EXERCISE OBJECTIVE
Exercise 4-3
When you have completed this exercise, you will be able to measure and demonstrate inductive phase shift. You will also observe the phenomenon of negative power associated with inductance in ac circuits.
DISCUSSION
As you saw in previous units, the voltages and currents in resistive ac circuits are in phase, and the power dissipated by resistors is active power in the form of heat. Now, just like the case when capacitance is present in an ac circuit, there will be a phase shift between voltage and current because of inductance. This phase shift is caused by the opposition of inductors to current changes.
When current flowing in an inductor starts to change, the inductor reacts by producing a voltage that opposes the current change. The faster the current changes, the greater is the voltage produced by the inductor to oppose the current change. In other words, the voltage across the inductor is proportional to the rate of change in current. Now, suppose that a sine-wave current flows in an inductor. At the instant the current goes through a minimum value (negative peak value), the current is no longer changing and the inductor voltage must be zero since the current rate of change is zero. Then, when the current is going to zero amplitude, its rate of change is maximum and the inductor voltage must be maximum. As a result, the current in an ideal inductor lags the voltage by 90E. The inductive phase shift of 90E between current and voltage is shown in Figure 4-8.
Inductive Phase Shift and Reactive Power
As mentioned earlier in Unit 2, reactive components that cause a phase shift between circuit voltage and current produce instantaneous power waveforms having negative and positive values, meaning that power is being returned to the source. The instantaneous power waveform for a purely inductive ac circuit is shown in Figure 4-9. This waveform also has equal areas of positive and negative power, like that for a capacitive ac circuit, and the average power over a complete period is zero. However, as you will see in this exercise, real inductors have some resistance and they will consume a small amount of active power. Consequently, positive and negative areas in the power waveform will not be exactly equal. Note that the instantaneous power waveform frequency is twice the ac source frequency, the same as for capacitive circuits.
Figure 4-9. Instantaneous Power in an Inductive AC Circuit.
EQUIPMENT REQUIRED
Refer to the Equipment Utilization Chart in Appendix C to obtain the list of equipment required for this exercise.
PROCEDURE
CAUTION!
High voltages are present in this laboratory exercise! Do not make or modify any banana jack connections with the power on unless otherwise specified!
G 1. Install the Power Supply, data acquisition module, and Inductive Load module in the EMS Workstation.
Inductive Phase Shift and Reactive Power
G
2. Make sure that the main switch of the Power Supply is set to the O (OFF) position, and the voltage control knob is turned fully ccw. Ensure the Power Supply is connected to a three-phase wall receptacle.G 3. Set up the circuit shown in Figure 4-10, and connect inputs E1 and I1 to measure the circuit voltage and current. Set the Inductive Load module for the value of LMIN given in Figure 4-10.
Figure 4-10. Inductive Phase Shift and Reactive Power in an AC Circuit.
G 4. Ensure that the POWER INPUT of the data acquisition module is connected to the main Power Supply, and that 220v power cable
is connected to the data acquisition module. Display the Metering screen. .
G 5. Turn on the main Power Supply and set the 24 V - AC power switch to the I (ON) position. Adjust the voltage control to 100 % and verify that the circuit parameters are displayed on the Metering application.
G 6. Note the rms values of the voltage and current, and the apparent power (S) displayed by the meters.
Inductive Phase Shift and Reactive Power
G
7. Is the apparent power equal to the product of the rms values of voltage and current?G
YesG
NoG
8. Click on the Oscilloscope button and display E1, I1, and P1 on CH1, CH2, and CH3. Ensure that the time base control is adjusted to show at least two complete cycles of the sine waves.G 9. Compare the current waveform with the voltage waveform. Are they both sine waves at the same frequency?
G
YesG
NoG
10. What is the phase shift between the voltage and current? Phase shift ' EG
11. Does the phase shift show that the inductor current lags the voltage by about 80E?G
YesG
NoNote: The resistance of the inductor wire causes the phase shift
to be less than the theoretical value of 90E and causes real
inductors to consume some active power.
G
12. Does the current waveform attain its maximum when the voltage is going through zero amplitude, and become zero when the voltage is going through its maxima?G
YesG
No4-20
G
13. Determine the period and frequency of the instantaneous power waveform?G 14. How does the frequency of the instantaneous power waveform compare with that of the ac source?
