Lab 4 - Non-Ideal Transformers

Lab 4 - Non-Ideal Transformers

Purpose

To determine the transformer properties via open-circuit, short-circuit, and load tests on a non-ideal iron core transformer. The voltage regulation and efficiency for various load conditions will be calculated and compared with the results of the load test.

Introduction

Since iron has non-linear magnetic characteristics, the iron core transformer is essentially a non-linear device, with internal losses and leakage. We will model the operation of the device with an appropriate linear equivalent circuit which accounts for both losses and leakage. Using this equivalent circuit, we then can predict transformer behavior with sufficient accuracy. Moreover, this equivalent circuit has parameters which may be determined by simple tests that we will perform.

Open circuit test (done with the secondary winding not connected)
Short circuit test (done with the secondary winding shorted with an ammeter)
Load Test (done with the secondary loaded using the rheostat)

Equivalent Circuit 3a (Open-Circuit)

Part 1: Equivalent Circuit Model (see test circuits for comparison)

At lower frequencies, the physical transformer can be represented by an equivalent circuit as shown in Figure 3c. If the voltage in the primary and the leakage reactance are neglected the approximate equivalent circuit 3d can be used to predict the performance of the transformer.

Open Circuit Model using 3a and 3d & 3b and 3d:

Equivalent Circuit 3b (Short-Circuit)

Equivalent Circuit 3c

Equivalent Circuit 3d

The results of the equivalent circuits will allow for the regulation and efficiency calculations required in the results section. Keep in mind the equivalent circuit is from the primary side. The test load (R_L and X_L ) must be multiplied by (N₁/N₂)² so that all the parameters are referred to the high-voltage (primary) side. Alternatively, some parameters may be transformed to the low-voltage side.

Be careful not to mix voltage and current from one side with the impedance value from the other side.

Part 2: Efficiency

η = output power/input power, where: input power = (outut power - losses)

W_o = V_o ∙ I_o∙ cos(θ_o)

The iron losses are obtained from the open-circuit test

the copper losses are obtained from the short-circuit test

Part 3: Regulation

The voltage regulation of a transformer, at a certain load, is defined as the percentage rise in the secondary voltage when the load is removed.

∈ = (V_{no load} - V_{full load} )/V_{full load}

Test Circuits

Circuit 3.1: Open-Circuit Test

Procedure

Testing:

Record the model number, voltage, current, and power ratings of the transformer.

Do not exceed these values.

Note that the power meters measure Voltage, Current, and Power.
The power meter will act in place of the multimeters typically used.
Be careful of which ports you use for each measurement.

Open-circuit Test:

Use AC for both voltage and Current. Use mA mode for the current measurement.

Connect the transformer as shown in Circuit 3.1.
Take readings of the primary Voltage, Current, and Power.
- Test with a primary voltage of 30V, 60V, 90V and 120V.

Circuit 3.2: Short-Circuit Test

Warning: Turn the autotransformer down and off before

carrying out the short circuit test.

Short-circuit Test:

For the short-circuit test apply the test voltage slowly

until the rated current is achieved in the secondary.

A small input will produce a large current in the secondary.

Less than 10 volts is enough to circulate the rated secondary current.

Connect the transformer as shown in Circuit 3.2.
Connect the secondary wires directly to the current meter.
Take readings of the primary Voltage, Current, and Power.
- Record values that produce 1, 2, 3, 4, & 5A in the secondary.

Load Test:

Connect the transformer as shown in Circuit 3.3
With a purely resistive load connected to the secondary:
Take readings of the Voltage, Current and Power for each coil.
Adjust the variable resistor and input voltage to:
- Produce 1, 2, 3, 4, & 5 Amps in the secondary.
- While maintaining 36V in the secondary.
- Record the values.
For each test, disconnect the load and:
- Adjust the input voltage to what it was with the load connected.
- Record the unloaded secondary voltage.
These readings will be used to determine the regulation of the transformer.

Circuit 3.3: Load Test

Results

Open Circuit Test

For the open-circuit test, plot X_M and R_C against the applied voltage. Separately plot primary input power against voltage.
Determine the transformer turns ratio N₁/N₂

Short-Circuit Test

For the short-circuit test, plot Z_E , R_E and X_E against I_SC . Separately plot primary input power against secondary short-circuit current.
Use primary and secondary current to determine the transformer turns ratio (N₂ /N₁).

Load Test

Calculate the actual efficiency at 1, 2, 3, 4 and 5 amps (using the measured input and load power).
The best result is obtained if Linear Interpolation is used to determine the value of R_c.
Calculate the Actual Voltage Regulation as a function of load current.

On separate plots, plot η and ∈ against I_Load from the Load Test. Plot both the actual values and values from the model and comment on any differences.

For each test, discuss your results. Include reference to the introductory theory, and where departures from the ideal transformers occur.

Questions

Why does the Open-Circuit test used to find Iron losses, and Short-Circuit test used to find the Copper losses?
Describe what is meant by efficiency and regulation in terms of the transformer properties analyzed above.
Why is the voltage in the primary lower with the load, than when unloaded?

From the model developed, calculate the efficiency you would expect at 1, 2, 3, 4 and 5 amps.

Using the transformer model, calculate the voltage regulation you would expect with a 1, 2, 3, 4 and 5 amp load with a power factor of 1.0.

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