LABORATORY 2
Electrical Power and Power Factor Correction
OBJECTIVES
1.
2.
3.
4.
Study complex power in single-phase AC system and understand power triangles.
Measure the phase angle and the power factor of an inductive load.
Study the requirements for power factor correction and understand the concept.
Perform power factor correction and verify the results using MicroCap circuit simulation
and laboratory measurements.
INFORMATION
1. Power factor definitions
The instantaneous power delivered to a load can be expressed as
p(t) = v(t) . i(t)
(Equation 2.1)
The instantaneous power may be positive or negative depending upon the sign of v(t) and i(t),
which is related to the sign of the signal at a given time. A positive value means that power
flows from the supply to the load, and a negative value indicates that power flows from the load
to the supply.
In the case of sine wave voltage and current, the instantaneous power may be expressed as
the sum of two sinusoids, or as the sum of two sinusoids with twice the frequency as shown
in the following equations.
v(t) = Vm cos (t)
i(t) = Im cos (t + )
p(t) = Vm Im cos () + Vm Im cos (2t+ )
p(t) = Vm Im cos  . (1+ cos2t) + Vm Im sin  cos (2t+ )
(Equation 2.2)
In the previous power equation, the first term on the right-hand side is known as real power or
active power and is measured in watts (W)
P= Vm Im cos ()
(Equation 2.3)
The second term on the right-hand side is called instantaneous reactive power, and its average
value is zero. The maximum value of the second term is known as the reactive power, and it is
measured in volt-ampere reactive (VAR)
Q = Vm Im sin (
2-1
(Equation 2.4)
The apparent power (S) is measured in volt-ampere (VA) and can be calculated from P and Q
as
S = Vm Im =
P2  Q2
(Equation 2.5)
Complex power in AC circuits can be given as
S = P  jQ = Vm Im cos () + j Vm Im sin ()
(Equation 2.6)
Here S indicates a complex number. The real part of the complex power is equal to the active
power (P) and the imaginary part is the reactive power (Q).
The cosine of the phase angle () between the voltage and the current is called the power factor
pf.
P
P
pf  cos   
(Equation 2.7)
S Vrms I rms
Hence, from the previous expressions, the equations associated with the active, reactive and
apparent power can be developed geometrically on a right triangle called a power triangle.
A power triangle using phasors is illustrated in Figure 2.1. In the phasor graph, the horizontal
axis represents the active power P and the vertical axis represents the reactive power Q. The
phasor graph also displays the complex power S. In this case the reactive power QL is positive,
since it’s caused by the inductive type of load and the power factor is lagging.
S
QL

P
Figure 2.1. Power triangle
2. Power Factor Correction
Power Factor Correction attempts to improve the power factor by the addition of capacitor(s) in
parallel with the load. These capacitors supply some or all of the reactive power to the inductive
load, which reduces the reactive power and therefore the current that the power supply delivers.
The capacitors are source of the reactive power QC , which is leading or negative– Figure 2.2. A
resulting reactive power QL-QC < QL which provides a smaller lagging angle  and larger
Power factor cos(), compared to the circuit before power factor correction in Figure 2.1.
The complete compensation of the lagging effect of the inductive load XL could be achieved by
adding more capacitance XC to the circuit, until QL- QC =0 and the power factor cos() =1, as
it is shown in Figure 2.3.
2-2
S

S
QL
P
QC
QL
P
Q

C
Figure 2.2. Power factor correction
Figure 2.3. Complete Power factor
compensation
Following Equations are useful in determining Power Factor corrections:
Impedance of the inductor:
X L  L  2fL
Impedance of the capacitor:
XC 
1
1

