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CHAPTER 2
Basic DC
Motor.
School of Computer and Communication
Engineering, UniMAP
Prepared By:
Amir Razif b. Jamil Abdullah
EMT 113: V-2008
1
2.0 Basic Direct Current (DC)
Motor.
2.1 Introduction to DC Machines.
2.2 Construction of DC Machines.
2.3 DC Motor.
2.4 DC Generator.
2
2.1 Introduction to DC Machine.
DC motors are dc machine used as motors.
DC generator are dc machines used as generators.
DC machine is most often used for a motor.
The major advantages of dc machines are the
(i) easy speed and
(ii) torque regulation.
 However, their application is limited to mills, mines and trains.
As examples, trolleys and underground subway cars may use dc
motors.
 In the past, automobiles were equipped with dc dynamos to
charge their batteries.




3
Cont’d…
 The same physical machine can operate as a motor or generator
depends on the direction of power flow in it.
 DC machine are generators that convert mechanical energy to
dc electric energy.
 DC machine are motors that convert dc electric energy to
mechanical energy.
 DC motors are used in cars, trucks, and aircrafts because they use
dc power system.
 DC motors are often compared by their speed regulation (SR)
which is defined as;
 nl   fl
SR 
 100%
 fl
4
Cont’d…
Speed Regulation (SR)
 SR is the measure of the shape of the motor’s torque-speed
characteristic.
(a) Positive SR means that the motor’s speed drops with
increasing load.
(b) Negative SR means that the motor’s speed increasing with
increasing load.
(c) The magnitude of the SR tells approximately how steep the
slope of the torque-speed curve is.
SR 
nnl  n fl
n fl
 100%
5
2.2 Construction of DC Machine.
 The physical structure of the machine consists of two parts;
(i) Stator or stationary part,
(ii) Rotor or rotating part.
Figure 2.1: Stator (left) and Rotor (right)
6
Cont’d…
 Frame is the stationary part
which provide physical support.
 Pole Piece which is projected
inward and provide the magnetic
flux in the machine.
 Pole shoes distributes flux
evenly over the rotor surface.
 The expose surface of the pole
shoes is the pole face.
 The distance between the pole
face and the rotor is called air
gap.
Figure 2.2: General Arrangement of a
DC Machine
7
Cont’d…
 There are two principal windings on the dc machine;
(i) armature windings,
(ii) field windings.
 The armature windings are defined as windings in which a
voltage is induced.
 The field windings are defined as the windings that produce the
main magnetic flux in the machine.
 The armature winding is located on the rotor, and the field
windings are located on the stator.
 The stator of the dc motor has poles, which are excited by dc
current to produce magnetic fields.
 In the neutral zone, in the middle between the poles, commutating
poles are placed to reduce sparking of the commutator.
 The commutating poles are supplied by dc current.
 Compensating windings are mounted on the main poles.
 These short-circuited windings damp rotor oscillations.
 The poles are mounted on an iron core that provides a closed
8
magnetic circuit.
Cont’d…
 The rotor has a ring-shaped laminated iron core with slots.
 Coils with several turns are placed in the slots. The distance
between the two legs of the coil is about 180 electric degrees.
 The coils are connected in series through the commutator
segments.
Commutator
 The ends of each coil are connected to a commutator segment.
 The commutator consists of
insulated copper segments
mounted on an insulated tube.
 Two brushes are pressed to the
commutator to permit current flow.
 The brushes are placed in the
neutral zone, where the magnetic
field is close to zero, to reduce
9
arcing.
2.2.1 Commutator and Brushes
Construction.
Commutator.
 The commutator in a dc machine is typically made of copper bars
insulated by a mica-type material.
Rotation
Ir_dc/2
Brush
Ir_dc/2
Ir_dc
Shaft
Pole
winding
|
1
2
8
N
3
7
6
S
4
5
Insulation
Rotor
Winding
Ir_dc
Figure 2.3: Details of the Commutator of a DC Motor.
Copper
segment
10
Cont’d…
Brushes.
 The brushes of the machine are made of carbon, graphite,
metal graphite or a mixture of carbon and graphite.
 The brushes have a high conductivity to reduce electrical losses
and low coefficient of friction to reduce excessive wear.
Operation.
 The commutator switches the current from one rotor coil to the
adjacent coil,
 The switching requires the interruption of the coil current.
 The sudden interruption of an inductive current generates high
voltages .
 The high voltage produces flashover and arcing between the
commutator segment and the brush.
11
Cont’d…
 The commutator switches the current from one rotor coil to the
adjacent coil,
 The switching requires the interruption of the coil current.
 The sudden interruption of an inductive current generates
high voltages .
 The high voltage produces flashover and arcing between the
commutator segment and the brush.
Figure 2.4: Details of the Commutator of a DC Motor.
