EXERCISE OBJECTIVE
Exercise 3-3
When you have completed this exercise, you will be able to measure and demonstrate capacitive phase shift. You will also observe the phenomenon of negative power associated with reactive power 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 however, unlike the case when only resistance is present in an ac circuit, there will be a phase shift between the circuit voltage and current because of the presence of capacitance. The phase shift is due to the fact that capacitors oppose changes in the voltage across their terminals.
As previously discussed, the charging-discharging process associated with capacitors, hence the capacitive current flow, is related to the fact that the applied voltage is changing. If we stop for a moment to consider what is happening when an ac voltage goes through a minimum value (negative peak value), we realize that for that particular moment the voltage is no longer changing. Hence, the capacitive current must be zero at that time, since the rate of change in the voltage is zero. Then, when the ac voltage is going through zero amplitude, its rate of change is maximum, and the current must therefore be maximum. As a result, the voltage lags the current by 90E. In the case of an ideal capacitor the phase shift is 90E. The
capacitive phase shift of 90E between voltage and current is shown in Figure 3-7.
Capacitive Phase Shift and Reactive Power
As mentioned earlier in Unit 2, reactive components like capacitors that cause a phase shift between circuit voltage and current will produce an instantaneous power waveform having negative values as well as positive. The negative power just means that power is being returned to the source. The instantaneous power waveform of a purely capacitive ac circuit is shown in Figure 3-8. The waveform has equal areas of positive and negative power and therefore the average power over a complete period is zero. The negative portion in the waveform indicates the presence of reactive power, and the reactive power will equal apparent power when there is no resistance present in the circuit. Note also that the instantaneous power waveform frequency is twice the ac source frequency.
Figure 3-8. Instantaneous Power in a Capacitive 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 Capacitive Load module in the EMS Workstation.
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.
Capacitive Phase Shift and Reactive Power
G
3. Set up the circuit shown in Figure 3-9, and connect inputs E1 and I1 to measure the circuit voltage and current. Set the Capacitive Load module for the value of CMAX given in Figure 3-9.Figure 3-9. Capacitive 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 the power cable
is connected to the data acquisition module. Display
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.
ES' V IS' A S (PQS1) ' VA
G
7. Is the apparent power equal to the product of the rms values of voltage and current?Capacitive Phase Shift and Reactive Power
G
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 step 10 confirm that the current leads the voltage by about 90E?G
YesG
NoG
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 maximum?G
YesG
NoG
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?
G 15. Does the instantaneous power waveform show that the areas of positive and negative power are approximately equal?
G
YesG
No3-20
G
16. Calculate the apparent power (S) by multiplying of the rms values of the current and voltage 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) = ES x IS' VA
Capacitive Phase Shift and Reactive Power
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 (Q) in the circuit?G
YesG
NoG
18. What is the total active power consumed by the circuit? PACTIVE' WG
19. Is the instantaneous power null when the current or the voltage is zero?G
YesG
NoG
20. Change the circuit capacitance by opening the three switches on one section of the Capacitive Load module.G 21. What effect does the change in capacitive reactance produce on the circuit current, voltage and reactive power?
G
22. Did the phase shift between the current and voltage change?G
YesG
NoG
23. Why is the instantaneous power waveform different in amplitude?G
24. Ensure that the Power Supply is turned off, the voltage control is fully ccw, and remove all leads and cables.CONCLUSION
You determined capacitive phase shift in an ac circuit using measurements of the current and voltage waveforms. You examined the instantaneous power waveform and saw that there was no active power dissipated in the capacitive circuit. Finally, observation of the circuit waveforms allowed you to confirm the theoretical behaviour
Capacitive Phase Shift and Reactive Power
REVIEW QUESTIONS
1. Capacitors store energy in the electric field set up between their plates when a voltage is applied across them.
a. True. b. False.
c. False, the energy is stored in the dielectric. d. True in ac circuits only.
2. The phase shift between current and voltage caused by a capacitor equals 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. In a purely capacitive ac circuit, when is the instantaneous power waveform equal to zero?
a. Whenever the voltage or the current is zero.
b. Whenever the voltage and current waveforms intersect. c. Whenever the rms voltage and current values are maximum. d. None of the above because the active power equals zero.
4. What is the reactive power in a purely capacitive ac circuit when the rms voltage and current values are 250 V and 3 A respectively?
a. 750 W. b. 750 VA. c. 750 var. d. 83.3 var.
5. The instantaneous power waveform for a circuit has equal positive and negative areas. What does this indicate?
a. That the circuit is resistive.
b. That the circuit contains only reactive components. c. That the active power is zero.
d. Both b and c.
Unit Test
1. What will be the voltage drop across a 100-Ω capacitive reactance when circuit current is 1.2 A?
a. 1200 V. b. 80 V. c. 120 V. d. 120 kV.
2. The capacitive reactance of a circuit can be doubled by a. increasing the source frequency by one-half. b. doubling the source voltage.
c. doubling the capacitance.
d. reducing the capacitance by one-half.
3. The formula XC'1/(2πfC) can be used to determine
a. the reactance of resistors.
b. the capacitive resistance of capacitors. c. the capacitive reactance of capacitors. d. the capacitive phase shift of a circuit.
4. Frequency and capacitance directly affect a. the resistance of a power source.
b. the amount of active power dissipated by a resistor. c. the polarity of the current flowing in a circuit. d. a circuit's capacitive reactance.
5. What formula is used to determine CEQ for parallel-connected capacitors?
a. CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
b. 1/CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
c. CEQ'C1+C2+C3+C4+....+CN.
d. 1/CEQ'C1+C2+C3+C4+....+CN.
6. What formula is used to determine CEQ for series-connected capacitors?
a. CEQ'C1+C2+C3+C4+....+CN.
b. 1/CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
c. CEQ'1/(C1+C2+C3+C4+....CN)
3-24
Unit Test (cont'd)
7. What is the equivalent capacitance of three 15-μF capacitors connected in series?
a. 45 μF. b. 4.5 μF. c. 50 μF. d. 5.0 μF.
8. What is the equivalent capacitance of three parallel-connected capacitors with values of 1 μF, 2 μF, and 4 μF?
a. 8 μF. b. 7 μF. c. 0.57 μF. d. 1.75 μF.
9. In a purely capacitive ac circuit, the phase shift between voltage and current is a. !90E if the current is used as reference.
b. +90E if the voltage is used as reference. c. +90E if the current is used as reference.
d. Either a or b, depending on which is used as reference.
10. What is the reactive power in a purely capacitive ac circuit with an rms voltage of 75 V and a current of 5 A?
a. 375 W. b. 375 VA. c. 375 var. d. 15 var.