C 2fC
(Equation 2.9)
 XL 

 R 
(Equation 2.10)
  tan 1 
Inductive Reactive Power
Z  RT  X L
V
I  S
Z
QL  I 2 X L
Capacitive Reactive Power
QC 
Total impedance of the circuit:
Total current from the source:
(Equation 2.8)
2
2
(Equation 2.11)
(Equation 2.12)
(Equation 2.13)
2
VS
XC
(Equation 2.14)
Equipment
1. PROTO-BOARD PB-503 (breadboard).
2. Function generator Wavetek FG3B.0
3. Digital Oscilloscope Tektronix TDS-210.
4. Resistors: 150, 22.
5. Capacitors: 10nF, 22nF, 47nF.
6. Inductor 3.3mH/ 6 
PRE-LABORATORY PREPARATION
1. Power Factor calculations of the inductive load
The circuit of Figure 2.4 represents a model of a power system. The load impedance ZL is build
of the inductor L1 3.3mH and resistor R1 150 . Resistor R2 represents simplified transmission
2-3
line with a neglectable inductance. Hence, the voltage across the resistor R2 is proportional
to the current trough the ZL, with the phase preserved.
For the circuit shown in Figure 2.4 consider VS =10Vp-p and f=10kHz.
Figure 2.4
Figure 2.5
1.1. Use phasor analysis methods to find VL and IL. Find the total complex power Stot provided by
the source VS and the power absorbed by the "load" SL. Remember to use rms values for
these calculations. All phase angles should be referenced to VS. Show your calculations in
section 1.1 of the LMS.
1.2. Using Equations 2.8 to 2.14, calculate the following parameters of the circuit in section 1.2
of the LMS and enter the results in Table 2.1 of the LMS:
 load impedance ZL
 load power factor angle 
 load power factor cos
 complex power absorbed by the load
 expected time shift between load voltage and current in msec.
Note: Take in consideration the internal resistance of the inductor of 6.
1.3. Draw the Power triangle of this circuit in section 1.5-a of the LMS.
1.4. Calculate the value of the parallel capacitance C1 as it is shown in Figure 2.5, in order to
correct the load pf to unity. Show your calculations in section 2 of the LMS.
1.5. Enter the calculated data in Table 2.2 for future comparison with the MicroCap simulations
and the experimental results.
2. MicroCap simulations:
2.1. Simulate the circuit in Figure 2.4 in MicroCap using sinusoidal voltage source Vs= 10Vp-p
and f=10kHz. Run Transient Analysis and apply the technique from Lab #1 to measure the
time difference  and calculate the power factor angle Calculate the load power factor
cos 
2.2. Enter the calculated data in Table2.1 for comparison with the Pre-Lab calculations and the
experimental results.
2.3. Modify the circuit by adding the power factor correction capacitor C1, calculated
theoretically, and run the Transient Analysis again.
2.4. Determine load power factor angle  calculate the load power factor cos for this
compensated circuit and record the results in Table 2.2
2-4
PROCEDURE
1. Power Factor Analysis
1.1. Build the circuit in Figure 2.6 on the Breadboard.
1.2. Connect the CH1 of the oscilloscope to measure the input voltage VS and the CH2 to
measure the output signal at resistor R2, as it is shown in Figure 2.6.
1.3. Set the input signal Vs to 10 Vp-p, and use oscilloscope vertical cursors to measure the
amplitudes and the time difference between the input voltage Vs and output voltage Vo.
Calculate the sift angle [deg]. Record the measured values in Table 2.1 of your LMS.
Calculate the power factor cos for this circuit.
1.4. Compare the simulated and measured data and make a comment in section 1.3 of the LMS.
Figure 2.6. Inductive load power factor measurement
Note: Do not turn the power on before your circuit has been checked by your TA!
When the layout has been completed, have your TA to check your circuit connections and get
his/her signature in your log book.
1.5. Use the VL and IL data collected in part 1 to compute the complex power Stot and SL in
section 1.4 of the LMS. Compare these results with the complex power calculated in Pre-lab.
From your measurements, determine the average power P and the reactive power Q delivered to
the load. Use the values of P and Q computed from the measurements to compute the power
factor from pf = P/|S|. Indicate whether the load power factor is leading or lagging.
1.6. Draw the Power triangle of this circuit based on your measurements results and calculations
in section 1.5-b of the LMS.
1.7. Complete the Part 1 of the experiment by answering the question in section 1.6 of the LMS.
2. Power Factor Correction
2.1. Modify the circuit built in part 1 of this experiment by connecting C1=10nF in parallel with
the load, as it is shown in Figure 2.7.
Figure 2.7. Power factor correction experiment
2-5
2.2. Connect the CH1 of the oscilloscope to measure the input voltage VS and the CH2 to
measure the output signal Vo at resistor R2, as it is shown in Figure 2.7.
2.3. Set the input signal Vs to 10 Vp-p, measure the time difference between the input and
output voltages Vo and calculate the sift angle [deg]. Calculate the power factor cos for this
circuit. Record the measured values in Table 2.2 of your LMS.
2.4. Replace the capacitor C1 =10nF with a capacitor C2=22nF and repeat the same
measurements. Calculate the power factor cos for this circuit. Record the measured values in
Table 2.2 of your LMS
2.5. Replace the capacitor C2 =22nF with a capacitor C3=47nF and repeat the same
measurements. Calculate the power factor cos for this circuit. Record the measured values in
Table 2.2 of your LMS.
2.8. Use the VL and IL data collected in part 2 to compute the complex power Stot and SL. Compare
these results with the complex power calculated in Pre-lab. From your measurements, determine
the average power P and the reactive power Q delivered to the load. Use the values of P and Q
computed from the measurements to compute the power factor from pf = P/|S|. Indicate whether
the load power factor is leading or lagging.
2-6
LAB MEASUREMENTS SHEET – LAB #2
Name _________________________
Student No_____________________
Workbench No_____
1. Power Factor calculations of the inductive load
1.1. Phasor analysis- measured complex power Stot and SL
1.2. Circuit parameters calculations based on Lab measurements
2-7
Table 2.1.
Calculated values*
MicroCap*
Measured values
Vs
Vo
us]

T
T
360 0
cos 
1.3. How close the calculated, experimental and simulated results are and what could cause the
discrepancy.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
1.4 Calculate the measured complex power Stot and SL
2-8
1.5-a.*Calculated Power Triangle diagram
1.5-b. Measured Power Triangle diagram
1.6. Compare measured to the estimated power triangle and comment on differences.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. Power factor correction calculations.
Table 2.2.
2-9
Calculated
values*
MicroCap*
C1
Measured values
10nF
22nF
47nF
Vs
Vo


T
T
360 0
cos 
3. Discussion: Interpret and analyze your observations and calculations. Discuss the trends
you see in the data.
________________________________________________________________________
________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
____________________________________________________________________
2-10
SIGNATURE AND MARKING TABLE – LAB #2
TA Name:___________________
Check
Task
boxes
Max.
Granted
TA
Marks
Marks
Signature
Pre-lab completed
50
Power factor measurements
20
Power factor corrections
20
Overall Report Preparation
10
TOTAL MARKS
100
2-11