Introduction
This article examines the sizing of electrical cables (i.e.
cross-sectional area) and its implementation in various international
standards. Cable sizing methods do differ across international standards (e.g.
IEC, NEC, BS, etc) and some standards emphasise certain things over others.
However the general principles underlying any cable sizing calculation do not
change. In this article, a general methodology for sizing cables is first
presented and then the specific international standards are introduced.
The proper sizing of an electrical (load bearing) cable is important to
ensure that the cable can:
·
Operate continuously under
full load without being damaged
·
Withstand the worst short
circuits currents flowing through the cable
·
Provide the load with a
suitable voltage (and avoid excessive voltage drops)
·
(optional) Ensure operation of
protective devices during an earth fault
This calculation can be done individually for each power cable that
needs to be sized, or alternatively, it can be used to produce cable sizing
waterfall charts for groups of cables with similar characteristics (e.g. cables
installed on ladder feeding induction motors).
All cable sizing methods more or less follow the same basic six step
process:
1) Gathering
data about the cable, its installation conditions, the load that it will carry,
etc
2) Determine
the minimum cable size based on continuous current carrying capacity
3) Determine
the minimum cable size based on voltage drop considerations
4) Determine
the minimum cable size based on short circuit temperature rise
5) Determine
the minimum cable size based on earth fault loop impedance
6) Select
the cable based on the highest of the sizes calculated in step 2, 3, 4 and 5
The first step is to collate the relevant information that is required
to perform the sizing calculation. Typically, you will need to obtain the
following data:
The characteristics of the load that the cable will supply, which
includes:
·
Load type: motor or feeder
·
Three phase, single phase or
DC
·
System / source voltage
·
Full load current (A) - or
calculate this if the load is defined in terms of power (kW)
·
Full load power factor (pu)
·
Locked rotor or load starting
current (A)
·
Starting power factor (pu)
·
Distance / length of cable run
from source to load - this length should be as close as possible to the actual
route of the cable and include enough contingency for vertical drops / rises
and termination of the cable tails
The basic characteristics of the cable's physical construction, which
includes:
·
Conductor shape - e.g.
circular or shaped
·
Conductor type - e.g. stranded
or solid
·
Conductor surface coating -
e.g. plain (no coating), tinned, silver or nickel
·
Number of cores - single core
or multicore (e.g. 2C, 3C or 4C)
How the cable will be installed, which includes:
·
Above ground or underground
·
Installation / arrangement -
e.g. for underground cables, is it directly buried or buried in conduit? for
above ground cables, is it installed on cable tray / ladder, against a wall, in
air, etc.
·
Ambient or soil temperature of
the installation site
·
Cable bunching, i.e. the
number of cables that are bunched together
·
Cable spacing, i.e. whether
cables are installed touching or spaced
·
Soil thermal resistivity (for
underground cables)
·
Depth of laying (for
underground cables)
·
For single core three-phase
cables, are the cables installed in trefoil or laid flat?
Step 2: Cable Selection Based
on Current Rating
Current flowing through a cable generates heat through the resistive
losses in the conductors, dielectric losses through the insulation and
resistive losses from current flowing through any cable screens / shields and
armouring.
The component parts that make up the cable (e.g. conductors, insulation,
bedding, sheath, armour, etc) must be capable of withstanding the temperature
rise and heat emanating from the cable. The current carrying capacity of a
cable is the maximum current that can flow continuously through a cable without
damaging the cable's insulation and other components (e.g. bedding, sheath,
etc). It is sometimes also referred to as the continuous current rating or
ampacity of a cable.
Cables with larger conductor cross-sectional areas (i.e. more copper or
aluminium) have lower resistive losses and are able to dissipate the heat
better than smaller cables. Therefore a 16 mm2 cable will
have a higher current carrying capacity than a 4 mm2 cable.
