Learning objective: Translate physical ohms into per-unit quantities and understand why base selection must be consistent.
Understand the idea
The per-unit system expresses voltage, current, impedance and power as ratios to chosen base quantities. It simplifies the comparison of equipment at different voltage levels and is especially useful for transformer and fault studies. For three-phase systems, use the line-to-line voltage base with the three-phase apparent-power base.
Worked example: given data
- Three-phase power base Sbase = 100 MVA.
- Line-to-line voltage base Vbase = 132 kV.
- A line reactance is X = 40 Ω. Find its per-unit value and the current base, then change to a 50 MVA power base with unchanged voltage base.
Detailed solution
Compute base impedance
For three-phase bases, Zbase = Vbase²/Sbase. Substituting kV and MVA gives (132²)/100 = 174.24 Ω. No additional √3 factor belongs in this formula.
Convert the line reactance
Xpu = X/Zbase = 40/174.24 ≈ 0.2296 pu. This is a dimensionless reactance on the stated base.
Calculate the current base
For a three-phase system, Ibase = Sbase/(√3 Vbase) = 100 × 10⁶/(√3 × 132 × 10³) ≈ 437.4 A.
Change to a new power base
The new base impedance is Zbase,new = 132²/50 = 348.48 Ω. Hence Xpu,new = 40/348.48 ≈ 0.1148 pu.
Cross-check using the base-change rule
Xpu,new = Xpu,old(Snew/Sold)(Vold/Vnew)². As the voltage base stays 132 kV, the old value is simply halved.
What the answer means
A physical reactance in ohms is unchanged by a change of base; only its numerical per-unit representation changes. With transformer networks, base voltages should be selected consistently according to the transformer ratios to avoid misleading comparisons.
Three mistakes to avoid
- Applying √3 twice when computing Zbase.
- Changing the power base but forgetting to update the numerical pu value.
- Mixing phase voltage with three-phase Sbase in the same formula.
Try a related question
A reactance is 20 Ω on the same original 100 MVA, 132 kV base. What is its per-unit value?
Show the worked-answer check
Xpu = 20/174.24 ≈ 0.1148 pu. It is half the 40 Ω reactance on that same base.
How to revise this concept
Try the same method on a two-transformer network with different voltage levels. First attempt the example on paper without opening the answer, then compare the intermediate steps. Explain each assumption before memorising a formula.
Content note: This is a newly prepared practice example, not an official GATE previous-year question. It was drafted with AI assistance for this educational website. Students should verify calculations and exam requirements against standard textbooks and official sources; educator review is recommended before publication.