### Overview

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

The objectives of this experiment are to find the equivalent circuit parameters of a three-phase induction motor using the per-phase equivalent circuit and tests similar to those used in transformer characterization. In electrical engineering, an equivalent circuit (or theoretical circuit) can be determined for a given system. The equivalent circuit retains all characteristics of the original system, and is used as a model to simplify calculations. Another objective is to operate the motor in the linear torque-speed region.

### Principles

The three-phase induction motor is fed by three-phase voltages or currents that induce three magnetic fields. These fields add up to a cumulative magnetic field, which rotates in space at constant amplitude and is termed the stator magnetic field. The magnetic field induces current in metal rotor bars or coils, which in turn induce their own magnetic field, termed the rotor magnetic field. The rotor hangs inside the stator, and the rotor magnetic field tries to lock to the rotating stator magnetic field, causing the rotor to spin. The rotor is typically made of rotor bars tied with end rings, forming what is commonly known as a "squirrel cage."

The per-phase equivalent circuit models the stator- and rotor-side winding resistance *R _{1}* and

*R*, respectively, leakage inductance due to leaked flux between the rotor and stator (

_{2}*L*is the stator leakage inductance, and

_{1}*L*is the rotor leakage inductance), mutual magnetizing inductance (

_{2}*L*or reactance

_{m}*X*), and core losses in the core loss equivalent resistance

_{m}*R*. These are similar to the transformer's equivalent circuit model, but include the effect of rotor magnetic field lag behind the stator, which is termed slip.

_{C}In order to find the equivalent circuit model of the motor, several tests (no-load, locked-rotor, DC, and load tests) should be performed. These tests require the knowledge of motor ratings. For the rated voltage of 208 V at 60 Hz, the following should be noted down from the nameplate: rated power (hp and W, where 1 hp = 746 W), rated current (A), and rated speed (RPM and rad/s). From these ratings, the rated torque (N·m) can be found by dividing the rated power in Watts over the rated speed in rad/s (1 RPM = 2π/60 rad/s), which is not shown on the nameplate.

To load the induction machine shaft, a DC generator (dynamometer setup) is mechanically coupled to the shaft. The induction motor acts as the prime mover of the generator. As the electrical load increases on the generator, the mechanical power increases into the generator and out of the induction motor, thus increasing the load on the induction motor shaft.

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### Procedure

1. DC Test

Note that a squirrel-cage induction machine has only stator terminals accessible.

- Turn on the low-power DC power supply and limit the current to 1.8 A.
- Turn the supply off.
- Connect the supply terminals across two of the induction motor terminals (labeled A, B, and C).
- Turn the supply on and record the output voltage and current.
- Repeat for the two other phase combinations.
- Note that the measured resistance is for two phases in series, thus the per-phase resistance is half the measurement.

2. No-Load Test

Test the induction machine with no load to find the per-phase magnetizing branch parameters *X _{m}* and

*R*For this test, make sure the load dynamometer has all its terminals disconnected, where it is generating no power and supporting no load.

_{C.}- Make sure the three-phase source is off.
- Check that the VARIAC is at 0% and then wire the VARIAC to the three-phase outlet, and connect the setup (Fig. 1).
- Double-check that the circuit connections are as shown in Fig. 1, and then turn on the three-phase source.
- Quickly increase the VARIAC output until each of the digital power meters reads around 208 V.
- Record the power, voltage, and current readings from both meters.
- Measure the speed using the strobe light (tune the strobe light to a reasonable speed), and label the measurement as ω
_{o}. - Record the torque reading in N·m or lb·ft, and label the measurement as T
_{o}just in case the torque transducer or torque-measuring apparatus is not well calibrated. This is the no-load torque. - Set the VARIAC back to 0% then turn off the three-phase source. Leave the rest of the circuit intact.

**Figure 1: Electrical setup for no-load test.** Please click here to view a larger version of this figure.

3. Locked-Rotor Test

Test the induction machine with a locked rotor in a manner similar to the short-circuit test of a transformer. Use this test to find the per-phase series resistances and leakage inductances. For this test, make sure the load dynamometer has all its terminals disconnected.

- Make sure the three-phase source is off.
- Check that the VARIAC is at 0%.
- Lock the rotor on the dynamometer side using a mechanical clamp or a zero-torque setting, if the dynamometer is digitally controlled.
- Note that the setup is still similar to that of Fig. 1, except with a locked rotor.
- Double-check that the circuit connections are as shown in Fig. 2.
- Turn on the three-phase source and the induction machine switch.
- Slowly and carefully increase the VARIAC until rated current is reached on one or both of the digital power meters.
- Record the power, voltage, and current readings from both meters.
- Set the VARIAC back to 0% then turn off the three-phase source. Leave the rest of the circuit intact.

**Figure 2: Setup for load test. **

4. Load Test

Use this test to trace the linear torque-speed characteristic of the induction machine. For this test, use the dynamometer with a shunt-field as a generator (more on this operating condition is given later in the DC machines video, but the armature is the generator output port).