Inductive Phase Shift and Reactive Power
G
15. Does the instantaneous power waveform have unequal areas of positive and negative power, thus demonstrating that real inductors consume active power?G
YesG
NoG
16. Calculate the apparent power (S) by multiplying the rms values of the voltage and the current displayed on the oscilloscope and compare it with the active power P [average (AVG) power value of P1 given in the waveform data box of the Oscilloscope screen].Apparent power (S) = EL x IL' VA
Active power (P) = W
G 17. Do the results of step 16 confirm that the apparent power and the active
power are different, due to the presence of reactive power in the circuit?
G
YesG
NoG
18. What is the total active power consumed by the circuit? PACTIVE' WG
19. When does the instantaneous power waveform go through zero amplitude?G 20. Does step 19 confirm that the instantaneous power is zero when the current or the voltage is zero?
G
YesG
NoG
21. Change the circuit inductance by opening the three switches on one section of the Inductive Load module.G 22. What effect does the change in inductive reactance produce on the circuit current, voltage and reactive power?
Inductive Phase Shift and Reactive Power
G
23. Did the phase shift between the current and voltage change?G
YesG
No4-22
G
24. Why is the instantaneous power waveform different in amplitude?G
25. Ensure that the Power Supply is turned off, the voltage control is fully ccw, and remove all leads and cables.CONCLUSION
You determined inductive phase shift in an ac circuit using measurements of the current and voltage waveforms. You demonstrated that some active power is dissipated in inductive circuits because of the resistance of the inductor wire. Finally, observation of the circuit waveforms allowed you to confirm the theoretical behaviour of the circuit current and voltage.
REVIEW QUESTIONS
1. Inductors store energy in a magnetic field created and sustained a. by current flowing through a coil of wire.
b. by voltage connected to the resistive part of the inductor. c. by connecting the inductor to a capacitor.
d. by connecting the ends of the inductor together.
2. The phase shift between current and voltage caused by an inductor is a. +90E, if the voltage is used as reference.
b. +90E, if the current is used as reference. c. !90E, if the voltage is used as reference. d. Both b and c.
3. When does the instantaneous power waveform cross through zero amplitude in an ideal inductive circuit?
a. When the voltage and current are both maximum. b. When the voltage and current waveforms intersect. c. When the rms values of voltage and current are maximum. d. Whenever the voltage or current is zero.
Inductive Phase Shift and Reactive Power
4. What is the reactive power in a purely inductive ac circuit when the rms voltage and current values are 80 V and 3 A?
a. 240 W. b. 240 VA. c. 240 var. d. 26.7 var.
5. The instantaneous power waveform for a circuit has unequal positive and negative areas. What can this indicate?
a. That the circuit is resistive, as well as being reactive. b. That the circuit contains only reactive components. c. That the apparent power is zero.
Unit Test
1. How much current will flow in an inductive ac circuit having a reactance of 60 Ω, when the circuit voltage is 120 V?
a. 20 A. b. 0.5 A. c. 2 A. d. 2 H.
2. How can the inductive reactance of a circuit be reduced by half without changing any circuit components?
a. By increasing the reactance by one-half. b. By reducing the source frequency by one-half. c. By increasing the source frequency by one-half. d. By reducing the source voltage by one-half.
3. How can inductive reactance be tripled in an ac circuit? a. By tripling the source voltage.
b. By reducing the source frequency by one-third. c. By tripling the inductance.
d. By reducing the inductance by one-third.
4. Inductive reactance can be determined from a. EL' 2πfLIL.
b. IL' EL/XL.
c. XL' 2πfL.
d. a, b, and c.
5. What is the formula for determining the equivalent inductance of inductors in parallel?
a. LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
b. 1/LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
c. LEQ'L1+L2+L3+L4+....+LN.
d. 1/LEQ'L1+L2+L3+L4+....+LN.
6. What is the formula for determining the equivalent inductance of inductors in series?
a. LEQ'L1+L2+L3+L4+....+LN.
b. 1/LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
c. LEQ'1/(L1+L2+L3+L4+....+LN).
4-26
Unit Test (cont'd)
7. What is the equivalent inductance of three 15-H inductors connected in series? a. 5.0 H.
b. 45 H. c. 4.5 H. d. 50 H.
8. What is the equivalent inductance of three parallel-connected inductors with values of 1 H, 2 H, and 4 H?
a. 7 H. b. 1.75 H. c. 0.57 H. d. 8 H.
9. In a purely inductive ac circuit, the voltage leads the current by a. 80E.
b. 90E. c. 270E. d. Both b and c.
10. What is the reactive power in a purely inductive ac circuit when the voltage and current values are 85 V and 10 A respectively?
a. 850 W. b. 850 VA. c. 850 var. d. 8.5 var.