151-EE-306-01-03-DC Machines
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Transcript of 151-EE-306-01-03-DC Machines
Chapter-4
DC Machines
Term-151
1
Direct Current (DC) Machines Fundamentals
Generator action: An emf (voltage) is induced in a
conductor if it moves through a magnetic field.
Motor action: A force is induced in a conductor that
has a current going through it and placed in a
magnetic field.
Any DC machine can act either as a generator or as a
motor.
2
DC Machines- Direction of Power Flow and Losses
3
DC Machines- Direction of Power Flow and Losses
4
DC Machines Analysis
Symbols that will be used.
= flux per pole
p = no. of poles
z = total number of active conductors on the armature
a = no. of parallel paths in the armature winding
n = speed of rotation of the armature in rpm
wm = speed in radians per second
5
The Internal Generated Voltage Equations
Of Real Machines
The induced voltage in any given machine depends on
three factors:
The flux Φ in the machine
The speed ω of the machine's rotor
A constant depending on the construction of the machine
The voltage out of a real machine = the number of conductors per current
path x the voltage on each conductor
6
EMF Equation
When the rotor rotates in the field a voltage is developed in the
armature.
The flux cut by one conductor
in one rotation
Therefore in n rotations, the
flux cut by one conductor
p
np
The flux cut per second by one
conductor
z
a
The number of conductors in
series
60
np
7
EMF Equation
EMF induced in the
armature windings
8
The Induce Torque Equations Of Real
Machines
The torque in any dc machine depends on three factors:
The flux Φ in the machine
The armature (or rotor) current IA in the machine
A constant depending on the construction of the machine
The torque on the armature of a real machine =the
number of conductors Z x the torque on each conductor
9
TORQUE EQUATION
EaIa=Tem - In the DC machine losses are
expressed as rotational losses
due to friction and windage (F&W).
- The torque equation can then be
rewritten as:-
SHAFT OUTPUT TORQUE = (Te -
TF&W)
10
Construction of DC Machines
11
Features of DC Machine
Field Winding
12
Construction of DC
Machines
13
Construction of DC Machines
Field system
Armature core
Armature winding
Commutator
Brushes
14
Field System
15
Field system
It is for uniform magnetic field within which the armature rotates.
Electromagnets are preferred in comparison with permanent magnets
They are cheap , smaller in size , produce greater magnetic effect and field strength can be varied
16
Field system consists of the following parts
Yoke
Pole cores
Pole shoes
Field coils
17
Armature core The armature core is cylindrical.
High permeability silicon steel stampings.
Lamination is to reduce the eddy current. loss
18
Armature winding
19
Armature winding
There are 2 types of winding
Lap and Wave winding
• A = P
• It is meant for high
current and low voltages.
• The armature windings are divided into number of sections equal to the number of poles.
• A = 2
• It is meant for low
current output and high voltages.
• 2 brushes
20
Commutator • Connect with external circuit.
• Converts ac into unidirectional current.
• Cylindrical in shape .
• Made of wedge shaped copper segments.
• Segments are insulated from each other.
• Each commutator segment is connected to armature conductors by means of a copper strip called riser.
• Number of segments equal to number of coils.
21
Carbon brush • Carbon brushes are used in DC
machines because they are soft materials.
• It does not generate spikes when they contact commutator.
• To deliver the current through armature.
• Carbon is used for brushes because it has negative temperature coefficient of resistance.
22
DC Machine Equivalent
Circuits
1. Magnetic equivalent
circuit
2. Electrical equivalent
circuit
23
1. Magnetic equivalent circuit
DC machine Cross-sectional view
DC machine Magnetic equivalent circuit
Flux-mmf relation in a dc machine
24
Electrical equivalent
circuit
DC Generator
25
DC Generator Equivalent circuit
The magnetic field produced by the stator poles induces a
voltage in the rotor (or armature) coils when the generator is
rotated.
This induced voltage is represented by a voltage source.
The stator coil has resistance, which is connected in series.
The pole flux is produced by the DC excitation/field current,
which is magnetically coupled to the rotor
The field circuit has resistance and a source
The voltage drop on the brushes represented by a battery 26
DC Generator Equivalent circuit
Equivalent circuit of a separately excited dc generator.
RfRa
Vbrush
VTEagVf
IfIag
Load
Mechanical
power in
Electrical
power out
27
DC Generator Equivalent circuit
The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated.
The dc field current of the poles generates a magnetic flux
The flux is proportional with the field current if the iron core is not saturated:
1 fK I
The rotor conductors cut the field lines that generate voltage in the coils.
ag a mE K 28
DC Generator Equivalent circuit
When the generator is loaded, the load current produces a
voltage drop on the rotor winding resistance.
In addition, there is a more or less constant 1 to 3 V voltage
drop on the brushes.
