Earth Loop Calculation

Form

A 3.7kW load with a PF of 0.64 is fed via a circuit of 8.8 metres wired in cable with line conductor of 4mm² and a CPC of 4mm².

The installation has a Ze of 0.38Ω.

Conductor installation & type is Not incorporated in cable - 70°C Thermoplastic (PVC)

Calculate Ib, In, the volt drop, the circuits Zs and fault current and whether the cables cpc is sufficient according to the adiabatic equation.

Form
Ze Circuit Length (metres) Live CSA (mm²) CPC CSA (mm²) Conductor Installation I (the earth fault current) t (the disconnection time from app 3) k (factor) Password

Zs Calculation

From Table I1 of the OSG obtain the resistance values for (R1+R2) (mΩ/m) for a 4mm² Line and 4mm² CPC cable.
Value found to be 9.22(mΩ/m)

Using this value multiply it by the length in metres and correct it by the factor for how the CPC is incorporated.

R1+R2 = \frac{9.22 \times 8.8 \times 1.04}{1000}

R1+R2 = 0.08 Ω

Now using the Ze given in the question calculate the Zs of the circuit at its farthest point.

Zs = Ze + R1 + R2

Zs = 0.38 + 0.08

Zs = 0.46 Ω

Now we need to compare this value with the max allowed for that breaker. From Table 41.3 (pg 68) of BS7671 a 32A Type B breaker has a Max EFLI of 1.37Ω.

Success! Our reading of 0.46Ω is less so complies and will have a disconnection time of 0.1s.

Design Current Ib and Protective Device Rating In

I_{b} = \frac{Watts}{Volts x PF}

I_{b} = \frac{3700}{230 x 0.64}

I_{b} = 25.14 A

We now need to choose a protective device that is rated the same or greater than this design current of 25.14A. We will chose a 32A breaker.

Fault Current Calculation

Fault Current = \frac{Voltage}{Zs}

Fault Current = \frac{230}{0.46}

Fault Current = 500 A

Adiabatic Calculation

s = \frac{\sqrt{I^{2} t}}{k}

s = \frac{\sqrt{500^{2} \times 0.1}}{143}

s = \frac{\sqrt{25000}}{143}

s = \frac{158.11}{143}

s = 1.11 {mm}^{2}

Success! Our CPC of 4mm exceeds this min calculated CPC size of 1.11mm so this cabling is OK.

Table 54.7

Minimum CSA of protective conductor in relation to CSA of associated line conductor

CSA of line conductor S	Minimum CSA of protective conductor if same material	Minimum CSA of protective conductor if different material
mm²	mm²	mm²
S ≤ 16	S	k1/k2 x S
16 < S ≤ 35	16	k1/k2 x 16
S > 35	S/2	k1/k2 x S/2

Table 41.3

Max Zs for Circuit Type B Breakers for Uo of 230V

Rating (A)	3	6	10	16	20	25	32	40	50	63	80	100	125
Zs (ohms)	14.57	7.28	4.37	2.73	2.19	1.75	1.37	1.09	0.87	0.69	0.55	0.44	0.35

Table I1 OSG pg 218

Line conductor	Protective conductor	Copper
1	-	18.10
1	1	36.20
1.5	-	12.10
1.5	1	30.20
1.5	1.5	24.20
2.5	-	7.41
2.5	1	25.51
2.5	1.5	19.51
2.5	2.5	14.82
4	-	4.61
4	1.5	16.71
4	2.5	12.02
4	4	9.22
6	-	3.08
6	2.5	10.49
6	4	7.69
6	6	6.16
10	-	1.83
10	4	6.44
10	6	4.91
10	10	3.66
16	-	1.15
16	6	4.23
16	10	2.98
16	16	2.30

Table I3 OSG pg 220

Conductor Installation	70°C Thermoplastic (PVC)	90°C Thermoplastic (PVC)	90°C Thermosetting
Not incorporated in a cable and not bunched (NOTE 1)	1.04	1.04	1.04
Incorporated in a cable or bunched (NOTE 2)	1.20	1.28	1.28

K Factors

Table 54.2 pg 200 BS7671

Values of k for insulated protective conductor not incorporated in a cable and not bunched with cables, or for separate bare protective conductor in contact with cable covering but not bunched with cables where the assumed initial temperature is 30°C.

Material of Conductor / Insulation of protective conductor or cable covering	70°C Thermoplastic	90°C Thermoplastic	90°C Thermosetting
Copper	143/133*	143/133*	176
Aluminium	95/88*	95/88*	116
Steel	52	52	64
Assumed Initial Temperature	30°C	30°C	30°C
Final Temperature	160°C/140°C*	160°C/140°C*	250°C

*Above 300mm².

Table 54.3 pg 200 BS7671

Values of k for insulated protective conductor incorporated in a cable or bunched with cables, where the assumed initial temperature is 70°C or greater.

Material of Conductor / Insulation material	70°C Thermoplastic	90°C Thermoplastic	90°C Thermosetting
Copper	115/103*	100/86*	143
Aluminium	76/68*	66/57*	94
Assumed Initial Temperature	70°C	90°C	90°C
Final Temperature	160°C/140°C*	160°C/140°C*	250°C

*Above 300mm².

Volt Drop

Volt Drop = mV/A/m x Ib x length

Volt Drop = \frac{11 x 25.14 x 8.8}{1000}

Volt Drop = 2.43 V

Earth Loop Calculation

Form

A 3.7kW load with a PF of 0.64 is fed via a circuit of 8.8 metres wired in cable with line conductor of 4mm² and a CPC of 4mm².

