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Per-unit calculator
Work out base impedance and current, convert between ohms and per-unit, and move an impedance from the equipment base to the system base. Free, no signup.
- Two-way ohm ↔ p.u. conversion
- Results update as you type
- Share any calculation as a link
Base impedance Zbase
—
Base current Ibase: —
Check the inputs: every value must be a positive number.
- Base admittance Ybase
- —
- Equipment impedance on the system base
- —
- Same impedance in ohms
- —
Three-phase bases: Sbase is three-phase power and Ubase is line-to-line voltage.
How the calculation works
In the per-unit system every quantity is divided by a base value. Choose a base power for the whole network and a base voltage for each voltage level; the base impedance and current follow from them.
- Base impedanceZbase = Ubase² / Sbase
- Base currentIbase = Sbase / (√3 · Ubase)
- Ohms to per-unitZpu = ZΩ / Zbase
- Change of baseZpu,new = Zpu,old · (Sbase,new / Sbase,old) · (Ubase,old / Ubase,new)²
Worked example
A 40 MVA, 110/20 kV transformer has uk = 10 %. On a 100 MVA, 110 kV system base:
| Base impedance at 110 kV | 121 Ω |
|---|---|
| Base current at 110 kV | 524.9 A |
| Transformer impedance on the system base | 0.25 p.u. |
| Same impedance in ohms (110 kV side) | 30.25 Ω |
The per-unit system is what makes hand calculations of load flow and short circuits manageable across several voltage levels.
Frequently asked questions
Why use the per-unit system?
Per-unit values of similar equipment fall in narrow ranges whatever their size, so mistakes are easy to spot. When the base voltages follow the transformer ratios, ideal transformers disappear from the equivalent circuit and a multi-voltage network becomes one circuit.
How do I choose the base values?
Use one base power for the whole network (100 MVA is common) and the nominal voltage of each voltage level as its base voltage. Across a transformer, the base voltages change in proportion to its rated voltage ratio.
On which base is a transformer’s uk given?
On its own rated power and rated voltage. Divide the percentage by 100 to get per-unit, then convert it to the system base with the change-of-base formula.
Are single-phase and three-phase per-unit values different?
No. With three-phase power and line-to-line voltage as bases, Zbase = Ubase² / Sbase gives the same per-unit impedance as the per-phase calculation.
Do I need per-unit values to use Electrisim?
No. You enter ratings and impedances in engineering units (kV, MVA, Ω/km, %) and the engines convert them internally. Results are shown in per-unit and in engineering units.