Power Factor Correction – Simulator Applet Updated 20 JUN 2019
A Practical Exercise Name:________________ Section: ____________
Page 1 of 13
T
T
Electrical
Power
Company
TT
IS
T
R1 =
560 Ohm
Induction motors with 20
ohms of internal resistance
T
Power line resistance
Heaters
Steel Mill
RL =
20 Ohm
XL =
188.5
OhmsR2 = 10 Ohm
Line
Voltage
ELine = 5V
I. Purpose.
1. Review the determination if the real, reactive and apparent power to a load.
2. Introduce the determination power factor.
3. Introduce a method for correcting a circuit’s power factor.
II. Equipment.
Circuit Simulator Applet
An introduction to the Circuit Simulator Applet
III. Pre-Lab Calculations
Step One: Introduction
• A very small steel company has been notified by the electrical power company that their steel
mill is drawing too much current from the electrical power grid. The grid can handle 20 mA.
• The electrical power company can upgrade the electrical power grid, but the small steel
company would have to pay for it. The small steel company determined that it would be too
costly to upgrade the electrical power grid, and has decided to re-configure their steel mill, so
the steel mill would draw less current from the electrical power grid.
Step Two: Impedance, Current, and Power Calculations.
□ Compute the impedance of the steel mill (the shaded portion of the circuit of Figure 1).
Figure 1
Zmill = ______________
13 Ohm
13
Power Factor Correction – Simulator Applet
Page 2 of 13
cos
sin
T S S
T T
T T
S I E
P S
Q S
=
= =
= =
=
□ Use Ohm’s law and the predicted impedance (Zmill) to calculate the source current assuming
that the electrical power company is supplying a line voltage of 5 VRMS at 30 kHz with zero
phase angle.
IS = _____________
□ Calculate the steel mill’s power factor (FP), and indicate whether it is leading or lagging.
FP = cos (θZ ) =
FP = ______________
LEADING LAGGING
□ Calculate the total reactive power, total active power, and total apparent power, using the
value of IS above and the 5V line voltage.
|ST| = ______________
PT = ______________
QT = ______________
| | | || |
| |
| |
Power Factor Correction – Simulator Applet
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2 2
1 1
2 2
C L
C C
C C
C
C
Q Q
V VQ X
X Q
X CfC fX
= −
= → = =
= → = =
Step Three: Power Factor Correction
□ Draw on Figure 1 where a capacitor would be connected to correct the power factor.
□ Calculate the capacitor’s value (F) required to correct the steel mill’s power factor to unity.
Capacitor’s value = ______________
□ Calculate the new impedance of the mill with this capacitor installed.
Zmill-corrected = ______________
□ Use Ohm’s law and this corrected impedance (Zmill-corrected) to calculate the new source
current.
IS-corrected = _____________
How was the source current affected by the correction to the power factor?
Stayed the same__________ Increased__________ Decreased___________
□ Calculate the new total apparent power of the mill, using the value of IS above and the 5V
line voltage.
|Scorrected| = ______________
Step Four: Instructor or lab assistant verification that pre-lab calculations are complete.
______________________________
Power Factor Correction – Simulator Applet
Page 4 of 13
IV. Lab Procedure. Time Required: 40 minutes. Check-off each step as you complete it.
Step One: Construct an AC series/parallel circuit
□ In the Circuit Simulator Applet, construct the ac series/parallel circuit in Figure 1.
The inductor is 1mH.
NOTE: It is important to draw the components as discussed in the Intro to Scope Function Lab.
If this is not done correctly, your phase angles may be 180o different from the Pre-Labs.
□ Set the Voltage Source to output a sine wave at 30 kHz, with a VP = 7.07 V.
□ Change the “Time step size(s)” to nanoseconds (n).
Refer to Step 1 of the Series AC Circuit Lab for a refresher on how to perform this task.
□ Insert a Scope Probe to measure the line voltage downstream of the power line resistor.
Adjust the voltage source amplitude until the Scope displays 5.00 VRMS (+/- 0.1 V).
