CH 4 DC Machines - Copy.pptx

Introduction:
 DC machines are generators that convert mechanical energy to dc electric energy and motors
that convert dc electric energy to mechanical energy.
 Although DC is not widely used by consumers, DC machines have played a major role in industry
over the years.
 Most dc machines are like ac machines in that they have ac voltages and currents within
them---dc machines have a dc output only because a mechanism exists that converts the
internal ac voltages to dc voltages at their terminals. Since this mechanism is called a
commutator, dc machinery is also known as commutating machinery.
 DC machines are characterized by their versatility. By means of various combinations of
shunt-, series-, and separately-excited field windings they can be designed to display a wide
variety of volt-ampere or speed-torque characteristics for both dynamic and steady-state
operation.
 Because of the ease with which they can be controlled, systems of dc machines have been
frequently used in applications requiring a wide range of motor speeds or precise control of
motor output.
 In recent years, solid-state ac drive system technology has developed sufficiently that these
systems are replacing dc machines in applications previously associated almost exclusively with
dc machines. However, the versatility of dc machines in combination with the relative simplicity
of their drive systems will insure their continued use in a wide variety of applications.

Cont’d
 DC Machine is most often used for a motor.
 The major advantages of dc machines are the easy speed and
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.

Cont’d
Three electrical machines (dc, induction, and synchronous) are used extensively
for electromechanical energy conversion. In these machines, conversion of
energy from electrical to mechanical form or vice versa results from the following
electromagnetic phenomena:
 When a conductor moves in a magnetic field, voltage is induced in the conductor
 When a current-carrying conductor is placed in a magnetic filed, the conductor experiences
a mechanical force.
These two effects occur simultaneously whenever energy conversion takes place
from electrical to mechanical or vice versa.
 In motoring action, the electrical system makes current flow through the conductors that
are placed in the magnetic filed. A force is produced on each conductor. If the conductors
are placed on a structure free to rotate, and electromagnetic torque will be produced,
tending to make the rotating structure rotate at some speed.
 If the conductors rotate in a magnetic field, a voltage will also be induced in each
conductor.

Cont’d
 In generating action, the process is reversed. In this case, the rotating
structure, the rotor, is driven by a prime mover (such as a steam turbine or a
diesel engine).
• A voltage will be induced in the conductors that are rotating with the rotor. If an
electrical load is connected to the winding formed by these conductors, a current I will
flow, delivering electrical power to the load.
• Moreover, the current flowing through the conductor will interact with the magnetic
field to produce a reaction torque, which will tend to oppose the torque applied by the
prime mover.
 Note that in both motoring and generating actions, the coupling magnetic
field is involved in producing a torque and an induced voltage.

Motional Voltage, e
• An expression can be derived for the voltage
induced in a conductor moving in a magnetic
field.
• As shown if a conductor of length l moves at a
linear speed v in a magnetic field B, the induced
voltage in the conductor is
𝑒 = 𝐵𝑙𝑣
Where B, l, and v are mutually perpendicular.
The polarity of the induced voltage can be
determined from the so called right-hand screw
rule. Turn the vector v toward the vector B. if the
a right-hand screw is turned in the same way, the
motion of the screw will indicate the direction of
positive polarity of the induced voltage.

Electromagnetic force, f
• For the current-carrying conductor in
figure a, the force (known as Lorentz
force) produced on the conductor is
• 𝑓 = 𝐵𝑙𝑖
• Where B, l, and I are mutually
perpendicular. The direction of the force
can be determined by using the right-
hand screw rule.
• Turn the current vector I toward the flux
vector B. if a screw is turned in the
same, the direction of the screw
represents the direction of the force, f.

Basic Structure of Electric Machines
• The structure of an electric machine has two
major components, stator and rotor, separated by
air-gap.

