Per-unit
Per-unit base quantities and conversion
- where
- base current (kA)
- three-phase base power (MVA)
- line-to-line base voltage (kV)
- base impedance (Ω)
- impedance in per unit
- impedance to convert (Ω)
Explain this equation
Sets up per-unit base quantities for a chosen MVA and voltage base, and converts an ohmic impedance to per unit. Per unit makes networks with several voltage levels easy to add up.
Sb is the three-phase base power and Ub the line-to-line base voltage. Ib is the line current that carries Sb at Ub, and Zb the impedance that would draw base current at base phase voltage. zpu is any impedance Z expressed as a fraction of Zb.
Ib = Sb/(√3·Ub) comes from three-phase power S = √3·U·I. Zb = Ub²/Sb follows from phase voltage over line current: (Ub/√3)/(Sb/(√3·Ub)). With MVA and kV the units work out to kA and Ω.
Sense check: on 100 MVA, Zb is 1.21 Ω at 11 kV, 10.89 Ω at 33 kV and 174.24 Ω at 132 kV; Ib is about 5.25 kA at 11 kV.
Watch out: keep the MVA base the same everywhere and change the voltage base across each transformer in its turns ratio.
Base current and base impedance for a chosen MVA and voltage base, and an ohmic impedance converted to per unit.
Enter your values to see the result.
Good to know
UK studies usually use 100 MVA base and nominal voltages (132, 33, 11 kV). The voltage base changes across each transformer in its turns ratio; the MVA base is the same everywhere.
Common mistake
Using a phase-to-neutral voltage with a three-phase MVA base. Use line-to-line kV with three-phase MVA throughout.
Limits
Three-phase balanced per-unit system with line-to-line voltage and three-phase power bases.
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.