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Experiment 4. Three-Phase Circuits
OBJECTIVE

To study the relationship between voltage and current in three-phase circuits.

To learn how to make delta and wye connections.

To calculate the power in three-phase circuits.
DISCUSSION
Students tend to approach three-phase circuits with a particular apprehension which is not at all
justified. Three-phase circuits, in the majority of cases, are symmetrical. They consist of three
identical branches, each of which has the same impedance. Each of these branches can be treated
exactly like a single-phase circuit. Consequently, three-phase circuits are not necessarily harder
to work with than single-phase circuits.
Unbalanced three-phase circuits represent an abnormal condition. Circuit analysis becomes
somewhat difficult and will not be covered in the laboratory experiments.
Three-phase systems are usually connected by either a delta (Δ) or a wye (Y) configuration. Each
of these connections has defined electrical characteristics and the designations delta and wye are
derived from the method of connection.
PROCEDURE
The grading in this section is 0.5 point for each correct answer.
1. Voltmeters
a. Circuit:
Open the Virtual Laboratory, and from the Virtual Lab, Welcome Window click on
Experiment 4 then Procedure 1 buttons. Your screen should look similar to Figure 4-1.
Using your Power Supply and AC Voltmeter connect the circuit shown in Figure 4-2. If
you are unsure how to make/remove connections, please refer to the Experiment 1
manual.
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Figure 4-1. Screen capture for Procedure 1.
Figure 4-2. Connection circuit for Procedure 1.
b. Measurements / Calculations:
i)
Adjust for 120 V AC as indicated by the variable AC power supply. Then, click on
the Run button. Measure and record each line-to-line voltage. If you receive
abnormal/unexpected results, check your wiring and voltage magnitude. Once you
have fixed your circuit, click the Run button again.
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VA to B = 207.661V ∠ 30 °
VB to C = 208.218V ∠−90 °
VA to C = 207.658V ∠−210°
ii) Calculate the average value of the line-to-line voltage.
Vline-to-line = 207.846V ∠0 °
iii)
Reconnect your three voltmeters to measure the voltage from each line-to-neutral.
Adjust for 120 V AC as indicated by the variable AC power supply. Then, click on
the Run button. Measure and record each line-to-neutral voltage. If you receive
abnormal/unexpected results, check your wiring and voltage magnitude. Once you
have fixed your circuit, click the Run button again.
VA to N = 119.785V ∠ 0 °
VB to N = 120.109V ∠−120°
VC to N = 120.106V ∠−240°
iv)
Calculate the average value of the line-to-neutral voltage.
Vline-to-neutral = 120.0V ∠ 0 °
v)
Calculate the ratio of the average line-to-line voltage to the average line-to-neutral
voltage.
Vline-to-line / Vline-to-neutral = 1.73205
vi)
Is this ratio approximately equal to
√3 ?
Yes, it is approximately the square root of three.
vii) Repeat Procedures 1 (i) and (iii), but this time, measure the voltages at the fixed
output terminals of your power supply. Be sure to hit the Run button after
changing the connections. If you receive abnormal/unexpected results, check your
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wiring and voltage magnitude. Once you have fixed you circuit, click the Run
button again.
VA to B = 207.661V ∠ 30 °
VA to N = 119.785V ∠ 0 °
VB to C = 208.219V ∠−90 °
VB to N = 120.109V ∠−120°
VA to C = 207.658V ∠−210°
VC to N = 120.107V ∠−240°
viii) Are the three fixed line-to-line voltage values similar to each other?
Yes, they are similar.
ix)
Are the three fixed line-to-neutral voltage values similar to each other?
Yes, they are similar.
x)
Is the voltage between any two terminals a single-phase voltage or a three-phase
voltage?
Three-phase voltage.
xi)
Close the Experiment 4 Procedure 1 window.
2. Three-phase Circuit: Wye connection
c. Circuit:
Click on the Experiment 4 Procedure 2 button. Your screen should look similar to Figure
4-3. By using the resistors, ammeters and voltmeters connect the wye circuit shown in
Figure 4-4. Do not connect the neutral of the resistance module to the neutral of the
power supply. The resistance value in each section is 400 Ω. If you are unsure how to
make/remove connections, please refer to the Experiment 1 manual.
d. Measurements/Calculations:
Adjust for 208 V AC (line-to-line) as indicated by the variable AC power supply. Then,
click on the Run button. Measure and record the voltages across and the currents through
the three load resistances RA, RB, and RC. If you receive abnormal/unexpected results,
check your wiring and voltage magnitude. Once you have fixed your circuit, click the
Run button again.
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VRA = 207.998V ∠ 0 °
IA = 0.52A ∠ 0 °
VRB = 207.998V ∠−120 °
IB = 0.52A ∠−120°
VRC = 207.998V ∠−2 4 0 °
