lec09 three phase
TRANSCRIPT
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THREE PHASE
CIRCUIT
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Objectives
Explain the differences between single-phase, two-phase and three-phase.
Compute and define the Balanced Three-
Phasevoltages. Determine the phase and line
voltages/currents for Three-Phase
systems.
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SINGLE PHASE TWO WIRE
pV
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SINGLE PHASE SYSTEM
A generator connected through a pairof wire to a loadSingle Phase TwoWire.
Vpis the magnitude of the sourcevoltage, and is the phase.
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SINLGE PHASE THREE WIRE
pV
pV
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SINGLE PHASE SYSTEM
Most common in practice: twoidentical sources connected to twoloads by two outer wires and the
neutral: Single Phase Three Wire. Terminal voltages have same
magnitude and the same phase.
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POLYPHASE SYSTEM
Circuit or system in which ACsources operate at the same
frequency but different phasesare known as polyphase.
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TWO PHASE SYSTEM THREE WIRE
pV
90pV
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POLYPHASE SYSTEM
Two Phase System:A generator consists of two coils placed
perpendicular to each other
The voltage generated by one lags theother by 90.
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POLYPHASE SYSTEM
Three Phase System:A generator consists of three coils placed
120apart.
The voltage generated are equal inmagnitude but, out of phase by 120.
Three phase is the most economical
polyphase system.
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IMPORTANCE OF THREE PHASE SYSTEM
All electric power is generated anddistributed in three phase.
One phase, two phase, or more than
three phase input can be taken fromthree phase system rather thangenerated independently.
Melting purposes need 48 phasessupply.
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IMPORTANCE OF THREE PHASE SYSTEM
Uniform power transmission and lessvibration of three phase machines.
The instantaneous power in a 3system
can be constant (not pulsating). High power motors prefer a steady
torque especially one created by a
rotating magnetic field.
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IMPORTANCE OF THREE PHASE SYSTEM
Three phase system is moreeconomical than the single phase.
The amount of wire required for a three
phase system is less than required for anequivalent single phase system.
Conductor: Copper, Aluminum, etc
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THREE PHASE GENERATION
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FARADAYS LAW
Three things must be present inorder to produce electrical current:a) Magnetic field
b) Conductorc) Relative motion
Conductor cuts lines of magnetic
flux, a voltage is induced in theconductor
Direction and Speed are important
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GENERATING A SINGLE PHASE
Motion is parallel to the flux.
No voltage is induced.
N
S
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N
S
Motion is 45to flux.
Induced voltage is 0.707 of maximum.
GENERATING A SINGLE PHASE
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GENERATING A SINGLE PHASE
x
N
S
Motion is perpendicular to flux.
Induced voltage is maximum.
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GENERATING A SINGLE PHASE
Motion is 45to flux.
N
S
Induced voltage is 0.707 of maximum.
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GENERATING A SINGLE PHASE
N
S
Motion is parallel to flux.
No voltage is induced.
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GENERATING A SINGLE PHASE
N
S
Notice current in the
conductor has reversed.
Inducedvoltage is
0.707 of maximum.
Motion is 45to flux.
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GENERATING A SINGLE PHASE
N
S
Motion is perpendicular to flux.
Induced voltage is maximum.
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GENERATING A SINGLE PHASE
N
S
Motion is 45to flux.
Induced voltage is 0.707 of maximum.
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GENERATING A SINGLE PHASE
Motion is parallel to flux.N
S
No voltage is induced.
Ready to produce another cycle.
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THREE PHASE GENERATOR
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As the rotor rotates, its magnetic fieldcuts the flux from the three coils andinduces voltages in the coils.
The induced voltage have equalmagnitude but out of phase by 120.
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GENERATION OF THREE-PHASE AC
N
xx
S
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THREE-PHASE WAVEFORM
Phase 2lags phase 1by 120 Phase 2leads phase 3by 120
Phase 3lags phase 1by 240
Phase 1leads phase 3by 240
Phase 1 Phase 2 Phase 3
120 120 120
240
120 120 120
240
GENERATION OF 3 VOLTAGES
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Phase 1Phase 2Phase 3
GENERATION OF 3VOLTAGES
Phase 1is ready to go positive.
