Cable rating

Chapter 4
Cable rating
An important part of any electrical design is the determination of the size of cables. The
size of cable to be used in a given circuit is governed by the current which the circuit has
to carry, so the design problem is to decide the size of cable needed to carry a known
current. Two separate factors have to be taken into account in assessing this, and the size
of cable chosen will depend on which factor yields the most suitable value in each
particular case.
A conductor carrying a current is bound to have some losses due to its own resistance.
These losses appear as heat and will raise the temperature of the insulation. The current
the cable can carry is limited by the temperature to which it is safe to raise the insulation.
Now the temperature reached under continuous steady state conditions is that at which
the heat generated in the conductor is equal to the heat lost from the outside of the
insulation. Heat loss from the surface is by radiation and conduction and depends on the
closeness of other cables and on how much covering or shielding there is between the
cable and the open atmosphere. Thus the heat loss and, therefore, the equilibrium
temperature reached depends on how the cable is installed; that is to say whether it is in
trunking, or conduit, on an exposed surface, how close to other cables, and so on. To
avoid tedious calculations, tables have been prepared and published (appendix to BS
7671) which list the maximum allowable current for each type and size of cable.
The tables give a current rating for each type and size of cable for a particular method
of installation and at a particular ambient temperature. For these basic conditions a cable
must be chosen the rated current of which is at least equal to the working current. For
other methods of installation and ambient temperatures the tables give various correction
factors. The fuse or circuit breaker rating has to be divided by these to give a rated
current and a cable then selected such that its tabulated current is at least equal to this
nominal current.
Particular care has to be taken where cable is run in a thermally insulated space. With
increasing attention to thermal insulation of walls this is likely to become a more
frequently occurring situation, and BS 7671 now require a cable to be de-rated when it is
used in such a situation.
As is explained in Chapter 9, every cable, which may be subject to overload, short
circuit, or earth fault, must be protected against overload and/or short circuit. A generic
term is overcurrent, which is any current that exceeds the rated value of current-carrying
capacity of the cable. The overcurrent may be caused by (a) an overload, which is an
overcurrent occurring in a circuit that is electrically sound; (b) a short circuit, which is an
overcurrent between live conductors having a potential between them in normal
circumstances, due to a fault of negligible impedance between them, or (c) an earth fault.
The working current must be such that if it is exceeded, the resulting rise in temperature
will not become dangerous before the protective device cuts off the current.
When a short circuit occurs, the cable is carrying the fault current during the time it
takes the protective device, whether a fuse or a circuit breaker, to operate and disconnect
the circuit. Because this time is very short, the cable is heated adiabatically and the
temperature rise depends on the fault current and the specific heat capacity of the cable.
The short circuit current depends upon the impedance of the source and the cables in the
short circuit. The earth fault current depends on the earth fault loop impedance, which is
explained in Chapter 9. This impedance is the sum of the impedance of the phase
conductor R1 and the impedance of the protective conductor R2 and the impedance of the
source. BS 7671 requires that both the earth-fault loop impedance, the short-circuit
impedance, and the time for the device to operate are such that its protective device will
operate before a dangerous temperature is reached.
In most cases the protective device will have a breaking capacity greater than the
prospective short-circuit current, and this allows one to assume that the current will be
disconnected sufficiently quickly to prevent overheating during a short circuit. The cable
size selected from the rating tables for the working current is then adequate.
If the protective device is selected for short-circuit protection only, then a check must
be made by means of the formula
where t=time in seconds in which protective device opens at a current of IA
k=a constant, given in the Regulations for different cables
S=minimum cross-sectional area of conductor in the cable, mm2
I=short circuit current, A.
If necessary the cable size must be increased above that provisionally selected from
the tables in order to satisfy this condition.
Alternatively, the cable size can be retained and a fuse or circuit breaker with a faster
operating time used.
The protection must also operate if the overcurrent is not a short circuit but a
comparatively small multiple of the working current, an overload. HRC fuses and circuit
breakers can take up to four hours to operate at a current 1.5 times their rated current. The
cable temperature will rise during this time and the working current must allow a safety
margin to take account of this. The rating tables in BS 7671 include the necessary margin
for HRC fuses and circuit breakers.
However, rewireable fuses (BS 3036) take longer to operate and a larger margin is
therefore necessary. The rating tables therefore include a factor by which cables must be
de-rated if rewireable fuses are going to be used to protect the cables.
The resistance of the conductor also results in a drop of voltage along its length.
Because of this drop, the voltage at the receiving end is less than that at the sending end.
Since all electrical equipment used in a building is designed to work on the nominal
voltage of the supply in the building, it is necessary to limit the amount by which the
Design of electrical services for buildings 70

