electrical machines 1...course ilos 1. describe the construction of the transformers. 2. explain the...
TRANSCRIPT
ELECTRICAL MACHINES 1 EPMN301
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Course Grading System
Marks
Final Exam Semester Work- 20 Mid-term- 15 Quizzes
- 15 Assignments- 10 Lab
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Course Schedule
Lecture: Sunday 11:00 - 1:00 (9301) Tutorial: Sunday 4:00-7:00 pm (9301) Office Hours: Tuesday & Wednesday 11-12 Quizzes: W2-W4-W6-W10-W12 Assignments: W3-W5-W11-W14 Lab: W9-W13 Mid-term: W8 Email: [email protected] Scholar page: https://goo.gl/pkSTxw
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Course ILOs
1. Describe the construction of the transformers.
2. Explain the theory of operation of the transformers.
3. Calculate the parameters of the transformers using the different tests.
4. Predict the performance of the transformers.
5. Discriminate between the construction and applications of special transformers.
6. Identify the general constructional features of DC machines.
7. Formulate the EMF and torque equations of DC machine.
8. Analyze the operation of different types of DC motors and generators.
9. Asses the performance of different types of DC motors.
10. Implement different methods of, starting, speed control and braking of DC motors.
11. Work effectively as a team member.
12. Use practical work in laboratory.
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References
A.E. Fitzgerald & Charles Kingsley, Electric Machinery, 7th Edition.
Stephan J. Chapman, Electric Machinery Fundamentals, 5th Edition.
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Course Contents
Revision: Basic Principles Transformers:o Construction, theory of operation & Equivalent circuit. o Per-Unit System, Tests, Efficiency & Regulation.o Special Transformers.o Three-phase transformers & Parallel operation.
DC Machines:o DC Machines fundamentalso EMF & Torque Equationso Types of DC Generators & DC Motorso Equivalent circuito External Characteristics of DC Machineso Starting & Speed control of DC Motors
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Revision: Basic Principles
AC Circuits Three-phase Circuits
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Revision: Basic Principles
Phasor Representation
1 sin( )mv V tω=
2 sin( )m ov V tω θ= +
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Revision: Basic Principles
Phasor Representation
1 0rmsV V= ∠
2 rms oV V θ= ∠
2m
rmsVV =
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Revision: Basic Principles
Phasor Representation
1V
2V
Phasor Diagram
1 1 0V V= ∠
2 2 oV V θ= ∠ oθ
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Revision: Basic Principles
Phasor Representation
1V
2V
1 2TV V V= +
oθ
1V
TV
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Revision: Basic Principles
Phasor Representation
oV V θ= ∠
V A jB= +
Polar form
Rectangular form
V
oθx
y
cos oA V θ=
sin oB V θ=
Real
Img
1tanoBA
θ −=
2 2V A B= +ojV V e θ=
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Revision: Basic Principles
Phasor Representation
1 1 1V A jB= + 2 2 2V A jB= +
1 2TV V V= ±
1 2 1 2( ) ( )TV A A j B B= ± + ± T T TV V θ= ∠
2 21 2 1 2( ) ( )TV A A B B= ± + ± 1 1 2
1 2
tanTB BA A
θ − ±=
±
1 1 1V V θ= ∠ 2 2 2V V θ= ∠
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Revision: Basic Principles
Phasor Representation
1 1 1V A jB= + 2 2 2V A jB= +
1 2TV V V= ×
1 1 2 2[ ] [ ]TV V or Vθ θ= ∠ × ÷ ∠
T T TV V θ= ∠
1 1 1V V θ= ∠ 2 2 2V V θ= ∠
1 2 1 2TV V or V θ θ= × ÷ ∠ ±
1 2TV V or V= × ÷
1 2Tθ θ θ= ±
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Revision: Basic Principles
Loads: R-L Load
V I(R j L)ω= +
LV I(R j X )= +
V IZ= Impedance
LZ R j X Z Φ= + = ∠
1tan LRω−Φ =2 2
LZ R X= +
V 0 VIZ Z
ΦΦ
∠= = ∠−
∠current lags voltage
VΦ
I
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Revision: Basic Principles
Loads: R-L Load
RV IR=
V IZ=
L LV IX=Φ
R
ZLX
Φ
I×
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Revision: Basic Principles
Loads: R-C Load
1V I(R j )Cω
= −
CV I(R j X )= −
CZ R j X Z Φ= − = ∠−
1 1/tan CRω−Φ =
2 2CZ R X= +
V 0 VIZ Z
ΦΦ
∠= = ∠
∠−current leads voltage
VΦ
I
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Revision: Basic Principles
Loads: R-C Load
RV IR=
V IZ=C CV IX=
Φ
R
Z CXΦ I×
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Revision: Basic Principles
Loads: R-L-C Load
L CV I [R j( X X )]= + −
L CZ R j( X X ) Z Φ= + − = ∠
1tan L CX XR
− −Φ =2 2
L CZ R ( X X )= + −L CX X> veΦ = +
L CX X< veΦ = −V 0 VI
Z ZΦ
Φ∠
= = ∠∠±
inductive load