12
2.2.2 Rotor Construction.
 The rotor or armature construction of a dc machine consists of a
shaft machined from a steel bar with a core built up over it.
 The core is composed of many lamination stamped from a steel
plate.
 The commutator is built onto the shaft of the rotor at one end of
the core.
 The armature coils are laid into the slots on the core, and their
ends are connected to the commutator segments.
Figure 2.5: Rotor of a DC Motor.
13
2.3 DC Motor.
Figure 2.6: Cutaway View of a DC Motor.
14
2.3.1 DC Motor Operation.
 In a dc motor, the stator poles are supplied by dc excitation
current, which produces a dc magnetic field.
 The rotor is supplied by dc current through the brushes,
commutator and coils.
 The interaction of the magnetic
Rotation
field and rotor current generates
Ir_dc/2
Ir_dc/2
Ir_dc
Pole
Brush
a force that drives the motor.
winding
Shaft
|
1
2
8
N
3
7
6
S
4
5
Insulation
Rotor
Winding
Ir_dc
Copper
segment
15
Cont’d…
DC Motor Operation
1
v
B
 The magnetic field lines enter
a
into the rotor from the north
S
N
pole (N) and exit toward the
30
Vdc
south pole (S).
b
 The poles generate a magnetic
v
field that is perpendicular to
Ir_dc
the current carrying conductors.
Figure 2.7: (a) Rotor current flow from
 The interaction between the field
segment 1 to 2 (slot a to b)
and the current produces a
B
Lorentz force,
a
 The force is perpendicular to
both the magnetic field and
N
S
30
Vdc
v
v
conductor
1
2
2
b
Ir_dc
Figure 2.7: (b) Rotor current flow16from
segment 2 to 1 (slot b to a)
Cont’d…
maintains the counterclockwise
rotation.
a
N
2
S
30
v
Vdc
1
v
b
Ir_dc
Figure 2.8: (a) Rotor current flow from
segment 1 to 2 (slot a to b)
v
S
30
a
B
N
2
commutator changes the
current direction, which
B
1
 The generated force turns the
rotor until the coil reaches the
neutral point between the
poles.
 At this point, the magnetic
field becomes practically zero
together with the force.
 However, inertia drives the
motor beyond the neutral zone
where the direction of the
magnetic field reverses.
 To avoid the reversal of the
force direction, the
DC Motor Operation
b
v
Ir_dc
Figure 2.8: (b) Rotor current flow
17
from segment 2 to 1 (slot b to a)
Vdc
Cont’d…
v
S
B
a
N
1
30
Vdc
2
b
v
Ir_dc
Figure 2.9: (a) Rotor Current Flow
From Segment 1 to 2 (slot a to b)
B
S
2
a
30
v
v
N
Vdc
1
 Before reaching the neutral
zone, the current enters in
segment 1 and exits from
segment 2.
 Therefore, current enters the
coil end at slot a and exits
from slot b during this stage.
 After passing the neutral zone,
the current enters segment 2
and exits from segment 1.
 This reverses the current
direction through the rotor
coil, when the coil passes the
neutral zone.
 The result of this current
reversal is the maintenance of
the rotation.
DC Motor Operation
b
Ir_dc
Figure 2.9: (b) Rotor Current Flow
18
From Segment 2 to 1 (slot b to a)
2.3.2 DC Motor Equivalent
(1)
Circuit.
 In a dc motor, the stator poles are
supplied by dc excitation current,
which produces a dc magnetic field.
(2)
 There are four major types of dc
motor in general used;
(1) Separately Excited DC Motor.
(2) Shunt DC Motor.
(3) Series DC Motor.
(4) Compounded DC Motor.
(3)
(4)
19
2.3.3 Separately Excited and Shunt
DC Motors.
 Figure 2.10 and Figure 2.11 show the equivalent circuit of
separately excited dc motor and shunt motor.
 The armature circuit is represented by the EA and RA.
 The field coil is represented by the LF and RF.
(1) Seperately Excited DC Motor
Figure 2.10: The Separately Excited DC Motor Equivalent Circuit.
 From the above figure,
IF 
VF
RF
VT  E A  I A RA
IL  IA
20
Cont’d…
 (2) Shunt DC Motor
Figure 2.11: The Equivalent Circuit of a Shunt
DC Motor.
 From the above figure,
VT
IF 
RF
VT  E A  I A RA
IL  I A  IF
21
Speed Torque Characteristics.
 Figure 2.11 is the equivalent circuit of DC
shunt motor. From Kirchhoff ’s voltage law,
 The internal generated voltage, EA.
 Solving for the above equation yields; ω,
VT  E A  I A RA
E A  K
VT  I AR A
 The loss of field excitation results in over

speeding for a shunt motor. Thus, care should
K
be taken to prevent the field circuit from
getting open.
 ind
 The armature current may be expressed as
IA 
follows:
K
 The speed–torque equation of a DC shunt
motor.
