Principle of earthing

- Principle of earthing

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.

The extent of the earth fault loop for a TT system is shown in

{Fig (1)}, and is made up of the following labelled parts.

Fig (1). The earth fault loop

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:

IF   =	Uo =	240 A	= 150 A
	Zs	1.6

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.

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. Thus the Tables of maximum earth-fault loop impedance .

- 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.

		Xl = 2(pi)fL and Xc  =	1
			2(pi)fC
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:

a) resistive and capacitive circuit - b) resistive and inductive circuit Fig (2). Impedance diagrams

 

These relationships can be shown in the form of a diagram applying Pythagoras' theorem as shown in {Fig 5.8}. 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	= (R² + X²)
	= (2² + 1²) =  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.

- Earth-fault loop impedance values

The over-riding requirement is that sufficient fault current must flow in the event of an earth fault to ensure that the protective device cuts off the supply before dangerous shock can occur. For normal 240 V systems, there are two levels of maximum disconnection time. These are:

For socket outlet circuits where equipment could be tightly grasped: 0.4 s

For fixed equipment where contact is unlikely to be so good: 5 s

The maximum disconnection time of 5 s also applies to feeders and sub-mains.

It must be appreciated that the longest disconnection times for protective devices, leading to the longest shock times and the greatest danger, will be associated with the lowest levels of fault current, and not, as is commonly believed, the highest levels.

Where the voltage is other than 240 V, [Table 41A] gives a range of disconnection times for socket outlet circuits, of which the lowest is 0.1 s for voltages exceeding 400 V.

In general, the requirement is that if a fault of negligible impedance occurs between a phase and earth, the earth-fault loop impedance must not be greater than the value calculated from..

	Zs <	Uo
		Ia
where	Zs =	the earth fault loop impedance (Ohms)
	Uo =	the system voltage to earth(V)
	Ia  =	the current causing automatic disconnection
	(operation of the protective device) in the required time [A]).

depend on the supply voltage and assume, as shown in the Tables, a value of 240 V. Whilst it would appear that 240 V is likely to be the value of the supply voltage in Great Britain for the foreseeable future, it is not impossible that different values may apply. In such a case, the tabulated value for earth fault loop impedance should be modified using the formula:-

	Zs =	Zt x	U
			U240
where	Zs =	is the earth fault loop impedance required for safety
	Zt =	is the tabulated value of earth fault loop impedance
	U =	is the actual supply voltage
	U240 =	is the supply voltage assumed in the Table.

As an alternative to this calculation, a whole series of maximum values of earth fault loop impedance i (from for disconnection within 0.4 s. The reader should not think that these values are produced in some mysterious way - all are easily verified using the characteristic curves

For example, consider a 20 A HRC fuse to BS88 used in a 240 V system. and indicates that disconnection in 0.4 s requires a current of about 130 A. It is difficult (if not impossible) to be precise about this value of current, because it is between the 100 A and 150 A current graduations.

Using these values,
Zs =	Uo	=	240	Ohms = 1.84 Ohms
	Ia		130

Reference to {Table(.1)} shows that the stated value is 1.8 Oh,s, the discrepancy being due to the difficulty in reading the current with accuracy. {Tables (.1) and(.2)} give maximum earth-fault loop impedance values for fuses and for miniature circuit breakers to give a minimum disconnection time of 0.4 s in the event of a zero impedance fault from phase to earth.

The reason for the inclusion of fixed equipment as well as distribution circuits in {Table (2)} will become apparent later in this sub-section.