Table 1. Example of base current rating table (Excerpt from IEC
60364-5-52)
International standards and manufacturers of cables will quote base
current ratings of different types of cables in tables such as the one shown on
the right. Each of these tables pertain to a specific type of cable
construction (e.g. copper conductor, PVC insulated, 0.6/1kV voltage grade, etc)
and a base set of installation conditions (e.g. ambient temperature,
installation method, etc). It is important to note that the current ratings are
only valid for the quoted types of cables and base installation conditions.
When the proposed installation conditions differ from the base
conditions, derating (or correction) factors can be applied to the base current
ratings to obtain the actual installed current ratings.
International standards and cable manufacturers will provide derating
factors for a range of installation conditions, for example ambient / soil
temperature, grouping or bunching of cables, soil thermal resistivity, etc. The
installed current rating is calculated by multiplying the base current rating
with each of the derating factors, i.e.
where is the
installed current rating (A)
is the base
current rating (A)
are the
product of all the derating factors
For example, suppose a cable had an ambient temperature derating factor
of kamb = 0.94 and a grouping derating factor of kg
= 0.85, then the overall derating factor kd = 0.94x0.85
= 0.799. For a cable with a base current rating of 42A, the installed current
rating would be Ic = 0.799x42 = 33.6A.
When sizing cables for non-motor loads, the upstream protective device (fuse or circuit breaker) is
typically selected to also protect the cable against damage from thermal overload. The protective device must therefore be selected to exceed the full
load current, but not exceed the cable's installed current rating, i.e. this
inequality must be met:
Where is the full
load current (A)
is the
protective device rating (A)
is the
installed cable current rating (A)
Motors are normally protected by a separate thermal overload (TOL) relay
and therefore the upstream protective device (e.g. fuse or circuit breaker) is not
required to protect the cable against overloads. As a result, cables need only
to be sized to cater for the full load current of the motor, i.e.
Where is the full
load current (A)
is the
installed cable current rating (A)
Of course, if there is no separate thermal overload protection on the
motor, then the protective device needs to be taken into account as per the
case for feeders above.
A cable's conductor can be seen as an impedance and therefore whenever
current flows through a cable, there will be a voltage drop across it, which
can be derived by Ohm’s Law (i.e. V = IZ). The voltage drop will depend on two
things:
·
Current flow through the cable
– the higher the current flow, the higher the voltage drop
·
Impedance of the conductor –
the larger the impedance, the higher the voltage drop
The impedance of the cable is a function of the cable size
(cross-sectional area) and the length of the cable. Most cable manufacturers
will quote a cable’s resistance and reactance in Ω/km. The following typical cable impedances for low
voltage AC and DC single core and multicore cables can be used in the absence
of any other data.
For AC systems, the method of calculating voltage drops based on load
power factor is commonly used. Full load currents are normally used, but if the
load has high startup currents (e.g. motors), then voltage drops based on
starting current (and power factor if applicable) should also be calculated.
For a three phase system:
Where is the three phase voltage drop (V)
is the
nominal full load or starting current as applicable (A)
is the ac
resistance of the cable (Ω/km)
is the ac
reactance of the cable (Ω/km)
is the load
power factor (pu)
is the
length of the cable (m)
For a single phase system:
Where is the single phase voltage drop (V)
is the
nominal full load or starting current as applicable (A)
is the ac
resistance of the cable (Ω/km)
is the ac
reactance of the cable (Ω/km)
is the load
power factor (pu)
is the
length of the cable (m)
For a DC system:
Where is the dc
voltage drop (V)
is the
nominal full load or starting current as applicable (A)
is the dc
resistance of the cable (Ω/km)
is the
length of the cable (m)
It is customary for standards (or clients) to specify maximum
permissible voltage drops, which is the highest voltage drop that is allowed
across a cable. Should your cable exceed this voltage drop, then a larger cable
size should be selected.
Maximum voltage drops across a cable are specified because load
consumers (e.g. appliances) will have an input voltage tolerance range. This
means that if the voltage at the appliance is lower than its rated minimum
voltage, then the appliance may not operate correctly.
In general, most electrical equipment will operate normally at a voltage
as low as 80% nominal voltage. For example, if the nominal voltage is 230VAC,
then most appliances will run at >184VAC. Cables are typically sized for a
more conservative maximum voltage drop, in the range of 5 – 10% at full load.
