 223 92.9 118 149
kg/m 0.387 0.744 0.610 0.218 1.984 0.819 1.063 1.325
µΩ 400.2 210.0 257.0 129.0 78.73 189.2 148.7 118.1
Indoor 205 285 300 420 540 390 440 490
Outdoor 285 390 400 560 715 505 570 640
25 25 25 32 32 32 38 38 38 44 44 44 50 50 50 50 50 50 64 64 64 75 75 75 75 75 75 75 89 89 89 100
2.65 4.07 6.36 1.63 3.26 6.36 1.63 3.26 7.64 1.63 3.26 7.64 1.63 2.04 4.07 4.87 6.41 10.2 2.04 4.07 10.2 1.63 2.04 2.65 4.07 4.89 5.40 10.2 2.65 5.40 12.7 3.26
189 272 380 154 291 506 186 356 730 219 421 882 250 312 597 702 892 1300 392 759 1700 380 472 610 912 1090 1200 2110 716 1410 3040 1000
1.684 2.431 3.38 1.378 2.59 4.51 1.65 3.178 6.498 1.955 3.74 7.84 2.227 2.775 5.30 6.25 7.93 11.5 3.48 6.89 15.1 3.40 4.21 5.43 8.13 9.69 10.78 18.7 6.37 12.64 27.05 8.93
12.5 16.2 19.3 17.6 30.2 43.8 31.3 54.9 90.7 50.6 90.6 157 76.6 93.4 165 189 227 287 187 339 632 267 328 417 606 704 761 1190 672 1250 2290 1230
0.976 1.26 1.51 1.10 1.89 2.74 1.63 2.86 4.73 2.26 4.04 7.01 2.99 3.65 6.46 7.39 8.85 11.2 5.85 10.6 19.8 6.95 8.55 10.9 15.8 18.3 19.8 30.9 15.0 27.8 51.0 23.9
92.95 64.52 45.93 114.8 60.14 35.00 94.37 49.43 24.06 80.48 41.77 19.90 70.42 56.42 29.52 25.04 19.68 13.56 44.83 23.18 10.33 46.26 37.29 28.87 19.25 16.18 14.65 8.311 24.60 12.47 5.785 17.50
555 665 785 540 745 985 635 880 1260 730 1020 1470 820 915 1270 1380 1560 1870 1110 1550 2310 1170 1300 1490 1830 2000 2080 2760 1700 2400 3500 2100
720 865 1020 695 955 1260 838 1138 1620 935 1300 1880 1050 1170 1620 1760 1980 2390 1420 1980 2960 1500 1670 1900 2320 2530 2660 3530 2170 3050 4470 2680
100 100 115 115 115 127 127 127 140 140 140 150 150 150
6.41 12.7 3.26 6.41 12.7 4.07 7.64 12.7 4.89 8.86 19.1 5.90 10.2 19.1
1910 3550 1130 2170 4050 1570 2860 4560 2065 3630 7220 2710 4540 7980
17.0 31.5 10.1 19.3 36.0 14.0 25.4 40.5 18.4 32.3 64.2 24.1 40.4 71.0
2200 3600 1760 3200 5350 2990 5150 7600 4740 7870 13600 7350 11600 18200
42.9 70.4 30.6 55.5 92.9 46.8 80.5 119 67.3 112 193 95.6 151 238
9.196 4.954 15.53 8.103 4.341 11.15 6.156 3.860 8.518 4.844 2.438 6.484 3.871 2.209
2910 3960 2330 3210 4400 2850 3850 4870 3340 4430 6240 4000 5180 6850
3710 5050 2970 4090 5610 3600 4850 6130 4000 5600 7900 4930 6370 8450
1. Current ratings are for 50°C temperature rise and 40°C ambient
Table 15. Current ratings, moments of inertia and section moduli - sections
SINGLE CHANNEL Width offlange fmm Thicknesstmm AreaAmm Approx.weight *kg/m Moment of inertiax 105 mm4 x-x 33.3 33.3 33.3 44.5 44.5 44.5 55.6 55.6 68.3 68.3 68.3 81.0 81.0 81.0 105 63.5 x 63.5 76.2 x 76.2 76.2 x 76.2 4.91 5.49 7.21 5.08 6.10 8.59 6.60 8.61 7.01 9.75 12.5 8.26 13.2 11.9 12.7 4.76 542 690 884 890 1050 1430 1450 1850 1850 2550 3180 2610 4010 4280 5140 542 4.82 6.15 7.86 7.92 9.35 12.7 12.9 16.4 16.8 22.7 28.3 23.2 35.7 38.0 45.7 4.81 5.06 6.30 7.78 14.5 16.9 22.3 36.4 45.4 68.9 90.9 111 129 191 272 413 3.62 Modulus of sectionx 105 mm3 Approx.d.c.resistanceat20°C Approx a.c. rating(A) TWO CHANNELS
y-y 0.543 0.673 0.822 1.60 1.86 2.42 4.05 5.02 7.30 10.7 12.9 15.9 23.7 34.3 51.7 0.957
x-x 0.133 0.165 0.204 0.286 0.333 0.439 0.573 0.796 0.901 1.19 1.45 1.46 2.18 2.68 3.61 0.0806
y-y 0.0226 0.0286 0.0358 0.0497 0.0583 0.0780 0.102 0.127 0.147 0.220 0.270 0.272 0.417 0.513 0.688 0.0533
µΩ/m 31.8 24.9 19.5 19.4 16.4 12.0 11.9 9.35 9.15 6.76 5.41 6.59 4.29 4.04 3.35 31.8
Test 1 2200 2500 2800 3200 3500 4000 4500 5000 5600 6300 6700 7000 7900 8900 10000 2750
Calculate 3000 3400 3800 4400 4800 5550 6150 6850 7700 8600 9200 9650 10850 12300 13750 3000
88.9 x 88.9 102 x 102 114 x 114 114 x 114 127 x 127 152 x 152
* 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.