Cont’d
• Stator: this part of the machine does not move and normally
is the outer frame of the machine.
• Rotor: this part of the machine is free to move and normally
is the inner part of the machine.
• Both stator and rotor are made of ferromagnetic materials. In
most machines slots are cut on the inner periphery of the
stator and outer periphery of the rotor structure.
• Conductors are placed in these slots. The iron core is used to
maximize the coupling between the coils (formed by
conductors) placed on the stator; to increase the flux density
of the machine and to decrease the size of the machine.
• If the stator or rotor (or both) is subjected to a time-varying
magnetic flux, the iron core is laminated to reduce eddy
current losses.

Cont’d
• The conductors placed in the slots of the stator or rotor are
interconnected to form windings.
• The winding in which voltage is induced is called the armature winding.
• The winding through which a current is passed is called the field winding.
• Permanent magnets are used in some machines to provide the major source of
flux in the machine.

Cont’d
• DC Machine:
• In the DC machine, the field winding is placed
on the stator and the armature winding on
the rotor.
• A dc current is passed through the field
winding to produce flux in the machine.
• Voltage induced in the armature winding is
alternating. A mechanical commutator and a
brush assembly function as a rectifier or
inverter, making the armature terminal
voltage unidirectional.
Field winding

Cont’d
• Induction Machine:
• In this machine the stator windings serve as both armature
windings and filed winding.
• When the stator windings are connected to an ac supply, flux
is produced in the air gap and revolves at a fixed speed
known as synchronous speed.
• This revolving flux induces voltage in the stator windings as
well as the rotor windings. If the rotor circuit is closed,
current flows in the rotor winding and reacts with the
revolving flux to produce torque. The steady state speed of
the rotor is very close to the synchronous speed.
• The rotor can have a winding similar to the stator or a cage-
type winding.
• The latter is formed by pacing aluminum or copper bars in the
rotor slots and shorting them at the ends by means of rings.

Cont’d
• Synchronous Machine:
• In this machine, the rotor carries the field winding and the stator carries the armature
winding.
• The field winding is excited by direct current to produce flux in the air gap. When the
rotor rotates, voltage is induced in the armature winding placed on the stator.
• The armature current produces a revolving flux in the air gap whose speed is the same
as the speed of the rotor-hence the name synchronous machine.

Cont’d
• The three major machines types, although they differ in physical construction and appear to be
quite different from each other, are in fact governed by the same basic laws. Their behavior can be
explained by considering the same fundamental principles of voltage and torque production.
• Various analytical techniques can be derived for them, but the forms of the equations will differ
merely to reflect the difference in construction of the machines.
• For example, analysis will show that in dc machines the stator and rotor flux distributions are fixed
in space and a torque is produced because of the tendency of these two flux to align.
• The induction machine is an ac machine and differs in many ways from the dc machine but works
on the same principle. Analysis will indicate that the stator flux and the rotor flux rotate in
synchronism in the air-gap and the two flux distributions are displaced from each other by a torque-
producing displacement angle. The torque is produced because of the tendency of the two flux
distributions to align with each other.
• It must be emphasized at the outset that ac machines are not fundamentally different from dc
machines. Their construction details are different, but the same fundamental principles underlie
their operation.

Evolution of DC Machines (Simple Loop Generator)
• The simplest elementary generator that can be built is an ac generator. Basic
generating principles are most easily explained through the use of the elementary ac
generator. For this reason, the ac generator will be discussed first. The dc generator will
be discussed later.
• An elementary generator (fig. 1) consists of a wire loop placed so that it can be rotated
at a constant speed in a uniform magnetic field provided by permanent magnet or
electromagnet.
• The two ends of the coil are connected to rings
called Slip Rings which are insulated from each
other and from the shaft.
• Two collecting brushes (of carbon or copper)
press against the slip rings. Their function to
collect the current induced in the coil and to
convey to external load.
• The generated voltage appears across these
brushes.
•

Working Theory
• The elementary generator produces a voltage in the following manner
(fig. 1-3). The armature loop is rotated in a clockwise direction.