These two voltage drops reduce the terminal voltage of the
generator. The terminal voltage is;
ag T ag a brushE V I R V
29
Electrical equivalent
circuit
DC Motor
30
DC Motor Equivalent circuit
Equivalent circuit of a separately excited dc motor
Equivalent circuit is similar to the generator only the current directions are different
RfRa
Vbrush
VTEamVf
IfIam
Mechanical
power out
Electrical
power in
DC Power
supply
31
DC Motor Equivalent circuit The operation equations are:
Armature voltage equation
T am am a brushV E I R V
The induced voltage and motor speed vs angular frequency
am a mE K 2m mn
The output power and torque are:
amamout IEP out
a am
m
PT K I
32
Classification of DC
Machines
33
34
Separately Excited DC Machine
E
RaIa +
--
+
VT
a)
E
-
+Field
F F
Armature
b) Separately Excited35
Series & Shunt DC Machine
E
-
+
Field
F F
Armature
c) Series
E
-
+
Field
F F
Armature
d) Shunt
A
A
36
Cumulative & Differential DC machine
E
-
+
Field FF
Armaturee) Cummulative Compound
A
A
S S
E
-
+
Field FF
Armature
d) Differential Compound
A
A
S S
37
Long Shunt & Short Shunt DC Machine
E
-
+
Field FF
Armature
f) Long Shunt
A
A
S S
E
-
+
Field FF
Armature
g) Short Shunt
A
A
S S
38
Exercise Problems
39
Exercise-1
A four-pole dc machine has an armature of radius 12.5 cm and an
effective length of 25cm. The poles cover 75 % of the armature
periphery. The armature winding consists of 33 coils, each having
seven turns. The coils are accommodated in 33 slots. The average
flux density under each pole is 0.75 T.
A. If the armature is lap wound, then
a) Determine the armature constant Ka.
b) Determine the induced armature voltage when the armature
rotates at 1000 rpm.
c) Determine the current in the coil and the electromagnetic torque
developed when the armature current is 400 A.
d) Determine the power developed by the armature.
B. If the armature is wave-wound, repeat parts (a) to (d) above. The
current rating of the coils remains the same as in the lap-wound.
40
Exercise-2
A 12-pole dc generator has a simplex wave-wound armature
containing 144 coils of 10 turns each. The resistance of each turn is
0.011 Ω. Its flux per pole is 0.05 Wb, and the machine is running at a
speed of 200 r/min.
(a) How many current/parallel paths are there in this machine?
(b) What is the induced armature voltage of this machine?
(c) What is the effective armature resistance of this machine?
(d) If a 1 kΩ resistor is connected to the terminals of this generator,
Determine the power output and the induced counter-torque on
the shaft of this generator.
41
4.3 DC Generators
42
Separately Excited DC Generator The operation equations are:
Stator or field side:
Armature voltage equation:
Load or terminal equation:
Current equation:
f fw fc
f f f
R R R
V I R
a t a a brush
a a m
E V I R V
E K
t t LV I R
a tI I
Power developed in the armature:
Load or terminal equation:
Current equation:
a g a aP P E I
Power delivered to the load:
Load or terminal equation:
Current equation:
L t t t t LP P V I V I 43
Characteristics Performance of the DC generators
are determined by terminal output parameter IL and VT
By Kirchhoff's voltage law, the terminal voltage is,
Since the internal generated voltage is independent of armature current, the generator terminal characteristics is a straight line.
Due to the armature voltage drop, the characteristics show drooping nature.
t a a a brushV E I R V a tI ITerminal characteristics of separately
excited DC generator
44
Shunt (Self-Excited) DC Generator The operation equations are:
Stator or field side:
Armature voltage equation:
Load or terminal equation:
Current equation:
tsh
sh
VI
R
a t a a brush
a a m
E V I R V
E K
t t LV I R
a L shI I I
Power developed in the armature:
Load or terminal equation:
Current equation:
a g a aP P E I
Power delivered to the load:
Load or terminal equation:
Current equation:
L t t t t LP P V I V I 45
Characteristics By Kirchhoff's voltage law, the
terminal voltage is,
Since the internal generated voltage is independent of armature current, the generator terminal characteristics is a straight line.
Due to the armature voltage drop, the characteristics show drooping nature.
t a a a brushV E I R V
a t shI I I
Terminal characteristics of shunt DC generator
46
Series (Self-Excited) DC Generator The operation equations are:
Stator or field side:
Armature voltage equation:
Load or terminal equation:
Current equation:
se a L tI I I I
( )a t a a se brush
a a m
E V I R R V
E K
t t LV I R
a t LI I I
Power developed in the armature:
Load or terminal equation:
Current equation:
a g a aP P E I
Power delivered to the load:
Load or terminal equation:
Current equation:
L t t t t LP P V I V I 47
Characteristics By Kirchhoff's voltage law, the
terminal voltage is,
As the load increases, the field
current rises, so EA rises rapidly The
IA (RA+Rs) drop goes up too, but
at first the increase in EA goes up
more rapidly than the IA(RA+Rs)
drop rises, so Vr increases.
( )t a a a se brushV E I R R V
a t seI I I
Terminal characteristics of series DC generator
After a while, the machine approaches
saturation, and EA becomes almost
constant. At that point, the resistive
drop is the predominant effect, and VT
starts to fall.
