Transformer Formulas: Current and Fault Level
Transformer formulas for turns ratio, full-load current, impedance and fault current, with a 1,000 kVA worked example and a table of currents by rating.
The formulas
| To find | Formula |
|---|---|
| Turns ratio | a = Np / Ns = Vp / Vs |
| Current ratio | Ip / Is = Vs / Vp |
| Full-load current (three-phase) | I = S × 1000 / (√3 × V) |
| Fault current at the terminals | Isc = I(full load) / (Z% / 100) |
| Efficiency | η = x × S × pf / (x × S × pf + P(iron) + x² × P(copper)) |
| Load at maximum efficiency | x = √(P(iron) / P(copper)) |
S is the rating in kVA, V the line-to-line voltage of that winding in volts, Z% the impedance in percent, and x the fraction of full load. The fault current assumes an infinite source behind the transformer, so it is an upper limit.
Worked example: 1,000 kVA, 11 kV / 415 V, Z = 5%
- Secondary: I = 1000 × 1000 / (√3 × 415) = 1,391 A
- Primary: I = 1000 × 1000 / (√3 × 11000) = 52.49 A
- Voltage ratio = 11000 / 415 = 26.51
- Fault current at the secondary terminals: 1,391 / 0.05 = 27.82 kA
Full-load current by rating
| Rating | At 415 V | At 11 kV |
|---|---|---|
| 100 kVA | 139.1 A | 5.249 A |
| 250 kVA | 347.8 A | 13.12 A |
| 500 kVA | 695.6 A | 26.24 A |
| 1000 kVA | 1,391 A | 52.49 A |
| 1600 kVA | 2,226 A | 83.98 A |
Frequently asked questions
Why is the primary current so much lower than the secondary current?
Power is nearly the same on both sides, so the winding with the higher voltage carries proportionally less current.
What does the impedance percentage mean?
It is the share of rated voltage that must be applied to the primary, with the secondary shorted, to drive full-load current. A lower value gives a higher fault current.
Is the fault current from this formula the real value?
It is an upper limit. The supply network and the cable add impedance, so the real fault current is lower.
At what load is a transformer most efficient?
When the copper loss equals the iron loss, which for distribution transformers is typically at about 40% to 60% of full load.
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