Note: Sliders can be added to the side bar on the right side of the screen by right clicking the
component (in this case the voltage source) and selecting “Sliders…”, then select “Max Voltage”
and insert the range for the slider, 5 to 10 volts.
Power Factor Correction – Simulator Applet
Page 5 of 13
ELine = ____________
□ Using the “View in Scope”, measure the phase difference between The power company voltage,
Es, and the voltage across the power line resistor, VR2.
Refer to Step 3 of the Intro to Scope Function Lab for a refresher on how to perform this task.
NOTE: For this circuit, because VR2 is so small, it may be easier to calculate Δt by stacking the
scopes and using the “Max Scale” feature.
□ Calculate Δt
Δt = _____________
□ Calculate the phase shift (θ) between the waveforms.
∆θ = (Δt /T) X 360◦
∆ θ = _________
0°
Adjust Slider until VScope Probe = 5 VRMS;
make small adjustments; it will take some
time for the scope to update the RMS
value
Power Factor Correction – Simulator Applet
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□ Using the “View in Scope”, determine the RMS voltage across R2, the power line resistor, and
then write VR2 in phasor form. The phase angle of VR2 is the phase angle measured above
(negative if lagging, positive if leading).
Refer to Step 2 of the Series AC Circuit Lab for a refresher on how to perform this task.
Vpower line resistor = ____________
□ Determine the actual IS based upon the measured Vpower line resistor and the resistance of the 10
ohm power line resistor.
IS = ____________
□ Determine the apparent power being consumed by the steel mill, using IS and the 5V line
voltage.
|ST| = ______________
□ How do these values of VR2, IS, and ST compare to the values calculated in step two of the pre-
lab section?
Exact__________ Very close__________ Very Different_________
Step Four: Power Factor Correction
□ Connect the variable capacitor in parallel with the steel mill. Similar to the Voltage Source, add
a slider to the capacitor with a range of 1 nF to 40 nF.
□ Initially setting a value of 1 nF.
|ST| = |ET||IT|
Power Factor Correction – Simulator Applet
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□ Select “View in Scope” for the voltage source, Es.
Note: For this step, you will only view the scope for the source, but you will compare the voltage, Es,
and current, IS, from the source. Remember that the purpose for adding of the capacitor is to counter the
reactance of the inductor such that the circuit looks purely resistive to the source. For a purely resistive
circuit, the voltage and current will be in phase. Therefore, the capacitance of the capacitor will need to
be adjusted until the source voltage and current are in phase.
□ Starting at 1nF, slowly slide the bar on the variable capacitor until you observe Es and IS are in
phase. It will take some take for the graph in the scope to update, so be patient.
□ Record the value of the variable capacitor.
Capacitor value = ________________
How does this experimentally determined value compare to the predicted capacitor value from
step three of the pre-lab calculations?
Exact__________ Very close__________ Very Different______
ES IS
Power Factor Correction – Simulator Applet
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□ Determine the actual IS and write it as a phasor using the values you just obtained in the previous
step.
IS-corrected= ____________
How was the source current affected by the correction to the power factor?
Stayed the same__________ Increased__________ Decreased___________
□ Determine the apparent power being consumed by the steel mill, using the new value of IS and
the 5 V line voltage.
|Scorrected| = ______________
How do these corrected values of IS and ST compare to the predicted values from step three of
the pre-lab calculations?
Exact__________ Very close__________ Very Different______
Step Five: Circuit Submission
□ Save the circuit to your computer and submit the circuit text file to your instructor for lab credit.
0°
Power Factor Correction – Simulator Applet
Page 9 of 13
T
T
Electrical
Power
Company
TT
IS
T
R1 =
560 Ohm
Induction motors with 20
ohms of internal resistance
T
Power line resistance
Heaters
Steel Mill
RL =
20 Ohm
XL =
188.5
OhmsR2 = 10 Ohm
Line
Voltage
ELine = 5V
Practical Exercise Submission Form Name:________________ Section: _____
III. Pre-lab calculations. Show all work.
Step Two: Impedance, Current, and Power Calculations.