voltage drops between the point of entry into the building and the outlet serving an
appliance. In other words, the voltage drop in the wiring must be kept reasonably low. BS
7671 require that the voltage drop in the wiring should not exceed a value appropriate to
the safe functioning of the equipment. BS 7671 limits the volts drop to 4 per cent of the
nominal voltage.
The drop in volts is obtained by Ohm’s law as the product of the actual current
flowing and the total resistance of the actual length of cable. One therefore wants to know
the resistance per unit length of cable. The cable-rating tables already mentioned give
this, but for convenience of use, instead of giving it as ohms per metre, they quote it as
voltage drop per amp per metre length of cable. This makes it a very simple and quick
matter to calculate the actual drop over the actual length for the actual current. If this is
more than the acceptable drop the larger size of cable must be chosen and the calculation
repeated.
Referring to BS 7671, Table 4A1 shows various accepted methods of installing wiring
systems; these are termed ‘reference methods’. Reference methods vary; reference
method 1 is sheathed cables clipped direct or lying on a non-metallic surface; reference
method 3 refers to cables installed in conduit or trunking; method 4 refers to single-core
cables enclosed in conduit installed in a thermally insulating wall or ceiling, the conduit
being in contact with the thermal insulation on one side.
From Table 4D2A, which is at slight variance from Table 4D5A, with the tabulated
rating of a 2.5mm2 single-phase multicore thermoplastic non-armoured 70°C PVC cable
(typically twin and earth) is, reference method 1 given 27A, reference method 3, 24A,
and reference method 4, 19.5A. Table 4D5A refers to installation method 15 and
reference method 1. Note the differences between installation and reference methods.
Note how the current rating of the cable increases as the installation method allows more
heat to be dissipated.
The assumed ambient temperature is 30°C. The maximum conductor operating
temperature is 70°C. Therefore it can be assumed that the above currents will raise the
temperature of the cable by 40°C.
The tables assume that the circuits are run individually. It is normal practice to run
more than one circuit in an enclosure or to bunch multicore (more than one core)
together. If the circuits were grouped with other circuits, or if multicore cables were
bunched with other multicores, the heat dissipation properties of the circuits or cables
would be reduced; the more cables there are in the group the dissipation properties of the
cable are reduced. Then if the cables were loaded to their ungrouped level when they are
grouped they would overheat. The number of grouped circuits must therefore be taken
into account. Table 4B1 gives correction factors to apply for grouping Cg. If an enclosed
circuit as in method 3 or 4 is taken, or it is bunched and clipped direct to a non-metallic
surface multicore (method 1) for two circuits or two multicore cables, the correction
factor is 0.80. This means that for two circuits, only allowed 80 per cent of the single
circuit current is allowed. For three circuits, the factor is 0.70 This means that for three
circuits, only 70 per cent of the single circuit or multicore current is allowed.
How is the factor applied?
Figure 4.1 represents one single-phase thermoplastic 70°C circuit enclosed in conduit
installed as reference method 3; the minimum fuse size is chosen from the range of fuses
from BS88, the minimum rating of fuse is 50A. For the fuse to protect the cable against
Cable rating 71


overload, the minimum cable rating, Iz, is 50A. Also, the minimum tabulated rating, It,
for the cable is also 50A. The methods of calculation in BS 7671 make ‘It’ the subject of
the formulae used.
If the cable is grouped with three other circuits (four in total), the correction factor is
0.65. The correction factor is applied as a divisor to the protective device rating.
Therefore the minimum rating Iz, or the minimum tabulated rating It of the cable will be
It=In/Cg=50/0.65=76.92A
Figure 4.1 Device rating related to
design current
Figure 4.1 Effect of grouping cables
In other words a cable which will carry 76.92A is acceptable, but the cable must be derated
to a factor of 0.65:
76.92×0.65=50
Therefore, in these conditions, the cable is rated at 50A. We are selecting a larger size of
cable because of the reduction in current carrying capacity due to grouping.
If the cable is installed in an ambient temperature of 30°C and loaded with the
maximum rated current, the final temperature will be 70°C. Then, if the cable is installed
at a temperature above 30°C, the starting temperature of the cable will be higher, and the
running temperature will also be higher. Therefore, to prevent the cable from
overheating, we must make adjustments to the current carrying capacity of the cable, if it
is installed in an ambient temperature above 30°C. Table 4C1 relates to correction factors
(Cg) for ambient temperature. For general purpose PVC at 35°C the correction factor is
0.94. This means that the cable may only be loaded to 94 per cent of its 30°C capacity.
Table 4C1 is for all protective devices other than rewireable fuses. For rewireable
fuses, Table 4C2 is applicable.
If the above circuit is run with three other circuits (four in total), there are two
correction factors to apply, one for grouping and one for ambient temperature above
30°C. The minimum rating of the cable will be
Iz=In/Cg×Ca=50/(0.94×0.65)=81.83A
Design of electrical services for buildings 72