Table 16. Moments of inertia, section moduli and current ratings - rods
Sectional area Weight Moment of inertia x 103 mm4 0.0636 0.2011 0.4909 1.018 2.485 5.153 11.50 19.17 30.17 73.66 152.7 306.8 482.8 773.3 1050 1553 Section modulus x 103 Approx resistance per m at 20°C Approx. d.c. current capacity (1) Approx. a.c. current rating (1)
mm 6 8 10 12 15 18 22 25 28 35 42 50 56 63 68 75
mm2 28.27 50.27 78.54 113.1 176.7 254.5 380.1 490.9 615.8 962.1 1385 1963 2463 3117 3632 4418
g/m 251.9 447.9 699.8 1008 1575 2267 3387 4374 5486 8572 12344 17495 21945 27775 32358 39363
mm3 0.0212 0.0503 0.0982 0.1696 0.3313 0.5726 1.045 1.534 2.155 4.209 7.274 12.27 17.24 24.55 30.87 41.42
µΩ 609.7 343.0 219.5 152.4 97.56 67.75 45.35 35.12 28.00 17.92 12.44 8.780 7.000 5.531 4.747 3.902
50°C temperature rise and 40°C ambient
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, ρ, at 30°C = 1.772µΩ.cm
Size mm 12.5 x 2.5 16 x 2.5 20 x 2.5 25 x 2.5 31.5 x 2.5 40 x 2.5 50 x 2.5 63 x 2.5 16 x 4 20 x 4 25 x 4 31.5 x 4 40 x 4 50 x 4 Temp rise (°C) 10 65 80 95 115 140 175 210 255 105 125 150 180 220 270 20 95 120 145 175 210 260 315 385 155 185 225 270 335 405 30 120 150 180 220 265 325 395 485 195 235 280 340 420 510 40 145 175 210 255 310 385 465 570 230 275 330 400 490 595 50 160 200 240 290 350 430 525 640 260 310 370 450 555 670 60 175 215 260 315 385 475 575 705 285 340 410 500 610 740
63 x 4 80 x 4 100 x 4 25 x 6.3 31.5 x 6.3 40 x 6.3 50 x 6.3 63 x 6.3 80 x 6.3 100 x 6.3 125 x 63 160 x 6.3 50 x 10 63 x 10 80 x 10 100 x 10 125 x 10 160 x 10 200 x 10 250 x 10 100 x 16 125 x 16 160 x 16 200 x 16 250 x 16 315 x 16
330 405 490 195 235 285 345 420 515 620 755 935 445 535 655 795 960 1190 1445 1755 1025 1235 1525 1850 2240 2740
495 605 735 290 350 425 515 625 770 930 1130 1405 665 805 985 1190 1440 1785 2165 2635 1535 1855 2290 2770 3360 4105
620 765 925 365 440 535 650 790 970 1175 1425 1770 835 1015 1240 1500 1815 2245 2725 3315 1935 2335 2880 3490 4230 5170
725 895 1085 425 515 630 760 925 1135 1375 1670 2070 980 1190 1455 1755 2125 2635 3195 3885 2270 2735 3375 4090 4955 6060
820 1010 1225 480 580 710 855 1040 1280 1550 1885 2335 1105 1340 1640 1980 2400 2970 3605 4380 2555 3085 3805 4610 5590 6830
900 1110 1350 530 640 780 940 1145 1405 1705 2070 2570 1215 1475 1800 2180 2640 3265 3965 4820 2815 3395 4185 5070 6150 7515
b. Ambient temp = 40°C Calculated from formula 1, Section 3 Temp. coeff. of resistance, a, at 40°C = 3.644 x 10–3 Temp. coeff. of resistivity, b, at 40°C = 3.656 x 10–3
Resistivity, ρ, at 40°C = 1.833 µΩ.cm
Size mm 12.5 x 2.5 16 x 2.5 20 x 2.5 25 x 2.5 31.5 x 2.5 40 x 2.5 50 x 2.5 63 x 2.5 16 x 4 20 x 4 25 x 4 31.5 x 4 40 x 4 50 x 4 63 x 4 80 x 4 100 x 4 25 x 6.3 31.5 x 6.3 40 x 6.3 50 x 6.3 63 x 6.3 80 x 6.3 100 x 6.3 125 x 6.3 160 x 6.3 50 x 10 63 x 10 10 65 80 95 115 140 170 205 255 100 120 145 180 220 265 325 400 485 190 230 280 340 410 505 610 745 920 435 530 20 95 115 140 170 210 255 310 380 155 185 220 270 330 395 485 595 725 285 345 420 505 615 755 920 1115 1385 655 795 30 120 145 180 215 260 320 390 480 190 230 280 335 415 500 610 750 915 360 435 530 640 775 955 1155 1405 1740 825 1000 Temp rise (°C) 40 140 175 210 250 305 380 460 560 225 270 325 395 485 585 715 880 1070 420 510 620 750 910 1122 1355 1645 2040 965 1170 50 160 195 235 285 345 425 515 635 255 305 365 445 545 660 810 995 1210 475 575 700 845 1030 1260 1530 1855 2305 1090 1320 60 175 215 260 315 380 470 570 695 280 335 405 490 600 730 890 1095 1330 525 630 770 930 1130 1390 1685 2045 2535 1200 1455