- Make sure the three-phase source and induction machine switch are off.
- Check that the VARIAC is at 0%.
- Remove the locking clamp from the rotor shaft.
- Connect the circuit (Fig. 2). Use R
_{L}=300Ω but keep S_{D }off. - Do not use the series field.
- Check the circuit, then turn on the three-phase source and the induction machine switch.
- Quickly increase the VARIAC output until each of the digital power meters reads around 208 V.
- Record the power, voltage, and current readings from both meters.
- Measure the speed and label it as ω
_{1}. To measure the speed, adjust the "Coarse" frequency knob on the strobe light until the shaft looks almost stationary, and then fine-tune the frequency setting using the "Fine" knob. - Record the torque reading and label it as T
_{1}. - Note that this operating point (ω
_{1}, T_{1}) is not the same as no load, because the field winding is also acting as a load in parallel with the armature. As S_{D }is turned later and R_{L}is decreased, the load is increased since the load current increases as R_{L}decreases. - Turn on S
_{D}. Measure the speed and label it as ω_{2}. - Record the torque reading and label it as T
_{2}. - Turn off S
_{D}. Change R_{L}to 200 Ω, then turn on S_{D}. - Measure the speed and label it as ω
_{3}. - Record the torque reading and label it as T
_{3}. - Turn on S
_{D}. Change R_{L}to 100 Ω. Turn on S_{D}. - Measure the speed and label it as ω
_{4}. - Record the torque reading and label it as T
_{4}. - Set the VARIAC to 0%, turn off the three-phase source, and disassemble the circuit.

AC Induction Motors are the workhorses of modern industry, as they are simple, rugged, and reliable. An induction motor has only two main parts. The first is the stationary part called the stator, which consists of stationary coils around a cavity. Suspended in the cavity is the rotor, which is a pair of end rings capping a cylindrical arrangement of bars. This is often called the squirrel cage. The electrical parameters of these two components provide information about the motor's efficiency and the relationship between torque and speed. This is essential for determining the best motor size and type for an application. This video will introduce the basics of induction motor operation and demonstrate how to determine an equivalent circuit model for a three-phase induction motor.

A three-phase AC induction motor uses three-phase power with each phase connected to its own separate set of stator coils. The coils are arranged in a pattern that generates one magnetic field for each phase of the supplied power. The resulting net magnetic field, called the stator magnetic field, rotates with constant angular velocity. The rotating magnetic flux induces current in the rotor, similar to the way that a transformer transfers power from the primary coil to the secondary. The current through the bars of the squirrel cage in turn creates its own magnetic field, called the induced rotor magnetic field. The interaction between these two fields produces a force on the rotor, which causes is to follow the stator magnetic field. Like an iron bar following the magnets around it. If the rotor exactly follows the magnetic field, like this bar, then the motor is synchronous. However, in an induction motor, the rotor lags behind the stator magnetic field. This lag, called slip, causes induction motors to be asynchronous. Thus, the induction motor will always turn more slowly than the synchronous speed. Torque increases with decreasing slip, or as motor speed decreases from synchronous until a certain point called the breakdown torque. With the addition of a load, the rotation speed decreases as slip increases, resulting in decreasing torque. The following experiments will show how to measure various electrical parameters of the induction motor in order to describe the motor using an equivalent circuit model.

Each of the following tests requires knowledge of the rotor ratings, which are printed on the motor's name plate. For the rated voltage of 208 volts at 60 hertz, record the rated power in both horsepower and watts. Also record the rated current in amps and the rated speed in both revolutions per minute and radians per second. The rated torque can be calculated and is equal to the rated power divided by the rated speed. Here the induction motor shaft drives a DC generator. The electrical load on the DC generator is directly related to the mechanical power into it. And in turn, acts as the mechanical load on the induction motor. First, set the DC power supply current limit to 1.8 amps, then turn it off. This DC test measures the resistance of just the stator winding since only the stator terminals are accessible for a squirrel cage induction motor. Connect the power supply output across stator terminals A and B. Turn on the power supply and record its output voltage and current. Repeat this procedure for the other two-phase combinations B and C, and C and A. For each of the phase combinations, calculate the resistance by dividing output voltage by output current. The result if for two phases in series, so the per phase resistance, R1, is half this value. The stator winding resistance depends on the motor power rating, and is six ohms for this motor.

Test the induction motor with no-load to obtain measurements needed for further calculations. First, disconnect all terminals of the DC generator, or dynamometer, so it generates no power and provides no mechanical load to the induction motor. With the three-phase power source off, assemble the apparatus. Set the variac to 0% output and connect it to the three-phase outlet. Turn on the three-phase power and quickly increase the variac output until each of the digital power meters reads about 208 volts. Record the power, voltage, and current measurements from both meters. The sum of the power measured by the two digital power meters is the power consumed by the three phases acting together. 1/3 of this is the power in one phase. Record the motor torque and designate it t-zero, the no-load torque. If the torque measurement apparatus is not well calibrated, t-zero may not necessarily equal zero. Next, use a strobe light to measure the motor's rotation speed with no-load, which is close to its synchronous speed of 1,800 RPM. Adjust the course and find frequency knobs until the shaft looks stationary. The motor speed is typically between the rated speed on the name plate and the synchronous speed. Convert the strobe light frequency from RPMs to the no-load angular rotation speed, omega zero. Set the variac back to 0% output, then turn off the three-phase power. Leave the rest of the apparatus intact.

