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3-Phase circuits Chpt 12 INEL 4075 Dr. Sandra Cruz-Pol Professor Electrical Engineering UPRM. Three-phase circuits. The 3- f circuits can be motors or generators and are the ones used nowadays to distribute electric power through all cities. They consists of: 3 sources - PowerPoint PPT Presentation
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3-Phase circuitsChpt 12Chpt 12INEL 4075INEL 4075
Dr. Sandra Cruz-PolProfessor Electrical Engineering UPRM
Three-phase circuitsThree-phase circuitsThe 3- circuits can be motors or generators and
are the ones used nowadays to distribute electric power through all cities. They consists of:– 3 sources– 3 transmission lines (3 or 4 wires)– 3 loads
• We use the frequency domain to work with 3-– Impedances& phasors
• Advantages:– Total power is constant with time, which is necessary
to keep large generators and motors running smoothly– More efficient and economic
Nikola Tesla
3- motor
Line voltages for positive phase sequence abc:
omc
omc
omb
omb
omama
VVtVtv
VVtVtv
VVtVtv
120 )240cos()(
120 )120cos()(
0 )cos()(
Assuming T.L. are lossless
Line currents are Ia, Ib and Ic
For Delta connection:For Delta connection:
omacca
omcbbc
ombaab
VVVV
VVVV
VVVV
2103
903
303
Compute the line-to-line voltages:
Connections: Connections: Y to Y to to YSystems is balanced when the loads,
currents, voltages are equal in all 3 phases. Then can do a per-phase equivalent circuit.
For balanced Y-Y systems;For balanced Y-Y systems;
cos3
P
0
0
2
Z
VP
PPP
but
PPP
I
V
ZZZZ
m
cba
cba
n
n
cba
Conversion Conversion to Y to Y
321
21
321
32
321
31
Z
Z
Z
ZZZ
ZZ
ZZZ
ZZ
ZZZ
ZZ
c
b
a
3
:balanced if
321
Z
ZZZ
ZZZZ
cba
Conversion Y to Conversion Y to
c
acbba
a
acbba
b
acbba
Z
ZZZZZZ
Z
ZZZZZZ
Z
ZZZZZZ
c3
c2
c1
Z
Z
Z
Y
Ycba
ZZZZ
ZZZZ
3
:balanced if
321
ReferencesReferences
• Wikipedia!
• Univ Zagreb
