Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-4, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
An Introduction to DC Generator Using
MATLAB/SIMULINK
Debabrata Pal
Assistant Professor, Aksum University, College of Engineering and Technology
Department of Electrical and Computer Engineering, Ethiopia, NE Africa
Abstract:This paper presents the modeling and analysis
of a dc generator in two different ways. First method is
keeping field flux constant and by varying the shaft
torque of the generator and second method is keeping
shaft torque constant and by varying the field flux of the
same generator.The performance of the generator under
various conditions as mentioned above are simulated
using MATLAB/SIMULINK environment and simulation
results demonstrate the feasibility of the proposed system.
Key words: DC Generator, Field flux, Shaft torque
MATLAB/SIMULINK.
1. Introduction
.
A dc generator is an electrical machine which converts
mechanical energy into direct current electricity. This
energy conversion is based on the principle of production
of dynamically induced emf. According to Faraday’s
laws of electromagnetic induction, whenever a conductor
is placed in a varying magnetic field (OR a conductor is
moved in a magnetic field), an emf (electromotive force)
gets induced in the conductor. The magnitude of induced
emf can be calculated from the emf equation of dc
generator. If the conductor is provided with the closed
path, the induced current will circulate within the path. In
a dc generator, field coils produce an electromagnetic
field and the armature conductors are rotated into the
field. Thus, an electromagnetically induced emf is
generated in the armature conductors. The direction of
induced current is given by Fleming’s right hand rule.
DC generators can be classified in two main categories,
separately
excited
and
self-excited.
In separatelyexcite type generator, field coils are
energized from an independent external DC source
and InSelf excited type dc generator, field coils are
energized from the current produced by the generator
itself. Initial emf generation is due to residual magnetism
in field poles. The generated emf causes a part of current
to flow in the field coils, thus strengthening the field flux
and thereby increasing emf generation. Self excited dc
generators can further be divided into three types - (a)
Series wound - field winding in series with armature
winding (b) Shunt wound - field winding in parallel with
armature winding (c) Compound wound - combination of
series and shunt winding [1]-[3].
Imperial Journal of Interdisciplinary Research (IJIR)
This paper mainly deals with a dc generator which is
controlled by shaft torque (field flux constant) and field
flux (shaft torque constant) using MATLAB/ SIMULINK
environment.
2.
Mathematical Modeling of DC
Generator
The different equations related to DC generator are given
below
𝐸𝑔 = 𝑘𝑔 𝑤𝑟 𝜑 (1)
𝑑𝑖
𝑉𝑡 = 𝐸𝑔 - 𝐿𝑎 𝑎 - 𝑅𝑎 𝐼𝑎 (2)
𝑑𝑡
𝑇𝐿 = 𝑘𝐿 𝜑𝐼𝑎
dw
Tshaft = TL +𝐽 r + Bwr (4)
dt
𝑉𝑡 = 𝐼𝑎 𝑅𝐿
(3)
(5)
Where 𝑉𝑡 = terminal voltage, 𝐸𝑔 = total generated voltage,
𝐿𝑎 = armature inductance, 𝑅𝑎 = armature resistance, 𝐼𝑎
= armature current,
𝑘𝑔 = voltage constant,
𝜑 =
stator/field flux,
wr = speed of the generator, 𝑅𝐿 =
load resistance, Tshaft = shaft torque,𝑇𝐿 = load torque, 𝐽
= moment of inertia, B = viscous friction, 𝑘𝐿 = load
torque.
The necessary differential equations will now be derived
by using above equations to simulate the dc generator.
𝑑𝐼𝑎
𝑑𝑡
𝑑𝑤 𝑟
𝑑𝑡
=
𝑘 𝑔 𝜑𝑤 𝑟
=
𝐿𝑎
𝑘 𝐿 φ𝐼𝑎
𝐽
–
( 𝑅𝑎 + 𝑅 𝐿 )
𝐿𝑎
𝐼𝑎
𝐵
𝑇 𝑠𝑕 𝑎𝑓𝑡
𝐽
𝐽
- 𝑤𝑟 +
(6)
(7)
3. Results and Discussion
The set of model equations given by ((6), (7)) are solved
to compute the instantaneous values of the performance
variables of the system. Let, the dc generator parameters
(coefficient of differential equations) are assigned to be𝐽
= 0.01kg-m2, B = 0.1N-m sec/rad, 𝑅𝑎 = 1 Ω, 𝐿𝑎 = 0.4 H,
𝑘𝑔 = 0.27 V-sec/rad, 𝑘𝐿 = 0.11 N-m/A, 𝑅𝐿 = 3Ω.
In first case, simulation has been carried out by varying
different shaft torques (20 N-m, 30N-m, 40N-m) and
Page 935
Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-4, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
10
50
0
2
4
6
8
10
6
8
10
Time(Sec)
300
5
0
0
1
2
3
4
5
6
Time(Sec)
7
8
9
10
5
Armature current(amp)
100
0
Rotor speed(r.p.m)
Terminal voltage(volt)
15
150
Generated power(watt)
keeping field flux constant (0.30 T).The simulation
results are shown in following figures.
