Week 8 Video Lecture – Power Factor Correction
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alternating_current_1.docx1. Watch the video
· Week 8 Video Lecture – Power Factor Correction
Consider the circuit demonstrated in this week’s presentation. Analyze the circuit to determine the following (include both polar and complex forms where applicable):
b. Zeq
R1 = 100 Ω
f = 100 Hz
C= 0.398uF
Xc = 1/(2*pi*f*C)
Xc = 1/(2*pi*100*0.398uF)
Xc = 400 Ω
· Since its capacitive we use the negative sign. We have now R1 and Xc we can no formulate Zeq. Because it’s a series circuit we take Zeq in the form Zeq = R1 + Xc
Zeq = R1 + Xc
Zeq = 100 - j400 Ω ( complex form )
Zeq magnitude = 413.310
Zeq angle = arctan ( -400/100) = -75.96
So our Zeq in polar form is as follows
Zeq = 412.310 ∟-75.96◦ Ω ( Polar form )
c. IT
Vs = 120
= Vs / Zeq
= 120 / (100-j400)
= 0.070588 +j0.28235 A ( complex form )
= 0.29104 ∟75.96◦ A ( Polar form )
d. IR1
IR1= 0.29104 ∟75.96◦ A
· Since it’s a series circuit IR1 should be the same with It and IC1
e. Ic1
IC1= 0.29104 ∟75.96◦ A
Since it’s a series circuit IR1 should be the same with It and IC1
f. Real Power (Watts)
P =IR12 R1
= (0.29104)^2 (100)
= 8.4705 W
g. Reactive Power (VARs)
Q = IXC2 Xc
= (0.29104)^2 ( 400)
33.8817 VAR
a. Apparent Power (Vas)
S =
S =
= 34.924 Vas
b. Power Factor
PF = R1/ Zeq
PF = 100 / 412.310
Construct the circuit in MultiSIM and run a Single Frequency Analysis to confirm your calculations for the phasor values in part 2. Capture a screenshot of the analysis for both Magnitude/Phase (polar) and Real/Imaginary (complex). Create a table with your expected and measured results.
Magnitude/Phase (polar)
Real/Imaginary (complex)
Table
Polar
|
|
Calculated |
Measured |
|
IC1
|
0.29104 ∟75.96◦ A |
0.29120 ∟75.96◦ A |
|
IR1
|
0.29104 ∟75.96◦ A
|
0.29120 ∟75.96◦ A
|
|
IT
|
0.29104 ∟75.96◦ A
|
0.29120 ∟75.96◦ A
|
complex
|
|
Calculated |
Measured |
|
IC1
|
0.070588 +j0.28235 A |
0.0706258 +j0.282423 A |
|
IR1
|
0.070588 +j0.28235 A |
0.0706258 +j0.282423 A |
|
IT
|
0.070588 +j0.28235 A |
0.0706258 +j0.282423A |
Measure the real power of the circuit and the power factor using a watt meter. Capture a screenshot of the watt meter readings.
Based upon the power factor, determine the value of the capacitors needed in each case to bring the power factor to the following values. Be sure to show your calculations.
PF = R1/ Zeq
Where
Zeq =
and
Xc =
R1 = 100 Ω
f = 1000 Hz
a. Power Factor = 0.85
solving above equitation
we get
C = 2.5680 µF
b. Power Factor = 0.95
solving above equitation
we get
C = 4.842 µF
c. Power Factor = 1.00
solving above equitation
we get
C = infinite
Or Xc should be very small
Let we take C=1F
Insert each of the capacitor values found in step 5 into the circuit one at time and confirm the power factor correction with a watt meter. Use a 5% tolerance for the capacitors. Capture a screenshot of the watt meter for each case. Create a table of expected and measured results. Comment on how well the desired power factor was achieved and any reasons for discrepancies.
For PF = 0.85
For PF = 0.95
For PF=1
Table
|
P.F |
Calculated (capacitor value ) |
Measured (power factor) |
|
0.85 |
2.5680 µF |
0.85464 |
|
0.95 |
4.842 µF |
0.95118 |
|
1 |
Infinite (taking 1 F) |
1 |