Phase 2is going more negative.
Phase 3is going less positive.
N
xx
S
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THREE PHASE QUANTITIES
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BALANCED 3VOLTAGES
120cos240cos)(
120cos)(
cos)(
tVtVtv
tVtv
tVtv
MMcn
Mbn
Man
Balanced three phase voltages: same magnitude (VM )
120phase shift
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BALANCED 3CURRENTS
Balanced three phase currents: same magnitude (IM )
120phase shift
240cos)(
120cos)(
cos)(
tIti
tIti
tIti
Mc
Mb
Ma
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PHASE SEQUENCE
120cos)(
120cos)(
cos)(
tVtv
tVtv
tVtv
Mcn
Mbn
Man
120
120
0
Mcn
Mbn
Man
VV
VV
VV
120
120
0
Mcn
Mbn
Man
VV
VV
VV
POSITIVESEQUENCE
NEGATIVESEQUENCE
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PHASE SEQUENCE
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EXAMPLE # 1
Determine the phase sequence ofthe set voltages:
110cos200
230cos200
10cos200
tv
tv
tv
cn
bn
an
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BALANCED VOLTAGE AND LOAD
Balanced Phase Voltage: all phasevoltages are equal in magnitude andare out of phase with each other by
120. Balanced Load: the phase
impedances are equal in magnitude
and in phase.
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THREE PH SE CIRCUIT
POWERThe instantaneous power is constant
)cos(3
cos2
3
)()()()(
rmsrms
MM
cba
IV
IVtptptptp
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THREE PH SE CIRCUIT
Three Phase Power,
SSSSS
3
CBAT
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THREE PHASE QUANTITIES
QUANTITY SYMBOL
Phase current I
Line current IL
Phase voltage V
Line voltage VL
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PHASE CURRENTS and LINE CURRENTS
Line current (IL) is the current ineach lineof the source or load.
Phase current (I) is the current ineach phaseof the source or load.
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THREE PHASE CONNECTION
SO C O CO C O
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SOURCE-LOAD CONNECTION
SOURCE LOAD CONNECTION
Wye Wye Y-Y
Wye Delta Y-
Delta Delta -
Delta Wye -Y
SOURCE LOAD CONNECTION
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SOURCE-LOAD CONNECTION
Common connection of source:WYEDelta connected sources: the
circulating current may result in the
delta mesh if the three phase voltagesare slightly unbalanced.
Common connection of load:DELTA
Wye connected load: neutral line maynot be accessible, load can not beadded or removed easily.
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WYE CONNECTION
WYE CONNECTED GENERATOR
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WYE CONNECTED GENERATOR
n
a
b
c
Vab
Vbc
Vca
Vbn
Vcn
Van
Ia
Ib
Ic
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WYE CONNECTED LO D
ZY
ZY
ZY
a
c
b
nLoad
ZY
ZYZ Y
a
b
c
Load
n
OR
BALANCED Y Y CONNECTION
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BALANCED Y-Y CONNECTION
PHASE CURRENTS AND LINE CURRENTS
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PHASE CURRENTS AND LINE CURRENTS
In Y-Y system:
L II
PHASE VOLTAGES V
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PHASE VOLTAGES, V
Phase voltage ismeasured betweenthe neutral and anyline: line to neutralvoltage
n
a
b
c
Vab
Vbc
Vca
Vbn
Vcn
Van
Ia
Ib
Ic
Van
Vbn
Vcn
PHASE VOLTAGES V
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PHASE VOLTAGES, V
an M
bn M
cn M
V V 0 volt
V V 120 volt
V V 120 volt
LINE VOLTAGES V
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LINE VOLTAGES, VL
Line voltage ismeasured between
any two of the threelines: line to linevoltage.