The locked rotor test measures the electrical parameters when the motor is fixed and unable to rotate. In this state, the largest difference in motion between the rotor and stator field occurs. For this test, use the set up of the no-load test and disconnect all terminals of the DC generator or dynamometer. With the three-phase power turned off and the variac at 0% output, lock the rotor on the DC motor side with the mechanical clamp. Except for the locked rotor, the apparatus is the same as for the no-load test. Turn on the three-phase power and the induction motor. Slowly increase the variac output to the rated current on the digital power meters. Record the power, voltage, and current from both meters. To finish, set the variac back to 0%, then turn off the three-phase power.

Effectively, the stator winding performs the same function as the primary coil of a transformer, and the rotor is equivalent to the secondary winding. The motor can therefore be modeled using an equivalent circuit similar to that of a transformer. However, the circuit is simplified to remove the ideal transformer portion and refers to the rotor components as a reflection of the stator. The per-phase equivalent circuit includes the stator winding resistance, R1, calculated from the DC test. The stator also exhibits opposition to changes in current and voltage called the reactance X1. The rotor parameters are reflected from the stator, including the reflected resistance, R2 prime, and rotor reflected reactance, X2 prime. The mutual magnetizing reactance, XM parameter is an equivalent for the magnetic flux in the air gap between the rotor and stator. Finally, a loss of power occurs between the stator and rotor, and is modeled as the core loss equivalent resistance, RC. All of these values can be calculated from the tests demonstrated, and are detailed in the tests protocol.

AC induction motors are widely used in a variety of applications, due to their simplicity, ruggedness, and reliability. An induction motor is often selected based on its linear torque speed under a changing mechanical load. The load test traces the linear torque speed characteristic as the mechanical load changes. For this test, a DC generator, or dynamometer, is connected to the induction motor so that it provides a controlled load on the rotor. The apparatus is assembled with a load resistance, R-L, of 300, 200, or 100 ohms. The power, voltage, and current measurements are recorded from the connected meters. Then, the torque reading and rotation speed are measured with and without the load resistance. A plot of the induction motor torque speed characteristics will be like these curves for the four classes of NEMA motors. An electron microscope requires an evacuated chamber to contain the sample and uses a vacuum pump which may have a small induction motor. The vacuum in the chamber enables transmission of electrons to the sample, and from the sample to the imaging apparatus. Finally, lathes and other machine shop equipment may use more powerful three-phase induction motors. Because of their simplicity and lack of mechanical commutation, induction motors can withstand heavy use with reduced likelihood of failure. This ruggedness is a clear advantage when fabricating metal parts.

You've just watched Jove's introduction to AC induction motors. You should now understand the basic principle of operation and how to perform the tests to determine their equivalent circuit parameters.

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### Results

A common mistake in finding the equivalent circuit parameters of induction machines is to use the three-phase measured power in calculations of the per-phase equivalent circuit, while one third of the power should be used: three phases consume the measured power, and thus, one third of the power is in one phase.

Calculations of the equivalent circuit parameters are similar to those of the transformers, but it is common to split *X _{1}* and

*X*per the NEMA frame of the machine. For example, if the motor is of NEMA frame A or D, then

_{2}'*X*and

_{1}*X*are assumed to be equal, while if the motor is of NEMA frame B, then

_{2}'*X*and

_{1}*X*are split as 40% and 60% of

_{2}'*X*, respectively, and if the motor is of NEMA frame C, then

_{eq}*X*and

_{1}*X*are split as 30%

_{2}'*and*

*70% of X*, respectively. It is expected to find that

_{eq}*X*and

_{1}*X*are 1-10% of

_{2}'*X*,

_{m}*R*and

_{1}*R*are on the order of mΩ to several Ω depending on the motor power rating, and

_{2}'*R*would be on the order of tens to hundreds of Ω, as it is several orders of magnitude larger than

_{C}*R*and

_{1}*R*.

_{2}'The linear region of the induction motor torque-speed curve is found using the load test and can be extrapolated from no-load to full- or rate-load conditions. A typical torque-speed curve is shown in Fig. 3 for several NEMA frames and the linear region is the right-most region close to the 90-100% speed.

**Figure ****3****: Typical torque-speed curves for various NEMA frames.**

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### Applications and Summary

Three-phase induction machines, especially induction motors, are the workhorses of modern industry. Appropriately characterizing an induction motor provides engineers and technicians with information on the motor's efficiency and torque-speed characteristics. These are essential in determining which motor size and frame best fits an application. Once a motor is characterized and the torque-speed curve is known from equivalent circuit parameters using the tests described, different NEMA frames have different curve shapes. For example, an elevator application requires high-starting torque; therefore, frames, such as NEMA frame D, are more suitable than A or B. When dealing with the induction motor's integral parts of larger systems that consume considerable amounts of energy (*e.g.*, chillers), knowing the equivalent circuit parameters of a motor can provide good estimates of the motor's efficiency and its contribution to energy consumption in that larger system.

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