Voltage drop calculations are carried out in accordance with CENELEC Technical Report CLC/TR 50480, Determination of cross-sectional area of conductors and selection of protective devices, dated February 2011.
Voltage drop checks confirm that the voltage at the load remains within acceptable limits after allowing for cable impedance, load current, circuit type and power factor.
CENELEC voltage drop equation
The voltage drop, expressed 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 |
Within myCableEngineering, complex arithmetic is used and the expression is evaluated as:
For the underlying AC power convention, see Complex Power in AC Circuits.
R and X are per line conductor. For example, the resistance of a single-phase two-core circuit, line and neutral, is 2R if the line and neutral conductors have equal resistance.
For parallel cables, R and X are the resultant per-line values. For example, if nph cables are installed in parallel and the resistance of one line conductor is Rc0ph, then R = Rc0ph / nph.
The equation above expresses relative voltage drop as a percentage of Uo. Multiplying by Uo gives the actual voltage drop for d.c. and single-phase circuits. For three-phase circuits, the result needs to be multiplied by √3.
Voltage drop by system type
Adjusting the CENELEC equation so that three-phase voltage drop is referred to line-to-line voltage gives the following expressions, with R, X and Z in ohms per metre.
| System | ΔU, V/m | ΔU, % per m |
|---|---|---|
| d.c. systems | ||
| a.c. systems, single-phase | ||
| a.c. systems, three-phase |
| R | Resistance of a single conductor, Ω/m |
| X | Reactance of a single conductor, Ω/m |
| Z | Impedance of a single conductor, Ω/m |
| Ib | Cable design current, A |
| Uo | Nominal line-to-neutral or line-to-earth voltage for single-phase a.c. or d.c., V |
| Un | Nominal line-to-line voltage for three-phase systems, V |
BS 7671 voltage drop tables
BS 7671, Requirements for Electrical Installations, gives voltage drop values in Appendix 4. The values are listed in mV/A/m, effectively mΩ. The single-phase values relate to line-to-neutral voltage, while the three-phase values relate to line-to-line voltage.
To convert BS 7671 three-phase table values so they can be used as the input resistance or reactance required by CENELEC TR 50480, divide the three-phase values by √3. No adjustment is required for single-phase values.
The BS 7671 table values are given at the maximum conductor operating temperature. myCableEngineering uses circuit theory to calculate impedance and then calculates voltage drop using CENELEC TR 50480. Testing shows that the difference between resistance calculated by circuit theory and the values in BS 7671 is small.
For more background on the standards used in myCableEngineering, see Cable Sizing Standards.
For the detailed BS 7671 table method, including correction factors and conversion of mV/A/m values to impedance, see BS 7671 Voltage Drop Calculations.
For detailed cable impedance formulae, including positive and zero sequence cases, see Cable Impedance.
For resistance calculation and IEC 60228 reference values, see Conductor Resistance.
For cable inductance and reactance background, see Cable Inductance.
For the reactance term used in impedance-based voltage drop calculations, see Cable Reactance.