Per-unit converter

Base current and impedance, and an impedance moved from one MVA and kV base to another.

Result

Z on the new base: 0.8pu
Z in ohms: 0.7618Ω

Base impedance: 0.9522Ω
Base current: 8,367A

Z on its own base: 0.08 pu

How per-unit values work

A per-unit value is a quantity divided by a chosen base. Pick a three-phase power base and a line-to-line voltage base for one part of the system, and every other base follows. Impedances then land near 1 or below, a transformer's impedance is the same number on both of its sides, and a whole system can be added up without carrying turns ratios through every step.

The two derived bases, for a three-phase MVA base and a line-to-line kV base:

I_\text{base} = \dfrac{S_\text{base}}{\sqrt{3}\,V_\text{LL}}

Z_\text{base} = \dfrac{V_\text{LL}^{2}}{S_\text{base}}

Equipment impedances are given on the equipment's own rating. Before you add a transformer, a generator and a line together, move each one to the common system base:

Z_\text{new} = Z_\text{old}\left(\dfrac{V_\text{old}}{V_\text{new}}\right)^{2}\left(\dfrac{S_\text{new}}{S_\text{old}}\right)

Worked example

A 20 MVA, 13.8 kV transformer has a nameplate impedance of 8%, which is 0.08 pu on its own rating. The study uses a 200 MVA system base at 13.8 kV. The voltage base is unchanged, so only the power ratio applies:

Z_\text{new} = 0.08 \times \left(\dfrac{13.8}{13.8}\right)^{2} \times \dfrac{200}{20} = 0.8\ \text{pu}

To read that back in ohms, find the base impedance on the new base and multiply:

Z_\text{base} = \dfrac{13.8^{2}}{200} = 0.9522\ \Omega \qquad Z = 0.8 \times 0.9522 = 0.7618\ \Omega

Notice the direction: a larger power base makes the per-unit impedance larger. The ohms do not change; only the yardstick does.

Mistakes this catches

Mixing a three-phase MVA base with a line-to-neutral kV base, which is off by a factor of three.
Forgetting the voltage-ratio square when a nameplate kV differs from the system base kV.
Adding a percent impedance to a per-unit impedance without dividing by 100.

Questions

Why does a transformer's per-unit impedance stay the same on both sides?

Because the base voltages on the two sides are chosen in the transformer's turns ratio. The impedance in ohms changes by the square of that ratio, and so does the base impedance, so their ratio, the per-unit value, does not change.

Is percent impedance the same as per-unit?

Yes, scaled by 100. A nameplate impedance of 8% is 0.08 pu on the transformer's own MVA and kV rating. Convert it to the system base before adding it to other impedances.

Should the base voltage be line-to-line or line-to-neutral?

With a three-phase MVA base, use the line-to-line kV. Z_base = kV² / MVA then gives ohms per phase directly. Mixing a three-phase MVA base with a line-to-neutral kV is the most common way to end up off by a factor of three.

For learning, not for design

PhasorPrep is an independent study resource. It is not affiliated with, endorsed by, or sponsored by NCEES. Questions are original and written for practice; they are not actual exam questions. Calculators are for learning, not for engineering design.

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