**Mr. Muhammad Faheem Meer from GM Cables & Pipes (Pvt) Ltd**

Voltage drop is the difference in voltage at sending and receiving end of a circuit and defined as the amount of voltage loss that occurs through all or part of a circuit. Dropping is due to increased resistance (impedance) in a circuit, typically caused by an increased load, or energy used to operate electric loads, in the form of extra connections, components, or high-resistance conductors.

Conventional voltage drop factor value of each type/size of cable is tabulated in mV/A/m in various standards and voltage drop in cable particular cable section can be determined using following formula;

Conventional Voltage drop (V_{d}) = (mV/A/m) x Length of section x load current /1000

Where,

(mV/A/m) is voltage drop factor of particular cable under use

BS 7671 however, provides further accuracy in the calculations and suggests to apply temperature correction and power factor correction to conventional voltage drop factor (mV/A/m), so that voltage drop is calculated for actual corrected current flowing in the circuit.

Temperature correction factor (C_{t}) according to BS 7671 can be calculated using following formula;

C_{t} = 230+t_{p}−(C_{a}^{2 }x C_{g}^{2} x C_{s}^{2} x C_{d}^{2} – I_{b}^{2} / I_{t}^{2}) x (tp−30)

—————————————————————

230+tp

Where,

*t _{p}* – the maximum permitted normal operating temperature in

^{o}C of the cable

*I _{b}* – load current (Amp) of the circuit (current intended to be carried by the cable

*I*– value to tabulated current (Amp) for the cable (BS 7671 appendix 4, tables)

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

_{a}*C _{g}* – rating factor for grouping

*C _{s}* – rating factor for soil thermal resistivity

*C _{d}* – rating factor for depth of burial

Similarly, the power factor is also split into active and reactive components in BS 7671;

Cos ɸ – active power factor component of load

Sin ɸ – reactive power factor component of load [Sin (Cos^{-1} (pf)]

To utilize temperature and power correction factors accurately, BS 7671 offers voltage drop factors separately in resistive and inductive components for cables above 16 mm^{2}.

Resistive component of voltage drop factor mV_{r }– (mV / A / m)_{r }

Reactive component of voltage drop factor mVx_{ }– (mV / A / m)_{x }

Values of resistive and reactive voltage drop components are given in cable data tables appendix 4 in BS7671. For cables up to 16 mm^{2}, conventional voltage drop mV (mV/A/m) remains applicable.

Using above formulae, voltage drop and percentage voltage drop of a given section according to BS 7671 is calculated as follows;

For cables having conductor cross-section up to 16 mm^{2};

Voltage Drop V_{d} = [ ( C_{t} x Cos ɸ ) x (tabulated mV/A/m) ] x L x I_{b}/ 1000

For cables having conductor x-section greater than 16 mm^{2}

- Drop V
_{d}= [C_{t}x Cos ɸ x (tabulated V_{r }) + Sin ɸ x (tabulated V_{x }] x L x I_{b}/ 1000

Percentage Voltage Drop (%V_{d}) = V_{d}/U_{o} x 100

U_{o} = Line Voltage

Voltage drop calculations according to BS 7671 are elaborated by following two exercises;

__Exercise – 1;__

To calculate voltage drop according to BS 7671 Eighteenth Edition (2018) of 600/1000 V, 4 core 50 mm2 Cu/XLPE/PVC cable 60 meter run laid flat in cable tray along with one more circuit at ambient temperature of 40^{o}C. Cable to be operated in 3 phase 400 V AC line voltage for 100 amps load having power factor of 0.87.

Solution;

Voltage Drop V_{d} = [ C_{t} x Cos ɸ x mV_{r} + Sin ɸ x mV_{x} ] x L x I_{b}/ 1000

Where,

C_{t} = Temperature Correction factor

C_{t} = 230+t_{p}−(C_{a}^{2 }x C_{g}^{2} x C_{s}^{2} x C_{d}^{2} – I_{b}^{2} / I_{t}^{2}) x (t_{p}−30)

—————————————————————

230+t_{p}

Where,

*t _{p}* – the maximum permitted normal operating temperature in

^{o}C of the cable

(90^{o}C for XLPE insulated cables and 70^{o}C for PVC insulated cables)

*I _{b}* – load current (Amp) of the circuit (current intended to be carried by the cable)

*I*– value to tabulated current (Amp) for the cable (BS 7671 appendix 4, tables)

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

_{a}*C _{g}* – rating factor for grouping

*C _{s}* – rating factor for soil thermal resistivity

*C _{d}* – rating factor for depth of burial

Cos ɸ – power factor of load

Sin ɸ – Sin [Cos^{-1} (pf)]

L – Length of cable in meters whose voltage drop is being calculated

mV_{r} – (mV / A / m)_{r } value of cable (table 4E3B BS 7671)

mV_{x} – (mV / A / m)_{x } value of cable (table 4E3B BS 7671)