80 x 10 100 x 10 125 x 10 160 x 10 200 x 10 250 x 10 100 x 16 125 x 16 160 x 16 200 x 16 250 x 16 315 x 16
645 780 945 1170 1420 1730 1010 1220 1500 1820 2205 2695
970 1170 1420 1755 2135 2595 1515 1825 2255 2730 3310 4045
1220 1475 1790 2215 2685 3265 1905 2300 2840 3435 4165 5095
1430 1730 2095 2595 3150 3830 2235 2700 3330 4030 4885 5975
1615 1955 2365 2930 3555 4320 2520 3045 3755 4545 5510 6740
1780 2150 2605 3225 3915 4755 2775 3350 4130 5005 6070 7415
c. Ambient temp = 50°C Calculated from formula 1, Section 3 Temp. coeff. of resistance, a, at 50°C = 3.516 x 10–3 Temp. coeff. of resistivity, b, at 50°C = 3.527 x 10–3 Resistivity, , at 50°C = 1.888 .cm
Size mm 12.5 x 2.5 16 x 2.5 20 x 2.5 25 x 2.5 31.5 x 2.5 40 x 2.5 50 x 2.5 63 x 2.5 16 x 4 20 x 4 10 65 75 95 110 135 170 205 250 100 120 20 95 115 140 170 205 250 305 375 150 180 30 120 145 175 210 260 320 385 470 190 230 Temp rise (°C) 40 140 170 205 250 305 375 455 555 220 265 50 155 195 230 280 340 420 510 625 250 300 60 175 210 255 310 375 465 565 690 275 330
25 x 4 31.5 x 4 40 x 4 50 x 4 63 x 4 80 x 4 100 x 4 25 x 6.3 31.5 x 6.3 40 x 6.3 50 x 6.3 63 x 6.3 80 x 6.3 100 x 6.3 125 x 6.3 160 x 6.3 50 x 10 63 x 10 80 x 10 100 x 10 125 x 10 160 x 10 200 x 10 250 x 10 100 x 16 125 x 16 160 x 16 200 x 16 250 x 16 315 x 16
145 175 215 260 320 390 475 185 225 275 335 405 500 605 730 910 430 520 635 770 935 1155 1400 1705 995 1200 1480 1795 2175 2660
215 265 325 390 480 590 715 280 340 415 500 610 745 905 1100 1365 645 780 955 1155 1400 1735 2105 2555 1495 1800 2220 2690 3265 3990
275 335 410 495 605 740 900 355 430 520 630 765 940 1140 1385 1720 815 985 1205 1455 1765 2185 2650 3220 1880 2270 2800 3390 4110 5025
320 390 480 580 705 870 1060 415 500 610 740 900 1105 1340 1625 2015 955 1155 1415 1710 2070 2565 3110 3780 2210 2665 3285 3980 4825 5900
365 440 540 655 800 980 1185 470 565 690 835 1015 1245 1510 1835 2275 1075 1305 1595 1930 2335 2890 3510 4265 2490 3005 3710 4490 5445 6655
400 485 595 720 880 1080 1315 515 625 760 920 1120 1370 1665 2020 2505 1185 1435 1755 2125 2575 3185 3865 4700 2745 3310 4085 4945 5995 7330
Note that only CDA Publications are available from Copper Development Association. Other reference material is available from the appropriate standards organisation or from a technical library service. National and International Standards Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9
National and International Standards
British and European Standards:
BS 23 Copper and copper-cadmium trolley and contact wire for electric traction. BS 7884 Copper and copper-cadmium stranded conductors for overhead electric traction and power transmission systems. BS 159 Busbar and busbar connections. BS 6931 Glossary of terms for copper and copper alloys. BS 1432 Copper for electrical purposes, strip with drawn or rolled edges.
