Expressing every quantity as a fraction of a chosen base turns messy multi voltage networks into simple arithmetic.
The per unit system expresses voltages, currents, powers and impedances as fractions of chosen base values. It removes transformer ratios from network calculations and makes fault studies far easier.
What Is the Per Unit System?
The per unit system is a method of expressing electrical quantities as a ratio of their actual value to a selected base value. A voltage of 10.45 kV on an 11 kV base becomes 0.95 pu, and an impedance is expressed the same way against a base impedance.
Two base values are chosen freely, usually power in MVA and voltage in kV. All other bases, such as current and impedance, follow from these two.
Nameplates already use this idea. A transformer marked 8 percent impedance simply has 0.08 pu impedance on its own rating.
Engineers use per unit values in every load flow and short circuit program. Understanding them makes the software results much easier to check.
Base Quantities and Formulas
Base MVA is the same everywhere in the network. Base kV changes across each transformer in proportion to its turns ratio, which is the trick that removes ratios from the calculation.
Three phase formulas use line voltage and total power, so the √3 terms appear only in the base current. This avoids the usual confusion described in three phase power calculation.
4 Brilliant Shortcuts of Per Unit Analysis
Shortcut 2 is useful for sanity checks. Transformer impedances usually fall between about 4 and 15 percent, so a value of 80 percent suggests a typing error.
Shortcut 3 makes hand checks of short circuit current quick and reliable before running software.
Change of Base Formula With Example
Z pu new = Z pu old × (MVA new ÷ MVA old) × (kV old ÷ kV new)²
Worked example:
Transformer 10 MVA, 11 kV, Z = 8 percent = 0.08 pu on own base
System base 100 MVA, same kV
Z pu new = 0.08 × 100 ÷ 10 = 0.8 pu
Fault at the transformer terminals, infinite source:
I fault = 1 ÷ 0.08 = 12.5 times rated current
Rated current = 10 MVA ÷ (√3 × 11 kV) = 524.9 A
I fault ≈ 6.56 kA
The change of base step is needed whenever equipment ratings differ from the common system base. Skipping it is the most common per unit mistake.
Real fault levels are lower because the source impedance adds to the transformer impedance. Add all pu impedances on the same base before dividing.
Typical Per Unit Impedances
| Equipment | Typical Impedance on Own Rating | Notes |
|---|---|---|
| Distribution transformer | About 4 to 6 percent | Lower value, higher fault level |
| Power transformer | About 8 to 15 percent | Chosen to limit fault current |
| Generator subtransient | About 10 to 25 percent | Decides first cycle fault current |
| Induction motor locked rotor | About 15 to 20 percent | Motors feed fault current too |
| Cables and lines | Depends on length | Convert from ohms per km |
These ranges help build quick estimates when data is missing. Always replace them with nameplate or test values for final studies.
Transformer impedance also sets how much voltage drops under load, linked to the turns ratio and secondary voltage.
Where the Per Unit System Is Used
Relay engineers turn per unit fault levels into relay currents for coordination studies.
Transformer selection uses the same data, including kVA rating from transformer kVA calculation.
Common Mistakes in the Per Unit System
Mixing values on different MVA bases without conversion is the classic error. Always write the base next to every pu value in your calculation sheet.
Another error is using the wrong kV base across a transformer. If the transformer ratio differs from the nominal kV ratio, use the voltage correction term in the change of base formula.
Finally, remember to convert results back to amps, volts or ohms at the end. A per unit answer alone means nothing to the person choosing a breaker.
Fault Current Calculator
This result assumes an infinite source. Add source impedance in per unit on the same base for a realistic value.
- Removes transformer ratios from calculations.
- Makes data errors easy to spot.
- Simplifies fault and load flow studies.
- Same values on both transformer sides.
- All values must share one MVA base.
- kV bases must follow transformer ratios.
- Convert back to real units at the end.
- Nameplate percent must be converted to pu.
Per Unit Representation Chapter PDF
Per Unit Values Explained on Video
Per Unit System FAQ
Related Articles
- Short Circuit Current Calculation
- Calculate Short Circuit Fault Current
- Load Flow Analysis for Industrial Plants
- What Is Impedance
- How to Calculate Three Phase Power
External References
- Base Changing Per Unit Impedance, Electrical PE Review
- Per Unit Representation Chapter, BS Publications
- Changing Base Across Transformers, GridAnalytica
- Per Unit Values, Wikipedia
What We Learn Today
- Pick base MVA and base kV, then derive base current and impedance.
- Change every impedance to the common base before combining.
- Fault current in pu is 1 divided by the total pu impedance.