Loss assumptions in OC and SC tests

In the OC test the measured power is taken as iron loss, and in the SC test as copper loss. Both assumptions are justified because in each test the neglected loss is a tiny fraction of the measured one.

No-load (OC) test: copper loss is negligible

 rated V  -->[W]--(A)--+ LV winding || HV winding  (open)

• The test is done on the LV side at rated voltage, with the HV side open.
• Rated voltage gives rated flux ($\phi_m = \frac{V}{4.44fN}$), so the full normal iron loss occurs (hysteresis loss $\propto B_m^{1.6}$, eddy-current loss $\propto B_m^2$, so $P_i$ varies roughly as $B_m^2$).
• The only current is the no-load current $I_0$, which is only 2-5% of rated current. The copper loss in the energised winding is $I_0^2R_1$.
• Since copper loss varies as the square of current, it is only about $(0.02$ to $0.05)^2 = 0.04\%$ to $0.25\%$ of the full-load copper loss, which is negligible. The HV winding carries no current at all.
• Hence $P_0 = P_i + I_0^2R_1 \approx P_i$.

Example: in a 10 kVA, 250 V transformer with $I_0 = 0.8$ A and $R_1 = 0.04\ \Omega$, the copper loss is $0.8^2 \times 0.04 = 0.026$ W against a wattmeter reading of 80 W, i.e. 0.03%.

Short-circuit (SC) test: iron loss is negligible

 low V  -->[W]--(A)--+ HV winding || LV winding (shorted)

• The LV side is shorted and a low voltage is applied to the HV side, raised until rated current flows. This voltage is only 5-10% of rated voltage, because only the small leakage impedance $Z_{01}$ limits the current.
• Rated current in both windings gives the full-load copper loss $I_1^2R_{01}$.
• The flux is proportional to the applied voltage, so the core works at only 5-10% of its normal flux density. Iron loss varies roughly as $B_m^2$, so it is only $(0.05$ to $0.1)^2 = 0.25\%$ to $1\%$ of the normal iron loss, which is negligible compared with the full-load copper loss.
• Hence $P_{sc} = P_{cu,FL} + P_{i,sc} \approx P_{cu,FL}$.

Summary

Because each neglected loss is far below 1% of the measured one, the error is within instrument accuracy. This lets the two losses be found separately while using little energy, so the efficiency and regulation at any load can be predicted.