BS 1433 Copper for electrical purposes, rod and bar. BS 1434 Copper for electrical purposes - commutator bar. BS 1977 High conductivity copper tubes for electrical purposes. BS EN 1652 Copper and copper alloys. Plate, sheet and circles for general purposes. BS EN 12165 Copper and copper alloys. Wrought and unwrought forging stock. BS EN 12166 Copper and copper alloys. Wire for general purposes. BS EN 12163 Copper and copper alloys. Rod for general purposes. BS EN 1652 Copper and copper alloys. Plate, sheet, strip and circles for general purposes. BS 4109 Copper for electrical purposes-wire for general electrical purposes and for insulated cables and cards. BS 4608 Copper for electrical purposes-rolled sheet, strip and foil. BS 5311 High voltage alternating-current circuit-breakers. BS EN 60439-2 Specification for low voltage switchgear and controlgear assemblies. Particular requirements for busbar trunking systems (busways). BS EN 1976 Copper and copper alloys. Cast unwrought copper products. BS EN 1978 Copper and copper alloys. Copper cathodes BS EN 60439-1 Specification for low-voltage switchgear and controlgear assemblies. Specification for type-tested and partially type-tested assemblies.
IEC Specifications
IEC 28 International standard of resistance for copper. IEC 137 Bushings for alternating voltages above 1000V. IEC 273 Dimensions of indoor and outdoor post insulators and post insulator units for systems with nominal voltage greater than 1000V. IEC 344 Guide to the calculation of resistance of plain and coated copper conductors of low frequency wires and cables. IEC 349 Factory-built assembler of low-voltage switchgear and controlgear.
American Specifications
C 29.1 Electric power insulators, test methods for. C 37.20 Switchgear assemblies including metal-enclosed bus. C 37.30 High voltage air switches insulators and bus supports, definition and requirements for. C 37.31 Indoor apparatus insulators, electrical and mechanical characteristics.
Section 2
BOWERS, J.E. and MANTLE, E.C.: Copper for Transformer Windings. J. Inst. Met., 91,1961/2, pp 142-146. BRANDES, E.A.: Smithells Metals Reference Book. 6th Edition, (Butterworths), 1983. COPPER DEVELOPMENT ASSOCIATION: Copper in Electrical Contacts. C.D.A. Pub. TN23, 1980. COPPER DEVELOPMENT ASSOCIATION: High Conductivity Coppers-Properties and Applications. C.D.A. Pub. TN29, 1981. COPPER DEVELOPMENT ASSOCIATION: High Conductivity Coppers Technical Data. C.D.A. Pub. TN27, 1981. COPPER DEVELOPMENT ASSOCIATION: Megabytes on Coppers, CD-ROM, 1994. RUSKIN, A.M.: On the Safety of Copper and Aluminium Busbars. I.E.E.E. Technical Conference on Industrial and Commerial Power Systems, Toronto, 6th May, 1975.
Section 3
BURNS, R.L.: Determination of Current-Carrying Capacity of Rectangular Copper Busbars. Pub. 224/77, Copper and Brass Information Centre, Australia, 1977. BURNS, R.L.: Determination of Current-Carrying Capacity of Rectangular Copper Busbars. Paper 1, Copper Busbar Symposium, Johannesburg, 21st Nov., 1978. CHIN, T.H. and HIGGINS TJ.: Equations for the Inductances and Current Distribution of MultiConductor Single-Phase and Polyphase Buses. A.I.E.E Paper 57-654, 1957. DWIGHT, H.B., ANDREW, G.W., and TILESTON, H.W.: Temperature Rise of Busbars Calculated and Test Results for Single and Built Up Bar Forms, Also Solid and Tubular Round and Square Tubular Forms. Cen. Elec. Rev., 43, pp 213-218. FUGILL, A.P.: Carrying Capacity of Enclosed Busbars. Elect. World, 99, 1932, pp 539-540. HOLME, R.: Electric Contact. (Gebers), Stockholm, 1946. MCADAMS, W.H.: Heat Transmission. (McGraw-Hill), 1933, p 44. MELSOM, S.W. and H.C. BOOTH: Current-Carrying Capacity of Solid Bars. Jour. I. E. E., 62, 1924, pp 909 915. MONTSINGER, V.M., and WETHERILL, L.: Effect of Colour of Tank on Temperature of Self Cooled Transformers. Trans. A.l.E.E., 49, 1930, pp 41-51. PABST, H.W.: Current-Carrying Capacity of Busbars. Elect. World, 94, Sept., 1929, pp 569-572. PABST H.W.: Current-Carrying Capacity of Hollow Conductors. Elect. J., July, 1931, pp 411-414. PRAGER, M., PEMBERTON, D.L., CRAIG, A.G., and BLESHMAN, N.A.: Thermal Considerations for Outdoor Bus Design. I.E.E.E. Trans., PAS-95, No. 4, July/Aug., 1976.
