What is the per-unit system?

The per-unit (pu) system expresses electrical quantities as fractions of a chosen base value. Z_base = kV²/MVA (ohms); I_base = MVA/(√3 × kV) (kA); V_base = kV (line-to-line). Per-unit values are dimensionless and simplify power system calculations by eliminating the need to refer quantities across transformer turns ratios.

How do you change the per-unit impedance base?

Z_pu_new = Z_pu_old × (MVA_new/MVA_old) × (kV_old/kV_new)². This converts an impedance given on one base (old MVA, old kV) to a new base (new MVA, new kV). This is required when combining equipment data from different manufacturers onto a common system base.

What is Z_base in power systems?

Z_base = kV²/MVA (line-to-line kV, three-phase MVA). For example, on a 13.8kV, 100MVA base: Z_base = 13.8²/100 = 1.9044 Ω. A transformer with 5% impedance on its own base of 13.8kV/100MVA has Z_pu = 0.05 per unit.

What reference covers the per-unit method?

IEEE Std 399-1997 (Brown Book: Recommended Practice for Industrial and Commercial Power Systems Analysis) Chapter 8 covers the per-unit method. It is also covered in IEEE Std 141-1993 (Red Book) and virtually every power systems textbook (Glover/Sarma, Stevenson, Bergen).

Per-Unit System Converter

Convert electrical quantities between actual values and per-unit. Change impedance base between different MVA/kV ratings. Per IEEE Std 399 (Brown Book) §8.

IEEE Std 399Brown Book §8IEEE Std 141Base Change

Actual Values

Enter actual electrical quantities to convert to per-unit.

System Base

Base MVA (3-phase)

Base kV (line-to-line)

Z_base

1.9044 Ω

I_base

4.1837 kA

Actual Voltage (kV, line-to-line)

Actual Impedance (Ω) — optional

Actual Current (kA) — optional

Active Power (MW) — optional

Reactive Power (MVAR) — optional

Per-Unit Results

Normalized to Base MVA = 100, Base kV = 13.8

V_pu (voltage)1.0000 pu

Z_pu (impedance)—

I_pu (current)—

P_pu (active power)—

Q_pu (reactive power)—

Z_base = kV² / MVA

I_base = MVA / (√3 × kV)

V_pu = V_actual / V_base

Z_pu = Z_actual / Z_base

The Per-Unit Method — IEEE Std 399

The per-unit (pu) system normalizes electrical quantities to dimensionless fractions of a chosen base. IEEE Std 399-1997 (Brown Book: Recommended Practice for Industrial and Commercial Power Systems Analysis) §8 establishes the standard method used in power system studies.

Worked example (base change): A 30 MVA transformer has 6% impedance on its own base (30 MVA, 13.8 kV). To combine with a 100 MVA system study base at 13.8 kV: Z_pu_new = 0.06 × (100/30) × (13.8/13.8)² = 0.2000 pu. The same transformer on 100 MVA base has 20% impedance — which is what the calculator returns.

The per-unit method eliminates transformer turns ratios from network equations, making multi-voltage system analysis tractable. It also allows direct comparison of impedances across different voltage levels.

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Disclaimer: This tool is for educational planning purposes. For precision power system studies, engage a licensed Professional Engineer. IEEE Std 399 and IEEE Std 141 govern the accepted practice for industrial power system analysis.

The Per-Unit Method — IEEE Std 399