n
a
b
c
Vab
Vbc
Vca
Vbn
Vcn
Van
Ia
Ib
Ic
Vab
Vbc
Vca
LINE VOLTAGES V
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LINE VOLTAGES, VL
ancnca
cnbnbc
bnanab
VVV
VVV
VVV
150V3V
90V3V
30V3V
Mca
Mbc
Mab
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PROPERTIES OF PHASE VOLTAGE
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PROPERTIES OF PHASE VOLTAGE
All phase voltages have the samemagnitude,
Out of phase with each other by 120
an bn cnV V V V = =
PROPERTIES OF LINE VOLTAGE
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PROPERTIES OF LINE VOLTAGE
All line voltages have the samemagnitude,
Out of phase with each other by 120
ab bc caV V V VL = =
RELATIONSHIP BETWEEN V and V
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RELATIONSHIP BETWEEN Vand VL
1. Magnitude
2. Phase
-VLLEADtheir corresponding Vby 30
LV 3 V
30VVL
EXAMPLE 1
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EXAMPLE 1
Calculate the line currents
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DELTA CONNECTION
DELTA CONNECTED SOURCES
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DELTA CONNECTED SOURCES
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DELT CONNECTED LO D
OR
BALANCED CONNECTION
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BALANCED-CONNECTION
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PHASE VOLTAGE V
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PHASE VOLTAGE, V Phase voltages are equal to the
voltages across the load impedances.
PHASE CURRENTS I
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PHASE CURRENTS, I
The phase currents are obtained:
CA
CA
BC
BC
AB
AB Z
V
I,Z
V
I,Z
V
I
LINE CURRENTS I
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LINE CURRENTS, IL
The line currents are obtained from thephase currents by applying KCL atnodes A,B, and C.
LINE CURRENTS I
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LINE CURRENTS, IL
BCCAc
ABBCb
CAABa
III
III
III
120II
120II
30I3I
ac
ab
ABa
PHASE
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PHASE
CURRENTS (I
)
LINE CURRENTS (IL)
CACA
BCBC
ABAB
Z
VI
Z
VI
Z
VI
120II
120II
30I3I
ac
ab
ABa
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PH SE DI GR M OF I
L
ND I
PROPERTIES OF PHASE CURRENT
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PROPERTIES OF PHASE CURRENT
All phase currents have the samemagnitude,
Out of phase with each other by 120
CABCABZVIIII
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RELATIONSHIP BETWEEN I and I
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1. Magnitude
2. Phase
- ILLAGtheir corresponding Iby 30
IIL 3
RELATIONSHIP BETWEEN Iand IL
30IIL
EXAMPLE
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EXAMPLE
A balanced delta connected load havingan impedance 20-j15 is connected toa delta connected, positive sequence
generator havingVab= 3300V.Calculate the phase currents of the loadand the line currents.
Given Quantities
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Given Quantities
0330V
87.3625j1520Z
ab
Phase Currents
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Phase Currents
A87.15613.2120II
A13.83-13.2120II
A36.8713.236.8725
0330ZVI
ABCA
ABBC
ABAB
Line Currents
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A87.12686.22120II
A13.311-86.22120II
87.686.22
A30336.8713.2
303II
ac
ab
ABa
Line Currents
BALANCED WYE-DELTASYSTEM
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BALANCED WYE-DELTASYSTEM
EXAMPLE 2
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EXAMPLE 2
A balanced positive sequence Y-connected source withVan=10010Vis connected to a -connected
balanced load (8+j4)per phase.Calculate the phase and line currents.
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THREE PH SE POWER
ME SUREMENT
EXAMPLE 3
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EXAMPLE 3
Determine the total power (P), reactive
power (Q), and complex power (S) at thesource and at the load
EXAMPLE #4
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EXAMPLE #4
A three phase motor can beregarded as a balanced Y-load. Athree phase motor draws 5.6 kW
when the line voltage is 220 Vandthe line current is 18.2 A. Determinethe power factor of the motor