7.13.12Calculating internal earth fault loop impedance#

7.13.12.1Using cable resistance and reactance#

Internal impedance is the impedance of the circuit from the electrical installation’s point of supply to any point in the electrical installation. The impedance of the earth fault loop path is the sum of the internal and external path impedances. This is the maximum impedance that will allow sufficient active-to-earth fault current to flow in the circuit causing the circuit protection to activate and clear the fault; hence:

ZTotal = ZExternal + ZInternal

Once the external impedance has been determined, the maximum allowable internal impedance can be calculated:

ZInternal = ZTotal − ZExternal

The internal cable impedance is calculated in the same way as the external cable impedance shown from the R and X values provided in the tables for the specific cables selected. Typically, AS/NZS 3008.1.1 contains the necessary tables.

7.13.12.2Using cable cross section#

When the length and cross-sectional area of the active and earth (or PEN) cores are known, the internal impedance can be determined from the sum of the active and earth conductor impedances.

The resistance of a material can be found from the following relationship:

R = ρ L / S

where

R = resistance in ohms

ρ = resistivity in ohms mm² / metre

L = length of the conductor in metres

S = area of conductor in mm²

At 50 Hz, and cables up to 35 mm² the reactance of the circuit will be small compared with resistance so the impedance is effectively resistive.

The impedance of the internal part of the circuit consisting of the active and earth conductors is therefore given by:

ZInternal = ρ L (Sp + Se) / (Sp Se)

If it is assumed that the active and earth conductors are the same length, which they will be if in the same cable, then:

ZInternal = ρ L (Sp + Se) / (Sp Se)

The maximum internal impedance ZInternal will be a maximum when the cable length is a maximum Lmax.

7.13.12.3Maximum cable length for ZInternal#

Where the internal cable cross sectional area is constant throughout the run, the maximum length of run can be calculated so that the allowable ZInternal can be optimised.

The total circuit impedance ZTotal is the impedance, at nominal phase voltage (400 / √3 V), that allows the current to flow that will activate the circuit protection within the disconnect time required.

ZTotal = Uo / Ia

and

ZTotal = ZInternal + ZExternal

therefore

Uo / Ia = ZInternal + ZExternal

ZInternal = (Uo / Ia) − ZExternal

but

ZInternal = ρ LMax (Sp + Se) / (Sp Se)

therefore

ρ LMax (Sp + Se) / (Sp Se) = (Uo / Ia) − ZExternal

and

LMax = (Sp Se) / (ρ (Sp + Se)) ((Uo / Ia) − ZExternal)

where

LMax = maximum cable length (m) for maximum ZInternal

Uo = nominal phase voltage (V)

Se = area of earth core (mm²)

Sp = area of phase core (mm²)

Ia = current to activate the circuit protection in the disconnect time (A)

ρ = resistivity of conductor material (ohm mm² / m)

ZExternal = calculated / measured external circuit impedance (Ω)

This is the maximum cable length for the allowable internal impedance and protection selected.