### Overview

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.

Transformers are stationary electric machines that step up or down AC voltage. They are typically formed of primary and secondary coils or windings, where the voltage on the primary is stepped up or down at the secondary, or the other way around. When a voltage is applied to one of the windings and current flows in that winding, flux is induced in the magnetic core, coupling both windings. With an AC current, AC flux is induced, and its rate of change induces voltage on the secondary winding (Faraday's law). Flux linkage between both windings depends on the number of turns of each winding; therefore, if the primary windings have more turns than the secondary winding, voltage will be higher on the primary than on the secondary, and vice versa.

This experiment characterizes a single-phase transformer by finding its equivalent circuit parameters. Three tests are performed: open-circuit test, short-circuit test, and the DC test.

### Principles

The transformer used in this experiment is rated at 115 V/24 V, 100 VA. The voltage rating comes from the ability of the insulation of each winding to safely handle specific voltages, while the VA rating or power (Watt) rating come from current handling capability of these windings, specifically wire thickness. It is important not to mix primary and secondary with high- and low-voltage nomenclature. For this experiment, the primary side is assumed to have the 115 V rating, while the secondary side is rated at 24 V. The 115 V side has two terminals labeled IN1 and IN2, while the secondary side has two terminals labeled OUT1 and OUT2.

The high-voltage side is commonly used for short-circuit testing to achieve more voltage resolution. For example, if a transformer is rated for 1200 V/120 V, a short-circuit on the 120 V probably has rated current flowing with less than 10% of the 1200 V, which makes a 0-120 V variable auto-transformer (VARIAC) on the 1200 V suitable for this test. The low-voltage side is commonly used for open-circuit testing, since this voltage is more accessible in the lab. Thus, this approach is followed as standard practice in this experiment.

The open-circuit test helps estimate the mutual inductance between two windings, as well as core power losses caused by flux induced in the core. The short-circuit test helps identify the leakage inductance of both windings, since maximum current is drawn in the short circuit, and some flux leaks from the core around the windings. The DC test helps measure wire resistance of both windings.

Subscription Required. Please recommend JoVE to your librarian.

### Procedure

1. DC Test

- Turn on the low-voltage DC power supply available on the bench.
- Set its voltage output to 0 V, and set the current limit to 0.8 A.
- Double-check the circuit connections, then connect the power supply output across the primary side windings (IN1 and IN2). Leave the secondary side windings (OUT1 and OUT2) open.
- Turn on the supply and slightly increase the voltage until the current limit is reached. Note that the supply might already be current-limited when the supply is turned on.
*Do not increase the current limit.* - Record the voltage and current readings from the power supply display.
- Set the voltage back to 0 V and disconnect the supply.
- Adjust the current limit to 4 A, then connect the supply output across the secondary side windings (OUT1 and OUT2). Leave the primary side windings (IN1 and IN2) open.
- Turn on the supply and slightly increase the voltage until the current limit is reached. Note that the supply might already be current-limited when the supply is turned on.
*Do not increase the current limit.* - Record the voltage and current readings from the power supply display. For this transformer, the input voltage is 3.5 V and the current is 0.8 A.
- Set the voltage back to 0 V, turn the supply off, and disconnect it.
- Measure the resistance across the primary windings with a multi-meter.
- Measure the resistance across the secondary windings with a multi-meter.
- It is common to have the higher voltage side resistance to be higher than the lower voltage side resistance due to the fact that power on both sides is ideally equal, and higher voltage means lower current and thus lower resistance. The DC test and measured resistance on the multi-meter should match closely.