IC = 0.52A ∠−24 0 °
Fig
ure 4-3. Screen Capture for Procedure 2.
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Figure 4-4. Connection circuit for Procedure 2.
i)
Are the currents and voltages reasonably well balanced?
Yes, they are.
ii)
Calculate the average value of load voltage.
Vload = 207.998V
iii)
What is the average value of the line-to-line voltage (from Procedure 1(ii))?
Vline-to-line = 360.3V
iv)
Calculate the ratio of the average line-to-line voltage to the average load voltage.
Vline-to-line / Vload = 1.73
v)
Is this ratio approximately equal to
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√3 ?
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Yes it is.
vi)
Calculate the power dissipated by each load resistance.
PRA = 108.16W
PRB = 108.16W
PRC = 108.16W
vii)
Calculate the total three-phase power PT.
PT = 187.34W
viii) Close the Experiment 4 Procedure 2 window.
3. Three-phase Circuit: Delta connection
e. Circuit:
Click on the Experiment 4 Procedure 3 button. Your screen should look similar to Figure
4-5. Connect the delta circuit shown in Figure 4-6. Figure 4-6(a) clearly shows the delta
arrangement while Figure 4-6(b) is a simplified version. The resistance used in each
section is 400 Ω. Connecting the circuit using wires with different colors can be helpful
for students to deal with three-phase circuit connections. When connecting this delta
circuit, it may be useful to make marks on Figure 4-6 (i.e., labeling each resistor with ‘R’
for the red end and ‘B’ for the black end).
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Figure 4-5. Screen capture for Procedure 3.
Figure 4-6(a). Connection circuit for Procedure 3.
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Figure 4-6(b). Simplified connection circuit for Procedure 3.
f. Measurements / Calculations:
Adjust for 120 V AC (line-to-line) as indicated by the variable AC power supply. Then,
click on the Run button. Measure and record the voltages across and the currents
through the three load resistances RAB, RBC, and RCA. If you receive abnormal/unexpected
results, check your wiring and the voltage magnitude. Once you have fixed your circuit,
click the Run button again.
VAB = 120.999V ∠ 3 0 °
IAB = 0.303A ∠6 0 °
VBC = 120.999V ∠−9 0°
IBC = 0.303A ∠−6 0°
VCA = 120.999V ∠−210 °
ICA = 0.303A ∠−180 °
i) Are the currents and voltages reasonably well balanced?
Yes they are.
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ii) Calculate the average value of load current.
Iload = 0.303A
iii) Close the Experiment 4 Procedure 3 window.
4. Three-phase Circuit: Delta-connected circuit line current
a. Circuit:
Click on the Experiment 4 Procedure 4 button. Your screen should look similar to Figure
4-7. Insert the three current meters in series with power supply terminals A, B and C
(variable), and connect the circuit according to Figure 4-8. If you are unsure how to
make/remove connections, please refer to the Experiment 1 manual. Connecting the
circuit using wires with different colors can be helpful for students to deal with threephase circuit connections.
Figure 4-7. Screen capture for Procedure 4.
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Figure 4-8. Connection circuit for Procedure 4.
g. Measurements / Calculations:
i)
Adjust for 120 V AC (line-to-line) as indicated by the variable AC power supply.
Then, click on the Run button. Measure and record the three line currents. If you
receive abnormal/unexpected results, check your wiring and the voltage magnitude.
Once you have fixed your circuit, click the Run button again.
IA = 0.519489A ∠−3 0°
IB = 0.519735A ∠−150 °
IC = 0.519623A ∠−27 0°
ii)
Calculate the average value of the line current.
Iline = 0.519616 A
iii)
Calculate the ratio of the average line current to the average load current (see
Procedure 3 b (ii)).
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Iline / Iload = 1
iv)
Is this ratio approximately equal to
√3 ?
No.
v)
Calculate the power dissipated by each load resistance.
PRAB = 62.3W
PRBC = 62.4W
PRCA = 62.4W
vi)
Calculate the total three-phase power PT.
PT = 187.2W
vii)
Close the Experiment 4 Procedure 4 window.
REVIEW QUESTIONS
1. In a wye-connected circuit, if the line-to-line voltage is 346 V, what is the line-to-neutral
voltage? (2)
199.8V
2. In a delta-connected circuit, the current is 20 A in each resistance load. What is the line
current? (2)
34.6 ∠−30° A
3. In a wye-connected circuit, the current is 10 A in each resistance load. What is the line
current? (2)
10A
4. Three loads, each having a resistance of 10 Ω, are connected in wye. The total three-phase
power is 3000 W. What is the line-to-line voltage? (2)
300V
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5. Three resistors each having a resistance of 11 Ω are connected in delta across a three-phase
440 V line. (4)
i)
What is the line current?
40A
ii)
What is the total three-phase power?
52.8kW
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