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Three-Phase AC Circuits Appendix: A (p.681). Significant Features of Three-Phase AC Circuits. Almost all ac power generation and transmission is in the form of three-phase ac circuits - PowerPoint PPT Presentation
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Significant Features of Three-Phase AC Circuits • Almost all ac power generation and transmission is in the form of three-
phase ac circuits
• AC power systems have a great advantage over DC systems in that their voltage levels can be changed with transformers to reduce transmission losses.
• Three-phase (3) ac power system consists of
– 3 ac generators
– 3 transmission lines
– 3 loads
• Advantages of having 3 power systems over 1ones:
– More power per pound of metal of electrical machines of 3.
– Power delivered to a 3 load is constant, instead of pulsating as it does in a 1 system.
Generation of 3 Voltages and Currents
A 3 generator consists of three 1 generators:
- voltage of all phases are equal in amagnitude- differing in phase angle from each aother by 120o.
Three-Phases of the Generator Connected to Three identical Loads
VA
VB
VC
Phasor diagram showing the voltages in each phase
Currents in the Three Phases and the Neutral
00
00
0
240240
120120
0
IZ
VI
IZ
VI
IZ
VI
c
b
a
0
240240
120120
240120
00
00
00
sinjcos
sinjcossinjcosI
III
IIII cbaN
Currents flowing in the three phases
It is possible to connect the negative ends of these three single phase generators and the loads together, so that they share a common return line, called neutral.
As long as the three loads are equal, the return current in the neutral is zero.
Balanced Power Systems
• In a balanced power system:
– Three generators have same voltage magnitude and phase difference is 120o.
– Three loads are equal and magnitude and angle.
• abc phase sequence: the voltages in the three phases peak in the order a, b and c. It is possible to have acb phase sequence.
Y and Connections
A connection of this sort is called Wye-connection.
Another possible connectionis delta-connection, in whichthe generators are connected
head to tail.
Z Z
Z
Z
Z
Z
Ic
Ib
Ia
In
Ia
Ib
Ic
Va
Va
Vb
Vb
Vc
Vc
+ +
+
-- -
-
-
-
+
+
+
Voltages and Currents in a Y-Connected 3 Circuit
Phase quantities: voltages and currents in a given phaseLine quantities: voltages between lines and current in the lines
Ib
Ic
Ia (=IL)VanVbn
Vcn
+ +
+
-- -
ResistiveLoad
n
I
Vca
Vab
Vbc
++
+
-
-
-
00
00
00
240120
120120
00
IIVV
IIVV
IIVV
ccn
bbn
aan
000 3031200 VVVVVV bnanab
Voltages and Currents in a Y-Connected 3 Circuit (cont’d)
VVLL 3
The relationship between the magnitude of the line-to-line voltage and the
line-to-neutral (phase) voltage in a Y-connected generator or load
IIL
In a Y-connected generator or load, the current in any line is the same as
the current in the corresponding phase.
Vab
Vbc
Vca
Van
Vcn
Vbn
Voltages and Currents in a -Connected 3 Circuit
VVLL
In a delta-connected generator or load, the line-to-line voltage between any two lines will be the same as the voltage in the corresponding phase.
IIL 3
In a delta-connected generator or load, the relationship between the magnitudes
of the line and phase currents:
IaIbcIb
Iab
Ic
Ica
Ibc
Ica
VA VB
VC
--
-
+
+
+
Ia
Iab
IbIc
Power Relationship in 3 Circuits
A balanced Y-connected load.
The 3 voltages applied to this load:
13
000
000
0
0
0
0
33
48022402402
24021201202
22
2402
1202
2
2402
1202
2
PcosVItPtPtPPtP
tcoscosVItsintsinVItitvtP
tcoscosVItsintsinVItitvtP
tcoscosVItsintsinVItitvtP
tsinIti
tsinIti
tsinIti
tsinVtv
tsinVtv
tsinVtv
aaatotal
ccnc
bbnb
aana
c
b
a
cn
bn
an
The 3 currents flowing in this load:
Instantaneous power supplied to each of the three phases:
Total power supplied to the 3 load:
3Power Equations Involving Phase Quantities
The 1 power equations:
sinIVQ
cosIVP
IVS
sinIVQ
cosIVP
IVS
3
3
3
3
3
3
1
1
1
The 3 power equations:
S
P=Scos
Q=Ssin
90o
3Power Equations Involving Line Quantities
VVandII LLL 3
cosIVcosI
VcosIVP
cosIVcosIV
cosIVP
LLLL
LL
LLLLLL
33
33
33
33
3
3
For a Y-connected load:
90o
For a delta-connected load: VVandII LLL 3
Therefore, regardless of the connection of the load:
LLL
LLL
LLL
IVS
sinIVQ
cosIVP
3
3
3
3
3
3
Analysis of Balanced 3 Systems
If a three-phase power system is balanced, it is possible to determine voltages and currents at various points in the circuit with a per
phase equivalent circuit.
• Neutral wire can be inserted, as no current would be flowing through it, thus, system is not affected.
• Three phases are identical except for 120o phase shift for each phases.
• It is thus possible to analyze circuit consists of one phase and neutral.
• Results would be valid for other two phases as well if 120o phase shift is included.
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