One must also consider if the cable is run in heat-insulating material, whether its ability
to dissipate heat will be impaired. To take this into consideration Table 52A gives the
correction factor to apply when a cable is enclosed in thermal insulation.
The correction factor Ci is applied to the length of the cable. The formula is now
amended to
Iz, or minimum It=In/Cg×Ca×Ci
When considering overload protection earlier, it was mentioned that when a rewireable
fuse was used, a factor of 0.725 is used. The formula is now amended to
Figure 4.3 Cables enclosed in thermal
insulation
minimum It=In/Cg×Ca×Ci×0.725
If any of the factors are not applicable, ignore them or replace with a 1.
Example 3 single-phase 240V 36A loads are to be supplied by means of 70°C
thermoplastic PVC twin and earth cables having copper conductors, 25m in length, in an
area having an ambient temperature of 35°C (Ca= 0.94). The cables are touching and
single-layer clipped to a non-metallic surface (for 3 circuits Cg=0.79). The overcurrent
device at the origin of the installation is a type-B MCB to BS EN 60898. Calculate the
minimum permissible cable size.
Reference method=1
Design current Ib=36A. Nominal rating of the device In=40A
Cg=0.79, Ca=0.94 Ca×Cg=C, where C=combined factor to apply
C=0.79×0.94=0.7426
minimum tabulated rating It=In/C 40/0.7426=53.86A
Consulting manufacturer’s appropriate table, or at the BS 7671 Table 4D5A, column
4, It=64A. Therefore, the minimum size with respect to current carrying capacity is
10mm2.
Regulation group 525–01, states that the voltage at the terminals of a piece of
equipment should be appropriate for the standard to which the equipment was
Cable rating 73


manufactured. If no value is stated, the voltage should be such that the equipment
operates safely. The safety aspect is satisfied if the volt drop between the terminals of the
incoming supply and the terminals of the equipment, if directly connected to the mains,
or the socket outlet, does not exceed 4 per cent of the nominal voltage of the mains.
We now need to check that the voltage drop in the 10mm2 cable is within these limits.
Table 4D2B gives voltage drop in millivolts per ampere per metre. To calculate the
voltage drop, multiply
Therefore, the minimum permissible size is 10mm2.
If the circuit was protected by a rewireable fuse to BS 3036, the design of the circuit
would be slightly different.
Reference method 1
Design current Ib=36A. Nominal rating of the device In=45A
Cg=0.79, Ca=0.97, Ca×Cg×0.725=C, where C=combined factor to apply
C=0.79×0.97×0.725=0.555
minimum tabulated rating It=In/C 45/0.555=81A
Now look at Table 4D5A, column 4, It=85. Therefore, the minimum size with respect
to current carrying capacity is 16mm2.
Therefore, the minimum permissible size is 16mm2 (10mm2 with type-B MCB to BS EN
60898). Note that semi-enclosed fuses should be rigorously avoided these days. BS 7671
expresses a preference for cartridge-type fuses.
In most cases, there will be a number of sub-mains from the electrical intake of the
building to distribution fuse boards, and from each of these there will be a number of
final circuits. The allowable voltage drop is the sum of the drops in the sub-mains and in
the final circuits, and there is no restriction on how it is shared between the two. The
position of each distribution board will affect the lengths both of sub-mains and of final
circuits and thus of the voltage drop in each of them. There is no single correct way in
which these parameters must be combined, and the design can only be done by a process
of trial and error tempered by the designer’s own experience and judgement. There is
plenty of scope for a designer to exercise his personal initiative and intuition in
positioning distribution boards and selecting cable sizes to arrive at an economical
design. In general, it is a better all-round solution to take the final distribution board as
Design of electrical services for buildings 74

near to the current, using equipment as possible, thus reducing the length of the final
circuits to a minimum.
If the overcurrent protection device at the origin of the circuit is for short-circuit
protection only, as would be the case for a motor circuit, then the formula stated in BS
7671 section 434–03 is employed:
where t=time taken to reach the limit temperature
K=is a factor taken from table 43A BS 7671
S=cross sectional area in mm2
I=fault current.
For example: a motor circuit is supplied by means of 4mm2 thermoplastic 70°C PVC
copper cables. The protection device at the origin of the circuit is a 50A BS 88–2.1 fuse.
The prospective short circuit current is 300A. The K value for thermoplastic 70°C PVC
copper cables is 115. The time for the cable to reach its limit temperature is
To take a typical BS 88 fuse, 300A, flowing through a 50A fuse would disconnect in
about 1.2. Therefore, the fuse would operate before the cable reached its limit
temperature, the cable being protected against short circuit.
Because of the cable resistance, 10m along the run the short-circuit current will be
attenuated to 263A, giving a time to reach the limit temperature of above 3s. The
disconnection time would, however, increase to about 2.5s. The cable is still protected.
Mention should also be made of the circuit protective conductor. The function of this
is described in Chapter 9. Under normal conditions it carries no current and it conducts
electricity only when an earth fault occurs and, then, only for the short time before the
protective device operates. BS 7671 gives two alternative ways of determining its size.
The first is by the use of the same formula as above, transposed to make S the subject of
the formula, as has been quoted above, for checking the short circuit rating of the live
conductor. Alternatively, the regulations give a table which relates the size of the
protective conductor to the size of the phase conductor. The effect is that for circuits up
to 16mm2, the protective conductor minimum size must be equal to the line or phase
conductor, for 25mm2 and 35mm2 phase conductors, the protective conductor must be at
least 16mm2, and for phase conductors over 35mm2 the cross section of the protective
conductor must be at least half the cross section of the phase conductor.
BS 7671 IEE Wiring Regulations particularly applicable to this chapter are:
Section 521–7
Section 522
Section 523
Section 524
Cable rating 75