introduction to three-phase power
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ECE 441 1
Introduction to Three-Phase Power
ECE 441 2
Typical Transformer Yard
ECE 441 3
Basic Three-Phase Circuit
ECE 441 4
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).
ECE 441 5
Three-Phase Power
ECE 441 6
Definitions
• 4 wires– 3 “active” phases, A, B, C– 1 “ground”, or “neutral”
• Color Code– Phase A Red– Phase B Black– Phase C Blue– Neutral White or Gray
ECE 441 7
Phasor (Vector) Form for abc
Va=Vm/0°
Vb=Vm/-120°
Vc=Vm/+120°
ECE 441 8
Phasor (Vector) Form for abc
Va=Vm/0°
Vb=Vm/-120°
Vc=Vm/+120°
Note that KVL applies .... Va+Vb+Vc=0
ECE 441 9
Three-Phase Generator
• 2-pole (North-South) rotor turned by a “prime mover”
• Sinusoidal voltages are induced in each stator winding
ECE 441 10
ECE 441 11
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
ECE 441 12
Look at a Y-Y System
ECE 441 13
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
ECE 441 14
Look at the Line and Load Voltages
ECE 441 15
CN
AB AN BN
BC BN CN
CA AN
V V V
V V V
V V V
Line Voltages Phase Voltages
ECE 441 16
-VBN
Vector addition to find VAB=VAN-VBN
ECE 441 17
-VBN
Using the Tip-to-Tail Method
VAB = VAN – VBN = √3VΦ
VΦ = Line-to-Neutral, or Phase Voltage
ECE 441 18
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
ECE 441 20
Look at the Delta-Connected Load
ECE 441 21
0
120
120BC
AB
CA
I I
I I
I I
ECE 441 22
bB
aA AB CA
BC AB
cC CA BC
I I I
I I I
I I I
Line Currents Phase Currents
ECE 441 23
-ICA
Vector Addition to find IaA=IAB-ICA
ECE 441 24
-ICA
Using the Tip-to-Tail Method
IaA = √3IΦ/-30°
ECE 441 25
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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