The Single Phase Transformer

Furthermore, the Steinmetz model can be augmented with a core loss term Rc in parallel with Xm that approximately accounts for the hysteresis and eddy current losses. The more appropriate form of transformer equivalent circuit is shown in figure 2.a below.

The resistance parameters R1 and R2 can be found by applying DC voltage to the respective windings. For example, if a DC voltage is applied to the primary winding, the Steinmetz model predicts the equivalent circuit shown in Figure 3. The primary resistance can then be determined by
The same procedure can be used to find the secondary resistance R2. Note that the turns ratio is needed to refer to this resistance to the primary. This is usually given by the transformer manufacturer.
If the secondary of the transformer is short-circuited, the equivalent circuit can be approximated as shown in Figure 4. In this case, the magnetizing impedance is assumed to be much larger than the secondary resistance and leakage impedance. This is typically a good assumption for practical transformer designs. From the voltage, current, and power measurements, the magnitude and angle of the short-circuit impedance can be determined as

Although it is possible to perform other tests on the transformer to determine a more exact relationship between Xl1 and Xl2, (10) is a good approximation. An alternate method of determining the leakage reactances is to set (7) equal to the short-circuit impedance magnitude which can be written as

The next test involves open-circuiting the secondary winding and applying the rated voltage to the primary winding. Under this condition, the Steinmetz equivalent circuit, including the core loss term, reduces to that shown in Figure 5. As can be seen, the open-circuit impedance is

1) Single-phase transformer: The Lab’s variable AC source is a complex device, which is designed to provide safe conditions of an experiment. It consists of a single-phase transformer, variac, and lamp bulb in series with the output.