This worked example shows how a BS 7671 voltage drop check can be carried out when the tabulated resistance and reactance voltage drop values are known. The example uses a 50 mm2 single-core armoured copper cable with a design current of 152 A over an 80 m route.
Problem
Check the voltage drop for a three-phase circuit and express the result both in volts and as a percentage of the 400 V line-to-line system voltage.
Given data
| Item | Value |
|---|---|
| Cable type | Table 4E3A, single-core armoured 90 °C thermosetting copper conductors |
| Conductor size | 50 mm2 |
| Route length, L | 80 m |
| Design current, Ib | 152 A |
| System voltage, U | 400 V line-to-line |
| Power factor, cos φ | 0.87 |
| Maximum conductor temperature, tp | 90 °C |
BS 7671 lookup values
| Value | Description |
|---|---|
| It = 222 A | Tabulated current rating |
| mVr = 0.86 mV/A/m | Resistive component of voltage drop |
| mVx = 0.29 mV/A/m | Reactive component of voltage drop |
| Ca = 0.96 | Ambient temperature correction factor |
| Cg = 1.00 | Grouping correction factor |
| Cs = 1.00 | Soil thermal resistivity correction factor, not buried |
| Cd = 1.00 | Burial depth correction factor, not buried |
Step 1: resolve the power factor components
The resistive component uses cos φ directly. The reactive component uses sin φ, calculated from the power factor.
Step 2: calculate the temperature correction factor
The correction factor accounts for the cable operating below its maximum permitted conductor temperature.
Step 3: calculate voltage drop
The BS 7671 voltage drop calculation combines the corrected resistive component and the reactive component.
Step 4: convert to percentage voltage drop
Result: the calculated voltage drop is 10.06 V, or 2.52% of the 400 V line-to-line voltage.
This result should be compared with the relevant permitted voltage drop for the circuit. For background on the method, see BS 7671 voltage drop and the general voltage drop article.