Electrical Wire Sizing Calculation
Introduction
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
General Methodology
All cable sizing methods more or less follow the same basic six step process:
- Gathering data about the cable, its installation conditions, the load that it will carry, etc
- Determine the minimum cable size based on continuous current carrying capacity
- Determine the minimum cable size based on voltage drop considerations
- Determine the minimum cable size based on short circuit temperature rise
- Determine the minimum cable size based on earth fault loop impedance
- Select the cable based on the lowest of the sizes calculated in step 2, 3, 4 and 5
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 )
Locked rotor or load starting current (A)
Starting power factor ()
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
Cable Construction
The basic characteristics of the cable’s physical construction, which includes:
Conductor material - normally copper or aluminium
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, XLPE, EPR
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?
Step 2: Cable Selection Based on Current Rating
Current flowing through a cable generates heat through the resistivity losses in the conductors, dielectric losses through the insulation and resistivity losses from current flowing through any cable screens / shields and armoring.
The cable components (particularly the insulation) 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. 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 resistivity 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.
Base Current Ratings
International standards and manufacturers of cables will quote base current ratings of different types of cables in tables such as the one shown below. Each of these tables pertain to a specific type of cable construction (e.g. copper conductor, XLPE insulated, 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.
Reference Installation Method
Reference installation method mentioned in above table is explained below:
Method A
A1 - Insulated single core conductors in conduit in a thermally insulated wall
A2 - Multicore cable in conduit in a thermally insulated wall
This method also applies to single core or multicore cables installed directly in a thermally insulated wall (use methods A1 and A2 respectively), conductors installed in molding, architraves and window frames.
Method B
B1 - Insulated single core con ductors in conduit on a wall
B2 - Multicore cable in conduit on a wall
This method applies when a conduit is installed inside a wall, against a wall or spaced less than 0.3 x D (overall diameter of the cable) from the wall. Method B also applies for cables installed in trunking / cable duct against a wall or suspended from a wall and cables installed in building cavities.
Method C
C - Single core or multi -core cable on a wooden wall
This method also applies to cables fixed directly to walls or ceilings, suspended from ceilings, installed on unperformed cable trays (run horizontally or vertically) and installed directly in a masonry wall (with thermal resistivity less than 2 K.m/W).
Method D
D1 - Multicore or single core cables installed in conduit buried in the ground
D2 - Multicore or single core cables buried directly in the ground
Method E
E - Multicore cable in free -air
This method applies to cables installed on cable ladder, perforated cable tray or cleats provided that the cable is spaced more than 0.3 x D (overall diameter of the cable) from the wall. Note that cables installed on unperformed cable trays are classifies d under Method C.
Method F
F - Single core cables touching in free -air
This method applies to cables installed on cable ladder, perforated cable tray or cleats provided that the cable is spaced more than 0.3 x D (overall diameter of the cable) from the wall. Note that cables installed on unperformed cable trays are classified under Method C.
Method G
When the ed inst lltinnditins differ from the Conditions, derating or correction) factors can e applied to the ase current ratings to obtain the actual installed current ratings.
International standards and cable manufacturers ill provide derating factors for a range of installation conditions, for example ambient /soil temperature, grouping or bunching of cables, soil thermal resistivity , etc. he installed current rating is calculated by multiplying the base current rating each of the derating factors, i.e.
here is the installed current rating A)
is the base current rating A)
are the product of all the berating factors or example, suppose a cable had an ambient temperature derating factor b = and a grouping debating factor of kg = . , then the overall derating factor d =
. x . = . . or a cable ith a base current rating of A, the installed current rating would be Ic = . x =
When si ing cables for loads, the upstream protective device fuse or circuit breaker) is typically selected to also protect the cable against damage from thermal overload. he
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)
A cable’s conductor can be seen as an impedance and as a result, he never current flows through a cable, there will be a voltage drop across it, derived by Ohm’s law i.e. V = IZ).
he 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
Cl Impedance
The impedance of the cable is a function of the cable cross-sectional area) and the length of the cable. cable manufacturers will quote a cable’s resistance and reactance in /km.
Calculating Voltage p or AC systems, the method of calculating voltage drops based on load power factor is commonly used. ull 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.
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 /km) is the ac reactance of the cable /km)
is the load power factor )
is the length of the cable m)
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 /km) is the ac reactance of the cable /km)
is the load power factor pu)
is the length of the cable m)
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 /km) is the length of the cable m)
Maximum Permission Voltage Drop:
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 nominal voltage. or example, if the nominal voltage is VAC, then most appliances will run at VAC. Cables are typically for a more conservative maximum voltage drop, in the range of at full load.
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 si e given a maximum permissibly voltage drop e.g. of nominal voltage at full
load) rather than the voltage drop itself. or example, by doing this it is possible to construct tables showing the maximum lengths corresponding to different cable si es 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. of V nominal voltage = . V).
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 /km)
is the ac reactance of the cable /km) is the load power factor )
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 /km)
is the ac reactance of the cable /km) is the load power factor )
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 /km) is the length of the cable m)
Step 4 Short circuit temperature
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 si ed to withstand the largest short circuit that it is expected to see.
Minimum Cable Size use to Short Circuit Temperature
The minimum cable 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. if international standards have different treatments of the temperature rise constant, but by way of example, IEC -5-54 calculates it as follows:
Initial and Final Conductor Temperatures
The initial conductor temperature is typically chosen to be the operating temperature of the cable. The final conductor temperature is typically chosen to be the limiting temperature of the insulation.
Short Circuit Energy
The short circuit energy is normally chosen as the maximum short circuit that the cable could potentially experience. we over for circuits with current limiting devices such as C fuses), then the short circuit energy chosen should be the maximum prospective le-through energy of the protective device, which can be found from manufacturer data.
Step 5: Earth Fault loop Impedance
Sometimes it is desirable or necessary) to consider the earth fault loop impedance of a circuit in the 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. or 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. < s and will definitely require earth fault protection).
we Over 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. or 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 ) 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
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. we over 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 )
is the impedance of the active conductor ) is the impedance of the earth conductor )
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 /km) and are the reactance of the active and earth conductors respectively /km) 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 ) 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 /km) and are the reactance of the active and earth conductors respectively /km)
that the voltage 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 bus bars. This voltage is commonly represented by applying some factor to the nominal voltage. A conservative value of = 0. can be used so that:
Where Vn is the nominal phase to earth voltage V)