*Cable data;*

Cable size 4 core 50 mm^{2} copper conductor

t_{p} – Maximum operating temperature = 90^{o}C (XLPE insulation)

I_{t} – Tabulated current carrying capacity of cable It = 192 A (table 4E2A column 9)

I_{b} – Load current of cable = 100 A (given)

U_{o} – Line voltage = 400 V

*C _{a}* – rating factor for ambient temperature = 0.91 (table 4B1)

*C _{g}* – rating factor for grouping = 0.88 (table 4C1)

*C _{s}* – rating factor for soil thermal resistivity (1 for cable tray)

*C _{d}* – rating factor for depth of burial (1 for cable tray)

L – Length of cable under calculation = 60m

Cos ɸ – active power factor of load = 0.87

Sin ɸ – Sin [Cos^{-1} (0.87)] = 0.49

mV_{r} – (mV / A / m)_{r } value of cable = 0.86 (table 4E2B column 4)

mV_{x} – (mV / A / m)_{x } value of cable = 0.135 (table 4E4B column 4)

*Calculations;*

C_{t} = 230+t_{p}−(C_{a}^{2 }x C_{g}^{2} x C_{s}^{2} x C_{d}^{2} – I_{b}^{2} / I_{t}^{2}) x (t_{p}−30)

—————————————————————

230+t_{p}

C_{t} = 0.930

Voltage Drop V_{d} = [ C_{t} x Cos ɸ x mV_{r} + Sin ɸ x mV_{x} ] x L x I_{b}/ 1000

V_{d} = 4.574 V

Percentage Voltage Drop (%V_{d}) = V_{d}/U_{o} x 100

= 1.14%

__Exercise – 2;__

To calculate voltage drop according to BS 7671 Eighteenth Edition (2018) of 600/1000 V, 4 core 120 mm^{2} Cu/PVC/SWA/PVC cable 70 meter run buried in ground in flat formation at 0.7 m depth at ground temperature of 35^{o}C. Cable to be operated in 3 phase 400 V AC line voltage for 150 amps load having power factor of 0.80.

Solution;

Voltage Drop V_{d} = [ C_{t} x Cos ɸ x mV_{r} + Sin ɸ x mV_{x} ] x L x I_{b}/ 1000

Where,

C_{t} = Temperature Correction factor

C_{t} = 230+t_{p}−(C_{a}^{2 }x C_{g}^{2} x C_{s}^{2} x C_{d}^{2} – I_{b}^{2} / I_{t}^{2}) x (t_{p}−30)

—————————————————————

230+t_{p}

Where,

*t _{p}* – the maximum permitted normal operating temperature in

^{o}C of the cable

*I _{b}* – load current (Amp) of the circuit (current intended to be carried by the cable)

*I _{t}* – value to tabulated current (Amp) for the cable (BS 7671 appendix 4, tables)

*C*– rating factor for ambient temperature

_{a}*C _{g}* – rating factor for grouping

*C _{s}* – rating factor for soil thermal resistivity

*C _{d}* – rating factor for depth of burial

Cos ɸ – power factor of load

Sin ɸ – Sin [Cos^{-1} (pf)]

L – Length of cable in meters whose voltage drop is being calculated

mV_{r} – (mV / A / m)_{r } value of cable (table 4E3B BS 7671)

mV_{x} – (mV / A / m)_{x } value of cable (table 4E3B BS 7671)

*Cable data;*

Cable size 4 core 120 mm^{2} copper conductor

t_{p} – Maximum operating temperature = 70^{o}C (PVC insulation)

I_{t} – Tabulated current carrying capacity of cable I_{t} = 192 A (table 4D4A column 5)

I_{b} – Load current of cable = 150 A (given)

U_{o} – Line voltage = 400 V

*C _{a}* – rating factor for ambient temperature = 0.84 (table 4B2)

*C _{g}* – rating factor for grouping = 1 (single circuit)

*C _{s}* – rating factor for soil thermal resistivity 1 (TR assumed as 2.5 K.m/W)

*C _{d}* – rating factor for depth of burial (1 table 4B4)

L – Length of cable under calculation = 70 m

Cos ɸ – power factor of load = 0.80

Sin ɸ – Sin [Cos^{-1} (0.8)] = 0.60

mV_{r} – (mV / A / m)_{r } value of cable = 0.33 (table 4D4B column 4)

mV_{x} – (mV / A / m)_{x } value of cable = 0.135 (table 4D4B column 4)

*Calculations;*

_{t} = 230+t_{p}−(C_{a}^{2 }x C_{g}^{2} x C_{s}^{2} x C_{d}^{2} – I_{b}^{2} / I_{t}^{2}) x (t_{p}−30)

—————————————————————

230+t_{p}

= 0.987

Voltage Drop V_{d} = [ C_{t} x Cos ɸ x mV_{r} + Sin ɸ x mV_{x} ] x L x I_{b}/ 1000

= 3.587 V

Percentage Voltage Drop (%V_{d}) = V_{d}/U_{o} x 100

= 0.897 %