HV cables
Three-phase voltage drop of an HV cable
- where
- line-to-line voltage drop (V)
- load current (A)
- route length (km)
- a.c. resistance at operating temperature (Ω/km)
- load power factor (lagging)
- reactance per phase (Ω/km)
- nominal line voltage (kV)
Explain this equation
Estimates the line-to-line voltage drop along a three-phase cable feeding a lagging load, in volts and as a percentage of the nominal voltage.
I is the load current and l the route length. R and X are the a.c. resistance and reactance per phase per km. cos φ is the load power factor, and the square root term is sin φ.
The phase drop is the component of I(R + jX) in line with the sending voltage, I(R cos φ + X sin φ). Multiplying by √3 converts phase drop to line drop. The percentage divides by Uₙ in volts, hence the 10³.
300 A over 2 km of 11 kV cable at 0.9 power factor gives about 120 V, roughly 1.1 %. Doubling the current or the length doubles the drop.
Use the resistance at operating temperature. This projected-drop form is accurate for drops of a few per cent and ignores charging current.
Approximate line-to-line voltage drop along a three-phase cable for a lagging load, ΔU = √3·I·l·(R cos φ + X sin φ).
Enter your values to see the result.
Good to know
Use the a.c. resistance at the expected conductor temperature (see the conductor resistance calculator) and the reactance for the actual formation and bonding. For a leading load enter the result with care: the X sin φ term changes sign. Capacitive charging current is ignored, which is reasonable for distribution lengths.
Common mistake
Using 20 °C d.c. resistance from a table, or using the single-phase formula (2·I·Z) for a three-phase circuit.
Limits
Approximate (projected) drop, accurate when the drop is a few per cent; ignores the quadrature component and shunt capacitance. For long HV/EHV cables use a full π-model load-flow.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.