What is the per-unit system?

The per-unit (pu) system expresses all electrical quantities as a ratio to a chosen base value. For example, a voltage of 1.05 pu means the actual voltage is 5% above the base voltage. It simplifies calculations in multi-voltage systems because transformer turns ratios disappear from the equations.

How is base impedance calculated?

Base impedance (Ω) = (Base kV)² / Base MVA. For a 100 MVA, 138 kV system: Z_base = 138² / 100 = 190.44 Ω. A 50 Ω impedance is therefore 50 / 190.44 ≈ 0.2625 pu.

How is base current calculated?

Base current (A) = Base MVA × 1000 / (√3 × Base kV) for a three-phase system. This gives the rated line current at the base voltage and base power.

Why do I need to change base?

Equipment datasheets give per-unit impedances on the equipment's own MVA and kV rating, which may differ from the system base. The base-change formula is: Z_pu_new = Z_pu_old × (MVA_base_new / MVA_base_old) × (kV_base_old / kV_base_new)².

Is this calculator for three-phase or single-phase systems?

It supports both. For three-phase analysis enter three-phase MVA and line-to-line kV (standard practice). For single-phase, enter single-phase kVA converted to MVA and the applicable voltage. The formulas are consistent with both conventions when used accordingly.

What does a per-unit value greater than 1.0 mean?

A pu value above 1.0 means the actual quantity exceeds the base value. For example, 1.1 pu voltage means the bus voltage is 10% above the nominal base voltage, which may indicate an overvoltage condition.

Per Unit System Calc

Name: Per Unit System Calc
Availability: InStock
Author: Nham Vu

Convert impedance, voltage, current, and power to and from per-unit values using selectable base quantities.

Quantity Type

Direction

System Base

Base MVA

Base kV (L-L)

Actual Impedance (Ω)

Base Change (Impedance)

Rescale a per-unit impedance from equipment base to system base.

Old MVA base

Old kV base

New MVA base

New kV base

Z_pu (on old base)

Enter values on the left and click Calculate to see results.

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Summary

Convert impedance, voltage, current, and power to and from per-unit values using selectable base quantities.

How it works

Select the quantity type: Impedance, Voltage, Current, or Power.
Choose conversion direction: Actual to Per-Unit or Per-Unit to Actual.
Enter the system base values (base MVA and base kV).
Enter the actual quantity or the per-unit value to convert.
The calculator computes the base quantity and returns the converted result.
For base changes, enter both old and new base values to rescale an existing per-unit impedance.

Use cases

Normalize transformer and generator impedances to a common system base.
Convert equipment nameplate ratings to system per-unit values.
Rescale per-unit impedances when changing the system base MVA or kV.
Verify load-flow study inputs by checking per-unit voltage and current.
Teach or study per-unit system concepts interactively.
Convert per-unit fault current back to actual amperes for protection relay settings.
Cross-check transmission line impedances against system base.
Quickly compute base impedance for a given MVA and kV rating.

Frequently Asked Questions

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Last updated: 2026-05-29 · Reviewed by Nham Vu