It may be more convenient to calculate the maximum length of a cable for
a particular conductor size given a maximum permissible voltage drop (e.g. 5%
of nominal voltage at full load) rather than the voltage drop itself. For
example, by doing this it is possible to construct tables showing the maximum
lengths corresponding to different cable sizes in order to speed up the
selection of similar type cables.
The maximum cable length that will achieve this can be calculated by
re-arranging the voltage drop equations and substituting the maximum
permissible voltage drop (e.g. 5% of 415V nominal voltage = 20.75V). For a
three phase system:
Where is the
maximum length of the cable (m)
is the maximum permissible three phase voltage drop (V)
is the
nominal full load or starting current as applicable (A)
is the ac
resistance of the cable (Ω/km)
is the ac
reactance of the cable (Ω/km)
is the load
power factor (pu)
For a single phase system:
Where is the
maximum length of the cable (m)
is the maximum permissible single phase voltage drop (V)
is the
nominal full load or starting current as applicable (A)
is the ac
resistance of the cable (Ω/km)
is the ac
reactance of the cable (Ω/km)
is the load
power factor (pu)
For a DC system:
Where is the
maximum length of the cable (m)
is the
maximum permissible dc voltage drop (V)
is the
nominal full load or starting current as applicable (A)
is the dc
resistance of the cable (Ω/km)
is the
length of the cable (m)
During a short circuit, a high amount of current can flow through a
cable for a short time. This surge in current flow causes a temperature rise
within the cable. High temperatures can trigger unwanted reactions in the cable
insulation, sheath materials and other components, which can prematurely
degrade the condition of the cable. As the cross-sectional area of the cable
increases, it can dissipate higher fault currents for a given temperature rise.
Therefore, cables should be sized to withstand the largest short circuit that
it is expected to see.
The minimum cable size due to short circuit temperature rise is
typically calculated with an equation of the form:
Where is the
minimum cross-sectional area of the cable (mm2)
is the
prospective short circuit current (A)
is the
duration of the short circuit (s)
is a short
circuit temperature rise constant
The temperature rise constant is calculated based on the material
properties of the conductor and the initial and final conductor temperatures
(see the derivation here). Different international standards have different treatments of the
temperature rise constant, but by way of example, IEC 60364-5-54 calculates it
as follows:
(for copper conductors)
(for aluminium conductors)
Where is the initial conductor temperature (deg C)
is the final conductor temperature (deg C)
The initial conductor temperature is typically chosen to be the maximum
operating temperature of the cable. The final conductor temperature is
typically chosen to be the limiting temperature of the insulation. In general,
the cable's insulation will determine the maximum operating temperature and
limiting temperatures.
As a rough guide, the following temperatures are common for the
different insulation materials:
Material
|
Max Operating Temperature oC
|
Limiting Temperature oC
|
PVC
|
75
|
160
|
EPR
|
90
|
250
|
XLPE
|
90
|
250
|
The short circuit energy is normally
chosen as the maximum short circuit that the cable could potentially
experience. However for circuits with current limiting devices (such as HRC
fuses), then the short circuit energy chosen should be the maximum prospective
let-through energy of the protective device, which can be found from
manufacturer data.
Sometimes it is desirable (or necessary) to consider the earth fault
loop impedance of a circuit in the sizing of a cable. Suppose a bolted earth
fault occurs between an active conductor and earth. During such an earth fault,
it is desirable that the upstream protective device acts to interrupt the fault
within a maximum disconnection time so as to protect against any inadvertent
contact to exposed live parts.
Ideally the circuit will have earth fault protection, in which case the
protection will be fast acting and well within the maximum disconnection time.
The maximum disconnection time is chosen so that a dangerous touch voltage does
not persist for long enough to cause injury or death. For most circuits, a
maximum disconnection time of 5s is sufficient, though for portable equipment
and socket outlets, a faster disconnection time is desirable (i.e. <1s and
will definitely require earth fault protection).
