Per-unit
Per-unit impedance change of base
- where
- per-unit impedance on the new and old base (pu)
- old and new base voltage (kV)
- new and old base power (MVA)
Explain this equation
Moves a per-unit or percentage impedance from one base to another, typically from a nameplate rating onto the study base of 100 MVA.
zold is the impedance on the old base, defined by Sold and Uold. Snew and Unew define the new base. The result znew is the same physical impedance in ohms, just expressed against a different reference.
The ohmic impedance is z·U²/S on either base. Setting the two equal gives znew = zold·(Uold/Unew)²·(Snew/Sold). The voltage ratio is squared because impedance base scales with voltage squared; the MVA ratio is not inverted because a larger MVA base has a smaller ohmic base.
Sense check: a 10% impedance on a 20 MVA transformer becomes 0.5 pu (50%) on 100 MVA when the voltage base is unchanged. A generator X″ of 0.25 pu on 18 kV, 500 MVA becomes 0.0405 pu on 20 kV, 100 MVA.
Watch out: this is a base change only and applies no IEC 60909 correction factors.
Converts a nameplate per-unit or percentage impedance onto the study base.
Enter your values to see the result.
Good to know
Transformer uk% is already per unit on its own rating and rated voltage. If the study voltage base equals the rated voltage, only the MVA ratio matters: 10% on 20 MVA becomes 0.5 pu on 100 MVA.
Common mistake
Inverting the MVA ratio. Moving to a larger base MVA makes the per-unit impedance larger.
Limits
Pure base conversion; it does not apply IEC 60909 correction factors (KT, KG).
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.