RICHARDS, T.L.: The Current Rating of Rectangular Copper Busbars with Metric Dimensions. Elec. Rev., 186, 6th Mar., 1970. (Also C.D.A. Pub. No. R39). SCHURIG, O.R. and FRICK, C.W.: Heating and Current-Carrying Capacity of Bare Conductors for Outdoor Service. Gen. Elec. Rev., 33, No. 3, Mar., 1930, pp 141-157.
Section 4
ARNOLD, A.H.M.: The Alternating Current Resistance of Parallel Conductors of Circular CrossSection. J. I. E. R., 77,1935, pp 49-50. ARNOLD, A.H.M.: The Altemating Current Resistance of Tubular Conductors. J.l.E.E., 78, 1936, pp 580-593. Discussion J.I.E.E., 79, 1936, pp 595-596. ARNOLD, A.H.M.: The Transmission of Altemating Current Power with Small Eddy Current Losses. J.I.E.E., 80, 1937, pp 395-400. ARNOLD, A.H.M.: Proximity Effects in Solid and Hollow Round Conductors. J.I.E.E., 88, 1941, pp 349-359 BILLHIMER, F.M.: Current Capacity of Copper Busbars. Elec. J. ,15, 1918, pp 94-96. Bulletin of the Bureau of Standards (Washington), 8,1912, pp 173-179. BURNS, R.L.: Current Rating of Open Type Three Phase Rectangular Busbars by Actual Test. Pub. 219/76, Copper and Brass Infommation Centre, Australia, 1976. BURNS, R.L.: A.C. Current Rating of Open Rectangular Copper Busbars by Calculation. Pub. 221/77, 1977, Copper and Brass Information Centre, Australia. COCKCROFT, J.D.: Skin Effects in Rectangular Conductors at High Frequencies. Proc. Roy. Soc. ,122, 1929, pp 533-542. DWIGHT, H.B.: Skin Effect of a Return circuit of Two Adjacent Strap Conductors. Elec. Jour. ,13, 1916, pp 157-158. DWIGHT, H.B.: Skin Effect in Tubular and Flat Conductors. Trans. A.l.E.E., 37, Pt. 2,1918, pp 1379-1403. DWIGHT, H.B.: Skin Effect and Proximity Effect in Tubular Conductors. Trans. A.l.E.E., 41, 1922, pp 189-198. DWIGHT, H.B.: Proximity Effect in Wires and Thin Tubes. Trans. A.l.E.E., 42, 1923, pp 850-859. DWIGHT, H.B.: Reactance and Skin Effect of Concentric Tubular Conductors. Trans. A.l.E.E., 61, 1942, p 513 ESCHBACH, O.E.: Handbook of Engineering Fundamentals. (J. Wiley and Sons). FORBES, H.C. and GORMAN, L. J.: Skin Effect in Rectangular Conductors. Elec. Engineering, Sept. 1933, pp 636-639. FUGILL, A.P.: Carrying Capacity of Enclosed Busbars. Elec. World, 99, 1932, pp 539-540. HIGGINS, T.J.: Formulas for the Geometric Mean Distance of Rectangular Areas and of Line Segments. J. App. Phys., 14, No. 4, 1943, p 188.
HIGGINS, T.J.: Theory and Application of Complex Logarithms and Geometric Mean Distances. Trans. A. I.E.E., 66, 1947, p 12. MAYE, E.: Industrial High Frequency Electric Power. (Chapman and Hall), p 167. SIEGEL, C.M. and HIGGINS, T.J.: Equations for Determining Current Distribution Among the Conductors of Buses Compromised of Double Channel Conductors. A.I.E.E. Paper 54-467, 1954. WADDICOR, H.: Principles of Electric Power Transmission. 3rd Edition, (Chapman and Hall), 1935. WAGNER, C.F.: Current Distribution in Multi-Conductor Single-Phase Buses. Elec. World, 79, 1922, pp 526-529. WILSON, W.: Discussion, J. l. E. E., 71, 1932, pp 341-342. WRIGHT, E.G.: A.C. Ratings of Rectangular Conductors. Elec. Rev., 199,. No 5, 30th July 1976.
