Dynamic analysis of dc machine
-
Upload
ramesh-babu -
Category
Education
-
view
593 -
download
0
description
Transcript of Dynamic analysis of dc machine
![Page 1: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/1.jpg)
PHYSICAL STRUCTURE9
/1/2
013 1
1:4
8 A
M
1
PR
B /S
CE
/De
pt. o
fEE
E
![Page 2: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/2.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
2
PE 9211 Analysis of Electrical Machines
![Page 3: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/3.jpg)
Dynamic Characteristics of Permanent Magnet DC Motor
Modes of Dynamic operation
1. Starting from stall
2. Changes in load torque
Condition: The machine supplied from a
constant β voltage source
9/1
/20
13 1
1:4
8 A
M
3
PR
B /S
CE
/De
pt. o
fEE
E
![Page 4: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/4.jpg)
Mathematical Model of a PMDC Motor: 9
/1/2
013 1
1:4
8 A
M
4
PR
B /S
CE
/De
pt. o
fEE
E
![Page 5: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/5.jpg)
This motor consists of two first order differential equation and two
algebraic equation
Armature current equation,
9/1
/20
13 1
1:4
8 A
M
5
PR
B /S
CE
/De
pt. o
fEE
E
![Page 6: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/6.jpg)
Speed equation,
9/1
/20
13 1
1:4
8 A
M
6
PR
B /S
CE
/De
pt. o
fEE
E
![Page 7: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/7.jpg)
9/1
/20
13 1
1:4
8 A
M
7
PR
B /S
CE
/De
pt. o
fEE
E
![Page 8: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/8.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
8
Simulink Model of PMDC Motor
Motor Parameters
![Page 9: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/9.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
9
Solving armature current equation
![Page 10: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/10.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
10
Solving Speed equation
![Page 11: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/11.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
11
![Page 12: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/12.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
12
Dynamic performance during starting
![Page 13: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/13.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
13
![Page 14: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/14.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
14
Dynamic Characteristics of DC Shunt Motor
![Page 15: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/15.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
15
![Page 16: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/16.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
16
Simulink Model of DC Shunt Motor:
Fig shows the Simulink model of DC Shunt Motor. It is constructed using
subsystems for solving each differential equations (i.e.) armature
current, field current and torque equation.
![Page 17: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/17.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
17
![Page 18: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/18.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
18
![Page 19: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/19.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
19
![Page 20: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/20.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
20
![Page 21: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/21.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
21
Time domain block diagrams and state equations
Shunt connected dc machine
W.K.T
ππ = ππππ + π³π¨π¨ π πππ π
+ π³π¨πππππ β β ββ π
ππ = πππΉπ + π³ππ π ππ
π π β β ββ π
π»π = π»π³ + π± π ππ
π π + π©πππ β ββ β π
![Page 22: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/22.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
22
Equations (1),(2) and (3) can be written in terms of its time constants
ππ = ππ π + π³π¨π¨
ππ
π
π π ππ + π³π¨πππππ
ππ = ππ π + ππ π ππ + π³π¨πππππββββββ π
π―πππ, π βΆπ
π π
ππ = πΉπ π + π³ππ
πΉπ
π ππ
ππ = πΉπ π + ππ π ππβββββββ(5)
π»π β π»π³ = ( π©π + π± π) ππ ββ β β π
![Page 23: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/23.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
23
ππ βΆ Armature time constant
ππ βΆ Field time constant
πΊππππππ πππ πππππππππ π , π πππ π πππ ππ ,
ππ, πππ ππ πππππ π
ππ =
πππ
πππ + π ππ β π³π¨πππππ β β ββ π
ππ =
ππΉπ
πππ + π ππ β ββ β π
ππ =π
π±π + π©π π»π β π»π³ ββ β β π
![Page 24: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/24.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
24
Time domain block diagram of a shunt connected dc machine
![Page 25: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/25.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
25
πΊππππππ πππ πππππππππ π , π πππ π πππ π ππ
π π, π ππ
π π
πππ π ππ
π π πππππ π
From (1)
π πππ π
= βππ
π³π¨π¨
ππ β π³π¨π
π³π¨π¨
ππππ + π
π³π¨π¨
ππβ ππ
From (2)
π ππ
π π= β
πΉπ
π³ππ
ππ + π
π³ππ
ππβ ππ
From (3)
π ππ
π π= β
π©π
π±ππ +
π³π¨π
π±ππππ β
π
π±π»π³ β β(ππ)
State equation of shunt dc machine
![Page 26: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/26.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
26
π
ππππππ
=
βπΉπ
π³πππ π
πβππ
π³π¨π¨π
π πβπ©π
π±
ππππππ
+
πβπ³π¨πππ
π³π¨π¨
π³π¨πππππ
π±
+
π
π³πππ π
ππ
π³π¨π¨π
π πβπ
π±
ππ
ππ
π»π³
State equations in matrix form or vector matrix form
Note: The second term on the right side contains the product of state
variables causing the system to be nonlinear.
![Page 27: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/27.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
27
Permanent Magnet dc Machine
ππ ππ ππππππππππ
π³π¨πππ ππ ππππππππ ππ ππ
ππ ππ π πππππππππ ππ
Strength of the magnetReluctance of the ironNo. of turns in the armature winding
![Page 28: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/28.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
28
W.K.T
Above eqns. (1) and (2) can be written in terms of its time constants
![Page 29: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/29.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
29Time domain block diagram of a permanent magnet DC machine
![Page 30: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/30.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
30
State Equation of a permanent magnet DC machine
From (1)
From (2)
![Page 31: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/31.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
31
The form in which the state equations are expressed in above eqn.
is called the fundamental form.
OR
![Page 32: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/32.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
32
Advantages to using the state space representation compared with other methods.
1.The ability to easily handle systems with multiple inputs and outputs;
2.The system model includes the internal state variables as well as the output variable;
3.The model directly provides a time-domain solution, the matrix/vector modeling is very efficient from a computational standpoint for computer implementation
![Page 33: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/33.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
33
![Page 34: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/34.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
34
![Page 35: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/35.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
35
404349
![Page 36: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/36.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
36
![Page 37: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/37.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
37
![Page 38: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/38.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
38
![Page 39: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/39.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
39
![Page 40: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/40.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
40
![Page 41: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/41.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
41
34
![Page 42: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/42.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
42
![Page 43: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/43.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
43
![Page 44: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/44.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
44
34
![Page 45: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/45.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
45
![Page 46: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/46.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
46
![Page 47: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/47.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
47
![Page 48: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/48.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
48
![Page 49: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/49.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
49
![Page 50: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/50.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
50
34
![Page 51: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/51.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
51
![Page 52: Dynamic analysis of dc machine](https://reader034.fdocuments.in/reader034/viewer/2022042518/5594d3201a28ab7e798b45b3/html5/thumbnails/52.jpg)
9/1
/20
13 1
1:4
8 A
MP
RB
/SC
E /D
ep
t. ofE
EE
52