EARTH FAULT LOOP IMPEDANCE

The path followed by fault current as the result of a low impedance occurring between the phase
conductor and earthed metal is called the earth fault loop. Current is driven through the loop impedance by the supply voltage.

l. - the phase conductor from the transformer to the installation
2. - the protective device(s) in the installation
3. - the installation phase conductors from the intake position to the fault
4. - the fault itself (usually assumed to have zero impedance)
5. - the protective conductor system
6. - the main earthing terminal
7. - the earthing conductor
8. - the installation earth electrode
9. - the general mass of earth
10. - the Supply Company's earth electrode
11. - the Supply Company's earthing conductor
12. - the secondary winding of the supply transformer
For a TN-S system (where the Electricity Supply Company provides an earth terminal), items 8 to 10 are
replaced by the PE conductor, which usually takes the form of the armouring (and sheath if there is one)
of the underground supply cable.

For a TN-C-S system (protective multiple earthing) items 8 to 11 are replaced by the combined neutral and earth conductor.
For a TN-C system (earthed concentric wiring), items 5 to 11 are replaced by the combined neutral and earth wiring of both the installation and of the supply.
It is readily apparent that the impedance of the loop will probably be a good deal higher for the TT
system, where the loop includes the resistance of two earth electrodes as well as an earth path, than for the other methods where the complete loop consists of metallic conductors.

The importance of loop impedance

The earth fault loop impedance can be used with the supply voltage to calculate the earth-fault current.
IF =Uo
Zs
where IF = fault current, A
Uo = phase voltage, V

Zs = loop impedance
For example, if a 240 V circuit is protected by a 15 A semi-enclosed fuse and has an earth-fault loop
impedance of 1.6 Ohms, the earth-fault current in the event of a zero impedance earth fault will he:

This level of earth-fault current will cause the fuse to operate quickly. From  the time taken for
the fuse to operate will be about 0.15 s. Any load current in the circuit will be additional to the fault current and will cause the fuse to operate slightly more quickly. However, such load current must not be taken into account when deciding disconnection time, because it is possible that the load may not be connected when the fault occurs.
occurs.
Note that there is no such thing as a three-phase line/earth fault, although it is possible for three faults to occur on the three lines to earth simultaneously. As far as calculations for fault current are concerned, the voltage to earth for standard UK supplies is always 240 V, for both single-phase and three-phase
systems.

The resistance/impedance relationship
Resistance, measured in ohms, is the property of a conductor to limit the flow of current through it when a voltage is applied.
I = U
R
where I = current, A
U = applied voltage. V
R = circuit resistance, Ohms
Thus, a voltage of one volt applied to a one ohm resistance results in a current of one ampere.
When the supply voltage is alternating, a second effect, known as reactance (symbol X) is to be
considered. It applies only when the circuit includes inductance and/or capacitance, and its value,
measured in ohms, depends on the frequency of the supply as well as on the values of the inductance
and/or the capacitance concerned. For almost all installation work the frequency is constant at 50 Hz.
Thus, inductive reactance is directly proportional to inductance and capacitive reactance is inversely
proportional to capacitance.

where Xl = inductive reactance (Ohms)
Xc =capacitive reactance (Ohms)
(pi) =the mathematical constant (3.142)
f =the supply frequency (Hz)
L =circuit inductance (H)
C =circuit capacitance (F)


Resistance (R) and reactance (Xl or Xc) in series add together to produce the circuit impedance (symbol
z), but not in a simple arithmetic manner. Impedance is the effect which limits alternating current in a
circuit containing reactance as well as resistance.
Z =U
I
where Z =impedance (Ohms)
U =applied voltage (V)
I =current (A)
It follows that a one volt supply connected across a one ohm impedance results in a current of one
ampere.
When resistance and reactance are added this is done as if they were at right angles, because the
current in a purely reactive circuit is 90° out of phase with that in a purely resistive circuit. The
relationships between resistance, reactance and impedance are:

These relationships can be shown in the form of a diagram applying Pythagoras' theorem as shown in
above}. The two diagrams are needed because current lags voltage in the inductive circuit, but leads it in the capacitive. The angle between the resistance R and the impedance Z is called the circuit phase angle, given the symbol a (Greek 'phi'). If voltage and current are both sinusoidal, the cosine of this angle, cos a, is the circuit power factor, which is said to be lagging for the inductive circuit, and leading for the capacitive.

In practice, all circuits have some inductance and some capacitance associated with them. However, the
inductance of cables only becomes significant when they have a cross-sectional area of 25 mm² and
greater. Remember that the higher the earth fault loop impedance the smaller the fault current will be.
Thus, if simple arithmetic is used to add resistance and reactance, and the resulting impedance is low
enough to open the protective device quickly enough, the circuit will be safe. This is because the
Pythagorean addition will always give lower values of impedance than simple addition.
For example, if resistance is 2 Ohms and reactance 1 Ohm, simple arithmetic addition gives
Z = R + X – 2 + 1 = 3 Ohms
and correct addition gives
Z = Ö(R² + X²) = Ö(2² + 1²) = Ö 5 = 2.24 Ohms
If 3 Ohms is acceptable, 2.24 Ohms will allow a larger fault current to flow which will operate the
protective device more quickly and is thus even more acceptable.