The installation has a Ze of 0.38Ω.

Conductor installation & type is Not incorporated in cable - 70°C Thermoplastic (PVC)

Calculate Ib, In, the volt drop, the circuits Zs and fault current and whether the cables cpc is sufficient according to the adiabatic equation.

Zs Calculation

From Table I1 of the OSG obtain the resistance values for (R1+R2) (mΩ/m) for a 4mm² Line and 4mm² CPC cable.
Value found to be 9.22(mΩ/m)

Using this value multiply it by the length in metres and correct it by the factor for how the CPC is incorporated.

Now using the Ze given in the question calculate the Zs of the circuit at its farthest point.

Now we need to compare this value with the max allowed for that breaker. From Table 41.3 (pg 68) of BS7671 a 32A Type B breaker has a Max EFLI of 1.37Ω.

Success! Our reading of 0.46Ω is less so complies and will have a disconnection time of 0.1s.

Success! Our reading of 0.46Ω is less so complies and will have a disconnection time of 0.1s.

Design Current Ib and Protective Device Rating In

We now need to choose a protective device that is rated the same or greater than this design current of 25.14A. We will chose a 32A breaker.

Fault Current Calculation

Adiabatic Calculation

Success! Our CPC of 4mm exceeds this min calculated CPC size of 1.11mm so this cabling is OK.

Success! Our CPC of 4mm exceeds this min calculated CPC size of 1.11mm so this cabling is OK.

Table 54.7

Minimum CSA of protective conductor in relation to CSA of associated line conductor

Table 41.3

Max Zs for Circuit Type B Breakers for Uo of 230V

Table I1 OSG pg 218

Table I3 OSG pg 220

K Factors

Table 54.2 pg 200 BS7671

Values of k for insulated protective conductor not incorporated in a cable and not bunched with cables, or for separate bare protective conductor in contact with cable covering but not bunched with cables where the assumed initial temperature is 30°C.

*Above 300mm².

Table 54.3 pg 200 BS7671

Values of k for insulated protective conductor incorporated in a cable or bunched with cables, where the assumed initial temperature is 70°C or greater.

*Above 300mm².

Volt Drop

Pass! Our reading of 2.43V is below the 11.5V max for non lighting so passes.

Pass! Our reading of 2.43V is below the 11.5V max for non lighting so passes.

Pass! Our reading of 2.43V is below the 6.9V max for lighting so passes.

Pass! Our reading of 2.43V is below the 6.9V max for lighting so passes.

Earth Loop Calculation

Form

A 3.7kW load with a PF of 0.64 is fed via a circuit of 8.8 metres wired in cable with line conductor of 4mm² and a CPC of 4mm².

The installation has a Ze of 0.38Ω.

Conductor installation & type is Not incorporated in cable - 70°C Thermoplastic (PVC)

Calculate Ib, In, the volt drop, the circuits Zs and fault current and whether the cables cpc is sufficient according to the adiabatic equation.

Zs Calculation

From Table I1 of the OSG obtain the resistance values for (R1+R2) (mΩ/m) for a 4mm² Line and 4mm² CPC cable. Value found to be 9.22(mΩ/m)

Using this value multiply it by the length in metres and correct it by the factor for how the CPC is incorporated.

Now using the Ze given in the question calculate the Zs of the circuit at its farthest point.

Now we need to compare this value with the max allowed for that breaker. From Table 41.3 (pg 68) of BS7671 a 32A Type B breaker has a Max EFLI of 1.37Ω.

Success! Our reading of 0.46Ω is less so complies and will have a disconnection time of 0.1s.

Success! Our reading of 0.46Ω is less so complies and will have a disconnection time of 0.1s.

Design Current Ib and Protective Device Rating In

We now need to choose a protective device that is rated the same or greater than this design current of 25.14A. We will chose a 32A breaker.

Fault Current Calculation

Adiabatic Calculation

Success! Our CPC of 4mm exceeds this min calculated CPC size of 1.11mm so this cabling is OK.

Success! Our CPC of 4mm exceeds this min calculated CPC size of 1.11mm so this cabling is OK.

Table 54.7Minimum CSA of protective conductor in relation to CSA of associated line conductor

Table 41.3Max Zs for Circuit Type B Breakers for Uo of 230V

Table I1 OSG pg 218

Table I3 OSG pg 220

K Factors

Table 54.2 pg 200 BS7671

Values of k for insulated protective conductor not incorporated in a cable and not bunched with cables, or for separate bare protective conductor in contact with cable covering but not bunched with cables where the assumed initial temperature is 30°C.

*Above 300mm².

Table 54.3 pg 200 BS7671

Values of k for insulated protective conductor incorporated in a cable or bunched with cables, where the assumed initial temperature is 70°C or greater.

*Above 300mm².

Volt Drop

Pass! Our reading of 2.43V is below the 11.5V max for non lighting so passes.

Pass! Our reading of 2.43V is below the 11.5V max for non lighting so passes.

Pass! Our reading of 2.43V is below the 6.9V max for lighting so passes.

Pass! Our reading of 2.43V is below the 6.9V max for lighting so passes.

From Table I1 of the OSG obtain the resistance values for (R1+R2) (mΩ/m) for a 4mm² Line and 4mm² CPC cable.
Value found to be 9.22(mΩ/m)

Table 54.7

Minimum CSA of protective conductor in relation to CSA of associated line conductor

Table 41.3

Max Zs for Circuit Type B Breakers for Uo of 230V