VT
RA
m 


2 ind
K ( K )
22
Cont’d…
 This equation is just a straight line with a negative slope. The
resulting torque–speed characteristic of a DC shunt motor is
shown in Figure 2.12.
Figure 2.12: Torque-Speed Characteristic of a Shunt
or Separately Excited DC Motor with Compensating
Windings to Eliminate Armature Reaction
 In an actual machine, however, as the load increases, the flux
is reduced because of armature reaction. Since the denominator
terms decrease, there is less reduction in speed and speed
regulation is improved somewhat.
Figure 2.13: The Torque-Speed Characteristic of the
Shunt Motor with Armature Reaction.
23
2.3.3.2 Speed Control of Shunt
DC Motor.
 Changing the field resistance
- Assume that the field resistor increases and observe the response.
- If the field resistance increases, then the field current decreases
(IF = VT/RF increaces ), and as the field current decreases, the
flux Φ decreases with it.
- A decrease in flux causes an instantaneous decrease in the
internal generated voltage, EA = KΦ ω, which causes large
increase in machine’s armature currents, since
VT  E A
IA 
RA
- The induced torque in a motor is given by  ind  KI.A Since the
flux Φ in shunt DC motor decreases while the current IA increases.
The increase in current predominates over the decrease in flux, and
the induced torque rises:
 ind  KI A
24
Cont’d…
 Since  ind  load, the motor speed up.
 However, as the motor speeds up, the internal generated voltage
EA rises, causing IA to fall. As IA falls, the induced torque τind
falls too, and finally τind again equals τload at a higher steady state
speed than originally.
Summary
(1) Increasing RF causes IF (  VR ) to decrease.
(2) Deceasing IF decreases Φ.
(3) Decreasing Φ lowers EA (  K ).
(4) Decreasing EA increases IA (  V  E / R ).
(5) Increasing IA increases τind (  K  I ), with the change in IA
dominant over the change in flux.
(6) Increasing τind makes   , and the speed ω increases.
(7) Increasing Φ to increases EA = K Φ ω again.
(8) Increasing EA decreases IA.
(9) Decreasing IA decreases τind until  ind   load at a higher speed
25
ω.
T
F
T
A
A
ind
load
A
Cont’d…
Figure 2.14: The effect of field resistance
speed control on a shunt motor’s torque
speed characteristic: over the motor’s
normal operating range.
 As the flux in the machine decreases, the no load speed of the
motor increases, while the slope of the torque speed curve
becomes steeper.
 Naturally, decreasing RF would reverse the whole process, and the
speed of the would drop.
26
2.3.3.4 Changing the Armature
Voltage.
Figure 2.15: Armature voltage control
of a shunt (or separately excited) dc
motor.
Summary
(1) An increase in VA increases IA [= (VA  – EA)/ RA].
(2) Increasing IA increases  ind ( KI A )
(3) Increasing τind makes  ind  load
increasing ω.
(4) Increasing ω increases EA (=Kω  )
(5) Increasing EA decreases IA [ = (VA – EA)/ RA]
(6) Decreasing IA decreases τind until  ind   load
at a higher
ω.
27
Cont’d…
Figure 2.16: The effect of armature voltage speed
control on a shunt motor’s torque speed characteristic
 The effect of an increase in VA on the torque speed characteristic
of separately excited is shown in Figure 2.16.
 The no load speed of the motor is shifted by this method of
speed control, but the slope of the curve remains constant.
28
2.3.4 Series DC Motor.
Figure 2.17: The Equivalent Circuit of
DC Motor.
 A series dc motor is a dc motor whose field windings consists of
a relatively few turns connected in series with the armature
circuits, Figure 2.17.
 The generated voltage EA across the armature has a polarity
opposite to the applied voltage, VT.
29
2.3.4.1 Induced Torque in Series
DC Motor.
 The induced or developed torque is given by,  ind  KI A
 The flux in this motor is directly proportional to its armature
current. Therefore, the flux in the motor can be given by
  cI A
 where c is a constant of proportionality. The induced torque in
this machine is thus given by
 ind  KI A  KcI A
2
 This equation shows that a series motor give more torque per
ampere than any other dc motor, therefore it is used in
applications requiring very high torque, example starter motors
in cars, elevator motors, and tractor motors in locomotives.
30
2.3.4.2 Terminal Characteristic of
a Series DC Motor.
 The terminal characteristic of a series dc motor is based on the
analysis on the assumption of a linear magnetization curve, and
the effects of saturation of the graph.
