Transcript phase current - Deeteekay Community

ELECTRICAL CIRCUIT
ET 201
 Become familiar with the operation of a
three phase generator and the
magnitude and phase relationship.
 Be able to calculate the voltages and
currents for a three phase Wye and
Delta connected generator and load.
1
THREE PHASE
SYSTEMS
2
23.1 – Introduction
If the number of coils on the rotor is increased
in a specified manner, the result is a
polyphase ac generator, which develops
more than one ac phase voltage per rotation of
the rotor
An ac generator designed to develop a single
sinusoidal voltage for each rotation of the shaft
(rotor) is referred to as a single-phase ac
generator
In general, three-phase systems are preferred
over single-phase systems for the transmission
of power for many reasons, including the
following:
3
Introduction
1. Thinner conductors can be used to transmit the same
kVA at the same voltage, which reduces the amount of
copper required (typically about 25% less) and in turn
reduces construction and maintenance costs.
2. The lighter lines are easier to install, and the
supporting structures can be less massive and farther
apart.
3. Three-phase equipment and motors have preferred
running and starting characteristics compared to
single-phase systems because of a more even flow of
power to the transducer than can be delivered with a
single-phase supply.
4. In general, most larger motors are three phase
because they are essentially self-starting and do not
require a special design or additional starting circuitry.4
Introduction
The frequency generated is determined by the
number of poles on the rotor (the rotating part
of the generator) and the speed with which the
shaft is turned.
Throughout the United States the line frequency
is 60 Hz, whereas in Europe (incl. Malaysia) the
chosen standard is 50 Hz.
On aircraft and ships the demand levels permit
the use of a 400 Hz line frequency.
The three-phase system is used by almost all
commercial electric generators.
5
Introduction
 Most small emergency generators, such as the
gasoline type, are one-phased generating systems.
 The two-phase system is commonly used in
servomechanisms, which are self-correcting control
systems capable of detecting and adjusting their
own operation.
 Servomechanisms are used in ships and aircraft to
keep them on course automatically, or, in simpler
devices such as a thermostatic circuit, to regulate
heat output.
 The number of phase voltages that can be
produced by a polyphase generator is not limited to
three. Any number of phases can be obtained by
spacing the windings for each phase at the proper
angular position around the stator.
6
23.2 – Three-Phase Generator
The three-phase generator has three induction
coils placed 120° apart on the stator.
The three coils have an equal number of turns,
the voltage induced across each coil will have the
same peak value, shape and frequency.
7
Three-Phase Generator
At any instant of time, the algebraic sum of
the three phase voltages of a three-phase
generator is zero.
8
Three-Phase Generator
The sinusoidal expression for each of the
induced voltage is:
9
Phase expression
• In phase expression:
EM
EA 
0
2
EB 
EM
2
  120
EC 
EM
2
120
• Where:
EM
: peak value
EA, EB and EC : rms value
10
Connection in Three Phase System
•
A 3-phase system is equivalent to three
single phase circuit
• Two possible configurations in three
phase system:
1. Y-connection (star connection)
2. ∆-connection (delta connection)
11
Three-phase Voltages Source
Y-connected source
∆-connected source
12
Three-phase Load
Y-connected load
∆-connected load
13
23.3 – Y-Connected Generator
If the three terminals denoted N are connected
together, the generator is referred to as a Yconnected three-phase generator.
14
Y-Connected Generator

The point at which all the terminals are connected is
called the neutral point.

1.
Two type of Y-connected generator:
Y-connected, three-phase, three-wire generator
(a conductor is not attached from this point to the load)
Y-connected, three-phase, four-wire generator
(the neutral is connected)
2.

