The Per-Unit System

A network runs from 400 V to 400 kV, and impedances refer across a transformer by the square of the turns ratio. The same ohmic value means completely different things at different levels, and every calculation crossing a transformer needs a referral that can be got wrong.

Two bases are chosen freely — conventionally base MVA and base kV — and base current and base impedance follow. Base MVA is picked once for the whole system; base kV changes at every transformer, in the turns ratio.

That last choice is the point. With base voltages in the turns ratio, 1 p.u. on one side is 1 p.u. on the other, the ideal transformer vanishes, and only its leakage impedance remains in series.

Values cluster tightly, so an out-of-range result is visibly wrong without knowing which voltage level you are on. A result of 0.4 p.u. is obviously an error; a result of 52.8 kV requires context to judge.

Nameplate impedance is already per-unit — but on the equipment's own rating. A 20 MVA transformer at 11% becomes 55% on a 100 MVA system base. Converting bases is the one calculation per-unit does not remove, and it is where mistakes concentrate.

• Base kV is the line voltage, not the phase voltage.
• Base MVA is the three-phase total, not per phase.
• With those two choices, every √3 cancels and three-phase per-unit arithmetic looks exactly like single-phase.

Mixing line and phase bases is the classic error, and it shows up as a stray factor of √3 or 3 — large enough to notice, and easy to rationalise away if you are not expecting it.

A delta-star transformer introduces a 30° phase shift that per-unit does not remove, and it matters for unbalanced fault studies using symmetrical components.

And because every base must be consistent across the network, one wrong base propagates silently through a whole study. The results still look plausible, which is exactly what makes that error dangerous.