Table (1) - Maximum earth-fault loop impedance for 240 V socket outlet circuits protected by fuses
Fuse rating (A)	Maximum earth-fault loop impedance (Ohms)
-	Cartridge BS 88	Cartridge BS 1361	Semi-enclosed BS3036
5	-	10.9	10.0
6	8.89	-	-
10	5.33	-	-
15	-	3.43	2.67
20	1.85	1.78	1.85
30	-	1.20	1.14
32	1.09	-	-
40	0.86	-	-
45	-	0.60	0.62

Table (2) - Maximum earth-fault loop impedance for 240 V circuits -protected by miniature circuit breakers to give compliance with 0.4 s disconnection time
-	Maximum earth-fault loop impedance (Ohms)
Device rating (A)	MCB type 1	MCB type 2	MCB type 3 and type C	MCB type B	MCB type D
5	12.00	6.86	4.80	-	2.40
6	10.00	5.71	4.00	8.00	2.00
10	6.00	3.43	2.40	4.80	1.20
15	4.00	2.29	1.60	-	0.80
16	3.75	2.14	1.50	3.00	0.75
20	3.00	1.71	1.20	2.40	0.60
25	2.40	1.37	0.96	1.92	0.48
30	2.00	1.14	0.80	-	0.40
32	1.88	1.07	0.75	1.50	0.38
40	1.5	0.86	0.60	1.20	0.30

The severity of the electric shock received when there is a phase to earth fault (indirect contact) depends entirely on the impedance of the circuit protective conductor. Since this volt drop is equal to fault current times protective conductor impedance, if the protective conductor has a lower impedance the shock voltage will he less. Thus it can be sustained for a longer period without extreme danger.

Socket outlet circuits can therefore have a disconnection time of up to 5 s provided that the circuit protective conductor impedance's are no higher than shown in {Table (3)} for various types of protection.

The reasoning behind this set of requirements becomes clearer if we take an example. {Table 5.3} shows that a 40 A cartridge fuse to BS 88 must have an associated protective conductor impedance of no more than 0.29 Ohms if it is to comply. from which we can see that the current for operation in 5 s is about 170 A. The maximum volt drop across the conductor (the shock voltage) is thus 170 x 0.29 or 49.3 V.

Table (3) - Maximum impedance of circuit protective conductors to allow 5 s disconnection time for socket outlets
-	Maximum impedance of circuit protective conductor
Rating (A)	Fuse BS 88	Fuse BS 1361	Fuse BS 3036	MCB type 1	MCB type 2	MCB type 3 & C	MCB type B	MCB type D
5	-	3.25	3.25	2.50	1.43	1.00	-	0.50
6	2.48	-	-	2.08	1.19	0.83	1.67	0.42
10	1.48	-	-	1.25	0.71	0.50	1.00	0.25
15	-	0.96	0.96	0.83	0.48	0.33	-	-
16	0.83	-	-	0.78	0.45	0.31	0.63	0.16
20	0.55	0.55	0.63	0.63	0.36	0.25	0.50	0.12
25	0.43	-	-	-	-	-	-	0.10
30	-	0.36	0.43	0.42	0.24	0.17	-	-
32	0.34	-	-	0.39	0.22	0.16	0.31	0.08
40	0.26	-	-	0.31	0.18	0.13	0.25	0.06
45	-	0.18	0.24	0.28	0.16	0.11	0.22	0.06

Table (4) - Maximum earth-fault loop impedance for 240 V fixed equipment distribution circuits protected by fuses
-	Maximum earth-fault loop impedance
Device rating (A)	Cartridge BS 88	Cartridge BS 1361	Semi-enclosed BS 3036
5	-	17.1	-
6	14.1	-	-
10	7.74	-	-
15	-	5.22	5.58
16	4.36	-	-
20	3.04	2.93	4.00
30	-	1.92	2.76
32	1.92	-	-
40	1.41	-	-
45	-	1.00	1.66
50	1.09	-	-

Application of the same reasoning to all the figures gives shock voltages of less than 50 V. This limitation on the impedance of the CPC is of particular importance in TT systems where it is likely that the resistance of the earth electrode to the general mass of earth will be high.

The breaking time of 5 s also applies to fixed equipment, so the earth-fault loop impedance values can be higher for these circuits, as well as for distribution circuits. For fuses, the maximum values of earth-fault loop impedance for fixed equipment are given in {Table (4)}.