 The assumption of a linear magnetization curve implies that the
flux in the motor given by;
 The derivation of a series motor’s torque-speed characteristic
starts with Kirchhoff ’s voltage law:
  cI
A
VT  E A  I A ( RA  RS )
 From the equation;  ind  KI A  KcI A
the armature current can be expressed as:
IA 
2
 ind
Kc
31
Cont’d…
 Also, EA = K, substituting these expression in previous
equation yields;
VT  K 
 ind
Kc
( RA  RS )

 We know,
IA 
c
 Substituting from the above equations and the induced torque
equation can written as
 ind
K 2
 
c
 Therefore, the flux in the series motor can be written as :
c

 ind
K
32
Cont’d…
 From the previous equations yields,
 ind
c
VT  K
 ind  
( RA  RS )
K
Kc
 The resulting torque–speed relationship is

VT
1
Kc  ind

R A  RS
Kc
 One disadvantage of series motor can be seen immediately from
this equation. When the torque on this motor goes to zero, its
speed goes to infinity.
 In practice, the torque can never go entirely to zero, because of
the mechanical, core and stray losses that must be overcome.
33
Cont’d…
 However, if no other load is connected to the motor, it can turn
fast enough to seriously damage itself.
 Never completely unload a series motor, and never connect one to
a load by a belt or other mechanism that could break.
Figure 2.18: The Ideal Torque-Speed Characteristic of
a Series dc Motor
34
2.3.4.3 Speed Control of the DC
Motor.
 Controlling speed.
- Change the terminal voltage of the motor.
- If the terminal voltage is increased, the speed also increased,
resulting in a higher speed for any given torque.
- This is only one efficient way to change the speed of a series
motor.
R R
V
1

T
Kc  ind

A
S
Kc
 By the insertion of a series resistor into the motor circuit, but this
technique is very wasteful of power and is used only for
intermittent period during the start-up of some motor.
35
Cont’d…
 The rotor conductors cut the field lines that generate voltage in
the coils.
E ag  2 N r B  g v
 The motor speed and flux equations are :
v 
Dg
2
 ag  B  g D g
36
2.3.5 Compound DC Motor.
shunt
series
shunt
series
Figure 2.19: The Equivalent Compound DC Motor (a) Long-Shunt Connection
(b) Short-Shunt Connection
 A compound DC motor is a motor with both a shunt and a series
field
 Two field windings: One is connected in series with armature
(series field) and the other is connected in parallel with the
armature (shunt field).
 The shunt field is always stronger than the series field in a
cumulative compound motor the mmf of the two fields add in a
differential compound motor the series field is connected so the37
mmf opposes the mmf of the shunt field
Cont’d…
 The Kirchhoff ’s voltage law equation for a compound dc motor
is:
VT  E A  I A ( R A  RS )
 The currents in the compounded motor are related by :
IA  IL  IF
VT
IF 
RF
 The net magnetomotive force given by
F net = F F ± FSE - FAR
Where,
FF = magnetmotive force (shunt field)
FSE = magnetomotive force (series field)
FAR = magnetomotive force (armature reaction)
38
Cont’d…
 The effective shunt field current in the compounded DC motor
given by:
N SE
FAR
*
IF  IF 
IA 
NF
NF
NSE = winding turn per pole on series winding
NF = winding turn per pole on shunt winding
 The positive (+) sign is for cumulatively compound motor
 The negative (-) sign is for differentially compound motor
39
2.3.5.1 Torque Speed Characteristic.
 The cumulatively compounded motor has a higher starting torque
than a shunt motor (whose flux is constant) but a lower starting
torque than a series motor (whose entire flux is proportional to
armature current).
 It combines the best features of both the shunt and the series
motors.
 Like a series motor, it has extra torque for starting; like a shunt
motor, it does not over speed at no load.
 At light loads, the series field has a very small effect, so the motor
behaves approximately as a shunt dc motor.
 As the load gets very large, the series flux becomes quite important
and the torque speed curve begins to look like a series motor’s
characteristic.
40
Cont’d…
Figure 2.20: The Torque-Speed
Characteristic of a Cumulatively
Compounded dc Motor Compared to
Series and Shunt Motors with the Same
Full-Load Rating.
Figure 2.21 The Torque-Speed
Characteristic of a
Cumulatively Compounded dc
Motor Compared to a Shunt
Motor with the Same No-Load
Speed.
41
Cont’d…
 In a differently compounded DC motor, the shunt magnetomotive
force and series magnetomotive force subtract from each other.
 This means that as the load on the motor increase, IA increases
and the flux in the motor decreased.
 As the flux decrease, the speed of the motor increases. The
increase in speed causes another increase in load and IA, Further
decreasing the flux, and increasing the speed again.
 The techniques available for control of speed in a cumulatively
compounded dc motor are the same as those available for a shunt
motor:
Change the field resistance, RF
Change the armature voltage, VA
Change the armature resistance, RA
 The arguments describing the effects of changing RF or VA are
very similar to the arguments given earlier for the shunt motor.
