Introduction to Three-Phase Power
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Typical Transformer Yard
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Basic Three-Phase Circuit
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What is Three-Phase Power?
• Three sinusoidal voltages of equal
amplitude and frequency out of phase with
each other by 120°. Known as “balanced”.
• Phases are labeled A, B, and C.
• Phases are sequenced as A, B, C
(positive) or A, C, B (negative).
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Three-Phase Power
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Definitions
• 4 wires
– 3 “active” phases, A, B, C
– 1 “ground”, or “neutral”
• Color Code
– Phase A
– Phase B
– Phase C
– Neutral
Red
Black
Blue
White or Gray
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Phasor (Vector) Form for abc
Vc=Vm/+120°
Va=Vm/0°
Vb=Vm/-120°
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Phasor (Vector) Form for abc
Vc=Vm/+120°
Va=Vm/0°
Vb=Vm/-120°
Note that KVL applies .... Va+Vb+Vc=0
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Three-Phase Generator
• 2-pole (North-South)
rotor turned by a
“prime mover”
• Sinusoidal voltages
are induced in each
stator winding
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How are the sources connected?
• (a) shows the sources
(phases) connected in
a wye (Y).
– Notice the fourth
terminal, known as
Neutral.
• (b) shows the sources
(phases) connected in
a delta (∆).
– Three terminals
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Look at a Y-Y System
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Definitions
• Zg represents the internal
generator impedance per
phase
• Zl represents the
impedance of the line
connecting the generator
to the load
• ZA,B,C represents the load
impedance per phase
• Zo represents the
impedance of the neutral
conductor
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Look at the Line and Load Voltages
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VAB  VAN  VBN
Line Voltages
VBC  VBN  VCN
Phase Voltages
VCA  VCN  VAN
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Vector addition to find VAB=VAN-VBN
-VBN
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Using the Tip-to-Tail Method
-VBN
VΦ = Line-to-Neutral,
or Phase Voltage
VAB = VAN – VBN = √3VΦ
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Conclusions for the Y connection
• The amplitude of the line-to-line voltage is
equal to √3 times the amplitude of the
phase voltage.
• The line-to-line voltages form a balanced
set of 3-phase voltages.
• The set of line-to-line voltages leads the
set of line-to-neutral (phase) voltages by
30°.
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Summary
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Look at the Delta-Connected Load
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I AB  I 0
I BC  I   120
I CA  I 120
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I aA  I AB  I CA
Line Currents
I bB  I BC  I AB
Phase Currents
I cC  I CA  I BC
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Vector Addition to find IaA=IAB-ICA
-ICA
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Using the Tip-to-Tail Method
-ICA
IaA = √3IΦ/-30°
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Conclusions for the Delta Connection
• The amplitude of the line current is equal
to √3 times the phase current.
• The set of line currents lags the phase
currents by 30°.
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