capacitive load
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Revision: Basic Principles
Loads
inductive load capacitive load
Pure inductive load Pure capacitive load
L CX X>
L CX X<
inductive load
capacitive load
Resistive load
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Revision: Basic Principles
AC Power
p( t ) v( t ) i( t )= ×
( ) 2 sin( )v t V tω=
( ) 2 sin( )i t I tω= ±Φ
( ) [cos( ) cos(2 )]p t VI tω= Φ − ±Φ
cosavgP VI= Φ Active Power (W)
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Revision: Basic Principles
Active and Reactive Power
( ) [cos( ) cos(2 )]p t VI tω= Φ − ±Φ
For pure resistive load:
0Φ =
( ) [1 cos(2 )]p t VI tω= −
avgP VI=
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Revision: Basic Principles
Active and Reactive Power
For pure inductive load:
90oΦ = −
( ) cos(2 90 )op t VI tω= −
( ) sin(2 )p t VI tω=
avgP zero=
( ) [cos( ) cos(2 )]p t VI tω= Φ − ±Φ
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Revision: Basic Principles
Active and Reactive Power
For pure capacitive load:
90oΦ =
( ) cos(2 90 )op t VI tω= +
( ) sin(2 )p t VI tω= −
avgP zero=
( ) [cos( ) cos(2 )]p t VI tω= Φ − ±Φ
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Revision: Basic Principles
AC Power: Inductive Load
2 cosP I R VI= = Φ
2S VI I Z= =2 sinL LQ I X VI= = Φ
Φ
RV IR=
V IZ=L LV IX=
Φ
Apparent Power (VA)
Active Power (W)
Reactive Power (VAR)
I×
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Revision: Basic Principles
AC Power: Capacitive Load
RV IR=
V IZ= C CV IX=ΦΦ
2 cosP I R VI= = Φ
2S VI I Z= =
2 sinC CQ I X VI= = Φ
Apparent Power (VA)
Active Power (W)
Reactive Power (VAR)
I×
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Revision: Basic Principles
Complex Power & Power Factor
Φ
*S P jQ VI= ± =
Leading Load
* *( )I I I= ∠ Φ = ∠±Φ
Lagging Load
S
P
QΦ
QS
Pcos sinS VI jVIφ φ= ±
cosPpower factorS
= = Φ
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Revision: Basic Principles
PPower FactorS
=
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Revision: Basic Principles29
Revision: Basic Principles
sin( )mv V tω=
2 Tπ ω=2T πω
= (sec)
3-phase AC Supply
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The three-phases are called: A-B-C or R-S-T or R-Y-B
Balanced 3-phase supply: the three voltages are equal in magnitude and are 120o out of phase.
sin( )a mv V tω=
sin( 120 )ob mv V tω= −
sin( 240 )oc mv V tω= −
sin( 120 )oc mv V tω= +
0aV V= ∠
120bV V= ∠−
120cV V= ∠
Revision: Basic Principles31
Revision: Basic Principles
A-B-C A-C-B
Positive sequence Negative sequence
0aV V= ∠
120bV V= ∠−
120cV V= ∠
0aV V= ∠
120bV V= ∠
120cV V= ∠−
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Revision: Basic Principles
abV
bcV
caVanV
bnV
cnV
Line-to-neutral
Line-to-line
ab an bnV V V= − bc bn cnV V V= − ca cn anV V V= −
0anV V= ∠
120bnV V= ∠−
120cnV V= ∠
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3 30ab an bnV V V V= − = ∠
3 90bc bn cnV V V V= − = ∠−
3 150ca cn anV V V V= − = ∠
3 ( 30)LL LnV V θ= ∠ +
Revision: Basic Principles34
Revision: Basic Principles
abV
bcV
caVLine-to-line
0abV V= ∠ 120bcV V= ∠− 120caV V= ∠
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Revision: Basic Principles
Balanced Star Load (ZA = ZB = ZC)
abV
bcV
caV anV
bnV
cnV
aI
bI
cI
ab bc ca LV V V V= = = an bn cnV V V Vφ= = =3LVVφ =
a b c LI I I I= = = an bn cnI I I Iφ= = =LI Iφ =
VI
Zφ
φφ
=
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Revision: Basic Principles
Balanced Delta Load (ZA = ZB = ZC)
ab bc ca LV V V V= = = LV Vφ =
a b c LI I I I= = = ab bc caI I I Iφ= = =
abV
bcV
caV caIabI
bcI
aI
bI
cI
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Revision: Basic Principles
b bc abI I I= −
c ca bcI I I= −
caIabI
bcI
aI
bI
cI
3a b c LI I I I Iφ= = = =
ab bc caI I I Iφ= = =
3 30a ab caI I I Iφ= − = ∠−
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YY
YD
DD
YD
Revision: Basic Principles39
Star-Star Balanced System0a b cI I I I zero+ + = =
n NV V zero= =
Revision: Basic Principles40
Star-Star Balanced System
Single phase equivalent circuit
Revision: Basic Principles41
Star-Delta Balanced System
3YZZ ∆=
Revision: Basic Principles42
Star-Delta Balanced System
Single phase equivalent circuit
3YZZ ∆=
Revision: Basic Principles43
Revision: Basic Principles
Star
Delta3-phase power = 3 x per phase power
3LV Vφ= LI Iφ =
LV Vφ= 3LI Iφ=
3 cos 3 cosL LP V I V Iφ φ= Φ = Φ
3 sin 3 sinL LQ V I V Iφ φ= Φ = Φ
3 3 L LS V I V Iφ φ= =
Active Power (W)
Reactive Power (VAR)
Apparent Power (VA)
PPower FactorS
=
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