42
2.3.5.2 DC Motor Efficiency.
 Prior to calculating the efficiency of a dc motor, determine the
following losses.
 Type of losses;
(1) Copper losses (I2R losses).
(2) Brush drop losses.
(3) Mechanical losses.
(4) Core losses.
(5) Stray losses.
Pconv = Pdev = EAIA=indω
Pin
Pout
VTIL
I2R losses Mechanical Core loss Stray losses
losses
43
Cont’d…
(1)Electrical or Copper Losses:
Copper losses are the losses that occur in the armature and field
windings of the machine. The copper losses for the armature and
field winding are given by :
Armature Loss; PA = IA2RA
Field Loss;
PF = IF2RF
The resistance used in these calculations is usually the winding
resistance at normal operating temperature
(2) Brush Losses:
The brush drop loss is the power loss across the contact potential at
the brushes of the machines. It is given by the equation:
PBD = VBDIA
(3) Magnetic or Core Losses:
These are the hysteresis and eddy current losses occur in the metal
of the motor.
44
Cont’d…
(4) Mechanical losses:
These are friction and windage losses.
- Friction losses include the losses caused by bearing friction and
the friction between the brushes and the commutator.
- Windage losses are caused by the friction between rotating parts
and air inside the DC machine’s casing.
(5) Stray load losses:
These are other losses that cannot be placed in one of the previous
categories.
Motor efficiency :


Poutput
Pinput
X 100%
Pinput  Plosses
Pinput
X 100%
45
2.3.5.3 Speed Regulation.
 The speed regulation is a measure of the change speed from noload to full load. The percent speed regulation is defined as,
Speed Regulation (SR):
 nl   fl
SR 
X 100%
 fl
or
 nl   fl
SR 
X 100%
 fl
(1) + Ve SR means that the motor speed will decrease when the
load on its shaft is increased.
(2) - Ve SR means that the motor speed increases with increasing
load.
46
2.4 DC Generators.
 DC generators are dc machines used as generator.
 There are five major types of dc generators, classified according
to the manner in which their field flux is produced:
(1) Separately Excited Generator: In separately excited generator, the
field flux is derived from a separately power source independent of the
generator itself.
(2) Shunt Generator: In a shunt generator, the field flux is derived by
connecting the field circuit directly across the terminals of the
generators.
(3) Series Generator: in a series generator, the filed flux is produced by
connecting the filed circuit in series with the armature of the generator.
(4) Cumulatively Compounded Generator: In a cumulatively
compounded generator, both a shunt and series field is present, and their
effects are additive.
(5) Differentially Compounded Generator: In differentially
compounded generator: In a differentially compounded generator, both a
shunt and a series field are present, but their effects are subtractive. 47
Cont’d…
Figure 2.22(a): The Equivalent Circuit of a DC Generator
Figure 2.22(b): A Simplified Equivalent Circuit of a DC Generator, with
RF Combining the Resistances of the Field Coils and the Variable Control
48
Resistor
2.4.1 DC Generator Operation.
 In a dc motor, the stator poles are supplied by dc excitation
current, which produces a dc magnetic field.
49
v
B
a
S
N
1
30
Vdc
2
b
v
Ir_dc
Figure 2.23: (a) Rotor Current Flow
From Segment 1 to 2 (slot a to b)
B
a
S
2
 The N-S poles produce a dc
magnetic field and the rotor coil
turns in this field.
 A turbine or other machine
drives the rotor.
 The conductors in the slots cut the
magnetic flux lines, which induce
voltage in the rotor coils.
 The coil has two sides; one is
placed in slot a, the other in slot b.
DC Generator Operation
30
v
v
N
Vdc
1
Cont’d…
b
Ir_dc
Figure 2.23: (b) Rotor Current 50
Flow
From Segment 2 to 1 (slot b to a)
Cont’d…
DC Generator Operation
1
v
B
 In Figure 2.24(a), the
a
conductors in slot a are cutting
S
N
30
the field lines entering into the
Vdc
rotor from the north pole,
b
 The conductors in slot b are
v
cutting the field lines exiting
Ir_dc
from the rotor to the south pole. Figure 2.24: (a) Rotor current flow from
segment 1 to 2 (slot a to b)
 The cutting of the field lines
generates voltage in the
B
a
conductors.
N
 The voltages generated in the two S
30
Vdc
v
v
sides of the coil are added.
1
2
2
b
Ir_dc
Figure 2.24: (b) Rotor current flow
51
from segment 2 to 1 (slot b to a)
Cont’d…
DC Generator Operation
1
v
B
 The induced voltage is connected
a
to the generator terminals
S
N
30
Vdc
through the commutator and
brushes.
b
 In Figure 2.25(a), the induced
v
Ir_dc
voltage in b is positive, and in a is
negative.
