EE 452, Power Systems Laboratory, Lab #1



Lab 2

Power Transformers

Objectives

• To understand the voltage-current relationships of an ideal transformer.

• To understand how to refer impedances through an ideal transformer.

• To perform the open-circuit and short-circuit tests to obtain the physical model of the transformer.

Background Theory

Voltage and Current Relationships

An electrical transformer is constructed from copper windings around an iron core. Generally, there are two layers of windings; one for the primary winding with N1 turns of wire, and one for the secondary winding with N2 turns. The schematic symbol for the ideal transformer is show in Figure 2.1.

[pic]

Figure 2.1 Ideal Transformer

For the ideal transformer, the primary and secondary voltages are related to the number of turns on the primary and secondary windings:

[pic] (2.1)

The primary and secondary currents have the inverse relationship:

[pic] (2.2)

Impedance Referral

If an impedance Z2 is connected across the secondary winding of a transformer, it may be expressed as the ratio of secondary voltage to secondary current:

[pic] (2.3)

With Equations 2.1, 2.2, and 2.3, the ratio of primary voltage to primary current is written as

[pic] (2.4)

Equation 2.4 reveals that the secondary impedance appears as a modified impedance on the primary side. Circuit analysis is facilitated when the secondary impedance is referred to the primary side and the ideal transformer is eliminated from the circuit. This procedure is illustrated in Figure 2.2.

[pic]

Figure 2.2 Secondary impedance referred to the primary.

Physical Transformers

The ideal transformer is lossless: all energy is transferred through the device. Physical transformers, however, have internal inductances and resistances that result in power dissipation and lower secondary voltages. The physical transformer model, shown in Figure 2.3, is approximated as an ideal transformer with series and parallel passive circuit elements.

[pic]

Figure 2.3 Physical Transformer Circuit

The magnetizing elements, Lm and Rm, are due to the current drawn by the transformer without a load connected to the secondary. The magnetizing inductance draws the current that is necessary to sustain the magnetic field in the core. The magnetizing resistance models the losses due to currents induced in the core. Since the magnetizing elements cause losses in the iron core, they are often referred to as “iron losses”. The series element Rs, models the copper losses, the resistive losses in the copper coils. The series element Ls, models the leakage inductance, corresponding to the small fraction of the flux generated by the primary coil which is not coupled through the core to the secondary windings (leakage flux). The values of these elements are determined by the open circuit and short circuit tests of the physical transformer.

Short-circuit Test

In the short circuit test, the terminals of the secondary winding are shorted together. The secondary and primary voltages in the ideal transformer of the model are therefore zero. Because of the short circuit, a very small source voltage on the primary is sufficient to cause rated current to flow through the transformer windings.

[pic]

Figure 2.4 Effect of secondary short circuit

Thus, the average power delivered by the source is contained in the series resistance

[pic] (2.5)

and reactive power is contained in the series reactance:

[pic] (2.6)

Open Circuit Test

In the open circuit test, the secondary winding is unconnected. Hence, the primary and secondary currents in the ideal transformer of the model are zero. In order to compute the values of Xm and Rm, we must represent the parallel elements as a series circuit . . .

[pic]

Figure 2.5a Represent core effects as Series circuit

And sum impedances:

[pic]

Figure 2.5b Combining Impedances

We can now compute Xss and Rss as before:

[pic] (2.7)

[pic] (2.8)

Using the values of Rs and Xs from the short circuit test, Rm and Xm may be computed.

Since Ls represents leakage flux, coupling coefficient k can be computed using

[pic] (2.9)

Laboratory Procedure

Turns Ratio

Determine the nominal turns ratio of each primary winding (105, 115, 125 V) with each secondary winding (6, 12, 18, 24 V) on the Todd Systems transformer.

Connect the adjustable AC supply and the transformer as shown in Figure 2.6. Apply rated voltage (105 V) to the 105V primary of the transformer and measure the RMS voltage at each secondary tap. Repeat the same procedure and measurements with the 115V and 125 V primaries. Calculate all the available turns ratios with the measured primary and secondary voltages.

[pic]

Figure 2.6 Circuit for Measuring Tap Voltages

Short-Circuit Test: Measurement of Winding Losses

With the AC power supply turned off, connect the 50 mV, 50 A shunt (0.001 ohm) across the 24 V secondary as shown in Figure 2.7. Bring up the voltage slowly until 25 mVAC appears across the shunt as measured by the DMM, corresponding to the rated transformer secondary current of 25 A. Measure the real and apparent powers again, along with the source voltage. With these measurements, calculate the reactive power and the series resistance, the series reactance, and the series inductance.

[pic]

Figure 2.7 Short Circuit Test

Open Circuit Test: Measurement of Core Losses

Connect the variable AC supply and the power analyzer to the transformer as shown in Figure 2.8. Measure the real and apparent powers with rated voltage applied. With these measurements, calculate the reactive power, the magnetizing resistance, the magnetizing reactance, and the magnetizing inductance.

[pic]

Figure 2.8 Open Circuit Test

THE LAB WRITE UP SHOULD CONFORM TO DEPARTMENTAL STANDARDS AS DESCRIBED IN THE GUIDELINES FOR LABORATORY REPORTS. INCLUDE THE FOLLOWING :

• Draw the equivalent circuit model of the 125/24 transformer with all resistances and inductances labeled with their calculated values.

• Diagrams

• Measurements

• Calculations

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