No separate values are given for miniature circuit breakers. will reveal that there is no change at all in the current causing operation between 0.4 s and 5 s in all cases except the Type 1. Here, the vertical characteristic breaks off at 4 s, but this makes little difference to the protection. In this case, the values given in{Table(2)} can be used for fixed equipment as well as for socket outlet circuits. An alternative is to calculate the loop impedance as described above.

- Protective conductor impedance

It has been shown in the previous sub-section how a low-impedance protective conductor will provide safety from shock in the event of a fault to earth. This method can only be used where it is certain that the shock victim can never be in contact with conducting material at a different potential from that of the earthed system in the zone he occupies. When overcurrent protective devices are used as protection from electric shock, the protective conductor must be in the same wiring system as, or in close proximity to, the live conductors. This is intended to ensure that the protective conductor is unlikely to he damaged in an accident without the live conductors also being cut.

{Figure (9)} shows a method of measuring the resistance of the protective conductor, using a line conductor as a return and taking into account the different cross-sectional areas of the phase and the protective conductors.

Fig (3) - Measurement of protective conductor resistance

Taking the cross-sectional area of the protective conductor as Ap and that of the line (phase or neutral) conductor as Al , then

Rp = resistance reading x	Al
	Al + Ap

For example, consider a reading of 0.72 Ohms obtained when measuring a circuit in the way described and having 2.5 mm² line conductors and a 1.5 mm² protective conductor. The resistance of the protective conductor is calculated from:

Rp =  R x	Al	= 0.72 x 2.5	Ohms
	Al + Ap	2.5 + 1.5
=	0.72 x 2.5	Ohms =	0.45 Ohms
	4.0

- Maximum circuit conductor length

The complete earth-fault loop path is made up of a large number of parts as shown in {Fig (1)}, many of which are external to the installation and outside the control of the installer. These external parts make up the external loop impedance (Ze). The rest of the earth-fault loop impedance of the installation consists of the impedance of the phase and protective conductors from the intake position to the point at which the loop impedance is required.

Since an earth fault may occur at the point farthest from the intake position, where the impedance of the circuit conductors will be at their highest value, this is the point which must be considered when measuring or calculating the earth-fault loop impedance for the installation. Provided that the external fault loop impedance value for the installation is known, total impedance can be calculated by adding the external

Table (5) - Resistance per metre of copper conductors at 20°C for calculation of R1 + R2
Conductor cross-sectional area (mm²)	Resistance per metre run  (m ohms / m)
1.0	18.1
1.5	12.10
2.5	7.41
4.0	4.61
6.0	3.08
10.0	1.83
16.0	1.15
25.0	0.727
Note that to allow for the increase in resistance with increased temperature under fault conditions the values of {Table 5.5} must be multiplied by 1.2 for p.v.c.

impedance to that of the installation conductors to the point concerned. The combined resistance of the phase and protective conductors is known as R1+ R2. The same term is sometimes used for the combined resistance of neutral and protective conductors. In the vast majority of cases phase and neutral conductors have the same cross-sectional area and hence the same resistance.

For the majority of installations, these conductors will be too small for their reactance to have any effect (below 25 mm² cross-sectional area reactance is very small), so only their resistance's will be of importance. This can be measured by the method indicated in {Fig (3)}, remembering that this time we are interested in the combined resistance of phase and protective conductors, or can be calculated if we measure the cable length and can find data concerning the resistance of various standard cables. These data are given here as {Table (5)}.

The resistance values given in {Table (5)} are for conductors at 20°C. Under fault conditions the high fault current will cause the temperature of the conductors to rise and result in an increase in resistance. To allow for this changed resistance, It should be mentioned that the practice which has been adopted here of adding impedance and resistance values arithmetically is not strictly correct. Phasor addition is the only perfectly correct method since the phase angle associated with resistance is likely to he different from those associated with impedance, and in addition impedance phase angles will differ from one another. However, if the phase angles are similar, and this will be so in the vast majority of cases where electrical installations are concerned, the error will be acceptably small.

It is often assumed that higher conductor temperatures are associated with the higher levels of fault current. In most cases this is untrue. A lower fault level will result in a longer period of time before the protective device operates to clear it, and this often results in higher conductor temperature.