2.25: (a) Rotor current flow from
segment 1 to 2 (slot a to b)
 The positive terminal is
B
connected to commutator
a
segment 2 and to the conductors
S
N
30
Vdc
in slot b.
v
v
 The negative terminal is
b
connected to segment 1 and to
Ir_dc
the conductors in slot a.
1
2
2
2.25: (b) Rotor current flow from
segment 2 to 1 (slot b to a) 52
B
a
S
N
30
Vdc
2
b
v
Ir_dc
Figure 2.26:(a) Rotor Current Flow
From Segment 1 to 2 (slot a to b)
B
a
S
2
 This changes the polarity of the
induced voltage in the coil.
 The voltage induced in a is now
positive, and in b is negative.
v
1
 When the coil passes the neutral
zone:
 Conductors in slot a are then
moving toward the south
pole and cut flux lines exiting
from the rotor.
 Conductors in slot b cut the
flux lines entering the in slot
b.
DC Generator Operation
30
v
v
N
Vdc
1
Cont’d…
b
Ir_dc
Figure 2.26: (b) Rotor Current Flow
53
From Segment 2 to 1 (slot b to a)
v
B
a
S
N
1
30
Vdc
2
b
v
Ir_dc
Figure 2.27: (a) Rotor current flow
from segment 1 to 2 (slot a to b)
B
a
S
2
 The simultaneously the
commutator reverses its
terminals, which assures that the
output voltage (Vdc) polarity is
unchanged.
 In Figure 2.27(b) the positive
terminal is connected to
commutator segment 1 and to
the conductors in slot a.
 The negative terminal is
connected to segment 2 and
to the conductors in slot b.
DC Generator Operation
30
v
v
N
Vdc
1
Cont’d…
b
Ir_dc
Figure 2.27: (b) Rotor current flow
from segment 2 to 1 (slot b to54
a)
2.4.2 DC Generator Equivalent
Circuit.
 Figure 2.28 is the DC equivalent circuit of a DC motor. Where
(1) EA and a resistor RA is the armature which is represented by an
ideal voltage source.
(2) The brush voltage drop is represented by a small battery Vbrush
opposing the direction of the current flow in the machine.
(3) The field coils, which produce the magnetic flux in the
generator, are represented by inductor LF and RF.
(4) The separate resistor Radj represents an external variable
resistor used to control the amount of current in the filed circuit.
Figure 2.28: Equivalent Circuit
of a DC Motor.
55
Cont’d…
 The brush drop voltage is often only a very tiny fraction of the
generated voltage in the motor and can be neglected. The
approximate value is included in the value of RA.
 The internal resistance of the filed coils is sometimes lumped
together with the variable resistor, and the total is called RF ,
Figure 2.29 below.
 Figure 2.29 is the simplified equivalent circuit of Figure 2.28.
Figure 2.29: A Simplified Equivalent Circuit eliminating the Brush Voltage Drop
and Combining Radj with the Field Resistance .
56
Cont’d…
 The internal generated voltage in this motor is,
E A  K
 EA is directly proportional to the flux in the motor and speed of
the motor.
 Refer to Figure 2.30, the field current in dc motor produces a
field magnetomotive force given by F = NF IF.
Figure 2.30: The magnetization curve of a ferromagnetic material (Φ versus F )
 This magnetomotive force produces a flux in the motor in
accordance with its magnetization curve.
57
Cont’d…
 The field current is directly proportional to the magnetomotive
force and since EA is directly proportional to the flux, it is
customary to present the magnetization curve as a plot EA versus
field current for a given speed ω0 , Figure 2.31.
Figure 2.31: The Magnetization Curve of a dc Machine Expresses as a Plot of EA
Versus IF, for a fixed speed ω0
 The induced torque developed by the motor is
 ind  KI A
58
2.4.3 Separately Exited DC
Generators.
Figure 2.32: Separately Excited DC Generator
 A separately excited DC generator is a generator whose filed
current is supplied by a separately external DC voltage source
where,
VT = Actual voltage measured at the terminals of the generator.
IL = current flowing in the lines connected to the terminals.
EA = Internal generated voltage.
IA = Armature current.
59
2.4.3.1 Terminal Characteristic of a
Separately Excited DC Generator.
Figure 2.33: The Terminal Characteristic of a Separately Excited DC Generator (a)
with and (b) Without Compensating Windings (EA = K).
 For DC generator, the output quantities are its terminal voltage
and line current. The terminal voltage is VT = EA – IARA
 Since the internal generated voltage EA is independent of IA, the
terminal characteristic of the separately excited generator is a
straight line.
60
2.4.3.2 Control of Terminal Voltage.
 The terminal voltage of a separately excited DC generator can be
controlled by changing the internal generated voltage EA of the
machine.
