Power quality and networks
Three-phase power and line current
- where
- apparent power (kVA)
- active power (kW)
- power factor
- reactive power (kvar)
- line current (A)
- line-to-line voltage (kV)
Explain this equation
Converts a balanced three-phase load given in kW and power factor into kVA, kvar and line current. Use it to size cables, switchgear and CTs, or to check a feeder loading against its rating.
P is the real power doing work, Q the reactive power exchanged with magnetic and electric fields, and S the vector sum of the two that the conductors actually carry. cos φ is the ratio P/S.
Power in a balanced three-phase circuit is three times the per-phase power. Writing it with line-to-line voltage, which is √3 times the phase voltage, leaves √3 in the denominator: I = S/(√3·U). With S in kVA and U in kV the result is directly in amperes.
Sense check: at 11 kV each MVA is about 52 A; at 33 kV about 17.5 A; at 400 V about 1443 A. Halving the power factor at the same kW doubles the current.
Watch out: if you use phase-to-neutral voltage, divide by 3, not √3.
Converts a balanced three-phase load in kW and power factor into kVA, kvar and line current at a given line-to-line voltage.
Enter your values to see the result.
Good to know
With S in kVA and U in kV the current comes out directly in amperes. For a load given in kVA, set pf to 1 and enter the kVA as P to get the current. Line current is the same in star and delta connections when written in terms of the line-to-line voltage.
Common mistake
Using phase voltage with √3, or line voltage without it. I = S/(√3·U) needs U line-to-line; I = S/(3·U) needs U phase-to-neutral.
Limits
Balanced sinusoidal three-phase load. Harmonic currents and unbalance are not included; use a power-quality study for those.
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.