Voltage drop is calculated in accordance with CENELEC technical report CLC/TR 50480 "Determination of cross-sectional area of conductors and selection of protective devices", dated February 2011.
The voltage drop (as a percentage) is given by:
ΔU = cable voltage drop, %
Uo = nominal line to neutral voltage, V
R = cable resistance, Ω
X = cable reactance, Ω
Ib = cable design current, A
b = circuit factor (=2 for d.c. and single-phase, =1 for three-phase)
Note: within myCableEngineering, we use complex arithmetic and the above is evaluated as:
Note: R and X are per line conductor. For example, the resistance of a single-phase two core circuit (live and neutral) would be 2R (assuming the live and neutral circuits are of equal resistance). For parallel cables, R and X are the per line resultant values. For example, nph cables in parallel, with the resistance of one line conductor is Rc0ph then the R = Rc0ph/nph.
The above equation), has the relative voltage drop expressed as a percentage of Uo. Multiplying by Uo will give the actual voltage drop for d.c. and single-phase circuits and for three-phase circuits, this needs to be multiplied by √3.
Adjusting the CENELEC equation to take into account referring the voltage drop to line-line voltage for three-phase systems, setting R, X in ohms, and using complex forms gives:
||ΔU, % per m
|a.c. systems, single-phase
|a.c systems, three-phase
- the resistance of a single conductor, Ω/m
- the reaction of a single conductor, Ω/m
- the impedance of single conductor , Ω/m
- cable design current, A
- the nominal line to neutral/earth voltage (for single-phase a.c. or d.c.), V
- the nominal line to line voltage (for three-phase systems), V
BS 7671 Voltage Drop Tables
BS7671 "Requirements for Electrical Installations", the IET Wiring Regulations, Appendix 4 voltage drop tables, values are given in mV/A/m (or effectively mΩ). However, these tables are related to the line to neutral voltage for single-phase circuits and line to line voltage for three-phase circuits.
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.
Note: the values in the tables are given at the maximum conductor operating temperature. myCableEngineering uses circuit theory (see Impedance
) to calculate impedance and voltage drops are calculated using CENELEC 50480. Our testing shows that the difference in resistance calculation by circuit theory and that given in BS 7671 is small.