Current base
Ibase = Sbase / (√3 Vbase)
The short answer
Per-unit is a common scale for unlike equipment
Power systems combine generators, transformers, lines, motors, and loads operating at different voltage and power levels. In physical units, quantities must be referred from one voltage level to another before they can be combined.
A per-unit quantity is the actual quantity divided by its base quantity:
Xpu
=
XactualXbase
A voltage of 0.98 per unit is 98 percent of the selected voltage base. An impedance of 0.10 per unit is 10 percent of the selected impedance base. Eight percent impedance is therefore 0.08 per unit.
When voltage bases follow transformer nominal ratios, the ideal transformer ratio is absorbed into the base quantities. The transformer does not disappear from the model. Its impedance, phase shift, tap position, grounding, losses, and controls still matter.
How are the base quantities selected?
For a balanced three-phase system, engineers commonly select a three-phase apparent-power base, Sbase, and a line-to-line voltage base, Vbase. The corresponding current and impedance bases are:
Impedance base
Zbase = Vbase2 / Sbase
The same MVA base is normally used throughout the system. Voltage bases change between voltage levels according to transformer ratios. Most errors come from inconsistent base selection or conversion, not from the equations themselves.
A short example
Assume a 100 MVA base and a 13.8 kV voltage base:
Zbase = 13.82 / 100 = 1.9044 Ω
An impedance of 0.10 per unit represents 0.19044 Ω on this base.
At 138 kV on the same 100 MVA base, the impedance base is 190.44 Ω. The same 0.10 per-unit impedance represents 19.044 Ω on the high-voltage side. The physical impedance changes when referred through the transformer. The per-unit value remains 0.10 because the voltage bases were selected consistently.
When must impedance be converted to a new base?
Equipment impedance is usually provided on the equipment’s own MVA and voltage ratings. Before using it in a system model, convert it to the system base:
Zpu,new = Zpu,old × (Sbase,new / Sbase,old) × (Vbase,old / Vbase,new)2
If the old and new voltage bases are equal, the voltage term is one. For example, 0.10 per unit on a 50 MVA base becomes 0.20 per unit on a 100 MVA base when the voltage base is unchanged:
0.10 × (100 / 50) = 0.20
Using a nameplate value without checking its original base is a common source of error.
What are the common mistakes?
Scale and convention
Mixing three-phase and per-phase conventions, or treating 8 percent as 8.0 per unit instead of 0.08 per unit, creates avoidable errors.
Base conversion
Using equipment impedance without converting its MVA or voltage base can distort the system model.
Transformer representation
Voltage bases should follow nominal ratios. Phase shifts, vector groups, grounding, taps, and controls remain part of the model.
False confidence
A clean per-unit result does not prove that topology, grounding, control states, equipment data, and limits are correct.
Should results always be reported as per-unit quantities?
No. Per-unit quantities are useful for modeling and comparison, but final engineering decisions often require physical quantities such as kilovolts, amperes, fault duty in kA or MVA, ohms, protection secondary values, and operating margins.
A sound workflow may perform calculations in the per-unit system, then convert decision-relevant results back to physical units for verification and communication.
Concise interview answer
What should you say?
The per-unit system normalizes electrical quantities to selected power and voltage bases. It simplifies calculations across transformer voltage levels, makes equipment parameters easier to compare, and helps identify scaling and data errors. Its usefulness depends on consistent base selection, correct base conversion, and conversion back to physical units when evaluating equipment duty or operating limits.
Free readiness diagnostic · MRK-002
Can you use the per-unit system without losing physical meaning?
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