BS 7671 , Appendix 4 (Informative), gives a procedure for calculating the voltage drop in low voltage cables. This procedure is based on looking up resistive and reactive voltage drops in a table and determining the cable voltage drop from these values.

## Voltage Drop Calculation

The tables in BS 7671 give the voltage drops for different cables in mV/A/m (or effectively mΩ/m) for various cable types and installation arrangements. Voltage drop figures are related to the cable's maximum operating temperature and the line to neutral voltage for single phase circuits and line to line voltage for three phase circuits. Values for both resistive (*R*), reactive (*X*) and total impedance (*Z*) voltage drops are given.

Typical BS 71 Voltage Drop Table

Note: the figures in the tables apply to frequencies from 49 to 61 Hz for a.c. cables and assume armour is bonded at both ends for single core armoured cables. For conductors less than 16 mm^{2}, the tables ignore inductance and only resistive voltage drops are given.

Typically the cable voltage drop is found by multiply the figures given in the table by the intended cable operating current and its length. This approach leads to significant inaccuracies where the cable is operating substantially below its rated value due to the cable having a lower operating temperature. If power factor is not correctly considered, errors in calculated voltage drop will also be apparent.

Only the resistance of the cable is affected by temperature. To correct the for the operating temperature of the cable, we can use:

${C}_{t}=\frac{230+{t}_{p}-\left({C}_{a}^{2}{C}_{g}^{2}{C}_{s}^{2}{C}_{d}^{2}-{\displaystyle \frac{{I}_{b}^{2}}{{I}_{t}^{2}}}\right)\left({t}_{p}-30\right)}{230+{t}_{p}}$

*t _{p}* - the maximum permitted normal operating temperature of the cable

*I*- design current of the circuit (current intended to be carried by the cable)

_{b}*I*- value to tabulated current (BS 7671 appendix 4, tables)

_{t}*C*- rating factor for ambient temperature

_{a}*C*- rating factor for grouping

_{g}*C*- rating factor for soil thermal resistivity

_{s}*C*- rating factor for depth of burial

_{d}Combining the temperature correction factor, with the power factor,$\mathrm{cos}\left(\varphi \right)$ the voltage drop (in mV) is given by:

$vd={I}_{b}*L*{C}_{t}\mathrm{cos}\left(\varphi \right)\left(\mathrm{tabluated}\right(mV/A/m{)}_{r})+\mathrm{sin}(\varphi )(\mathrm{tabulated}(mV/A/m{)}_{x})$

vd - voltage drop across the cable in mV (divide by 1000 for V)

$\mathrm{cos}\left(\varphi \right)$ - the power factor of the circuit

*L* - length of the cable, m

Note: power factor is 1 and the tabulated (mV/A/m)_{x} is 0 for a d.c. circuit. For cable CSA less than 16 mm^{2}, BS 7671 ignores inductance and (mV/A/m)_{x} can be taken as zero. For three phase circuits, the voltage drop is related to the line-line voltage - to relate to the line-neutral voltage divide by √3.

To obtain the voltage drop as a percentage, divide by the nominal voltage for d.c. circuits, the line-neutral voltage for single phase circuits and the line-line voltage for three phase circuits.

From BS 7671 Appendix 4, Table 4Ab, the voltage drop between the origin of any installation and load point should not be greater than:

Lighting | Other Uses | |
---|---|---|

Low voltage installation supplied directly from a public LV distribution system | 3% | 5% |

Low voltage installation supplied from a private LV supply | 6% | 8% |

Note: for installation runs longer than 100 m, the above can be increased by 0.005% per metre beyond 100m, without any increase being greater than 0.5%.

### Example Calculation

To illustrate the above, consider a single core, 50 mm^{2} copper XLPE armoured cable, supplying a 400 V three phase load of 152 A with pf=0.87. Assume the cable is installed in trefoil on a ladder with an ambient of 35 °C, not grouped with any other cables and 80 m in length.

To view the detailed calculation for the cable, please see BS 7671 Voltage Drop Calculation. This calculation shows that the absolute voltage drop is 10.06 V (referenced to the line-line voltage). As a percentage the voltage drop is 2.52%.

**myCableEngineering.com** - sizing the same cable with myCableEngineering, using a generic cable gives the same voltage drop (10.07 V and 2.52%). Using a BS 6724 cable gives 2.46%. These types of variation are due to BS 7671 using a one-size-fits-all approach, whereas in myCableEngineering voltage drop is calculated based on each cables actual physical characteristics.

## Deriving Impedance & CENELEC 50480

Voltage drop in cables is always related to the impedance of the cable. Consequently, it is possible to drive an equivalent impedance for the mV/A/m values given in the BS 7671 tables. To convert the three phase table values so that they relate to the input resistance (or reactance) required by CENELEC 50480 it is necessary to divide the BS 7671 three phase values by √3 (the square root of three). No adjustment is required for single phase values.

Given values of voltage drop for three phase balanced systems are related to the line voltage.

$R=(mV/A/m{)}_{r}/(2*1000)$ and $X=0$

- for a d.c. circuit

$R=(mV/A/m{)}_{r}/(2*1000)$ and $X=(mV/A/m{)}_{x}/(2*1000)$

- for a singe phase a.c. circuit

$R=(mV/A/m{)}_{r}/(\sqrt{3}*1000)$ and $X=(mV/A/m{)}_{x}/(\sqrt{3}*1000)$

- for a singe phase a.c. circuit

(mV/A/m)_{r} - tabulated resistive mV/A/m from BS 7671

(mV/A/m)_{x} - tabulated reactive mV/A/m from BS 7671

R - resistance per conductor in Ω/m

X - reactance per conductor in Ω/m

Note: the values given in BS 7671 for resistive voltage drop are at the cables maximum operating temperature (i.e. 90 °C for thermosetting cables). These can be adjusted to the required temperature by standard formulae. See Conductor Resistance for details on how to adjust for temperature.