Electric and Electronic Department Supply Cable Sizing Calculation, C5

V. Supply Cable Sizing Calculation

5.1 Introduction

5.1.1 Generality

Figure 5.1 Cable Overview

This course 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 emphasize certain things over others. However the general principles
underlying any cable sizing calculation do not change. In this course, a general
methodology for sizing cables is first presented and then the specific
international standards are introduced.

5.1.2 Why do the calculation?

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

5.1.3 When to do the calculation?

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

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groups of cables with similar characteristics (e.g. cables installed on ladder

feeding induction motors).

5.2 General Methodology

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.

5.2.1 Step 1: Data Gathering

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:

Load Details

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

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Cable Construction

The basic characteristics of the cable's physical construction, which includes:

 Conductor material - normally copper or aluminum

 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
 Insulation type - e.g. PVC (Poly Vinyl Chloride) , XLPE (Cross
linked polyethylene), EPR (Ethylene Propylene Rubber)
 Number of cores - single core or multicore (e.g. 2C, 3C or 4C)

Installation Conditions

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?

5.2.2 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.

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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.

5.2.2.1 Base Current Ratings

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Example of base current rating table (Except 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.

In the absence of any guidance, the following reference based current ratings
may be used.

5.2.2.2 Installed Current Ratings

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.

In the absence of any guidance, the following reference derating factors may be
used.

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5.2.2.3 Cable Selection and Coordination with Protective Devices

Feeders

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

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.

5.2.3 Step 3: Voltage Drop

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:

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 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

5.2.3.1 Cable Impedances

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.

5.2.3.2 Calculating Voltage Drop

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)

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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)

5.2.3.3 Maximum Permissible Voltage Drop

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.

5.2.3.4 Calculating Maximum Cable Length due to Voltage Drop

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:

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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)

5.2.4 Step 4: Short Circuit Temperature Rise

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

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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.

5.2.4.1 Minimum Cable Size Due to Short Circuit Temperature Rise

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 aluminum conductors)

Where i is the initial conductor temperature (deg C)

f is the final conductor temperature (deg C)

5.2.4.2 Initial and Final Conductor Temperatures

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

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insulation will determine the maximum operating temperature and limiting

temperatures.

As a rough guide, the following temperatures are common for the different
insulation materials:

Table 5.7

Material Max Operating Temperature oC Limiting Temperature oC

PVC 75 160
EPR 90 250
XLPE 90 250

5.2.4.3 Short Circuit Energy

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) (HRC: high rupturing capacity), 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.

5.2.5 Step 5: Earth Fault Loop Impedance

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

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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.

5.2.5.1 The Earth Fault Loop

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)

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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).

5.2.5.2 Maximum Cable Length

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)

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5.3 Worked Example

In this example, we will size a cable for a 415V, 30kW three-phase motor from
the MCC to the field.

5.3.1 Step 1: Data Gathering

The following data was collected for the cable to be sized:

 Cable type: Cu/PVC/GSWB/PVC, 3C+E, 0.6/1kV

 Operating temperature: 75oC
 Cable installation: above ground on cable ladder bunched together
with 3 other cables on a single layer and at 30oC ambient
temperature
 Cable run: 90m (including tails)
 Motor load: 30kW, 415V three phase, full load current = 61A,
power factor = 0.85
 Protection: use fuse of rating = 80A, max prospective fault I2t =
90,000 A2s , 5s melt time = 550A

5.3.2 Step 2: Cable Selection Based on Current Rating

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, 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.

5.3.3 Step 3: Voltage Drop

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:

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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.

5.3.4 Step 4: Short Circuit Temperature Rise

The cable is operating normally at 75oC 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 160oC. 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 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.

5.3.5 Step 5: Earth Fault Loop Impedance

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.

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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.

Waterfall Charts

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

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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.

International Standards

IEC

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.

NEC

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

BS 7671 (2008) "Requirements for Electrical Installations - IEE Wiring

Regulations" is the equivalent standard for IEC 60364 in the United Kingdom.

AS/NZS

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.

Computer Software

Cablesizer is a free online application for sizing cables to IEC standards.

Most of the major electrical analysis 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).

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Appendix

Table 5.1: Current carrying capacity, in A, in continuous service for cables

based on maximum conductor operating temperature of 80°C (ambient
temperature 45°C)

Table 5.2: Current carrying capacity, in A, in continuous service for cables

based on maximum conductor operating temperature of 85°C (ambient
temperature 45°C)

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Table 5.3: Current carrying capacity, in A, in continuous service for cables

based on maximum conductor operating temperature of 95°C (ambient
temperature 45°C)

Table 5.4: Correction factors for various ambient air temperatures

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Table 5.5: Correction factors for short-time loads

Table 5.6: Correction factors for intermittent service

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