Working Theory
• We will consider the following cases:
Case 1: When the loop is in position no. 1. (This will be considered
the zero-degree position.)
i. At 0º the armature loop is perpendicular to the magnetic field.
ii. The conductors (AB and CD) of the loop are moving parallel to
the field.
iii.The instant the conductors are moving parallel to the magnetic
field, they do not cut any lines of flux. Therefore, no emf is
induced in the conductors, and the meter at position A
indicates zero. This position is called the NEUTRAL PLANE.

Working Theory
• Case 2: When the loop at position 2.
i. As the armature loop rotates from position 1 (0º) to
position 2 (90º), the conductors cut through more and
more lines of flux, at a continually increasing angle.
ii. At 90º, the coil sides AB and CD are at right angles to the
flux and are therefore cutting through a maximum number
of lines of flux at maximum angle.
iii. The result is that between 0º and 90º , the induced emf in
the conductors builds up from zero to a maximum value.
iv. Observe that from 0º to 90º , the AB conductor cuts DOWN
through the field. At the same time the CD conductor cuts
UP through the field. The induced emfs in the conductors
are series-adding. This means the resultant voltage across
the brushes (the terminal voltage) is the sum of the two
induced voltages.
v. The meter at position 2 reads maximum value.

Working Theory
i. As the armature loop continues rotating from 90º (position
2) to 180º (position 3), the conductors which were cutting
through a maximum number of lines of flux at position 2
now cut through fewer lines. They are again moving parallel
to the magnetic field at position 3. They no longer cut
through any lines of flux.
ii. As the armature rotates from 90º to 180º , the induced
voltage will decrease to zero in the same manner that it
increased during the rotation from 0º to 90º . The meter
again reads zero.
iii.From 0º to 180º the conductors of the armature loop have
been moving in the same direction through the magnetic
field. Therefore, the polarity of the induced voltage has
remained the same. This is shown by points 1 through 3 on
the graph.

Working Theory
i. As the loop rotates beyond 180º (position 3), through 270º
(position 4), and back to the initial or starting point (position
1), the direction of the cutting action of the conductors
through the magnetic field reverses. Now the AB conductor
cuts UP through the field while the CD conductor cuts DOWN
through the field. As a result, the polarity of the induced
voltage reverses. Following the sequence shown by graph
points C, D, and back to A, the voltage will be in the
direction opposite to that shown from points A, B, and C.
The terminal voltage will be the same as it was from A to C
except that the polarity is reversed (as shown by the meter
deflection at position D). The voltage output waveform for
the complete revolution of the loop is shown on the graph in
figure 1-3.
ii. This cycle repeats with each revolution of the coil.

DIRECTION OF INDUCED EMF AND CURRENT
• We use Right-hand rule to determine the direction of induced emf.

• Consider the simple loop generator and imagine the the coil to be
rotating in clockwise direction.

• When the plane of the coil is at right angles to the lines of flux as shown
below, then, the direction of velocity of both sides of the coil is parallel
to the direction of the field lines so, there is no cutting for field lines.
Then flux linkages with the coil is minimum. Hence; there is no induced
EMF in the coil.

• As the coil continues rotate further, the rate of change of flux linkages
(and hence induced EMF in it) increases. When 90° is reached the coil
plane is parallel to the lines of the flux. As seen, the rate of change of
flux linkages is maximum. Henc maximum EMF is induced in the coil at
90°. The direction of flow current(0-90) is ABXYCD as shown.

• In the next quarter revolution i.e from 90 to 180, the rate of change of
flux linkages decreases. Hence, the induced EMF decreases gradually to
zero and the direction of ABXYCD.

• In the next half revolution i.e. from 180-360, the variations in the magnitude of EMF
are similar to those in the first half revolution but it will be found that the direction of
indeed current is from D to C and B to A. Hence, the current is flowing along DCYXBA
which his just the reverse of the previous direction of flow.
• So we find that the current which we obtain from such a simple generator reverses its
direction after every half revolution.

Cont’d
• The e.m.f. generated in the previous simple loop generator is alternating one.
If, somehow, connection of the coil side to the external load is reversed at the
same instant the current in the coil side reverses, the current through the load
will be direct current. This is achieved by a device called commutator.
• So we can have a simple loop d.c. generator by replacing the slip rings in ac
generator by a commutator. This is the main difference between construction of
ac and dc generators.
• In fact, a commutator is a mechanical rectifier. It mechanically reverses the
armature loop connections to the external circuit.

