Transformer no-load operation and ideal transformer properties

No-load operation of a single-phase transformer

With the secondary open ($I_2 = 0$), the primary draws a small no-load current $I_0$ (2–5% of rated) from the supply. It does two jobs, so it has two components:

• Magnetising component $I_m = I_0\sin\phi_0$: in phase with the flux, lags $V_1$ by 90°; it sets up the core flux.
• Core-loss (working) component $I_c = I_0\cos\phi_0$: in phase with $V_1$; it supplies hysteresis and eddy losses (and a very small $I_0^2 R_1$).

$$I_0 = \sqrt{I_m^2 + I_c^2}, \qquad P_0 = V_1 I_0\cos\phi_0 \approx \text{core loss}$$

        V1
        ^
        |    I0
        |   /
     Ic |  /  phi0 (about 75-85 deg)
        | /
        +--------> phi, Im
        |
        v E1, E2

The no-load power factor is low (0.1–0.3 lag). The shunt branch of the equivalent circuit is $R_0 = V_1/I_c$ and $X_0 = V_1/I_m$.

Properties of an ideal transformer

1. Zero winding resistance (no $I^2R$ loss).
2. No leakage flux; all flux links both windings.
3. Core of infinite permeability, so negligible magnetising current.
4. No hysteresis or eddy current loss.
5. 100% efficiency, zero regulation, and $V_1/V_2 = N_1/N_2 = I_2/I_1$.