Lecture 0 -Three Phase Circuits Lecture (1).pdf

It is an engineering Circuits Chapter for three phase circuits.

1. Three Phase AC Circuits
Mohamed Ahmed

2. Why Three Phase?
• Using three-phase circuits, the power delivery capacity tripled
(increased by 200%) by increasing the number of conductors
from 2 to 3 (increased by 50%). Therefore, power density
(power per unit volume) and specific power (power per unit
mass) is large compared with single phase.
• Smooth flow of power (instantaneous power is constant).
• Constant torque (reduced vibrations).
• Furthermore, as will be seen later, a three-phase supply
allows for using three-phase induction motors, which are self
starting. Note that single-phase induction motors are not self
starting and need auxiliary tools to start them from standstill.
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3. Three Phase Circuits
• A three-phase sinusoidal voltage source is
composed of three single-phase sinusoidal
voltage sources with the same amplitude
and frequency, but phase-shifted by 120
o
with respect to one another.
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4. Three Phase Circuits
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5. Three Phase Circuits
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6. THREE PHASE
CONNECTIONS
Three Phase Circuits
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7. Three Phase Connections
• Star or wye (Y) Connection:
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8. Three Phase Connections
(Y-Connection)
• Line to Line Voltages
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9. Three Phase Connections
(Y-Connection)
• Relation between Three phase voltages
and Currents:
Balanced three phase Load
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10. Three Phase Connections
(Y-Connection)
• Relation between Three phase voltages
and Currents:
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11. Three Phase Connections
(Y-Connection)
• Where, Z
phase
is the impedance per phase
and I
phase
is the rms values of the phase
current.
• In Y-connection, the current in each line is
equal to the current in the corresponding
phase.
line phase
II

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12. Three Phase Connections
(∆-Connection)
• Delta (∆) Connection
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13. Three Phase Connections
(∆-Connection)
For delta connected systems:
LD=OA
is the rms phase or line to line voltage
magnitude.
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14. Three Phase Connections
(∆-Connection)
• Relation between Three phase voltages
and Currents:
Balanced three phase Load
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15. Three Phase Connections
(∆-Connection)
• Line Currents:
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16. Three Phase Connections
(∆-Connection)
• Phasor diagram of currents in a 3-phase
∆-connected balanced load
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17. Three Phase Connections
(Summary)
Star (Y) Delta (∆)
Phase to neutral
voltage
8
?????
L8
?
L8
?????
?08
?????
L8
??
L8
?????
?0
Line to line
voltages
8
??
L8
??
L
38
?????
?30
?
8
??
L8
?????
L8
??
Phase Current
+
?????
L+
?
L
8
?????
<
?F? +
?????
L+
??
L
8
?????
<
?F?
L+
?????
?F?
Line Current+
????
L+
?????
+
????
L+
?
L
3+
?????
?F? F30
?
Where,
<L<??
Same analysis can be done for the rest of the system phases
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18. Equivalent Star and Delta
Connections
• In many cases during the course, we may
need to transform delta connected load to
a star load work with on a per-phase
basis.
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19. Equivalent Star and Delta
Connections
For a balanced Load:
<
1
L
<
?
3
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20. Single Line Equivalent Circuit • For balanced three phase circuits, a single
line equivalent which represents one
phase of the original system.
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21. Single Line Equivalent Circuit +
?
L+
?????
?F?
Power factor=cos(?)
• If the actual line currents I
A
, I
B
, and
I
C
are desired, their phase angles
may be found by adding to the
phase angles of V
AN
, V
BN
, and V
CN
• The method may be applied to a
balanced ∆-connected load if the
load is replaced by its Y-equivalent,
where,
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22. THREE PHASE
POWER
Three Phase Circuits
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23. Three-phase Power
• The three phase power is equal the sum of the phase powers
• If the load is balanced:
• Wye (star) system:
• Delta system:
c b a
P P P P   





phase phase phase
P 3 P 3 V I cos
LN LL L phase LN phase
V 3 V I I V V  








phase phase LL L
P 3 V I cos 3 V I cos
phase LL phase Line
V V I 3 I 








phase phase LL L
P 3 V I cos 3 V I cos
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24. Three-phase Power
• For any three phase load:
–Apparent power:
?????
?????
????
????
–Reactive power:
?????
?????
????
????
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25. 3/9/2014
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Power factor correction
• Power factor (p.f.) correction is the process of
making a unity power factor (p.f. = 1).
• In order to correct the power factor in any system, a
reactive (either inductive or capacitive) will be added
to the load.
• If the load is inductive, then a capacitance is added.
• If the load is capacitive, then an inductor is added.
• Correcting the P.F. WILL NOT affect the active
power

26. EXAMPLES
Three Phase Circuits
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27. 3/9/2014
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Example (1)
A 345 kV, three phase transmission line delivers 500 MVA,
0.866 lagging power factor, to a three phase load connected to
its receiving end terminals. Assume the load is Y connected and
the voltage at the receiving end is 345 kV, find:
• The load impedance per phase.
• The line and phase currents.
• The total real and reactive power.
Three-phase Circuits

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1
()
345 500
0 , I 836.7
333345
836.7 cos (0.866) 836.7 30
238 30 206 119
( ) Star connected load, 836.7 30
( ) 3 cos( ) 433 MW
3 sin( ) 249.9 MVAR
L
L
LL
LL
V
aZ
I
kV S MVA
VV A
VkV
I
Zj
bII
cP VI
QVI











 
 

 



29. Three phase circuits
Example (2):
A three phase Y-connected generator supplies
a 10kVA load at 230V. The generator has an
internal impedance of 0.5+j1.2 ohms per phase.
a) Calculate the generator voltage for a 0.8
lagging power factor load.
b) Calculate the generator voltage for a 0.8
leading power factor load.
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30. March 9, 2014
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11
11
1.2 , 0.5 ,
230
0 132.8 0
3
) cos (0.8) cos (0.8)
33
25.1 36.87
( ) 161.76 5.878
) cos (0.8) cos (0.8)
33
25.1
ph
phLL
ph ph
phLL
ii
load
rated rated
loadload
o
o
gload i i
rated rated
loadload
XR
VV
SS
aI
VV
IA
VV IR
j
X
SS
bI
VV
I


 

  




36.87
( ) 128.7114.22
ph ph
o
o
gload i i
A
VV IR
j
X 