Action Of Commutator
• A commutator is a conducting ring split into segments; each segment is electrically conne
cted to one terminal of the loop. It is mounted on the shaft , but is electrically insulated fr
om it. The brushes are stationary and make sliding contact with the segments.
• Fig. below shows a commutator having two segments C1 and C2. It consists of a
cylindrical metal ring cut into two halves or segments C1 and C2 respectively separated
by a thin sheet of mica. The commutator is mounted on but insulated from the rotor
shaft.
• The commutator can also be called a split Ring.
• The rings of the commutator are so arranged that during half the revolution of the coil,
each half ring remain in contact with a particular brush. while during the next half
revolution, when the current is reversed, the same half ring is in contact with other the
brush.

Action Of Commutator
• The ends of coil sides AB and CD are connected to the segments C1 and C2 respectively as shown
in Fig. (1.4). Two stationary carbon brushes rest on the commutator and lead current to the
external load. With this arrangement, the commutator at all times connects the coil side under S-
pole to the +ve brush and that under N-pole to the -ve brush.
In Fig. (1.4), the coil sides AB and CD are under N-pole and S-
pole respectively. Note that segment C1 connects the coil side
AB to point P of the load resistance R and the segment C2
connects the coil side CD to point Q of the load. Also note the
direction of current through load. It is from Q to P
After half a revolution of the loop (i.e., 180° rotation), the coil
side AB is under S-pole and the coil side CD under N-pole as
shown in Fig. (1.5). The currents in the coil sides now flow in
the reverse direction but the segments C1 and C2 have also
moved through 180° i.e., segment C1 is now in contact with
+ve brush and segment C2 in contact with -ve brush.
Note that commutator has reversed the coil connections to the
load i.e., coil side AB is now connected to point Q of the load
and coil side CD to the point P of the load. Also note the
direction of current through the load. It is again from Q to P.

Action Of Commutator (Cont’d)
• Thus the alternating voltage generated in the loop will appear as direct voltage across
the brushes. The reader may note that e.m.f. generated in the armature winding of a
d.c. generator is alternating one. It is by the use of commutator that we convert the
generated alternating e.m.f. into direct voltage. The purpose of brushes is simply to
lead current from the rotating loop or winding to the external stationary load.
• The variation of voltage for the dc generator across the brushes with the angular
displacement of the loop will be as shown in Fig. below.
• The output is not a steady direct voltage but has a pulsating
character. It is because the voltage appearing across the
brushes varies from zero to maximum value and back to
zero twice for each revolution of the loop.
• A pulsating direct voltage such as is produced by a single
loop is not suitable for many commercial uses.
• What we require is the steady direct voltage. This can be
achieved by using a large number of coils connected in
series. The resulting arrangement is known as armature
winding.

CONSTRUCTION OF D.C. GENERATOR
 The d.c. generators and d.c. motors have the same general construction. Any d.c.
generator can be run as a d.c. motor and vice-versa.
 All d.c. machines have five principal components viz., (i) field system(Stator) (ii)
armature core (iii) armature winding (Rotor) (iv) commutator (v) brushes [See Fig.].

Classification of DC Machines
• The field circuit and the armature circuit can be interconnected in
various ways to provide a wide variety of performance characteristics-
an outstanding advantage of dc machines.
• Also, the field poles can be excited by two field windings, a shunt field
winding and a series field winding.
• The shunt winding has a large number of turns and takes only a small
current (less than 5% of the rated armature current).
• The series winding has fewer turns but carries a large current.

