Magnetically Coupled Circuits XIII.Frequency Response. XIV.The Laplace Transform XV.[r]
(1)Electric Circuit Theory
(2)Three-phase Circuits - sites.google.com/site/ncpdhbkhn
Contents
I. Basic Elements Of Electrical Circuits II. Basic Laws
III Electrical Circuit Analysis IV Circuit Theorems
V Active Circuits
VI Capacitor And Inductor VII First Order Circuits VIII.Second Order Circuits
IX Sinusoidal Steady State Analysis X AC Power Analysis
XI Three-phase Circuits
XII Magnetically Coupled Circuits XIII.Frequency Response
(3)Three-phase Circuits 1 Introduction
2 Three-phase Source 3 Three-phase Load
(4)Introduction (1) • Polyphase:
– Phase: branch, circuit or winding – Poly: many
• Three-phase: three phases • Advantages:
– Machine: less space & less cost
– Transmission & distribution: less conducting material – Power delivered to a three-phase load is always constant – Single phase source from three-phase source
(5)Three-phase Source (1)
t vAA’ vBB’ vCC’
' sin
AA m
v =V ωt
o ' sin( 120 )
BB m
v =V ωt −
o ' sin( 120 )
CC m
v =V ωt +
Stator
A
A’
B’ B
C C’
(6)Three-phase Source (2)
Three-phase Circuits - sites.google.com/site/ncpdhbkhn
t vAA’ vBB’ vCC’
' sin
AA m
v =V ωt
o ' sin( 120 )
BB m
v =V ωt −
o ' sin( 120 )
CC m
v =V ωt +
' ' '
o o o o
o
(sin sin cos120 cos sin120 sin cos120 cos sin120 ) (sin 2 sin cos120 )
1
sin 2sin 0
2
AA BB CC
m
m
m
v v v
V t t t t t
V t t
V t t
ω ω ω ω ω ω ω ω ω + + = = + − + + = + − = + =
' ' ' 0
AA BB CC
v + v + v =
(7)Three-phase Source (3)
t vAA’ vBB’ vCC’
' sin
AA m
v =V ωt
o ' sin( 120 )
BB m
v =V ωt −
o ' sin( 120 )
CC m
v =V ωt +
' ' ' 0
AA BB CC
v + v + v =
'
AA
V
'
BB
V
120o
120o 120o
ω
'
CC
V Symmetrical (balanced) Three-phase Source:
- Same magnitude - Same frequency
(8)Three-phase Source (4)
Three-phase Circuits - sites.google.com/site/ncpdhbkhn
A A’
B’
B C
C’
Load C
Load A
Load B
A
A’ B’
B C
C’ N
Star connection
A A’
B’
B
C
C’
(9)Three-phase Source (5) A
A’ B’
B C
C’ N
A
B
C
A A’
B’
B
C
C’
A
B
(10)Three-phase Source (6)
Three-phase Circuits - sites.google.com/site/ncpdhbkhn 10
vAB, vBC, vCA: line voltages
iA, iB, iC: line currents/phase currents
A B C N vAB vBC vCA iA iB iC vA vB vC
vA, vB, vC: phase voltages
A A’ B’ B C C’ vA vB vC iC iA iB iBC iCA iAB
vA, vB, vC: line voltages/phase voltages
iA, iB, iC: phase currents