Open circuit and short circuit tests

The open circuit (OC) and short circuit (SC) tests find the equivalent circuit parameters, the losses and the efficiency of a transformer without loading it fully. They need very little power, which is only the loss of the transformer.

Open circuit test (no-load test)

Purpose: to find the core loss $P_i$, no-load current $I_0$ and the shunt branch $R_0$, $X_0$.

        W   A
 AC o---(W)--(A)----+----------+
 supply            (V)   HV winding open
 o-----------------+----------+
        LV winding (rated V)

Procedure: the HV winding is left open, and rated voltage $V_0$ at rated frequency is applied to the LV winding (this is safer and needs lower-range instruments). A wattmeter, ammeter and voltmeter are connected on the LV side.

Calculations:

$$P_0 = V_0I_0\cos\phi_0,\quad I_w = I_0\cos\phi_0,\quad I_\mu = I_0\sin\phi_0$$ $$R_0 = \frac{V_0}{I_w},\qquad X_0 = \frac{V_0}{I_\mu}$$

Since $I_0$ is small (2 to 5% of rated), the copper loss $I_0^2R_1$ is negligible. So the wattmeter reading $P_0$ is the core (iron) loss, constant at all loads.

Short circuit test

Purpose: to find the full-load copper loss $P_{cu}$ and the equivalent resistance, reactance and impedance $R_{eq}$, $X_{eq}$, $Z_{eq}$.

        W   A
 AC o---(W)--(A)----+----------+
 supply (low V,    (V)   LV winding
 via variac)             short-circuited
 o-----------------+----------+
        HV winding

Procedure: the LV winding is short-circuited with a thick conductor. A low voltage $V_{sc}$ (about 5 to 10% of rated) is applied to the HV winding and slowly increased by a variac until the rated full-load current $I_{sc}$ flows. Wattmeter, ammeter and voltmeter are on the HV side.

Calculations:

$$Z_{eq} = \frac{V_{sc}}{I_{sc}},\qquad R_{eq} = \frac{P_{sc}}{I_{sc}^2},\qquad X_{eq} = \sqrt{Z_{eq}^2 - R_{eq}^2}$$

Because the applied voltage is low, the flux and hence the core loss are very small (core loss varies as $B^2$). So the wattmeter reading $P_{sc}$ is the full-load copper loss.

Uses of the results

• Equivalent circuit parameters, from which regulation is found: $\text{VR} \approx \dfrac{I(R_{eq}\cos\phi \pm X_{eq}\sin\phi)}{V}$.
• Efficiency at any load: $\eta = \dfrac{xS\cos\phi}{xS\cos\phi + P_i + x^2P_{cu}}$.
• The maximum efficiency load $x = \sqrt{P_i/P_{cu}}$.
• Together, the two tests give the transformer's full performance while drawing only the loss power from the supply. This is their advantage over a direct load test.