2. Open-circuit Test

- Make sure the three-phase source is off.
- Connect the circuit for the open-circuit test (Fig. 1). Use a digital power meter.
- Make sure the VARIAC is at 0%.
- Double-check that the circuit connections are as expected from Fig. 1, and then turn on the three-phase source.
- Slowly adjust the VARIAC knob until the voltage reading on the digital power meter reaches 24 V.
- Record the voltage, current, real power, and power factor of the power meter.
- Set the VARIAC back to 0%, turn off the three-phase source, and disconnect the VARIAC output.
- In the open-circuit or no-load test, the magnetizing reactance (
*X*) and core loss resistance (_{m}*R*) are found from the current (_{C}*I*), voltage (_{OC}*V*), and power (_{OC}*P*) measurements as follows:_{OC}

*R*=_{C}*V*_{OC}^{2}*/P*(1)_{OC}

and*X*=_{m}*V*_{OC}^{2}*/Q*(2)_{OC}

where*Q*_{OC}^{2}=*(V*)_{OC}I_{OC}^{2}-^{ }*P*_{OC}^{2}(3)

**Figure 1: DC test schematic. **Please click here to view a larger version of this figure.

3. Short-circuit Test

- Make sure the three-phase source is off.
- Connect the circuit for the short-circuit test (Fig. 2). Make sure IN1 and IN2 are connected to the VARIAC output.
- Make sure the VARIAC is at 0%.
- Calculate the rated input current of the transformer. This is found by dividing the VA rating by the voltage rating on the input side. For example, if the input is 115 V and the VA rating is 100 VA, the input current rating is 100/115= 0.87 A.
- Check the circuit, and then turn on the three-phase source.
- Slowly and carefully adjust the VARIAC knob until the current reading on the digital power meter reaches rated input current.
- Record the voltage, current, real power, and power factor on the power meter.
- Set the VARIAC back to 0%, turn off the disconnect switch, and disconnect the VARIAC output. Keep the VARIAC three-phase cable connected.
- Remove the short circuit placed across the transformer secondary.
- In the short-circuit test, the leakage reactance (
*X*+_{1}*X*) and wire resistance (_{2}'=X_{eq}*R*+_{1}*R*) of both windings are found from the current (_{2}'=R_{eq}*I*), voltage (_{SC}*V*), and power (_{SC}*P*) measurements as follows:_{SC}

*R*=_{eq}*P*/_{SC}*I*_{SC}^{2}(4)

and*X*=_{eq}*Q*/_{SC}*I*_{SC}^{2}(5)

where*Q*_{SC}^{2}=*(V*)_{SC }I_{SC}^{2}-^{ }*P*_{SC}^{2}(6) *X*is assumed to be equal to_{1}*X*', while_{2}*R*and_{1}*R*can be used from the DC test (or at least one of them). If the DC test is not performed, it is common to assume that_{2}'*R*and_{1}*R*are equal._{2}'

**Figure 2: Short-circuit test schematic.** Please click here to view a larger version of this figure.

4. Load Test

Load tests show how the current and voltage values correlate between the input and output sides of the transformer where ideally,* V _{1}/V_{2 }*=

*I*=

_{2}/I_{1}*N*=

_{1}/N_{2}*a*where

*N*is the number of turns, subscripts 1 and 2 are for the primary and secondary sides, respectively, and

*a*is the turns ratio. The impedance on the secondary side reflected to the primary side is

*R'*=

*a*

^{2}

*R*or

*X'*=

*a*

^{2}

*X.*

- Make sure the three-phase source is off.
- Connect the circuit for the load test (Fig. 3). Make sure IN1 and IN2 are connected to the VARIAC output.
- Make sure the VARIAC is at 0%.
- Connect an oscilloscope differential voltage probe across the primary with a 1/200 setting. Adjust the probe measurement for 0 V offset with an appropriate scaling factor.
- Connect an oscilloscope current probe to measure the load current. Adjust the probe measurement for 0 mV offset with a 1X scaling factor for a 100 mV/A setting.
- Check the circuit, and then turn on the three-phase disconnect switch.
- Slowly adjust the VARIAC knob until
*V*reads 115 V._{P} - Record the voltage, current, real power, and power factor of both digital power meters.
- Capture the oscilloscope screen with at least three cycles shown.
- Turn off the three-phase source and set the VARIAC at 0%.
- Replace the 100 Ω resistor with three 100 Ω resistors in parallel.
- Turn on the three-phase source and slowly adjust the VARIAC knob until
*V*_{P}reads 115 V. - Record the two digital power meter readings only (no oscilloscope screen capture).
- Set the VARIAC back to 0%, turn off the disconnect switch, and disconnect the setup.