VT = EA – IARA
 If EA increases, VT will increase, and if EA decreases, VT will
decreases. Since the internal generated voltage, EA = KΦω, there
are two possible ways to control the voltage of this generator;
(1) Change the speed of rotation.
If ω increases, then EA = KΦω increases, so VT = EA IARA increases too.
(2) Change the field current.
If RF is decreased, then the field current increases (IF =VF/RF
). Therefore, the flux Φ in the machine increases. As the flux
rises, EA= K ω must rise too, so VT = EA – IARA increases.
62
2.4.4 Shunt DC Generator.
 A shunt DC generator is a DC generator that supplies its own
field current by having its field connected directly across the
terminals of the machine.
I A  IF  IL
VT  E A  I A RA
 VT
I F  
 RF



Figure 2.34 : The Equivalent Circuit
of a Shunt DC Generator.
63
2.4.4.1 Voltage Built up in a Shunt
Generator.
 Assume the DC generator has no load connected to it and that the
prime mover starts to turn the shaft of the generator.
 The voltage buildup in a DC generator depends on the presence
of a residual flux in the poles of the generator.
 This voltage is given by;
E A  K res 
 This voltage, EA is essentially applied to the field circuit, and it
causes a current IF to flow in the field coils.
 This field current produces a magnetomotive force in the poles,
which increases the flux in them.
 EA, then VT higher causes and increase IF, which further
increasing the flux  and so on.
 The final operating voltage is determined by intersection of the
field resistance line and saturation curve. This voltage buildup
64
process is depicted in the next slide
Cont’d…
Figure 2.35: Voltage Built up on Starting in a Shunt DC
Generator.
65
Cont’d…
 Several causes for the voltage to fail to build up during starting
which are;
(1) Residual magnetism. If there is no residual flux in the
poles, there is no Internal generated voltage, EA = 0V and the
voltage will never build up.
(2) Critical resistance. Normally, the shunt generator builds up
to a voltage determined by the intersection of the field resistance
line and the saturation curve.
- If the field resistance is greater than critical resistance, the
generator fails to build up and the voltage remains at the residual
level.
- To solve this problem, the field
resistance is reduced to a value
less than critical resistance.
Refer Figure 9-51 page 605
(Chapman)
66
Cont’d…
 The direction of rotation of the generator may have been reversed, or the
connections of the field may have been reversed. In either case,
the residual flux produces an internal generated voltage EA. The
voltage EA produce a field current which produces a flux
opposing the residual flux, instead of adding to it.
 Under these conditions, the flux actually decreases below res
and no voltage can ever build up.
67
2.4.4.2 Terminal Characteristics of
DC Shunt Generator.
Figure 2.36: The Terminal
Characteristic of a Shunt DC
Generator
 As the load on the generator is increased, IL increases and so IA =
IF + IL also increase.
 An increase in IA increases the armature resistance voltage drop
IARA, causing VT = EA -IARA to decrease.
 However, when VT decreases, the field current IF in the machine
decreases with it. This causes the flux in the machine to decrease;
decreasing EA. Decreasing EA causes a further decrease in the 68
terminal voltage, VT = EA - IARA
2.4.4.3 Voltage Control for Shunt
DC Generator.
 There are two ways to control the voltage of a shunt generator:
(1) Change the shaft speed, ωm of the generator.
(2) Change the field resistor of the generator, thus changing the
field current.
 Changing the field resistor is the principal method used to control
terminal voltage in real shunt generators. If the field resistor RF is
decreased, then the field current IF = VT/RF increases.
 When IF , the machine’s flux , causing the internal generated
voltage EA. EA causes the terminal voltage of the generator to
increase as well.
69
2.4.4.4 The Series DC Generator.
Figure 2.37 : The Equivalent
Circuit of a Series DC Generator
 A series DC generator is a generator whose field is connected in
series with its armature. Because the field winding has to carry the
rated load current, it usually have few turns of heavy wire.
 The shunt generator tends to maintain a constant terminal
voltage. While the series generator has tendency to supply a
constant load current.
 The Kirchhoff ’s voltage law for this equation;
VT  E A  I A ( RA  RS )
70
2.4.4.5 Terminal Characteristics of
a Series Generator.
Figure 2.38 : A Series Generator
Terminal Characteristic with Large
Armature Reaction Effects
 The magnetization curve of a series DC generator looks very much
like the magnetization curve of any other generator.
 At no load, however, there is no field current, so VT is reduced to a
very small level given by the residual flux in the machine.
 As the load increases, the field current rises, so EA rises rapidly.
The IA (RA + RS) drop goes up too, but at the first the increase in EA
goes up more rapidly than the IA(RA + RS) drop rises, so VT increases.
 After a while, the machine approaches saturation, and EA becomes
almost constant. At that point, the resistive drop is the predominant
71
effect, and VT starts to fall.
