Per Unit System Calc
Z_base = kV² ÷ MVA and I_base = MVA × 1000 ÷ (√3 × kV) for three-phase (MVA × 1000 ÷ kV for single-phase). On a 100 MVA, 138 kV base, Z_base = 190.44 Ω and I_base = 418.37 A, so 50 Ω = 0.2625 pu. Change of base: Z_new = Z_old × (kV_old ÷ kV_new)² × (MVA_new ÷ MVA_old); 0.10 pu on 50 MVA, 132 kV becomes 0.1830 pu on 100 MVA, 138 kV.
Use the Per Unit System Calc
Quantity Type
Direction
System Base
Base Change (Impedance)
Rescale a per-unit impedance from equipment base to system base.
Enter values on the left and click Calculate to see results.
Per-Unit Impedance
Base Impedance
—
Ω
Base Current
—
A
Base Voltage
—
kV (L-L)
Formula Used
Base voltage across a transformer
The base MVA is the same in every zone; the base kV steps by the transformer's rated voltage ratio. Uses the system base MVA and the phase setting above.
| Zone | Base kV | Base Z (Ω) | Base I (A) |
|---|
Per-unit formulas
| Base quantity | Three-phase | Single-phase |
|---|---|---|
| Power | S_base = MVA 3φ | S_base = MVA 1φ |
| Voltage | V_base = kV line-to-line | V_base = kV of the circuit |
| Current | I = MVA·1000 / (√3·kV) | I = MVA·1000 / kV |
| Impedance | Z = kV² / MVA | Z = kV² / MVA |
| Change of base | Z_new = Z_old · (kV_old / kV_new)² · (MVA_new / MVA_old) | |
| Fault behind Z | I_f = I_base / Z_pu; S_f = MVA_base / Z_pu (1.0 pu prefault) | |
Worked example
System base 100 MVA, 138 kV (three-phase): Z_base = 138² ÷ 100 = 190.44 Ω and I_base = 100,000 ÷ (√3 × 138) = 418.37 A. A 50 Ω line is 50 ÷ 190.44 = 0.2625 pu, and 600 A is 600 ÷ 418.37 = 1.434 pu.
Change of base. A 50 MVA transformer with X = 10% on its 132 kV rating, on the 100 MVA, 138 kV base: 0.10 × (132/138)² × (100/50) = 0.10 × 0.9149 × 2 = 0.1830 pu, or 0.1830 × 190.44 = 34.85 Ω. A bolted fault behind it from a 1.0 pu infinite source draws 418.37 ÷ 0.1830 = 2,286 A, which is 100 ÷ 0.1830 = 546.5 MVA.
Across the transformer. With a 138/13.8 kV transformer, the low-side base is 13.8 kV, Z_base = 13.8² ÷ 100 = 1.9044 Ω and I_base = 4183.7 A. The per-unit values stay the same on both sides.
Summary
The Per Unit System Calculator converts power system quantities (impedance, voltage, current and power) between actual values and per-unit (pu) values on a chosen base. Three-phase systems use three-phase MVA and line-to-line kV; single-phase systems use single-phase MVA and the single-phase voltage. It also rescales a per-unit or percent impedance from a nameplate base to the system base, reports the bolted fault current and fault MVA behind that impedance, and carries the base voltage across a transformer so every voltage zone has consistent bases. Everything runs in your browser.
How it works
- Choose three-phase (MVA 3φ, kV line-to-line) or single-phase (MVA 1φ, kV of the single-phase circuit).
- Enter the base MVA and base kV. The tool shows Z_base = kV² ÷ MVA, I_base and the base voltage.
- Pick a quantity (impedance, voltage, current or power) and a direction, enter the value, and click Calculate.
- For a change of base, enter the impedance in pu or % on the equipment base (MVA and kV) and the new system base.
- The base-change result also gives the ohmic value, plus the bolted fault current and fault MVA behind that impedance at 1.0 pu voltage.
- In the transformer section, the base voltage on the far side = base kV × (rated kV far side ÷ rated kV near side).
Use cases
- Convert transformer and generator nameplate impedances (%Z) to a common system base.
- Compute base impedance and base current for a bus voltage level.
- Convert per-unit load-flow or fault-study results back to amps, kV and MVA.
- Estimate the fault current at a transformer secondary from its percent impedance.
- Carry base voltages through transformers into each zone of a one-line diagram.
- Check single-phase distribution transformer impedances in per unit.