BS – Cable Size Under Short Circuit Calculation

This section describes the fault current calculation that needs to be performed after the cable has been sized.

The adiabatic method shown below calculates maximum short circuit current. The larger the cable, the larger the current the cable can withstand without damage.

Step – I Calculate Source Short Circuit Current

ISC =   (Er * 1000) * (100)

                V * (Imp %)

Where:

V = Phase voltage (Vph * Ö3/2) for 1 phase, Line voltage Vl for 2 phase or Line voltage (Vl * Ö3) for 3 phase

Er = Equipment rating with units in kVA

Imp % = Equipment Impedance expressed as a percentage

Step – II Calculate Source Impedance

Zsc = V/Isc

Where:

Zsc = source impedance in ohms

Isc = phase current in amps

V = voltage in volts

Step – III Calculate Cable Impedance 1 (When cable catalogue has valid values)

If the cable catalogue data includes the resistive and reactive value then use the following equation:

Zc1 = (L/1000) * Ö[(Rc)2 + (Xc)2]

Where:

L = length in meters

Rc = resistance of active conductor (Ohms/km)

Xc = reactance of active conductor (Ohms/km)

Zc1 = cable impedance in Ohms

Step – IV Calculate Cable Impedance 1 (If No cable catalogue values)

If conductor resistive and reactive values are not available in the cable catalogue, then impedance values are taken from BS standard impedance tables.

Zc1 = ([(R * L * cosø) / A] + [X * L * sinø])

Where:

R = Resistivity of conductors in normal service, taken equal to the Resistivity at the temperature in normal service, i.e. 1.25 times the Resistivity at 20°C, or 0.0225Wmm2/m for copper and 0.036Wmm2/m for aluminium

L = route length of circuit, in metres

A = cross-sectional area of conductors, in mm2

cosø = power factor; in the absence of precise details, the power factor is taken as 0.8 (sin ø = 0.6)

X = reactance per unit length of conductors, which is taken to be 0.00008W/m in the absence of other details

Zc1 is in Ohms

If cables are in parallel (see the screen shot above) the ‘No. of Cables:’ value will be 2 or more (in future).

The equation to find the total impedance is:

1/ZTOTALc1 = 1/Zc1A + 1/Zc1B + 1/Zc1C …….+ 1/Zc1n

Where:

ZTOTALc1 = total impedance for cable in ohms

1/Zc1A = impedance for cable if ‘No. of Cables:’ value = 1, in ohms

1/Zc1B = impedance for cable if ‘No. of Cables:’ value = 2, in ohms

1/Zc1C = impedance for cable if ‘No. of Cables:’ value = 3, in ohms

1/Zc1n = impedance for cable if ‘No. of Cables:’ value = n, in ohms

Since system only allows 2 cables to be in parallel the equation can be simplified to:

ZTOTALc1 = Zc1/N

Where:

Zc1 is in Ohms

N = number of cables in parallel, N = 1 when no cable in parallel

Step - V Calculate Cable Impedance 2 (If No cable catalogue values)

In this example there is a cable between switchboard busbar SWB-2 and incomer MCC-1.

Before performing the calculation the system needs to check if it is a power cable.

Then if there is an impedance value for the cable.

Then if it is in parallel.

The calculation is exactly the same as the Cable Impedance 1 calculation.

Step – VI Calculate Total Impedance

Z = Zsc + ZTOTALc1N + ZTOTALc2 + ……. + ZTOTALcn

Where:

Z is total impedance for Isc in ohms

Zsc = source impedance in ohms

ZTOTALc1 = total impedance for cable in ohms

ZTOTALc2 = total impedance for cable in ohms

ZTOTALcn = total impedance for cable in ohms

Step – VII Calculate Short Circuit Current for Sized Cable

Isc = V/Z

Where:

Isc is short circuit current in amps

V is voltage in volts

Z is total impedance for Isc in ohms

Step - VIII Calculate Korg Factor

1. Find the Initial Temperature

   Initial Temperature = Conductor Temp (from the Lookup Current Rating Table)

2. Find the Final Temperature (default values are shown in the table below)

   	Limit	Insulation Type	Cond. Temp	Core Size
   Final Temperature	160	Thermoplastic	70	<= 300 mm2
   	140	Thermoplastic	70	> 300 mm2
   	250	Thermosetting	90
   	160	Mineral	70
   	250	Mineral	105

3. Find the Material K Factor (from Lookup table - see below)

   b is the reciprocal of temperature coefficient of resistance of the current carrying component at 0°C

   This K factor is based on BS 7454:1991+A1:2008.

   	Material	Material Factor	(b)
   K Factor Lookup	Cu	226	234.5
   	Al	148	228

   Refer to also the Beta value against materials

4. Find the Korg Factor using this formula:

   Korg = Ö[(Material Factor)2 * Log [(Final Temperature + b) / (Initial Temperature + b)]]

   

   A = Ö((Isc/P)2 * t)/Korg

Step – IX Calculate Core Size based on Short Circuit Current

A = Ö((Isc/P)2 * t)/Korg

Where:

A is the cross-sectional area of the current-carrying component, in square millimetres.

Isc is the short-circuit current

t is the duration of short circuit

Korg is constant

P is the number of conductors in parallel

The results of this calculation are displayed in the Sizing Result tab as shown below: