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Chapter 1 Three phase system
Week 2
Interconnections of three phase system (star and delta),
Relationship between line and phase valuesBalanced load
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v(t)
Vm
-Vm
t
Phasor
diagram
Which one is:Vm = ?
Vinst = ?
= ?
+V
-V
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3
A three-phase system is superior economically and
advantage, and for an operating of view, to a single-
phase system. In a balanced three phase system thepower delivered to the load is constant at all times,
whereas in a single-phase system the power pulsates
with time.
Three-Phase System
In a three phase system the source consists of three
sinusoidal voltages. For a balanced source, the three
sources have equal magnitudes and are phase
displaced from one another by 120 electrical degrees.
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Advantages of 3- compared to 1- system
High efficiency
For same power at the transmission line,
less conductor and lighter Construction and maintenance, minimum
(cheaper)
Starting behavior and operation of 3-equipment better or more stable than 1-
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Generation of Three-PhaseThree separate windings or coils with terminals R-R, Y-Y and B-B are
physically placed 120o apart around the stator.
Y
BY
B
Stator
Rotor
Y
R
B
R
R
N
S
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It has 3 conductor loops
that is R (red), Y (yellow) and
B (blue). The conductor loop will
move in circle and then cut
off the magnetic flux.
It will produces the
electromagnetic force e.m.fin the conductor.
Maximum e.m.f is when the
conductor loop is 90 with
magnetic flux line.
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v(t)
t
vR
vY
vB
The instantaneous e.m.f. generated in phase R, Y and B:
vR= VRsin tvY= VY sin (t -120
o)
vB= VB sin (t -240o)= VBsin (t +120
o)
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Phase sequences : RYB and RBY
120o
-120o
120o VR
VY
VB
o
)rms(RR0VV
o
)rms(YY120VV
o
)rms(B
o
)rms(BB
120V
240VV
VR leads VY, which in turn leads VB.This sequence is produced when the rotor rotates in
the counterclockwise direction.
(a) RYB or positive sequence
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(b) RBY or negative sequence
o
)rms(RR0VV
o
)rms(BB120VV
o
rmsY
ormsYY
V
V
120
240
)(
)(
V
VR leads VY, which in turn leads VB.This sequence is produced when the rotor rotates in
the clockwise direction.
V
120o
-120o120
o
VR
VB
Y
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Simulation of current flow in 3 phase system
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3 phase generator
http://localhost/var/www/apps/conversion/tmp/scratch_2/alternator1.swfhttp://localhost/var/www/apps/conversion/tmp/scratch_2/3phase.swf -
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Connection in Three Phase System Star and Delta
Star Connection ()
Also known as Y connection (wye)
Usually been used in system that needs high voltage and
low current
There are two types of Y connection, i.e:
i) 3 wire star connection
ii) 4 wire star connection
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R
Y
B
ZR
ZY ZB
3 wire star connection
Use 3 line wire, that are R, Y and B.
All of the conductor loop source is connected in similar reference
point S.
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R
Y
B
ZR
ZY ZB
Star/wye Connectiona)Three wire system
Voltage
source Load
No Neutral wire
E,N S
VRY
VYB
VBR
VRN
VYNVBN
VRS
VBSVYS
IR
IY
IB
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VRN
VBN
VYN
ZR
ZY ZB
R
B
NY
4 wire star connection
Use 4 line wire, that are R, Y , B and N.
N wire is connected to reference point S.
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Star Connection
b) Four wire system
VRN
VBN VYN
ZR
ZY ZB
R
BN
YNeutral wire
Voltage
source LoadVRY
VYB
VBR
VRN
VBNVYN
N
IR
IY
IB
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Star/wye connection of Load
Z1
Z3
Z2
R
B
Y
NLoad
Z3
Z1Z 2
R
Y
B
Load
N
or
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Delta Connection ()
Usually been used in system that need high line current and lowphase current.
Connect all the conductor in series.
No neutral line
Generator Load
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Delta Connection
R
Y
B
Y
B
R
Voltage
source
Load
VRY VBR
VYB
VRY
VBR
VYB
IYB
IRY
IBR
IRIR
IY
IY
IB
IB
IRY
IYB
IBR
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Delta connection of load
Zc
Za
Zb
R
B
Y
Load
Zc
Zb
Za
R
Y
B
Load
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Line Voltage (VL) : Potential different between two line.
Phase Voltage (Vph) : Potential different between two
phase or voltage across load in each phase.
Line Current (IL): Current flow in each line.
Phase Current (IPH): Current flow in each phase or load.
3 phase system definition
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Line Voltage
Potential between line to line, Star and
Delta
VRY
between line R and Y
VYB between line Y and B
VBR between line B and R
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Balance 3 phase systemIn balance three phase system:
The system will have same value of load in
each phase.
Each phase voltage will have same magnitude
and phase different 120.
Each phase current will have same magnitude
and phase different 120.
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Star connection
Line Voltage
VRY : Line voltage between R & Y
VYB : Line voltage between Y & B
VBR : Line voltage between B & R
Phase Voltage
VRN : Phase voltage R
VYN : Phase voltage Y
VBN : Phase voltage B
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Star connection
VRN is take as the reference point in positive rotation
120120
120120
00
PhBNBN
PhYNYN
PhRNRN
VVV
VVV
VVV
From Kirchhoff Law:
303
1201011200
Ph
Ph
PhPhYNRNRY
V
V
VVVVV
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Star connection
1503
903
PRNBNBR
PBNYNYB
VVVV
VVVV
As conclusion :
303 PLVV
For a balance star
connection.
Line voltage (VL) has magnitude 3 Vph and is leading phase voltage (VPH)
with 30.
With the same method ;
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Star connection
Phasor diagram for phase voltage and line voltage;
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Line Current = Phase Current
Current flow in each line is:
IR : Line current R.
IY: Line current Y.
IB: Line current B.
Phase current : Current that flow through each phase loop or
load.
For star connection;
Star connection
current)(Phasecurrent)(LinePLII
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Delta Connection
Line Voltage,
VRY
Voltage across conductor RR.VYB
Voltage across conductorYY.VBR
Voltage across conductorBB.
In delta connection, Line voltage is also thephase voltage , So:
voltage)(Phasevoltage)(LinePLVV
Delta Connection
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30
120120
120120
00
PBRBR
PYBYB
PRYRY
III
III
III
303
1200
:loadAt the
P
PP
BRRYR
I
II
III
Phase current , IRY, IYB dan IBR Current flow through each conductor loop in
each phase.And IRYalways be taken as the reference current, so ;
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903
1503
;Then
PYBBRB
PRYYBY
IIII
IIII
Line Current (IL) lagging current phase (IPH) with 30.Magnitude IL = 3 IPH.
303 PLII
For balance delta
connection
Conclusion :
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Delta Connection
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Example
A positive phase sequence three-phase
voltage source connected in a balanced Y has
a line voltage of VRY= 415 -45 Vrms.
Determine the phase voltage.
V(t) = Vmax sin (t 45o)
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Example
A balanced Y-connected load is supplied by a
balanced Y-connected source with a phase
voltage of VRN = 220 Vrms . If IR = 5 -30 A.
Determine the phase and line voltages, phaseand line currents. Subsequently, sketch
phasor diagram with positive sequence phase.
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A balanced -connected load issupplied by positive phase sequence
balanced three-phase -connected
source with VRY= 415 Vrms, If thecurrent flowing through phase RY, IRY
= 5 A, determine phase and line
voltages, phase and line currents.Hence sketch the phasor diagram.
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Example
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Balanced Load Connection in
3-Phase System
Balance Power Supply
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////// 321 ZZZ
321 ZZZ
Y Y connection
Y - connection
- connection - Y connection
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VRN
VBN
Z1
Z2 Z3
R
B
N
Y
VYN
IR
IY
IB
IN
BYRNIIII
For balanced load system,
IN = 0 and Z1 = Z2 = Z3
3
o
BN
B
2
o
YN
Y
1
o
RN
R
Z
120VI
Z
120VI
Z
0VI
BNYNRNphasa
phasaBN
phasaYN
phasaRN
VVVVwhere
120VV
120VV
0VV
Voltage and Current at Star Connected Balanced Loads
a)Four wire system
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Voltage and Current at Star Connected Balanced Loadsb) Three wire system
R
Y
B
Z1
Z 2 Z3
IR
IY
IB
VRY
VYB
VBR S
0IIIBYR
3
o
BS
B
2
o
YS
Y
1
o
RS
R
Z
120VI
Z
120VI
Z
0V
I
BSYSRSphasa
phasaBS
phasaYS
phasaRS
VVVVwhere
240VV
120VV
0VV
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Voltage and Current at Delta-Connected Balanced Loads
Z
Z
Z
R
Y
B
VRY
VYB
VBR
IR
IRY
IBR
IYB
IB
IY
Phase currents:
3
o
BR
BR
2
o
YB
YB
1
o
RY
RY
Z
120VI
Z
120VI
Z
0VI
Line currents:
YBBRB
RYYBY
BRRYR
III
III
III
lineBYR
phasaBRYBRY
IIIIand
IIIIwhere