The three conductors connected from A, B and C to the
load are called lines.
15
Y-connected, 3-phase, 3-wire
generator
16
Y-connected, 3-phase, 4-wire
generator
17
Y-Connected Generator
The voltage from one line to another is called
a line voltage
The magnitude of the line voltage of a
Y-connected generator is:
18
Definition of Phase Voltage
• In 3-phase system, for Y-connected, the voltage
from line to neutral point is called a
phase voltage.
EAN – phase A voltage
EBN – phase B voltage
ECN – phase C voltage
19
Definition of Line Voltage
• In 3-phase system, for Y-connected, the voltage
from one line to another is called a
line voltage.
EAB – voltage between
line A and B
EBC – voltage between
line B and C
ECA – voltage between
line C and A
20
Y-connected system
• Line voltage:
VAB ; VBC ; VCA
• Phase voltage:
VAN ; VBN ; VCN
21
Voltage in Y-connected system
For 3-phase Y-connected system, if the phase
voltage VAN is taken as the reference, so
VAN  VAN 0
VBN  VBN   120
VCN  VCN 120
22
Voltage in Y-connected system
• By applying Kirchhoff’s Voltage Law, the line
voltage can be written as
VAB  VAN  VBN
 VAN0  VBN   120
 VAN (10  1  120)
 VAN ((1  j0)  (0.5  j0.866))
 VAN (1.5  j0.866)
 VAN (1.73230)
VAB  3VAN30
23
Voltage in Y-connected system
• With the same method,
VBC  VBN  VCN
 3VBN   90
and
VCA  VCN  VAN
 3VCN 150
• The relationship between the line voltage and
the phase voltage can be represented as
VL  3Vφ30
VL : line voltage
Vφ : phase voltage
24
Current in Y-connected system
• For the Y-connected system, it should be
obvious that the line current equals the phase
current for each phase; that is
IL  Iφ
IL : line current
Iφ : phase current
25
23.4 – Phase Sequence
(Y-Connected Generator)
 The phase sequence can be determined by the
order in which the phasors representing the phase
voltages pass through a fixed point on the phasor
diagram if the phasors are rotated in a
counterclockwise direction.
26
3.4 – Phase Sequence
(Y-Connected Generator)
In phasor notation,
Line voltage:
VAB  VAB0 (reference )
VBC  VBC   120
VCA  VCA 120
VAN  VAN 0 (reference )
Phase voltage:
VBN  VBN   120
VCN  VCN 120
27
23.5 – Y-Connected Generator
with a Y-Connected Load
 Loads connected with three-phase supplies are of two
types: the Y and the ∆.
 If a Y-connected load is connected to a Y-connected
generator, the system is symbolically represented by Y-Y.
28
Y-Connected Generator with a YConnected Load
 If the load is balanced, the neutral connection can be
removed without affecting the circuit in any manner; that
is, if Z1 = Z2 = Z3 , then IN will be zero, IN = 0 .
 Since IL = V / Z the magnitude of the current in each
phase will be equal for a balanced load and unequal for
an unbalanced load. In either case, the line voltage is
29
EXAMPLE 1
• Calculate the line currents in the three-wire Y-Y
system as shown below.
30
Solution:
Single Phase Equivalent Circuit
Phase ‘a’ equivalent circuit
31
I Aa
VAN