However for circuits that do not have earth fault protection, the
upstream protective device (i.e. fuse or circuit breaker) must trip
within the maximum disconnection time. In order for the protective device to
trip, the fault current due to a bolted short circuit must exceed the value
that will cause the protective device to act within the maximum disconnection
time. For example, suppose a circuit is protected by a fuse and the maximum disconnection
time is 5s, then the fault current must exceed the fuse melting current at 5s
(which can be found by cross-referencing the fuse time-current curves).
By simple application of Ohm's law:
Where is the earth
fault current required to trip the protective device within the minimum
disconnection time (A)
is the phase
to earth voltage at the protective device (V)
is the
impedance of the earth fault loop (Ω)
It can be seen from the equation above that the impedance of the earth
fault loop must be sufficiently low to ensure that the earth fault current can
trip the upstream protection.
The earth fault loop can consist of various return paths other than the
earth conductor, including the cable armour and the static earthing connection
of the facility. However for practical reasons, the earth fault loop in this
calculation consists only of the active conductor and the earth conductor.
The earth fault loop impedance can be found by:
Where is the earth
fault loop impedance (Ω)
is the
impedance of the active conductor (Ω)
is the
impedance of the earth conductor (Ω)
Assuming that the active and earth conductors have identical lengths,
the earth fault loop impedance can be calculated as follows:
Where is the
length of the cable (m)
and are the ac
resistances of the active and earth conductors respectively (Ω/km)
and are the
reactances of the active and earth conductors respectively (Ω/km)
The maximum earth fault loop impedance can be found by re-arranging the
equation above:
Where is the
maximum earth fault loop impedance (Ω)
is the phase
to earth voltage at the protective device (V)
is the earth
fault current required to trip the protective device within the minimum
disconnection time (A)
The maximum cable length can therefore be calculated by the following:
Where is the
maximum cable length (m)
is the phase
to earth voltage at the protective device (V)
is the earth
fault current required to trip the protective device within the minimum
disconnection time (A)
and are the ac
resistances of the active and earth conductors respectively (Ω/km)
and are the
reactances of the active and earth conductors respectively (Ω/km)
Note that the voltage V0 at the protective device is
not necessarily the nominal phase to earth voltage, but usually a lower value
as it can be downstream of the main busbars. This voltage is commonly
represented by applying some factor to the
nominal voltage. A conservative value of = 0.8 can be
used so that:
Where Vn is the nominal phase to earth voltage (V)
In this example, we will size a cable for a 415V, 37kW three-phase motor
from the MCC to the field.
The following data was collected for the cable to be sized:
·
Cable type: Cu/PVC/GSWB/PVC,
3C+E, 0.6/1kV
·
Operating temperature: 75C
·
Cable installation: above
ground on cable ladder bunched together with 3 other cables on a single layer
and at 30C ambient temperature
·
Cable run: 90m (including
tails)
·
Motor load: 37kW, 415V three
phase, full load current = 61A, power factor = 0.85
·
Protection: aM fuse of rating
= 80A, max prospective fault I2t = 90 A2s
, 5s melt time = 550A
Suppose the ambient temperature derating is 0.89 and the grouping
derating for 3 bunched cables on a single layer is 0.82. The overall derating
factor is 0.89 0.82 =
0.7298. Given that a 16 mm2 and 25 mm2 have
base current ratings of 80A and 101A respectively (based on Reference Method E), which cable should be selected based on current rating
considerations?
The installed current ratings for 16 mm2 and 25 mm2
is 0.7298 80A = 58.38A
and 0.7298 101A =
73.71A respectively. Given that the full load current of the motor is 61A, then
the installed current rating of the 16 mm2 cable is lower
than the full load current and is not suitable for continuous use with the
motor. The 25 mm2 cable on the other hand has an installed
current rating that exceeds the motor full load current, and is therefore the
cable that should be selected.
Suppose a 25 mm2 cable is selected. If the maximum
permissible voltage drop is 5%, is the cable suitable for a run length of 90m?
