Block I - Three-Phase Squirrel Cage Induction Motor

Objectives

1. Measure power flow with a wattmeter.

2. Measure reactive power flow with a varmeter.

3. Measure starting current of squirrel cage induction motor.

4. Demonstrate motor reversal.

Background

Three-phase squirrel cage induction motors comprise the vast majority of all electric motors made in larger sizes, say 5 hp or more. They are rugged and reliable. It is not uncommon for such motors to be in daily use for more than half a century, with the only maintenance being a new set of bearings every ten years or so. They do not produce sparks like DC motors do, so they can be used in hazardous environments like oil refineries and grain elevators. They are efficient, with efficiencies around 90% for a few hp, increasing to perhaps 98% for the very large sizes. They are even relatively quiet compared with single-phase motors. You should notice the difference in noise level between this Block and the later one dealing with single-phase motors. A large fraction of these motors are specified by mechanical engineers for use in grinding, pumping, and blowing operations, so mechanical engineers need to know something about them.

The electrical input of the three-phase induction motor is modeled in Fig. 1. There are three windings on the stator (the stationary part of the motor). They are located 120^o apart in space around the perimeter of the stator. In Fig. 1 they are shown connected in wye, with the common or neutral point available. The windings can also be connected in delta, which of course does not have a neutral point. In practice, the neutral is not brought out of the motor even if it is wired in wye, so it is impossible to tell which way a motor is wired by an external examination. It does not make any difference in performance so probably only a few people in the manufacturing facility actually know which wiring technique was used. We will analyze the motor using the wye convention, with the analysis being valid for wye connected loads in general.

The motor nameplate always lists the line-to-line voltage V_L and the line current I_L, but analysis usually is performed using the line-to- neutral or phase voltage V_P. That is, we do single-phase analysis because it is easier and multiply by 3 or to get the desired three-phase quantities. The phase current I_P will lag the phase voltage V_P by an angle . The power factor is defined as

pf = cos ..........(1)

In the following set of equations, voltages and currents will be taken as their magnitudes, with all phase relationships treated by a function of . The average power supplied to one phase of the motor is V_PI_Pcos . The total average power supplied to the motor is then

P = 3 V_P I_P cos ..........(2)

Since V_L = V_P and I_P = I_L, we can also write (2) as

P = V_L I_L cos ..........(3)

We are also interested in two other quantities, the apparent power S and the reactive power Q, defined as

|S| = 3 V_P I_P = V_L I_L..........(4)

Q = 3V_P I_P sin = V_L I_L sin ..........(5)

Note that

In this Block we introduce two additional measuring instruments, the wattmeter, which measures P, and the varmeter, which measures Q. The apparent power is obtained by just multiplying the voltmeter and ammeter readings. We therefore have plenty of information to calculate the power factor and the angle . In fact we have enough information to perform some internal tests for consistent data. We can evaluate the left portion of (6) from the voltmeter and ammeter, and the right portion from the wattmeter and varmeter, and if the two sides do not agree, then something is wrong with our reading of at least one of the instruments. We will ask you to do some of these consistency checks in this experiment.

All three powers are dimensionally the same, but we write the units differently to remind us of the quantities we are dealing with. When we see VA, we are reminded of apparent power. Real or average power is expressed in Watts. VAR stands for Volt Ampere Reactive and indicates reactive power. The SI purist is a bit unhappy about using three different labels for something dimensionally the same, but this seems to be one of those places where clarity of communication is more important than dogmatic adherence to a set of rules.

The mechanical output power of the motor is given by

P_out = T _m ..........(8)

where P_out is in W, T is in Nm, and _m is in rad/s. In this lab we actually measure the speed with a Strobotac in rpm, and torque with a dynamometer in inch pounds, so the equivalent formula is

..........(9)

where P_out is still in W, T is in inch pounds, and n is in rpm. The efficiency of the motor is then given by

..........(10)

The stator field rotates at a synchronous speed

..........(11)

where f is the frequency in Hz and p is the number of poles. A four pole machine operating on a line voltage at 60 Hz would have a synchronous speed of 1800 rpm. The actual speed of the motor will be less than the synchronous speed by an amount proportional to the slip s, where

..........(12)

Slip gets larger as the mechanical load increases. Slip will be near zero when the motor is unloaded, and will be in the range of 3 to 6% at full load. Higher efficiency motors have smaller slip. If you are comparing two motors at the same power rating, and one has a rated speed of 1745 rpm and the other has a rated speed of 1755 rpm, you are safe in assuming that the 1755 rpm motor has the higher efficiency.

One of the few disadvantages of induction motors is their lagging power factor. Transformers are always specified in terms of apparent power, so a larger transformer is required to supply a given amount of real power when the power factor is low. The larger current flow also increases the copper losses for a given amount of real power. Utility companies can therefore reduce both capital and operating costs if the power factor is increased to a value close to unity. Utilities will often impose a power factor penalty on manufacturing plants if the power factor drops below perhaps 0.9. The standard way for a manufacturing plant to improve its power factor is to add a capacitor bank, since the capacitive VARs will counteract the inductive VARs of the motors.

The reactive power supplied by a capacitor C at voltage V is

..........(13)

Multiply this value by 3 to account for the three capacitors in a capacitor bank.

Example: An industrial load consists of 150 kVA (input) of induction motors operating at 0.6 pf lag. What is the kVAR rating of the capacitor bank necessary to raise the power factor to 0.9 lag?