200
100
4
0
3
0
2
4
Time(Sec)
2
Fig: 2 Response of DC generator with Tshaft = 30 N-m
and field flux(𝜑 )= 0.30 T (constant)
1
0
0
2
4
6
8
10
Time(Sec)
25
Terminal voltage(volt)
Generated power(watt)
50
40
30
20
10
0
0
2
4
6
8
20
15
10
5
0
10
0
2
4
Time(Sec)
150
100
50
0
2
4
6
8
6
8
10
6
8
10
6
8
10
6
4
2
0
10
0
2
4
Time(Sec)
20
15
200
Generated power(watt)
Fig: 1 Response of DC generator with Tshaft = 20 N-m
and field flux (𝜑)= 0.30 T (constant)
10
150
100
50
0
0
2
4
Time(Sec)
5
0
400
0
2
4
6
8
10
Time(Sec)
8
6
Rotor speed(r.p.m)
Terminal voltage(volt)
10
8
Time(Sec)
Armature current(amp)
8
10
Armature current(amp)
Rotor speed(r.p.m)
200
0
6
Time(Sec)
300
200
100
0
4
0
2
4
Time(Sec)
2
0
Fig: 3 Response of DC generator with Tshaft = 40 N-m
and field flux(𝜑) = 0.30 T (constant)
0
2
4
6
8
10
Time(Sec)
Imperial Journal of Interdisciplinary Research (IJIR)
Page 936
Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-4, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
Terminal voltage(volt)
20
15
200
Generated power(watt)
In second case, simulation has been carried out by
varying different field flux (0.30T, 0.40T, 0.50T) and
keeping shaft torque constant (30N-m). The simulation
results are shown in following figures.
150
100
50
0
0
2
4
10
6
8
10
6
8
10
Time(Sec)
5
0
0
2
4
6
8
10
Time(Sec)
Armature current(amp)
8
6
Rotor speed(r.p.m)
300
200
100
0
4
0
2
4
Time(Sec)
2
0
0
2
4
6
8
10
Time(Sec)
Fig: 5 Response of DC generator with field flux (𝜑) =
0.40T and Tshaft = 30N-m (constant)
30
Terminal voltage(volt)
Generated power(watt)
150
100
50
0
0
2
4
6
8
10
20
10
0
Time(Sec)
0
2
4
6
8
10
6
8
10
6
8
10
6
8
10
Time(Sec)
300
Armature current(amp)
Rotor speed(r.p.m)
10
200
100
0
0
2
4
6
8
10
15
10
2
4
100
0
2
4
Time(Sec)
0
2
4
6
8
10
300
Rotor speed(r.p.m)
10
Armature current(amp)
0
200
0
Time(Sec)
8
6
4
200
100
0
2
0
2
300
5
0
4
Time(Sec)
Generated power(watt)
Terminal voltage(volt)
20
6
0
Time(Sec)
Fig: 4 Response of DC generator with field flux ( ) = 0.3
T and Tshaft = 30N.m (constant).
25
8
0
2
4
Time(Sec)
0
2
4
6
8
10
Time(Sec)
Imperial Journal of Interdisciplinary Research (IJIR)
Fig: 6 Response of DC generator with field flux (𝜑)=
0.50 T and Tshaft = 30N-m (constant).
Page 937
Imperial Journal of Interdisciplinary Research (IJIR)
Vol-2, Issue-4, 2016
ISSN: 2454-1362, http://www.onlinejournal.in
4. Conclusion
This paper mainly shows different results such as voltage,
current, power and speed of the generator with respect to
time under different conditions in MATLAB/SIMULINK
environment. This work will help undergraduate students
to explore more about dc generator
.
REFERENCES
[1] Dr. P.S. Bimbhra, ‘Electrical Machines’,
KHANNA PUBLSHER
[2] D.P Kothari &I.J.Nagrath, ‘Electrical Machines’
TATA Mc GRAW HILL EDUCATION,2004.
[3] Horace Field Parshall& Henry Metcalfe Hobart
‘Electric Generators’ JOHN WILEY AND SONS,
New York, 1900.
[4] Devendra K. Chaturvedi, Modeling and simulation
of system using MATLAB and Simulink, CRC
Press Taylor and Francis group Boca Raton
London New York 2010.
Author Profile
Debabrata Pal was born in Bankura,
West Bengal, India. He has received his
B.Tech degree in Electrical Engineering
in 2005 from West Bengal University of
Technology, India and Master’s degree
in Electrical Systems in 2010 from
National Institute of Technology,
Durgapur, India. His research interest is
in Renewable Energy Sources, Control
Engineering and Machine Simulation.
He has been teaching in various universities in India for
more than eight years in various capacities (2005-2013).
He is currently Assistant Professor in the Department of
Electrical and Computer Engineering, College of
Engineering and Technology, Aksum University, Aksum,
Ethiopia. Mr. Pal has attended many seminars and
conferences in various parts of India.
Imperial Journal of Interdisciplinary Research (IJIR)
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