Section 5
ARNOLD, A.N.M.: The Transmission of Alternating Current Power with Small Eddy Current Losses. J.I.E.E . 80, 1937, pp 395 400. ARNOLD, A.H.M.: The Alternating Current Resistance of Hollow Square Conductors. J.I.E.E., 82, 1938, pp 537-545 . BOAST, W.B.: Transpositions and the Calculation of Inductance from Geometric Mean Distances. Trans. A.I.E.E., 69, 1950, pp 1531-1534. BOHN, D.l. rnd BABST, H.W.: Conductors of Heavy Alternating Currents. Iron and Steel Engineer, June, 1951. CONAUGLA, A.: Heat Losses in Isolated Phase Bus Enclosures. I.E.E.E. Paper 63-65, 1963. DEANS, W.: What Shape Conductors for Electrical Busbars? Power, Feb., 1943, pp 75-78. DWIGHT, H.B., ANDREW, G.W., snd TILESTON, H.W.: Temperature Rise of Busbars Calculated and Test Results for Single and Built Up Bar Forms, Also Solid and Tubular Round and Square Tubular Forms. Gen. Elec. Rev., 43, pp 213-218. FISCHER, L.E. and FRANK, R.L.: Paired Phase Busbars for Large Polyphase Currents. A.l.E.E. Paper 43-17, 1943. HOUSE, H.H. and WHIDDEN, P.: Self-lnductance of Bus Conductors with Complex CrossSections. A.I.E.E. Paper 57-797, 1957. KILLLIAN, S.C.: Induced Currents in High-Capacity Busbar Enclosures. Trans. A.I.E.E., 69,1950, p 1388. MORMIER, C.: Busbars and Low and Medium Voltage Connections. Rev. Elect. Mec. ,1952, 89, p 17. RICHARDS, T.L.: Current-Rating Tests on Double Angle Section Copper Conductors. Engineering, 184, 1957, p 823.
SKEETS, W.F. and SWERDLOW, N.: Minimising the Magnetic Field Surrounding Isolated Phase Bus by Electrically Continuous Enclosures. I.E.E.E. Paper 62-171, 1962. WAGNER, C.F.: Current Distribution in Multi-Conductor Single Phase Buses. Elect. World, 79, pp 526-529. WYMAN, B.W., and SHORES, R.B.: A New Isolated-Phase Metal-Enclosed Bus. Trans. A.l.E.E., 67, 1948, p 699.
Section 6
Asea Jour., Electromagnetic Forces on Busbars. 25, 1952, p 84. BATES, A.C.: Basic Concepts in the Design of Electrical Bus for Short-Circuit Conditions. A.l.E.E. Paper, 57-717. 1957. CHIN, T.H. and HIGGINS, T.J.: Equations for Evaluating Short-circuit Forces on Multi-Strap Single-Phase and Polyphase Buses for Supplying Low Frequency Induction Furnaces. DARLING, A.G.: Short-Circuit Calculating Procedure for Low Voltage A.C. Systems. A.l.E.E. Trans., 60, 1941, pp 1121-1135. DUNTON, W.F.: Electromagnetic Forces on Current-Carrying Conductors. J. Sci. Instr., 4, pp 440446. DWIGHT, H.B.: Repulsion Between Strap Conductors. Elect. World, 70, 1917, pp 522-524. EVERITT, L.M.R.: The Calculations of Short Time Ratings of Bare Electrical Conductors. J.I.E.E., 93, 1945, pp 380-387 . FRICK, C.W.: Electromagnetic Forces on Conductors with Bends, Short Lengths and CrossOvers. Gen. Elec. Rev., 36, 1933, pp 232242. KNOWLTON, A.E.: Standard Handbook for Electrical Engineers. 8th Edition, (McGraw-Hill), Tables 12-27, p 1144. LYTHALL, R.T.: Low-Voltage Breaking Capacity: Fault Current More Important than kVA Ruptured. Elec. Rev. ,119, No. 3100, 30th Apr. 1937, p 654. LYTHALL, R.T.: Low-Voltage Short Circuit Calculations: The Effect of Equivalent High-Voltage Reactance. Elec. Rev., 123, No. 3182, 18th Nov. 1938. PAPST, H.W.: Stresses in Buses During Short circuit. Elec. J., 31, 1934, pp 322-323. PILCHER, E.E.I.: Short circuit Forces on Busbars. World Power, 24, 1935, pp 116-123. SCHURIG, O.E. and SAYRE, M.F.: Mechanical stresses on Busbar Supports During ShortCircuits. A.l.E.E. Trans., 44, 1952, pp 217-237. SCHURIG, O.E., FRICK, C.W. and SAYRE, M.F.: Practical Calculations of Short-Circuit Stresses in Supports for Straight Parallel Bus Conductors. Gen. Elec. Rev., 29,1926, pp 534-544. SIEGEL, C.M. and HIGGINS, T.J.: Equations for the Inductance and Short-Circuit Forces of Buses Comprised of Double-Channel Conductors. Trans. A.I.E.E., 71, 1952, p 425. TANBERG, R.: Stresses in Bus Supports. Elect. J., 24, 1927, pp 517-525.
