EE 448 Laboratory Experiment 1
Single Phase AC Circuits
EE 448
Lab Experiment No. 1
03/24/2008
Single Phase AC Circuits
1
EE 448 Laboratory Experiment 1
Single Phase AC Circuits
I.
INTRODUCTION
OBJECTIVES:
•
Study the phasor relationship between Voltage and Current in a
single phase AC Circuit.
•
Study the concept of real power (P), reactive power (Q), apparent
power(S) and power factor (cosΦ).
•
Identify a method to improve the line side power factor with the help
of a capacitor bank.
BACKGROUND SUMMARY:
AC circuit elements consist of resistors (R), inductors (L) and
capacitors(C) which can be fed from either a 3 phase or 1 phase 60 Hz,
120V source. Resistor and inductor combination connected to a single
phase AC source results in a lagging current with respect to voltage. If R &
L are connected in series, the phasor sum of the voltages across L and R
equals the source voltage. In contrast if they are connected in parallel the
phasor sum of the currents drawn by R & L equals the source current.
Power factor of any load (source) is defined as the cosine of the angle
between the load(source) current and corresponding load(source) voltage.
By connecting a capacitor bank in parallel with such a RL circuit can
improve the power factor which in turn reduces the current drawn from
the source for a given power drawn by the resistor.
Power relations in a single phase system
Real power =Vrms *Irms cosΦ in watts (where Φ is angle between V and I)
Reactive power = Vrms *Irms * sin(Φ) in VARs
Apparent power = Vrms *Irms in VA
INSTRUMENTS and COMPONENTS:
Power Supply Module EMS 8821
AC Voltmeter Module EMS 8426
AC Current Meter ModuleEM.S 8428
Resistance Module
EMS 8311
Inductance Module EMS 8321
Capacitance Module EMS 8421
2
EE 448 Laboratory Experiment 1
Single Phase AC Circuits
II.
PRELAB EXERCISES
1. The machines we will be working with in this lab have these
resistances: R1 = 300Ω, R2 = 600Ω and R3 = 1200Ω. Identify the
parallel combinations of two of the resistors at a time to get equivalent
resistances of 200Ω, 240Ω and 400Ω. This will make using the lab
equipment easier.
2. If R1= 300Ω is connected in series with an inductive reactance of X1 =
j300Ω, what will be the impedance angle of this series combination?
3. In Fig. 2, If R1 and X1 are connected in parallel across a single phase
source. What capacitance C value should be connected in parallel to
get unity p.f. Assume the frequency of supply is 60Hz.
4. Draw the phasor diagrams for the voltages in figure 1. Take voltage
across the resistor (Vr) as the reference vector.
1
300
V1
120Vrms
60Hz
j300
2
Figure 1
5. For the circuit in Fig.2, draw the phasor diagram for the three currents
Is, Ir and I1 and prove that Is = √2(Ir).
Is
Ir
1
Il
V1
120Vrms
60Hz
300
j300
2
Figure 2
3
EE 448 Laboratory Experiment 1
Single Phase AC Circuits
6. For the circuit in Fig. 3 find
a)
All the currents
b)
Real power supplied by the source
c)
Reactive power supplied by the source
d)
Apparent power supplied by the source
e)
Power dissipated in the resistor
f)
Real and reactive power in the inductor
g)
Real and reactive power in the capacitor
h)
Power factor as seen by the source
Assume the source voltage as reference ‫ ׃‬120∟o°
Is
Il
Ir
Ic
2
V1
120Vrms
60 Hz
j300
300
-j200
1
Figure 3
III.
LABORATORY EXPERIMENT
NOTE:
Whenever an ammeter is used to measure current in a circuit, one should
try to get the most accurate reading. To get a more accurate measurement
the DMM(Digital Multi-Meter) should be used. However the DMM is only
rated for 3 AMPS MAX! The Lab-Volt ammeters are rated for 8 amps. In
most of our circuits the current is below 3 amps, but be sure to check your
calculations of the circuit to determine whether to use the DMM or LabVolt ammeter for your measurements.
1. Connect the circuit as shown in Figure 4. The transformer is necessary
to isolate the scope ground from the line voltage.
4
EE 448 Laboratory Experiment 1
Single Phase AC Circuits
2. Observe the voltage waveforms of Vs and Vr on the oscilloscope and
identify the phase difference between these two voltages.
3. Disconnect only the inductor and measure the phase difference between
Vs and Vr.
4. Now reconnect the inductor, remove the resistor and measure the phase
difference between Vs and V1. Does the data from the previous steps
match your calculations for step 4 of part II?
5. Connect the circuit as shown in Figure 5.
6. Measure the currents As, Ar and A1.
a. Does the data from steps e and f match your calculations from
step 5 of part II?
7. Calculate the power delivered to the circuit.
8. Calculate the p.f. of the load.
9. Make the circuit connections as shown in Figure 6. Connect R, L & C in
parallel according to the table given below. First three readings are for
R&L combinations. Last two readings are for R, L & C combinations.
NOTE:
The toggle switches on the inductance, resistance, and capacitive boxes
work as follows. A toggle switch in the down position means that item is
not in the circuit between the two banana plugs. When switched to the
up position, the item is part of the circuit. When two or more toggle
switches are up, those two or more items will be in the circuit connected
in parallel. Depending on whether it’s a resistor, inductor, or capacitor
box will determine the value of the parallel connection.
10. Record your measurements in the table below.
Use V = 120V
I
S
P
R
Xi
Xc
300
600
1200
600
600
j300
j300
j300
j300
j600
-j300
-j300
5
p.f.
Q=S*sin φ
EE 448 Laboratory Experiment 1
Single Phase AC Circuits
11. From looking at the table, which set of values will produce a unity power
factor?
12. Study your data and determine the capacitance value that gave you the
best power factor (closest to unity). Does this value match what you
predicted in step 3 of part II? Why or why not?
13. Again study your data and determine why it might be an important goal
to achieve a power factor that is as close to unity as possible.
14. Present the lab results using a spreadsheet computer program and attach
it with your lab report.
Resistor Module – 8311
Inductor Module – 8321
Transformer – 8341
AC Source – 8821
Figure 4
6
+
1
+
Ammeter
EE 448 Laboratory Experiment 1
Single Phase AC Circuits
2
-
2
R1
300
+
L1
j300
+
1
As
1
+
+
+
1
Voltmeter
3
4
-
Digital
Ammeter
Ar
-
2
2
Al
-
Ammeter
-
2
N
2
+
120 V 2
AC Source
3
8821
1
-
1
1
-
Figure 5
+
1
+
Digital
Ammeter
Resistor Module – 8311
Inductor Module – 8321
AC Source – 8821 (Power Supply)
2
-
1
1
3
3
Wattmeter
2
4
4
+
1
2
1
120 V 2
AC Source
3
8821
2
Voltmeter
2
3
R1
300
4
L1
j300
2
-
N
+
1
1
-
Figure 6
Resistor Module – 8311
Inductor Module – 8321
Capacitor Module – 8331
AC Source – 8821
7
C1
-j300