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Lesson 4: Three Phase Sources and
Loads
ET 332b ET 332b Ac Motors, Generators and Power Systems
1 Lesson 4_et332b.pptx
Learning Objectives
2 Lesson 4_et332b.pptx
After this presentation you will be able to:
Identify circuit impedances, voltages and currents using
the double subscript notation.
Perform calculations on wye connected three-phase
sources and loads.
Perform calculations on delta connected three-phase
sources and loads.
Construct phasor diagrams of three-phase sources and
loads.
Identify the time and phasor plots of a three phase set
of voltages and currents.
Double Subscript Notation
3 Lesson 4_et332b.pptx
Sources and voltage drops are defined by the terminal letter. Voltage drop
and polarity defined by order of subscripts
b
n
a
n
Van
Voltages considered positive if first node subscript is higher
potential than second node subscript
Vbn
Double Subscript Notation
4 Lesson 4_et332b.pptx
Identify current flow from point b to c
Ibc
bc
bc bc Z
V
I Vbc = difference in potential between points b and c. If
voltage at point b is taken as the reference point, then the
polarity is reversed.
Vbc
+ - Vcb=-Vbc
Three-Phase Three-Phase
7 Lesson 4_et332b.pptx
Time Plots of Three Phase Voltages and Phasors
Three-Phase Source Connections
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Wye – Connected, three-phase 3 sources
Determine the relationship between the magnitude and phase shift of
each source voltage and the current and voltage at the terminals of the
connection
c
n
b
n a
Ic
Ia
Ib
Van
Vcn
Vbn V ab
V ca
V bc
In wye connection:
IL=Ip
Where:
IL = line current Ip= phase current
Wye Connected Sources
(^9) Lesson 4_et332b.pptx
Voltage relationships Line-to-line voltage^ phasors
Vab Van Vbn
Vbc Vbn Vcn
Vca Vcn Van
In balanced systems Van Vbn Vcn
Perform phasor subtraction
to find the values
Van
Vbn
Vab
Vca
Vcn
Vbc
Wye Connected Sources
10 Lesson 4_et332b.pptx
Van
Vbn
Vab
Vcn
Vbc
Rotation
Wye connected line voltage magnitudes
ca cn
bc bn
ab an
V 3 V
V 3 V
V 3 V
Phase shifts
Line-to-line (line) voltages lead phase
voltages by 30 degrees for CCW rotation
V ab Vab 30
V bc Vbc 90
V (^) ca Vca 210
30 °
Vca
Example 4-1 Solution (2)
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In wye connection line current equals phase current
For “a” phase
Ans
Ans
Ans
For other phases
b)
Example 4-1 Solution (3)
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c) To find the neutral current, sum the currents at the load neutral point
Neutral
point
Convert to rectangular form to add
In balanced 3 system, neutral conductor carries no current. It is used for
safety and to handle unbalances
Ib
Ia
Ic
Example 4-1 Solution (4)
15 Lesson 4_et332b.pptx
Phasor diagram
All line-to-line voltages lead the
phase voltages by 30 degrees.
For resistive load, the phase
current is in phase with Vpn, the
phase-to-neutral voltage.
Delta Connected Sources
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Phase voltages are equal to line-to-
line voltages in delta connections
Where: VLL = line-to-line voltage
Vp = phase voltage
VLL VP
V LL
V p
So Vab Vbc Vca
To find relationship between phase and
line currents, perform KCL at every
corner node
Ibc
Delta Connection Example
19 Lesson 4_et332b.pptx
Example 4-2: For the delta connected load shown, a) find the phasor
values of phase and line currents for the circuit.: b) draw a phasor diagram of
the computed currents and given voltages R = 15 ohms in each phase.
Vab = 240 0 o
Vbc = 240 - 120 o
Vca = 240 - 240 o 240 0 o
240 - 240 o
240 - 120 o
Example 4-2 Solution (1)
20 Lesson 4_et332b.pptx
For this balanced system, compute the values for single phase and then shift
the angles for the other values
Now compute the line current
Example 4-2 Solution (2)
21 Lesson 4_et332b.pptx
Similarly for the line current
Phasor diagram for delta connected
load Example 4- 2
Resistive circuit, so phase currents are in
phase with voltages that produce it.
0 degrees
Line currents lags the phase
currents by the 30 degrees
degrees
Delta Connected Load-General Impedances
22 Lesson 4_et332b.pptx
Example 4- 3 : a) Find the phasor values of phase and line currents for the
circuit shown: b) draw a phasor diagram of the computed currents
and given voltages. Z = 30 - 39 o^ ohms.
Vab = 240 0 o
Vbc = 240 - 120 o
Vca = 240 - 240 o
End Lesson 4: Three Phase
Sources and Loads
ET 332a Ac Motors, Generators and Power Systems
25 Lesson 4_et332b.pptx
