![Page 1: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/1.jpg)
ELECTRICAL MACHINES 1 EPMN301
1
![Page 2: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/2.jpg)
Course Grading System
Marks
Final Exam Semester Work- 20 Mid-term- 15 Quizzes
- 15 Assignments- 10 Lab
2
![Page 3: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/3.jpg)
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
3
![Page 4: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/4.jpg)
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.
4
![Page 5: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/5.jpg)
References
A.E. Fitzgerald & Charles Kingsley, Electric Machinery, 7th Edition.
Stephan J. Chapman, Electric Machinery Fundamentals, 5th Edition.
5
![Page 6: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/6.jpg)
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
6
![Page 7: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/7.jpg)
Revision: Basic Principles
AC Circuits Three-phase Circuits
7
![Page 8: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/8.jpg)
Revision: Basic Principles
Phasor Representation
1 sin( )mv V tω=
2 sin( )m ov V tω θ= +
8
![Page 9: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/9.jpg)
Revision: Basic Principles
Phasor Representation
1 0rmsV V= ∠
2 rms oV V θ= ∠
2m
rmsVV =
9
![Page 10: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/10.jpg)
Revision: Basic Principles
Phasor Representation
1V
2V
Phasor Diagram
1 1 0V V= ∠
2 2 oV V θ= ∠ oθ
10
![Page 11: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/11.jpg)
Revision: Basic Principles
Phasor Representation
1V
2V
1 2TV V V= +
oθ
1V
TV
11
![Page 12: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/12.jpg)
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=
12
![Page 13: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/13.jpg)
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= ∠
13
![Page 14: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/14.jpg)
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= ±
14
![Page 15: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/15.jpg)
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
15
![Page 16: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/16.jpg)
Revision: Basic Principles
Loads: R-L Load
RV IR=
V IZ=
L LV IX=Φ
R
ZLX
Φ
I×
16
![Page 17: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/17.jpg)
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
17
![Page 18: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/18.jpg)
Revision: Basic Principles
Loads: R-C Load
RV IR=
V IZ=C CV IX=
Φ
R
Z CXΦ I×
18
![Page 19: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/19.jpg)
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
19
![Page 20: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/20.jpg)
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
20
![Page 21: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/21.jpg)
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)
21
![Page 22: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/22.jpg)
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=
22
![Page 23: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/23.jpg)
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
23
![Page 24: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/24.jpg)
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
24
![Page 25: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/25.jpg)
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×
25
![Page 26: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/26.jpg)
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×
26
![Page 27: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/27.jpg)
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
27
![Page 28: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/28.jpg)
Revision: Basic Principles
PPower FactorS
=
28
![Page 29: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/29.jpg)
Revision: Basic Principles29
![Page 30: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/30.jpg)
Revision: Basic Principles
sin( )mv V tω=
2 Tπ ω=2T πω
= (sec)
3-phase AC Supply
30
![Page 31: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/31.jpg)
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
![Page 32: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/32.jpg)
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= ∠−
32
![Page 33: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/33.jpg)
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= ∠
33
![Page 34: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/34.jpg)
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
![Page 35: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/35.jpg)
Revision: Basic Principles
abV
bcV
caVLine-to-line
0abV V= ∠ 120bcV V= ∠− 120caV V= ∠
35
![Page 36: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/36.jpg)
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
=
36
![Page 37: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/37.jpg)
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
37
![Page 38: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/38.jpg)
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= − = ∠−
38
![Page 39: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/39.jpg)
YY
YD
DD
YD
Revision: Basic Principles39
![Page 40: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/40.jpg)
Star-Star Balanced System0a b cI I I I zero+ + = =
n NV V zero= =
Revision: Basic Principles40
![Page 41: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/41.jpg)
Star-Star Balanced System
Single phase equivalent circuit
Revision: Basic Principles41
![Page 42: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/42.jpg)
Star-Delta Balanced System
3YZZ ∆=
Revision: Basic Principles42
![Page 43: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/43.jpg)
Star-Delta Balanced System
Single phase equivalent circuit
3YZZ ∆=
Revision: Basic Principles43
![Page 44: ELECTRICAL MACHINES 1...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](https://reader033.vdocuments.us/reader033/viewer/2022041814/5e59f248bdf183494d205824/html5/thumbnails/44.jpg)
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
=
44