TIMASCHEFF, A.S.: Standard Curves for Calculations of Forces Between Parallel and Perpendicular Conductors. Eng. J., Oct., 1953. VAN ASPEREN, C.H.: Mechanical Forces on Busbars Under Short Circuit Conditions. Trans. A.I.E.E., 42, 1923, pp 1091-1111. WAGNER, C.F. and EVANS, R.D.: Symmetrical Components. (McGraw-Hill). WILSON, W.: The Calculation and Design of Electrical Apparatus. (Chapman and Hall), London, 1940. WILSON, W.R. and MANKOFF, L.L.: Short-Circuit Forces in Isolated Phase Buses. A.l.E.E. Paper 54-138. 1954.
Section 7
CONSTABLE, F.H.: Growth of Oxide Films. Proc. Roy. Soc., 115, 1927-8, p 385. COPPER DEVELOPMENT ASSOCIATION: Joining of Copper and Copper Alloys. C.D.A. Pub. TN25, 1980. (now superseded by Publication No 98) DENAULT, C.L.: Electrical Contact of Busbar Joints. Elect. J., 30, 1933, pp 281-282. DONATI, E.: Overlapping Joints in Electric Furnace Circuits. L'Energia Elettrica, 12, No. 6,1935. DWIGHT, H.B. and WANG, T.K.: Reactance of Square Tubular Busbars.A.l.E.E. Trans., 57, 1938, pp762-765. FRICK, C.W.: Current-Carrying Capacity of Bare Cylindrical Conductors for Indoor and Outdoor Service. Gen. Elec. Rev., 34, 1931, pp 464-471. HALPERIN, H.: Economical Utilisation of Electric Power Equipment. Power App. and Systerns, Apr., 1953, p 203. JACKSON, R.A.: Electrical Performance of Aluminium and Copper Bolted Joints. Proc. I.E.E., 129, Pt. C, No . 4, Jul., 1982 pp 177-184. KOUWENHOVEN, W.B. and LITTLE, C.: Contact Resistance. Welding J., 31, No. 10, Oct. 1952, p 457. LANCTOT, E.K.: Temperature Rise and Joint Resistance of Three-Phase Bus Assemblies of Aluminium and Copper. A.l.E.E. Paper 57-718, 1957. LUKE, G.E.: The Resistance of Electrical Connections. Elec. J., 21, 1924, pp 66-69. MELSOM, S.W. and BOOTH, H.C.: The Efficiency of Overlapping Joints. J.I.E.E., 60,1922, pp 889-899. SAYERS, D.P., FORREST, J.S. and LANE, F.J.: 275 kV Developments on the British Grid System. Proc. I.E.E.. 99. Pt. II, No. 72,1953, p 582. WATSON, C.G.: Sags and Tensions in Overhead Lines. (Pitman), 1931. WENNER, F., NUSBAUM, G.W. and CRUIKSHANKS, B.C.: Electrical Resistance of Contacts Between Nuts and Bolts. Bur. Stand. J. Res. Wash., 5, 1930, pp 757-766.
Section 8
ASHDOWN, K.T. and SWERDLOW, N.: Cantilever-Loaded Insulators for Isolated Phase Bus. A.I.E.E. Paper 54-141, 1954. KILLIAN, S.C.: Mechanical Forces on Buses due to Fault Currents. Elect. World, Dec. 12th, 1942, pp 60-62. SCHURIG, O.R. and SAYRE, M.F.: Mechanical stresses on Busbar Supports During ShortCircuits. A.I.E.E., 44, 1952, pp 217-237. SCHURIG, O.E., FRICK, C.W. and SAYRE, M.F.: Practical Calculations of Short-Circuit Stresses in Supports for Straight Parallel Bus Conductors. Gen. Elec. Rev., 29, 1926, pp 534-544. TRIPP, W.A.: Forces on Conductors During Short-Circuit. Elect. J., Dec., 1937, pp 493-497.
