Calculation
Δu = uR·cosφ + uX·sinφ
Kapp's approximation uses only the resistive and inductive components of the short-circuit voltage together with the load's power factor.
Dubbel, Elektrotechnik, Abschnitt Transformatoren (Kappsches Dreieck, Δu ≈ ur·cosφ + ux·sinφ); Busch 2006, Abschnitt 8.3.3.3, Gl. (8.51) als Sonderfall R≈0
Transformer relative voltage change under load
Kapp's approximation uses only the resistive and inductive components of the short-circuit voltage together with the load's power factor.
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Result
Select a target and calculate.
Understand the inputs
- Relative voltage change Δu in % — Deviation of secondary voltage at rated load from no-load voltage, relative to rated voltage.
- Resistive short-circuit voltage uR in % — Resistive component of the per-unit short-circuit voltage, from copper loss at rated current.
- Reactive short-circuit voltage uX in % — Reactive component of the per-unit short-circuit voltage, from leakage inductance.
- Load power factor cos φ — Displacement factor of the connected load at rated current.
Example
uR=1.5%, uX=4% and cos φ=0.8 (inductive) give Δu=1.5·0.8+4·0.6=3.6%.
Assumptions and limits
Approximation for inductive load (lagging power factor) at rated current; capacitive loads, saturation and the neglected quadratic correction term are excluded.
Understand Transformer relative voltage change under load
This calculator estimates how far a transformer's secondary voltage drops at rated load compared with no load, using the classic Kapp approximation.
What does this quantity describe?
Per-unit short-circuit voltage splits into a resistive component uR (copper loss) and a reactive component uX (leakage inductance). For a load with power factor cos φ, the approximation is Δu=uR·cosφ+uX·sinφ.
Formula and variables
Δu = uR·cosφ + uX·sinφ
Δu = uR·cosφ + uX·sinφ
| Symbol / input | Meaning |
|---|---|
| Relative voltage change Δu in % | Deviation of secondary voltage at rated load from no-load voltage, relative to rated voltage. |
| Resistive short-circuit voltage uR in % | Resistive component of the per-unit short-circuit voltage, from copper loss at rated current. |
| Reactive short-circuit voltage uX in % | Reactive component of the per-unit short-circuit voltage, from leakage inductance. |
| Load power factor cos φ | Displacement factor of the connected load at rated current. |
Choose the inputs correctly
uR and uX are the resistive and reactive components of the per-unit short-circuit voltage, cos φ the power factor of the connected load at rated current.
How to use the calculator
Derive uR and uX from the short-circuit test or winding data; take cos φ from the known load characteristic.
Worked example
uR=1.5%, uX=4% and cos φ=0.8 (inductive) give Δu=1.5·0.8+4·0.6=3.6%.
Understand the result and units
An inductive (lagging) load increases Δu relative to a purely resistive load; with a capacitive load, Δu can even become negative (voltage rise).
uR, uX and cos φ are dimensionless (as percentages or ratios). Δu is output as a percentage.
Typical applications
Estimating voltage drop at the transformer output at full load, and a basis for selecting tap changers or voltage regulators.
Assumptions, limits and common mistakes
Approximation for inductive (lagging) load at rated current; capacitive loads, saturation effects and the quadratic correction term of the full Kapp formula are excluded.
Common mistake: Do not swap uR and uX; uX is markedly larger than uR for most transformers.
Frequently asked questions
What is “Transformer relative voltage change under load” used for?
Estimating voltage drop at the transformer output at full load, and a basis for selecting tap changers or voltage regulators.
Where do the input values come from?
uR and uX are the resistive and reactive components of the per-unit short-circuit voltage, cos φ the power factor of the connected load at rated current.
What does the result not cover?
Approximation for inductive (lagging) load at rated current; capacitive loads, saturation effects and the quadratic correction term of the full Kapp formula are excluded.