AC Power and Power Factor Correction
ECE 2100 Circuit Analysis
updated 4 April 2016
Pre-Laboratory Assignment
Consider the circuit of Figure 1. The ‘load’ consists of all circuit elements connected to
.
1. This lab uses potentially lethal voltages. REVIEW SAFE LABORATORY PROCEDURES.
Remember that capacitors must be handled carefully even when not connected as they store
energy!
2. For C1 = 0uF (no capacitor present), find the equivalent impedance of the load (consisting of R1
and L1) at the indicated frequency of 60 Hz. Express your result in rectangular and polar
coordinates.
3. Calculate the complex power of the load (consisting of R1 and L1), the power dissipated by the
resistor, and the inductor reactive power. As always, use proper units for all results.
4. Calculate the load (consisting of R1 and L) power factor. Indicate whether the power factor is
leading or lagging.
Figure 1. Power Factor Correction Circuit
5. Calculate the value of C1 needed to provide a unity load (now consisting of R1, L, and C1)
power factor.
6. Using your SPICE engine, demonstrate that the value of C1 computed in pre-laboratory step 5
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does indeed correct the power factor to 1. Do this by comparing the relative phase of the source
voltage ( ) and source current ( ) before and after adding the capacitor. Note that in
LTspice you can simply click on a node to plot the voltage or click on a voltage source to plot
the current through the voltage source (you will need to multiply the current trace for the voltage
source by (-1) as the current through the source is in the opposite direction of the indicated
current – LTspice uses the passive sign convention based on the source voltage polarity). An
example plot for C1 = 0uF is provided in Figure 2 (V is ( )and –I(V) is ( )).
7. Bring an electronic copy of your electronic simulation files to lab.
Figure 2. Example Plot for the Circuit of Figure 1
Procedures
Part One (SETUP)
1. ENSURE THAT THE BENCH POWER SUPPLY UNIT IS OFF and that the AC voltage
source is set to the ZERO position. Do not turn on power until instructed to do so.
2. Verify that the variable power resistor is set to 50Ω using your DMM. Record the value of the
resistance.
3. BEFORE PROCEEDING DISCHARGE ALL POSSIBLE CAPACITOR SUBSTITUTION
BOX COMBINATIONS THROUGH R1.
4. DO NOT TURN ON THE BENCH POWER SUPPLY. Build the circuit of Figure 1 without
the capacitor.
5. DO NOT TURN ON THE BENCH POWER SUPPLY. Connect a DMM to measure the
source voltage
(AC RMS of course) and another DMM to measure the resistor voltage (AC
RMS of course)
.
6. HAVE THE INSTRUCTOR CHECK YOUR CIRCUIT.
Part Two (Measurement of Resistor Voltage)
7. Ensure that the bench power supply is set to 0 and turn it on. SLOWLY rotate the dial until the
source voltage is at 40V RMS as indicated by the source voltage-measuring DMM. IF THE
VOLTAGE DOES NOT SLOWLY INCREASE STOP! HAVE THE INSTRUCTOR
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CHECK YOUR CIRCUIT AND HAVE THE INSTRUCTOR APPLY THE VOLTAGE.
DO NOT EXCEED 40V.
8. Record the magnitude of the source and resistor voltages. TURN OFF POWER TO THE
BENCH POWER SUPPLY AND RETURN THE DIAL TO 0.
Part Three (Measurement of Inductor Voltage and Current)
9. DO NOT TURN ON THE BENCH POWER SUPPLY. Setup a DMM to measure the
inductor voltage
(AC RMS of course) and another DMM to measure the source current
(AC RMS of course).
10. HAVE YOUR INSTRUCTOR CHECK YOUR CIRCUIT. YOUR INSTRUCTOR WILL
TURN ON THE BENCH POWER SUPPLY AND SLOWLY INCREASE ITS VOLTAGE
TO 40V.
11. Record the inductor voltage and current.
12. TURN OFF POWER TO THE BENCH POWER SUPPLY AND SET THE DIAL TO 0.
Part Four (Computations)
13. Using the information from step 11, compute the impedance of the inductor
the inductance L1.
and the value of
. Assume that the
14. Update your LTspice schematic with the measured values of R1, L1, and
angle of is zero. Compute the magnitude and phase of ( ) and compare to your simulation
result.
15. Compute the complex power
that the angle of is zero.
of the load using measured values of R1, L1, and
. Assume
16. Calculate the power factor of the load.
17. Compute the value of C1 that will provide a unity power factor.
Part Five (Power Factor Correction)
18. DO NOT TURN ON THE BENCH POWER SUPPLY.
19. Set the capacitor substitution box to the value needed to achieve a unity power factor but do not
connect it to the circuit.
20. Setup a DMM to measure the resistor voltage
(AC RMS of course) and another DMM to
measure the source current
(AC RMS of course).
21. HAVE YOUR INSTRUCTOR CHECK YOUR CIRCUIT. YOUR INSTRUCTOR WILL
TURN ON THE BENCH POWER SUPPLY AND SLOWLY INCREASE ITS VOLTAGE
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TO 40V.
22. Record the resistor voltage and source current.
23. TURN OFF THE BENCH POWER SUPPLY AND RETURN THE DIAL TO 0.
24. Compute the resistor power.
25. DO NOT TURN ON THE BENCH POWER SUPPLY.
26. Connect the capacitor substitution box in parallel with the load of R1 and L1. Insure that that
current-measuring DMM is measuring the source current and not just the current through the
series combination of R1 and L1.
27. HAVE YOUR INSTRUCTOR CHECK YOUR CIRCUIT. YOUR INSTRUCTOR WILL
TURN ON THE BENCH POWER SUPPLY AND SLOWLY INCREASE ITS VOLTAGE
TO 40V.
28. Record the resistor voltage and source current.
29. TURN OFF THE BENCH POWER SUPPLY AND RETURN THE DIAL TO 0V.
DISCHARGE ALL POSSIBLE CAPACITOR SUBSTITUTION BOX COMBINATIONS
THROUGH R1.
30. Compute the resistor power.
Analysis
1. Provide a phasor diagram for the capacitor, inductor, and resistor complex powers for two cases:
a. C1=0, and
b. C1 corresponding to the unity power factor case.
2. Why are the resistor powers the same in steps 24 and 30 (they should be) even though the source
currents are different? Why might this be desirable?
Credits and Copyright
Adapted from material developed by current and former ECE faculty, including Professor Joseph
Kelemen.
© 2016 Damon A. Miller. All rights reserved.
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