Section 9
ARNOLD, A.H.M.: The Inductance of Linear Conductors of Rectangular Section. J.I.E.E., 70, 1932, pp 579 586. BOGARDUS, L.R.: Resistance Welder Feed has Low Reactance Drop. Elec. World, 10th Sept. 1938, p 702. DEANS, W.: What Shape Conductors for Electrical Busbars? Power, Feb., 1943, pp 75-78. DWIGHT, H.B.: Reactance of Strap Conductors. Elec. Rev., 70, 1917, p 1087. DWIGHT, H.B.: Reactance Values for Rectangular Conductors. Elec. J., 16, 1919, p 255. DWIGHT, H.B.: Reactance and Skin Effect of Concentric Tubular Conductors. Trans. A.I.E.E., 61, 1942, p 513 DWIGHT, H.B.: Geometric Mean Distance for Rectangular Conductors. Trans. A.I.E.E., 65, 1946, p 328. DWIGHT, H.B. and WANG, T.K.: Reactance of Square Tubular Busbars. Trans. A.l.E.E., 57, 1938, p 762. Discussion, p 765. Elec. Times: Transformers for Electric Furnaces. 5th Dec. 1940, p 375. GRAY, A.: Absolute Measurements in Electricity and Magnetism. 2nd Edition, (MacMillan), 1921, Chapter XIII. GROVER, F.W.: The Calculation of Inductance and Reactance of Single Layer Coils and Spirals Wound with Wire of Large Cross Section. Proc. I.R.E. (US), 17, No. 11, Nov. 1929, p 2053. GROVER, F.W.: Inductance Calculations. (Van Nostrand), 1946. HIGGINS, T.J.: Formulas for the Inductance of Rectangular Tubular Conductors. Trans. A.I.E.E., 60, 1941, p 1046. HIGGINS, T.J.: Formulas for the Inductance of Rectangular Tubular Conductors. J.App. Phys. , 13, No. 11,1942, p 1046.
HIGGINS, T.J.: Formulas for the Calculation of the Inductance of Linear Conductors of Structural Shape. Trans. A.l.E.E., 62, Feb., 1943, p 53. HIGGINS, T.J.: Formulas for the Geometric Mean Distance of Rectangular Areas and of Line Segments. J. App. Phys.!eu!, 14, No. 4, 1943, p 188. HIGGINS, T.J.: The Design of Busbars for Industrial Distribution Systems and Epitomisation of Available Data. Trans. A.l.E.E., 64, 1945, p 385. HIGGINS, T.J.: Theory and Application of Complex Logarithms and Geometric Mean Distances. Trans. A.l.E.E., 66, 1947, p 12. HIGGINS, T.J. and MESSINGER H.P.: Equations for the Inductance of Three-Phase Co-Axial Buses Comprised of Square Tubular Conductors. J. App. Phys. ,18, 1947, p 1009. KARAPETOFF, V.: The Inductance of Cables and Transmission Lines. (McGraw-Hill), 1914. LYTHALL, R.T.: Low Voltage Short-Circuit Calculations: The Effect of Equivalent High-Voltage Reactance. Elec. Rev., 123, No. 3182, 18th Nov. 1938. LYTHALL, R.T.: The J and P Switchgear Book. (Johnson and Phillips Ltd.), 1947, p 271. MAXWELL, J.C.: On the Geometrical Mean Distance of Two Figures in a Plane. Trans. Roy. Soc. Edin., 26, 1872, p 729. MESSINGER, H.P. and HIGGINS, T.J.: Formulas for the Reactance of Co-Axial Buses Comprised of Square Tubular Conductors. Trans. A.l.E.E., 65, 1946, p 328. MILLER, W.H.: Three-Phase Rectangular Conductors-A Simplified Reactance Formula. Electrician, 20th June 1947, p 1681. O'RAHILLY, A.: A Note on Self-Inductance. J.l.E.E.,86, No. 518, Feb. 1940, p 179. Discussion, June 1940, p 567. ROSA, E.B.: On the Geometrical Mean Distances of Rectangular Areas and the Calculation of Self-Inductance. N. B. S. Bull., 3, 1907, p 1. ROSA, E.B. and GROVER, F.W.: Formulas and Tables for the Calculation of Mutual and Self Inductance (Revised and Extended). N. B. S. Bull., 8, 1912, Paper No. 169. ROTH, E.D.: Champ Magnetique et Inductance d'un Systeme de Barres Rectangulaires Paralleles. Rev. Gen. de l'Elec, 44, No. 9, 3rd Sept. 1938, p 275. SCHURIG, O.R.: Engineering Calculation of Inductance and Reactance for Rectangular Bar Conductors. Gen Elec. Rev., 36, No 5, May 1933, pp 228-231. SCHWANTZ, W.G. and HIGGINS T.l.: Formulas for Calculating the Inductance of Channels Located Back to Back. Trans. A.l.E.E., 65, 1946, p 893. SIEGEL, C.M. end HIGGINS, T.J.: Equations for the Inductance and Short-Circuit Forces of Buses Comprised of Double-Channel Conductors. Trans. A.I.E.E., 71, 1952, p 425.
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