48
Short Shunt DC Generator The operation equations are:
Series field side:
Shunt field current
Armature voltage equation:
Load or terminal equation:
Current equation:
se L tI I I
a t a a se se brush
a a m
E V I R I R V
E K
t t LV I R
a L shI I I
Power developed in the armature:
Load or terminal equation:
Current equation:
a g a aP P E I
Power delivered to the load:
Load or terminal equation:
Current equation:
L t t t t LP P V I V I
t se sesh
sh
V I RI
R
49
Long Shunt DC Generator The operation equations are:
Series field side:
Shunt field current
Armature voltage equation:
Load or terminal equation:
Current equation:
se aI I
( )a t a a se brush
a a m
E V I R R V
E K
t t LV I R
a L shI I I
Power developed in the armature:
Load or terminal equation:
Current equation:
a g a aP P E I
Power delivered to the load:
Load or terminal equation:
Current equation:
L t t t t LP P V I V I
tsh
sh
VI
R
50
Characteristics
51
4.4 DC Motors
52
HW-3
Draw the equivalent circuits of
various DC motors & derive
their voltage, current and
power equations. Draw their
performance characteristics.
Due Date: Monday, November 16, 2015
53
Performance of DC
Machines
54
DC Generator A DC generator is a machine that takes in mechanical input
power to produce electrical power output.
The performance of a dc generator is assessed by means of the following:
Generator Efficiency:
Voltage Regulation:
100 100 100out in out
in in out
P P Losses P
P P P Losses
, ,
,
100t NL t FL
t FL
V VVR
V
55
DC Motor: A DC motor is a machine that produces mechanical output
power from the applied electrical input.
The performance of a dc motor is assessed by means of the following:
Motor Efficiency:
Speed Regulation:
100 100 100out in out
in in out
P P Losses P
P P P Losses
, ,
,
100m NL m FL
m FL
n nSR
n
56
Power Flow & Losses in
a DC Machine
57
Efficiency Calculations
Losses in DC Machines
58
All these losses appear as heat and thus raise the temperature of the machine. They
also lower the efficiency of the machine.
Constant Losses
Variable Losses
Electrical or Copper Losses (I2R Losses)
Armature copper loss:
59
These losses occur due to currents in the armature and field windings of the dc machine.
Brush Losses:
There is also brush contact loss due to brush contact resistance (i.e., resistance between the surface of brush and surface of commutator). This loss is generally included in armature copper loss.
It can also be calculated explicitly by the following relation.
2
A a aP I R
2
sh sh shP I R
2
se se seP I R
Shunt field copper loss:
Series field copper loss:
BD BD aP V I
Core or Iron Losses
60
As iron core of the armature is continuously rotating in a magnetic field, there are some losses taking place in the core. This loss consists of Hysteresis loss and Eddy current loss.
When the armature core rotates in the magnetic field, an emf is also induced in the core (just like it induces in armature conductors), according to the Faraday's law of electromagnetic induction. Though this induced emf is small, it causes a large current to flow in the body due to low resistance of the core. This current is known as eddy current. The power loss due to this current is known as eddy current loss.
Hysteresis loss is due to reversal of magnetization of the armature core. When the core passes under one pair of poles, it undergoes one complete cycle of magnetic reversal. The frequency of magnetic reversal if given by, f=PN/120. The loss that takes place due to repeated magnetization & demagnetization of the iron core contributes to the hysteresis loss.
Hysteresis loss:
Eddy current loss:
Mechanical Losses
61
The mechanical losses in a dc machine are the losses associated with
mechanical effects.
These losses are due to friction and windage.
(i) friction loss e.g., bearing friction, brush friction etc.
(ii) windage loss i.e., air friction of rotating armature.
These losses depend upon the speed of the machine. But for a given speed,
they are practically constant.
Mechanical and core losses are together considered as rotational losses .
The Power-Flow Diagram of DC Generator
62
The Power-Flow Diagram of DC Motor
63
Exercise Problems
64
Exercise-1
A separately excited dc generator running at 1200 rpm & delivers
12kW at 240 V as terminal voltage. The armature resistance is 0.3
ohms. Each brush takes 1 V drop. Pmech=600 W, Pcore=300 W and
Pstray=200 W. The field circuit resistance is 200 ohms and DC field
voltage is 250 V.
65
a) Draw the equivalent circuit and the corresponding power
flow diagram.
b) Find the induced voltage.
c) Determine the converted or developed power and the
induced torque.
d) Find the efficiency of the machine.
Exercise-2
A 220 V shunt DC motor has an armature resistance of 0.2 ohms and
a field resistance of 110 ohms. At no-load the motor runs at 1000
rpm and it draws a line current of 7 A. At full-load, the input to the
motor is 11 kW.
66
a) Draw the equivalent circuit.
b) Find the rotational losses.
c) Find the speed, speed regulation and developed torque at full
load.
d) Find the efficiency of the motor.
HW-4
67
Questions #:
4.2, 4.16, 4.17, 4.18, 4.25, 4.26,4.39,
4.40 found on pages 192-198 of the
text book.