; ZT  (5  j 2)  (10  j8)  16.15521.8
ZT
I Aa
1100

 6.81  21.8
16.15521.8
I Bb  I Aa   120
 6.81  141.8A
I Cc  I Aa   240
 6.81  261.8  6.8198.2A
32
23.6 – Y-Connected Generator
with a ∆-Connected Load
 There is no neutral connection for the Y-∆ system
shown below.
 Any variation in the impedance of a phase that
produces an unbalanced system will simply vary the
line and phase currents of the system.
33
Y-Connected Generator with a
∆-Connected Load
 For a balanced load, Z1 = Z2 = Z3.
 The voltage across each phase of the load is equal to the line
voltage of the generator for a balanced or an unbalanced
load: V = EL.
34
Y-Connected Generator with a
∆-Connected Load
 Kirchhoff’s current law is employed instead of Kirchhoff’s
voltage law.
The results obtained are:
 The phase angle between a line current and the nearest
phase current is 30°.
35
EXAMPLE 2
A balanced positive sequence Yconnected source with
VAN=10010 V is connected to a
-connected balanced load
(8+j4)  per phase. Calculate the
phase and line currents.
36
Solution:
Balanced WYE source, VAN = 10010 V
Balanced DELTA load, Z = 8 + j4 
Phase and line currents = ??
37
Phase Currents
Vab
I ab 
ZΔ
Vab= voltage across Z
= VAB= source line voltage
 VAB  3 VAN30
Vab  173.240 V
173.240
 I ab 
 19.3613.43 A
8  j4
38
Phase Currents
I ab  19.3613.43 A
 I bc  I ab 13.43  120
I bc  19.36  106.57 A
 I ca  19.3613.43  120
I ca  19.36133.43 A
39
Line Currents
I Aa  3 I ab   30
 3 (19.36) 13.43  30
I Aa  33.53   16.57 A
 I Bb  I Aa   120  33.53   136.57 A
 I Cc  I Aa   120  33.53 103.43 A
40
23.7 – ∆-Connected Generator
In the figure below, if we rearrange the coils of
the generator in (a) as shown in (b), the system
is referred to as a three-phase, three-wire.
41
∆-Connected Generator
∆-connected ac generator
In this system, the phase and line voltages are
equivalent and equal to the voltage induced
across each coil of the generator:
E AB  E AN and e AN  2 E AN sin t
EBC  EBN and eBN  2 EBN sin( t  120)
ECA  ECN and eCN  2 ECN sin( t  120)
or
EL = Eg
Only one voltage (magnitude) is available instead
of the two in the Y-Connected system.
42
∆-Connected Generator
 Unlike the line current for the Y-connected generator, the
line current for the ∆-connected system is not equal to the
phase current. The relationship between the two can be
found by applying Kirchhoff’s current law at one of the
nodes and solving for the line current in terms of the phase
current; that is, at node A,
IBA = IAa + IAC
or
IAa = IBA - IAC = IBA + ICA
43
∆-Connected Generator
The phasor diagram is shown below for a
balanced load.
In general, line current is:
44
Definition of Phase Current
• In 3-phase system, for ∆-connected, the current
that flow from one phase to another is called a
phase current.
IBA – phase A current
ICB – phase B current
IAC – phase C current
45
Definition of Line Current
• In 3-phase system, for ∆-connected, the current
that flow through the line is called a line current.
IAa – line A current
IBb – line B current
ICc – line C current
46
∆-connected system (generator)
• Line current:
IAa ; IBb ; ICc
• Phase current:
for generator:
IBA ; IAC ; ICB
47
∆-connected system (load)
• Line current:
IAa ; IBb ; ICc
• Phase current:
for load:
Iab ; Ibc ; Ica
48
Current in ∆-connected system
(Generator side)
For 3-phase ∆-connected system (generator), if
the phase current IBA is taken as the reference,
so
IBA  IBA 0
I CB  ICB   120
I AC  I AC120
49
Current in ∆-connected system
(Generator side)
• By applying Kirchhoff’s Current Law, the
line current can be written as
I Aa  I BA  I AC
 I BA 0  I BA 120
 I BA (10  1120)
 I BA (1  j0  (0.5  j0.866))
 I BA (1.5  j0.866)
 I BA (1.732  30)
I Aa  3I BA   30 A
50
Current in ∆-connected system
(Generator side)
• With the same method,
I Bb  I CB  I BA
 3I CB   150
and
I Cc  I AC  I CB
 3I AC90
51
Current in ∆-connected system
(Load side)
For 3-phase ∆-connected system (load), if the
phase current Iab is taken as the reference, so
Iab  Iab 0
I bc  I bc  120
Ica  Ica 120
52
Current in ∆-connected system
(Load side)
• By applying Kirchhoff’s Current Law, the
line current can be written as
I Aa  I ab  I ca
 I ab 0  I ab 120
 I ab (10  1120)
 I ab (1  j0  (0.5  j0.866))
 I ab (1.5  j0.866)
 I ab (1.732  30)
I Aa  3Iab   30 A
53
Current in ∆-connected system
(Load side)
• With the same method,
I Bb  I bc  I ab
 3I bc  150
and
I Cc  I ca  I bc
 3I ca 90
54
Relationship between the phase
current and the line current
(∆-connected system)
• The relationship between the line current and
the phase current can be represented as
I L  3Iφ  30
Where;
IL : line current
Iφ : phase current
55
Voltage in ∆-connected system
• For the ∆-connected system, it should be
obvious that the line voltage equals the phase
voltage for each phase; that is
VL  Vφ
VL : line voltage
V : phase voltage
56
23.8 – Phase Sequence (∆- Connected
Generator)
 Even though the line and phase voltages of a ∆ connected system are the same, it is standard
practice to describe the phase sequence in terms of
the line voltages
 In drawing such a diagram, one must take care to
have the sequence of the first and second
subscripts the same
 In phasor notation,
VAB = VAB 0o
VBC = VBC 120o
VCA = VCA 120o
57
23.9 - ∆-Connected Generator with
a ∆-Connected Load
58
EXAMPLE 3
A balanced delta connected load
having an impedance 20 - j15  is
connected to a delta connected,
positive sequence generator having
VAB = 3300 V. Calculate the phase
currents of the load and the line
currents.
59
Solution:
 ZΔ  20  j15   25  36.87
 VAB  3300 V
60
Phase Currents
Vab
3300
I ab 

 13.236.87A
ZΔ 25  38.87
I bc  I ab   120  13.2 - 83.13A
I ca  I ab   120  13.2156.87A
61
Line Currents
I Aa  I ab 3  30

 13.236.87 3  30
 22.866.87 A

I Bb  I Aa   120  22.86 - 113.13 A
I Cc  I Aa   120  22.86126.87 A
62
23.9 - ∆-Connected Generator with
a Y-Connected Load
63
EXAMPLE 4
• A balanced Y-connected load with a
phase impedance 40 + j25  is supplied
by a balanced, positive-sequence Δconnected source with a line voltage of
210 V. Calculate the phase currents.
Use VAB as reference.
64
Solution:
• the load impedance, ZY and the source voltage, VAB are
 ZY  40  j25  47.1732 
 VAB  2100 V
65
Solution:
• When the ∆-connected source is transformed to
a Y-connected source,
VAB
Van 
  30
3
2100

 1  30
3
 121.2 - 30 V
66
Solution:
• The line currents are
I Aa
Van 121.2  30


 2.57 - 62 A
ZY
47.1732
I Bb  I Aa   120  2.57 - 182 A
I Cc  I Aa   120  2.5758 A
67
Summary of Relationships in
Y and ∆-connections
Y-connection
Voltage
VL  3Vφ
magnitudes
Current
IL  Iφ
magnitudes
VL leads Vφ by 30°
Phase
sequence
∆-connection
VL  Vφ
I L  3I φ
IL lags Iφ by 30°
68