TOPIC-01 · Engineering guide
Transformer Voltage Regulation Percent
For load fraction 1, power factor 0.8 lagging, R = 2% and X = 4%, the no-load equivalent voltage magnitude is sqrt(1.082) per unit. Regulation percent is (sqrt(1.082) − 1) × 100.
Formula, variables and conditions
θ = acos(pf) I_real = λ × pf I_imag = −λ × sign × sin(θ), where sign is +1 lagging and −1 leading V_real = 1 + I_real × Rpu − I_imag × Xpu V_imag = I_real × Xpu + I_imag × Rpu regulation% = (hypot(V_real, V_imag) − 1) × 100
Variables and units
- λ: load fraction, output-current magnitude divided by rated output current, from 0 to 1.
- pf: power factor from 0 to 1.
- R% and X%: series resistance and reactance on one consistent per-unit base. At least one must be greater than zero.
- Reference side: primary or secondary. It names the base; it does not change the arithmetic.
Conditions
- The same per-unit equations are used for single-phase and for a balanced three-phase positive-sequence model.
- Rpu = R% / 100 and Xpu = X% / 100.
- Stored formulas are F-TVREG-001, F-TVREG-002 and F-TVREG-003. Model version 1.0.0. Source SRC-061.
Worked example
Golden fixture: single-phase or the same per-unit numbers, reference side secondary, full load, lagging.
- Load fraction λ
- 1
- Power factor
- 0.8 lagging
- R / X
- 2% / 4%
- Phasor check
- V_real = 1.04 and V_imag = 0.02
- Magnitude
- sqrt(1.082) per unit
- Regulation
- (sqrt(1.082) − 1) × 100
The unrounded result is (sqrt(1.082) − 1) × 100, about 4.019%. A display rounded to two decimal places can show 4.02%. Quote the expression when the extra digits matter.
Boundaries and common mistakes
Boundaries
- The same inputs with a leading load give magnitude sqrt(0.986), so regulation is negative in this model.
- Unity power factor with the same R and X gives magnitude sqrt(1.042).
- Zero load fraction gives 0% regulation.
- Excitation current, saturation, temperature, harmonics, taps, regulators, source impedance and unbalance are excluded.
- SRC-061 is a course-note PDF checked on 2026-10-14. It is model context, not a standard and not an equipment test.
Common mistakes
- Adding the turns ratio and the regulation percent as if they were one result.
- Forgetting the lagging/leading sign. The imaginary current flips with that choice.
- Reading a rounded 4.02% display as more precise than (sqrt(1.082) − 1) × 100.