A 25 mm2 cable has an ac resistance of 0.884
Ω/km and an ac reactance of 0.0895
Ω/km. The voltage drop across the cable is:
A voltage drop of 7.593V is equivalent to , which is lower than the maximum permissible voltage dorp of 5%.
Therefore the cable is suitable for the motor based on voltage drop
considerations.
The cable is operating normally at 75C and has a prospective fault
capacity (I2t) of 90,000 A2s.
What is the minimum size of the cable based on short circuit temperature rise?
PVC has a limiting temperature of 160C. Using the IEC formula, the short
circuit temperature rise constant is 111.329. The minimum cable size due to
short circuit temperature rise is therefore:
In this example, we also use the fuse for earth fault protection and it
needs to trip within 5s, which is at the upper end of the adiabatic period
where the short circuit temperature rise equation is still valid. Therefore,
it's a good idea to also check that the cable can withstand the short circuit
temperature rise for for a 5s fault. The 80A motor fuse has a 5s melting
current of 550A. The short circuit temperature rise is thus:
Therefore, our 25 mm2 cable is still suitable for this
application.
Suppose there is no special earth fault protection for the motor and a
bolted single phase to earth fault occurs at the motor terminals. Suppose that
the earth conductor for our 25 mm2 cable is 10 mm2.
If the maximum disconnection time is 5s, is our 90m long cable suitable based
on earth fault loop impedance?
The 80A motor fuse has a 5s melting current of 550A. The ac resistances
of the active and earth conductors are 0.884 Ω/km and 2.33 Ω/km) respectively.
The reactances of the active and earth conductors are 0.0895 Ω/km and 0.0967
Ω/km) respectively.
The maximum length of the cable allowed is calculated as:
The cable run is 90m and the maximum length allowed is 108m, therefore
our cable is suitable based on earth fault loop impedance. In fact, our 25 mm2
cable has passed all the tests and is the size that should be selected.
Table 2. Example of a cable waterfall chart
Sometimes it is convenient to group together similar types of cables
(for example, 415V PVC motor cables installed on cable ladder) so that instead
of having to go through the laborious exercise of sizing each cable separately,
one can select a cable from a pre-calculated chart.
These charts are often called "waterfall charts" and typically
show a list of load ratings and the maximum of length of cable permissible for
each cable size. Where a particular cable size fails to meet the requirements
for current carrying capacity or short circuit temperature rise, it is blacked
out on the chart (i.e. meaning that you can't choose it).
Preparing a waterfall chart is common practice when having to size many
like cables and substantially cuts down the time required for cable selection.
A professional, fully customisable Excel spreadsheet template for cable
sizing waterfall charts can be purchased from Tradebit.
The template is based on the calculation procedure described in this
page and includes waterfall charts for:
·
Three-phase motor loads
·
Three-phase feeder loads
·
Single-phase feeder loads
Screenshots from Cable Sizing Waterfall Chart
Template
|
|
Three-phase
motors
|
Single-phase
feeders
|
IEC
60364-5-52 (2009) "Electrical installations in buildings -
Part 5-52: Selection and erection of electrical equipment - Wiring
systems" is the IEC standard governing cable sizing.
NFPA 70 (2011)
"National Electricity Code" is the equivalent standard for IEC 60364
in North America and includes a section covering cable sizing in Article 300.
BS 7671 (2008)
"Requirements for Electrical Installations - IEE Wiring Regulations"
is the equivalent standard for IEC 60364 in the United Kingdom.
AS/NZS 3008.1 (2009)
"Electrical installations - Selection of cables - Cables for alternating
voltages up to and including 0.6/1 kV" is the standard governing low
voltage cable sizing in Australia and New Zealand. AS/NZS 3008.1.1 is for
Australian conditions and AS/NZS 3008.1.2 is for New Zealand conditions.
Cablesizer is a free online application for sizing cables to NEC and IEC
standards.
Most of the major power systems
analysis software packages (e.g. ETAP, PTW, etc) have a
cable sizing module. There also exists other (offline) software packages that
include cable sizing (for example from Solutions Electrical UK).