Per-Unit Base Conversion Calculator
Convert a per-unit impedance from one MVA and voltage base to another. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates impedance on new base from impedance on old base, old MVA base, old voltage base, new MVA base and 1 more input. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Typical use: put transformer and source impedances on one common system base before adding them.
Cross-check: 10 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Textbook power and energy identity (single-phase, three-phase, power factor, per-unit); no governing standard |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 10 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Impedance on old base (pu) | 0.08 |
| Old MVA base | 10 MVA |
| Old voltage base | 11 kV |
| New MVA base | 100 MVA |
| New voltage base | 11 kV |
- Znew = 0.08 × (100 / 10) × (11 / 11)² = 0.8 pu
Assumptions
- Same physical impedance, different base
Typical use: put transformer and source impedances on one common system base before adding them.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Impedance on old base (pu) | (number) | greater than 0 | |
| Old MVA base | MVA | greater than 0 MVA | |
| Old voltage base | kV | greater than 0 kV | |
| New MVA base | MVA | greater than 0 MVA | |
| New voltage base | kV | greater than 0 kV |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Impedance on new base (pu) | (number) | Shown to 5 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with old mva base
| Old MVA base (MVA) | Impedance on new base |
|---|---|
| 1 | 8 |
| 2.5 | 3.2 |
| 5 | 1.6 |
| 10 | 0.8 |
| 20 | 0.4 |
| 40 | 0.2 |
| 100 | 0.08 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60909-0 (short-circuit currents)
- IEEE Std 519 (harmonic limits)
Check results against your utility's connection requirements and the equipment data sheets. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter impedance on old base (pu), old MVA base, old voltage base, new MVA base and new voltage base. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Same physical impedance, different base.
Which calculators should I use next?
Common next steps are Per-Unit Base Values and Fault Level (kA to MVA). The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 10 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Per-Unit Formulas: Base Values and Impedance: Per-unit system formulas: base current and base impedance from MVA and kV
- Short-Circuit Formulas: Fault Level by MVA: Short-circuit formulas using the MVA method: transformer fault level, adding the source, three-phase fault current
More Power Systems calculatorsAll engineering calculatorsPer-Unit Base Conversion in Elecmetric