2.4.5 Cumulatively Compound DC
Generator.
Figure 2.39 : The Equivalent
Circuit of a Cumulatively
Compounded DC Generator with a
Long Shunt Connection
 A cumulatively compounded DC generator is a DC generator with
both series and shunt fields, connected so that the magnetomotive
forces from the two fields are additive.
72
Cont’d…
 The total magnetomotive force on this machine is given by
Fnet = FF + FSE - FAR
where FF = the shunt field magnetomotive force
FSE = the series field magnetomotive force
FAR = the armature reaction magnetomotive force

NFI*F = NFIF + NSEIA - FAR
I
*
F
N SE
FAR
 IF 
IA 
NF
NF
73
Cont’d…
 The other voltage and current relationships for this generator
are;
I A  IF  IL
VT  E A  I A ( RA  RS )
VT
IF 
RF
74
Cont’d…
The Cumulatively Compounded DC Generator
 Another way to hook up a cumulatively compounded generator. It
is the “short-shunt” connection, where series field is outside the
shunt field circuit and has current IL flowing through it instead of
IA.
Figure 2.40 : The Equivalent Circuit of a Cumulatively DC Generator
with a Short Shunt Connection
75
Cont’d…
The Terminal Characteristic of a Cumulatively
DC Generator
 When the load on the generator is increased, the load current IL
also increases.
 Since IA = IF + IL, the armature current IA increases too. At this
point two effects occur in the generator:
(1) As IA increases, the IA (RA + RS) voltage drop increases as well.
This tends to cause a decrease in the terminal voltage,
VT = EA –IA (RA + RS).
(2) As IA increases, the series field magnetomotive force
FSE = NSEIA increases too. This increases the total
magnetomotive force Ftot = NFIF + NSEIA which increases the flux
in the generator. The increased flux in the generator increases EA,
which in turn tends to make VT = EA – IA (RA + RS) rise.
76
Cont’d…
Voltage Control of Cumulatively Compounded DC Generator
 The techniques available for controlling the terminal voltage of a
cumulatively compounded DC generator are exactly the same as the
technique for controlling the voltage of a shunt DC generator;
(1) Change the speed of rotation.
An increase in  causes EA = K to increase, increasing the
terminal voltage VT = EA – IA (RA + RS).
(2) Change the field current.
A decrease in RF causes IF = VT/RF to increase, which increase
the total magnetomotive force in the generator. As Ftot increases, the
flux  in the machine increases, and EA = K increases. Finally, an
increase in EA raises VT.
77
Cont’d…
Analysis of Cumulatively Compounded DC Generators
 The equivalent shunt field current Ieq due to the effects of the
series field and armature reaction is given by
N SE
FAR
I eq 
IA 
NF
NF
 The total effective shunt field current is
I F*  I F  I eq
78
Cont’d…
Field Resistance
IA (RA + RS)
VT at no load condition will be the point at which
the resistor line and magnetization curve intersect.
As load is added to the field current Ieq and the
resistive voltage drop [IA(RA + RF)].
The upper tip triangle represents the internal
generated voltage EA.
The lower line represents the terminal voltage VT
79
Cont’d…
The Differentially Compounded DC Generator
I A  IL  IF
VT
IF 
RF
VT  E A  I A ( RA  RF )
Figure 2.41: The equivalent circuit of a differentially
compounded DC generator
A differentially compounded DC generator is a generator with both
shunt and series fields, but this time their magnetomotive forces
subtract from each other.
80
Cont’d…
The net magnetomotive force is
Fnet = FF – FSE – FAR
Fnet = NFIF – NSEIA - FAR
And the equivalent shunt field current due to the series field and
armature reaction is given by : N
FAR
SE
I eq  
IA 
NF
NF
The total effective shunt field current in this machine is
I  I F  I eq
*
F
or
N SE
FAR
I  IF 
IA 
NF
NF
*
F
81
Cont’d…
Voltage Control of Differentially Compounded DC Generator
 Two effects occur in the terminal characteristic of a differentially
compounded DC generator are
(1) As IA increases, the IA (RA + RS) voltage drop increases as well.
This increase tends to cause the terminal voltage to decrease VT.
(2) As IA increases, the series field magnetomotive FSE = NSEIA
increases too. This increases in series field magnetomotive force
reduces the net magnetomotive force on the generator, (Ftot =
NFIF – NSEIA), which in turn reduces the net flux in the generator.
A decrease in flux decreases EA, which in turn decreases VT.
 Since both effects tend to decrease VT, the voltage drop drastically
as the load is increased on the generator as shown in next slide
82
Cont’d…
 The techniques available for adjusting terminal voltage are exactly
the same as those for shunt and cumulatively compounded DC
generator:
(1) Change the speed of rotation, m.
(2) Change the field current, IF.
83