□ Compute the impedance of the steel mill (the shaded portion of the circuit of Figure 1).
Figure 1
Zmill = ______________
□ Use Ohm’s law and the predicted impedance (Zmill) to calculate the source current assuming
that the electrical power company is supplying a line voltage of 5 VRMS at 30 kHz with zero
phase angle.
IS = _____________
□ Calculate the steel mill’s power factor (FP), and indicate whether it is leading or lagging.
FP = cos (θZ ) =
FP = ______________
LEADING LAGGING
13 Ohm
13
Power Factor Correction – Simulator Applet
Page 10 of 13
2 2
1 1
2 2
C L
C C
C C
C
C
Q Q
V VQ X
X Q
X CfC fX
= −
= → = =
= → = =
cos
sin
T S S
T T
T T
S I E
P S
Q S
=
= =
= =
=
□ Calculate the total reactive power, total active power, and total apparent power, using the
value of IS above and the 5V line voltage.
|ST| = ______________
PT = ______________
QT = ______________
Step Three: Power Factor Correction
□ Draw on Figure 1 where a capacitor would be connected to correct the power factor.
□ Calculate the capacitor’s value (F) required to correct the steel mill’s power factor to unity.
Capacitor’s value = ______________
□ Calculate the new impedance of the mill with this capacitor installed.
Zmill-corrected = ______________
| | | || |
| |
| |
Power Factor Correction – Simulator Applet
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□ Use Ohm’s law and this corrected impedance (Zmill-corrected) to calculate the new source
current.
IS-corrected = _____________
How was the source current affected by the correction to the power factor?
Stayed the same__________ Increased__________ Decreased___________
□ Calculate the new total apparent power of the mill, using the value of IS above and the 5V
line voltage.
|Scorrected| = ______________
Step Four: Instructor or lab assistant verification that pre-lab calculations are complete.
______________________________
IV. Lab Procedure.
Step One: Construct an AC series/parallel circuit
□ Insert a Scope Probe to measure the line voltage downstream of the power line resistor.
Adjust the voltage source amplitude until the Scope displays 5.00 VRMS.
ELine = ____________
□ Measure the phase difference between the power company voltage, Es, and the voltage across
the power line resistor, VR2.
□ Calculate Δt
Δt = _____________
□ Calculate the phase shift (θ) between the waveforms.
∆θ = (Δt /T) X 360◦
∆ θ = _________
0°
Power Factor Correction – Simulator Applet
Page 12 of 13
□ Determine the RMS voltage across R2, the power line resistor, and then write VR2 in phasor form.
The phase angle of VR2 is the phase angle measured above (negative if lagging, positive if
leading).
Refer to Step 2 of the Series AC Circuit Lab for a refresher on how to perform this task.
Vpower line resistor = ____________
□ Determine the actual IS based upon the measured Vpower line resistor and the resistance of the 10
ohm power line resistor.
IS = ____________
□ Determine the apparent power being consumed by the steel mill, using IS and the 5V line
voltage.
|ST| = ______________
□ How do these values of VR2, IS, and ST compare to the values calculated in step two of the pre-
lab section?
Exact__________ Very close__________ Very Different_________
Step Four: Power Factor Correction
□ Record the value of the variable capacitor.
Capacitor value = ________________
How does this experimentally determined value compare to the predicted capacitor value from
step three of the pre-lab calculations?
Exact__________ Very close__________ Very Different______
□ Determine the actual IS and write it as a phasor using the values you just obtained in the previous
step.
IS-corrected= ____________
How was the source current affected by the correction to the power factor?
Stayed the same__________ Increased__________ Decreased___________
|ST| = |ET||IT|
0°
Power Factor Correction – Simulator Applet
Page 13 of 13
□ Determine the apparent power being consumed by the steel mill, using the new value of IS and
the 5 V line voltage.
|Scorrected| = ______________
How do these corrected values of IS and ST compare to the predicted values from step three of
the pre-lab calculations?
Exact__________ Very close__________ Very Different______
Step Five: Circuit Submission
□ Save the circuit to your computer and submit the circuit text file to your instructor for lab credit.