**Figure 3: Load test schematic.** Please click here to view a larger version of this figure.

Single phase transformers are used in power supplies and other equipment to convert AC voltages and currents from one value to another. Transformers are critical for providing electrical isolation which is necessary for the safe operation of many laboratory instruments and medical devices. If the input and output do not share a common terminal, then the transformer can transfer power with complete physical separation. This prevents electricity on the hazardous high-voltage side of a system from reaching circuits and people on the safe low-voltage side. Understanding the components within a transformer is important for transformer analysis and design. This video will demonstrate how to measure electrical parameters of transformer components by performing various tests.

A transformer has a pair of input terminals connected to a primary winding or coil and a pair of output terminals connected to a secondary winding. A core consisting of steel, ferrite or even simply air magnetically couples the two windings. A voltage across one winding causes current to flow through it, creating a magnetic field. Magnetic flux, which is the amount of magnetic field passing through an area is then coupled through the core to the secondary winding where it induces a voltage. This principal is called mutual induction. Faraday's Law states that flux's rate of change times the number of windings is equal to the induced voltage. Also called the Electromotive Force or EMF. A DC voltage across the primary winding is constant therefore the resulting magnetic flux is also constant and the rate of change is zero. However an AC voltage produces a magnetic flux with a non-zero rate of change and consequently induces a voltage. In other words an AC voltage is required for the transformer to operate. The transformer turns ratio is the number of turns of wire on the primary winding divided by the number of turns on the secondary winding. The ratio of voltage across the primary to voltage across the secondary is equal to the turns ratio. Depending on the turns ratio a transformer can step up voltage, step down voltage or keep it the same. The ratio of current through the primary to current through the secondary is equal to the inverse of the turns ratio. For example if the primary coil has three turns and the secondary has 30 turns, the turns ratio is 0.1. Thus 120 volts on the primary of this transformer becomes 1200 volts on the secondary. 10 amps through the primary becomes 1 amp through the secondary. Finally if the secondary coil has a load of impedance Z2, the primary coil has an apparent or reflective load, Z2 prime. The value of this reflective load is the impedance on the secondary side multiplied by the square of the turns ratio. A transformer can be considered a pair of coupled inductors which ideally transfers energy without loss from one coil to the other. However a real transformer has leaked magnetic flux or leakage inductance which does not contribute to the transfer of energy between windings. Furthermore a real transformer experiences power dissipation and heating from winding resistances. Magnetic flux induced in the core is an additional source of heat due to core loss resistance. To avoid damage a specified maximum power input is used called the VA rating or the product of input voltage and the current which is power. Now that the basics of a transformer have been introduced, let's take a look at how to measure a transformer's electrical parameters.

The transformer used in this experiment is rated to tolerate a maximum of 115 volts on the primary winding and a maximum of 24 volts on the secondary winding. Furthermore, this transformer has a power rating of 100VA meaning that it can accept a maximum of 100 watts of power. This DC test measures the resistance of each winding for use in the equivalent circuit model of the transformer. First set the low-voltage DC power supply voltage output to zero volts and the current limit to 0.8 amps. Then turn the supply off. Connect the power supply output across the primary winding. Do not connect anything to the secondary winding. Turn on the DC power supply and increase the voltage gradually until the current limit is reached. Record the voltage and current readings from the display of the power supply. Calculate the resistance of the primary winding by dividing the voltage by the current. Set the power supply voltage back to zero volts and turn it off. Connect the power supply across the secondary winding leaving an open circuit on the primary winding. Set the current limit on the power supply to four amps. Then increase the voltage gradually until the current limit is reached. Record the voltage and current readings from the display of the power supply. Calculate the resistance of the secondary winding. Set the power supply voltage back to zero volts, turn it off and disconnect it from the transformer. Finally use a multi-meter to confirm the calculated resistances across the primary and secondary windings.