The key to doing power factor correction problems is to remember that the real power remains constant. Capacitors draw only reactive power, not real power. The real power in this case is

The reactive power being supplied to the motors is

The apparent power with the capacitors in place will be

The angle is

= arccos(0.9) = 25.84^o

The total reactive power supplied to the combination is

The difference must be supplied by the capacitors.

Note that it will not be practical to `fine tune' the capacitor bank to get exactly -76.41 kVAR. Capacitor banks are sold in nominal values like -75 and -90 kVAR. If you wanted to make sure the power factor would be at least 0.9, then you would specify the next larger size. If that happened to be -90 kVAR for this example, the total reactive power becomes 30 kVAR, with a new apparent power

The new power factor is

Discussion and Calculations

1. A three-phase 208 V (line-to-line) induction motor draws 50 kVA at 0.7 pf lag. It is desired to add capacitors in the arrangement shown in Fig. 2 to increase the power factor to 0.9 lag. (These capacitors are in the delta arrangement, which is the normal configuration for motors of 480 V and below.)

   a) What is the necessary kVAR rating of the capacitor bank?

   b) What is the current into the motor I_Lm?

   c) What is the current supplied by the utility I_L?

   d) What is the current in each capacitor?

   e) What is the necessary value of each capacitor in µF?

2. The circuit for the Fluke clamp-on current probe is shown in Fig. 3. It is a 1000:1 turn ratio transformer. For this circuit, if the rms input current is 1A, what is the rms output current? What is the peak output voltage across the 10 resistor?

   The Fluke probe is diode protected against open circuits on the output, but assume for a moment that it is not. If the load resistance were changed from 10 to 1 Mega, what would the rms output voltage be for 1A input? Why do you suppose that people insist on keeping current transformers short circuited when not connected to a low impedance load?

3. Motor "G" is rated at 1/4 HP at 1725 rpm. How many inch-pounds (force) of torque is this? (Use formulas in experiment H).

Instructional Activity in Class

1. Assemble the circuit in Fig. 4. Belt machine G to the dynamometer. Turn the three-phase variable autotransformer to zero and turn on the three-phase breaker. Turn up the three-phase variable autotransformer slowly, watching all the meters to make sure none are being stressed due to improper wiring. If the induction motor has not started by the time the line-to-line voltage across it has reached 30 to 40 volts, turn down the variable autotransformer and check with the instructor.

   Check the calibration on your current transformer by noting the peak voltage into the oscilloscope for an rms current through the 0-5 AC AMPS meter of about 2A. Do not exceed a line-to-line voltage of 120 volts. Set the oscilloscope in the storage mode to record starting current from the current transformer. Adjust the three-phase variable autotransformer for 60 volts line-to-line. Open and close the three-phase breaker to record starting current. Record in your notebook the peak amplitude of voltage across the 10 resistor, the corresponding peak current, and the number of cycles required to reach steady state. Repeat for line-to-line voltages of 90 and 120 volts.

2. Note the direction of motor rotation with the present connections. Interchange phases B and C as shown in Fig. 5. Turn up the variable autotransformer and observe the direction of rotation.

3. With the variable autotransformer adjusted for 120 volts line-to-line and the motor running, pull phase C out of the variable autotransformer. What is the new line current in phase A? How would you describe motor operation.

4. Turn the variable autotransformer down to zero. Turn it back up, being careful not to exceed 5 A in phase "a". The circuit is given in Fig. 6. What happens? Will spinning the rotor by hand start the motor? Turn the variable autotransformer to zero.

5. Add a 42 µF capacitor between T2 and T3 on the motor as in Fig. 7. Turn up the variable autotransformer, being careful not to exceed 150 volts line-to-line or 5A in phase A. What happens?

6. If the connection from the autotransformer to point T2 is moved to T3 as in Fig. 7, what happens to the direction of rotation?

7. Assemble the circuit in Fig. 8. The varmeter and the 100 W wattmeter requires utility power to operate so turn on the toggle switch by the varmeter. Make sure the neutral of the varmeter is connected to the neutral of the three-phase variable autotransformer, or else your readings may be incorrect. If the varmeter reads downscale, flip the switch marked "INDUCTIVE - CAPACITIVE".

   Turn on the AC power to the small variable autotransformer on the dynamometer. Record data for five settings of this variable autotransformer: 0 lb-in (no load), 3 lb-in, 6 lb-in, 8 lb-in, and full load. Turn the three-phase variable autotransformer up so the motor is running with the line-to-line voltage set at 120 V. For each of the four settings, record the wattmeter and varmeter readings, rpm, line current, and the dynamometer torque. Don't forget to multiply the wattmeter and varmeter readings by the appropriate constants. The constants are given by the dials near the meters. Leave the circuit connected until Lab Activity 8 is completed.

8. Compute (during the lab if you have time) the total apparent power in VA by two methods V I and , the power factor, the slip, the power delivered to the dynamometer, and the motor efficiency, for each of the four load settings in Lab Activity 7. Do the two methods of computing apparent power yield consistent results?

Conclusion

1. Explain how you checked calibration of the clamp-on current probe.

2. Explain how direction of rotation is reversed for a three-phase induction motor.

3. List any instances where it might be necessary to operate a three-phase induction motor on single-phase.