Transformers: Equivalent Circuit, Losses & Testing
Open-circuit and short-circuit tests, equivalent circuit parameters, efficiency and all-day efficiency — the standard BHEL/Siemens opener.
Key formulas
V1/V2 = N1/N2 = K; E = 4.44 · f · N · Φm
Turns ratio / EMF equation: EMF per turn must be equal on both windings; K is the transformation ratio.
P_cu = P_i → η_max at load fraction x = √(P_i / P_cu,rated)
Maximum efficiency condition: Classic numerical: find the load at which efficiency peaks given iron and full-load copper losses.
VR% = (V₂NL − V₂FL)/V₂FL × 100; ≈ (I·Re·cosφ ± I·Xe·sinφ)/V₂ × 100
Voltage regulation: Plus sign for lagging load, minus for leading — the standard approximate formula in interviews.
Cheat sheet
- ▸O.C. test (LV side, one winding open) measures core (iron) losses and gives the shunt branch: R0 (no-load resistance) and X0 (magnetising reactance).
- ▸S.C. test (HV side, other winding shorted, low voltage applied) measures copper losses at rated load and gives the series branch: Re (equivalent resistance) and Xe (leakage reactance).
- ▸Iron loss is constant (depends on flux/frequency); copper loss varies as load². Maximum efficiency occurs when variable loss = constant loss.
- ▸Transformers are rated in kVA, not kW, because losses depend on current (copper) and voltage (iron), not on the load's power factor.
- ▸All-day efficiency = energy output / energy input over 24 h — used for distribution transformers that stay energised at light load, so iron loss dominates.
- ▸Voltage regulation = (V_no-load − V_full-load) / V_full-load × 100; it can be negative for leading-power-factor loads.
O.C. vs S.C. test
| Aspect | Open-Circuit test | Short-Circuit test |
|---|---|---|
| Excitation | Rated voltage on LV, other side open | Small voltage on HV, other side shorted |
| Measures | Iron loss, R0, X0 (magnetising branch) | Copper loss, Re, Xe (series branch) |
| Current drawn | Very small (no-load current) | Rated current at reduced voltage |
| Side energised | LV (safe, easy supply) | HV (current is limited, instruments safe) |
| Power consumed | ≈ core loss | ≈ copper loss at rated load |
Visual
Equivalent circuit (referred to primary):
R1 X1 R2' X2'
o--/\/\--/\/\--+--/\/\--/\/\--+--o
| |
R0 | X0 | (shunt: core loss + magnetising)
| |
+------ E1 (mutual flux branch)Top 4 campus interview questions
MCQ mastery quiz
1. The open-circuit test of a transformer primarily measures…
2. Maximum efficiency occurs when…
3. The short-circuit test is performed by energising the…
4. Voltage regulation of a transformer is negative when the load power factor is…