The open circuit test measures the mutual reactants or the opposition to a change in current from the core loss resistance. Core loss resistance is the equivalent circuit parameter for power dissipation and approximates power losses in the core of the transformer. With the three-phase power source off and the Variac set to zero percent, assemble the circuit as shown. Then use a digital power meter to measure open-circuit current and voltage on the primary side. Turn on the three-phase power source and slowly adjust the Variac's control knob to increase voltage until the digital power meter reads 24 volts. Record the open-circuit voltage, open-circuit current, open-circuit real power and power factor. Use these values to calculate equivalent circuit parameters for the transformer. The core loss resistance, RC is calculated from the open-circuit voltage and open-circuit power. The mutual reactance XM is calculated similarly using open circuit voltage, power and current.

The short circuit test measures the leakage reactants and can also determine the wire resistance of both windings. First calculate the rated input current of the transformer by dividing the VA rating by the voltage rating for the input side. With the power source off, and Variac at zero percent output assemble the circuit as shown. This time use the digital power meter to measure short circuit current and voltage. Turn on the three-phase power source and slowly adjust the Variac to increase voltage until the current reading on the digital power meter reaches the rated input current. Record the short circuit voltage and current as well as the short circuit real power and the power factor. The leakage reactants is the sum of the primary side reactants and the reflected secondary side reactants which are assumed to be equal. Calculate the leakage reactants with the measurements from the short circuit test. Finally calculate the total wire resistance of both windings as the sum of the resistance of the primary winding and the reflected resistance of the secondary side winding.

Transformers are very useful electrical devices which have applications in the area of power conversion and electrical isolation for safety. The load test measures the ratio of voltage across the primary to voltage across the secondary as well as the ratio of current through the primary to current through the secondary. The circuit was assembled with a 100 Ohm resistor connected to the secondary side and the current and voltage measured on both sides. With the primary side at 115 volts, the voltage, current, real power and power factor were measured on both sides. The ratio of the primary voltage to secondary voltage should ideally equal the turns ratio. A study of the olfactory sensory neurons of mice used ultraviolet light from a xenon flash tube to dissociate certain compounds. The circuitry to drive a flash tube required high voltages generated with a step-up transformer. As with all high-voltage equipment, safe design uses transformers for electrical isolation to prevent accidental short circuits between components with dangerous voltages and other electronics in the circuit.

You've just watched Jove's introduction to single-phase transformers. You should now understand how a transformer works as well as how to measure its equivalent circuit parameters. Thanks for watching!

Subscription Required. Please recommend JoVE to your librarian.

### Results

By performing the DC, open-circuit, short-circuit, and load tests, the transformer's equivalent circuit parameters were identified; therefore, simulating, operating, and analyzing realistic transformer behavior become possible.

The short circuit test is usually performed by applying an increasing voltage on the high voltage side, since only small voltages on that side may cause rated current to flow on the shorted low voltage side. This is useful in operating the transformer at rated current and, therefore, testing for current carrying capability.

For this test, the short circuit voltage is 11.9 V, the short circuit current is 0.865 A, and the short circuit power is 7.11 W. The short circuit measurements are then used to calculate leakage reactance, which is 9.94Ω in this case. The resulting primary side and reflected side reactances are each 4.97Ω. The total wire resistance is calculated as 9.502Ω. Subtracting the resistance of the primary winding (4.375Ω) gives 5.127

As for the open-circuit test, it is useful in ensuring that transformer voltage insulation capabilities are met when running rated voltages. Other tests, such as high-pot insulation tests for insulation material breakdown, mechanical vibration tests, etc., are also performed but for more advanced applications.

For this transformer, the open circuit voltage is 23.8 V, the open circuit current is 335.5 mA and the open circuit power is 2.417 W. From these measurements, the core loss resistance, *R _{c},* and mutual reactance,

*X*, can be calculated as 234.35Ω and 74.67Ω respectively.

_{m}Subscription Required. Please recommend JoVE to your librarian.

### Applications and Summary

The described tests are critical in evaluating the impedance of a transformer and in determining its equivalent circuit parameters. Since transformer applications vary from simple chargers to high power AC transmission, appropriately characterizing different transformers for various applications is essential. Transformer impedance is used in power systems to determine possible fault impedances on either side of a transformer, approximate the efficiency of a transformer, calculate its line and load regulation, and simulate the transformer as part of larger electrical systems.

Subscription Required. Please recommend JoVE to your librarian.