Cont’d
• The various connections of the field circuit and armature circuit are
shown below:

• Converters that are used to continuously translate electrical input to mechanical out
put or vice versa are called electrical machines.
Motor
Generator
• The process of translation is known as electromechanical energy conversion. Thus, the
process is reversible.
• The same physical machine can operate as either a motor or a generator-it is simply a
question of the direction of the power flow through it.
• DC machines are characterized by their versatility. They can be designed to display a
wide variety of volt-ampere or speed-torque characteristics for both dynamic and
steady-state operation.
H. A. Suud ECEg4221 Fall 2015 34
DC Motors and DC Generators

DC Motors
INTRODUCTION TO DC MOTORS:
• There were several reasons for the continued popularity of dc motors.
• One was that dc power systems are still common in cars, trucks, and aircraft.
• Another application for dc motors was a situation in which wide variations in speed are
needed. Before the widespread use of power electronic rectifier-inverters, dc motors
were unexcelled in speed control applications.
• Even if no dc power source were available, solid-state rectifier and chopper circuits
were used to create the necessary dc power, and dc motors were used to provide
the desired speed control.
• Today, induction motors with solid-state drive packages are the preferred choice over dc
motors for most speed control applications. However, there are still some applications
where dc motors are preferred.

• DC motors are often compared by their speed regulations. The speed regulation ( ) of a
motor is defined by
• It is a rough measure of the shape of a motor’s torque-speed characteristic
• A positive speed regulation means that a motor’s speed drops with increasing load, and a
negative speed regulation means a motor 's speed increases with increasing load.
• The magnitude of the speed regulation tells approximately how steep the slope of the
torque- speed curve is.
36
SR
*100%
nl fl
fl
SR
 



*100%
nl fl
fl
n n
SR
n



• DC motors are, of course, driven from a dc power supply.
• Unless otherwise specified, the input voltage to a dc motor is
assumed to be constant, because that assumption simplifies the
analysis of motors and the comparison between different types of
motors.
• There are five major types of dc motors in general use :
1. The separately excited dc motor
2. The shunt dc motor
3. The permanent-magnet dc motor
4. The series dc motor
5. The compounded dc motor
37

THE EQUIVALENT CIRCUIT of a DC MOTORS:
• The equivalent circuit of a dc motor is shown in Figure below.
• In this figure , the armature circuit is represented by an ideal
voltage source and resistor .
• This representation is really the Thevenin equivalent of the
entire rotor structure, including rotor coils, interpoles, and
compensating windings, if present.
38
A
E A
R
A
R

• The brush voltage drop is represented by a small battery opposing the
direction of current flow in the machine.
• The field coils, which produce the magnetic flux in the generator/motor, are
represented by inductor and resistor .
• Separate resistor represents an external variable resistor used to control
the amount of current in the field circuit.
• There are a few variations and simplifications of this basic equivalent circuit.
• The brush drop voltage is often only a very tiny fraction of the generated
voltage in a machine. Therefore, in cases where it is not too critical, the
brush drop voltage may be left out or approximately included in the value of
. Also, the internal resistance of the field coils is sometimes lumped together
with the variable resistor, and the total is called .
39
brush
V
f
L f
R
adj
R
A
R
F
R

• The internal generated voltage is given by the equation
and the induced torque developed by the machine is given by
• The Kirchhoff ‘s voltage law equation of the armature circuit &
the machine’s magnetization curve, are all the tools necessary
to analyze the behavior & performance of a dc motor.
40
A
E K

ind A
K I
 

ASSIGNMENT:
DERIVE MATHEMATICAL
EQUATIONS FOR THE INTERNAL
GENERATED VOLTAGE AND
INDUCED TORQUE EQUATIONS OF
REAL DC MACHINES

THE MAGNETIZATION CURVE of a DC MOTORS:
• The internal generated voltage is directly proportional to the
flux & the speed of rotation of the machine.
How is related to the field current in the machine?
• The field current in a dc machine produces a field magneto
motive force given by .
A
E
 f f
N I
F
A
E
 This magneto-motive force
produces a flux in the machine in
accordance with its magnetization
curve.

• Since the field current is directly proportional to the magneto
motive force and since is directly proportional to the flux, it
is customary to present the magnetization curve as a plot of
versus field current for a given speed .
42
A
E
0

A
E
 It is worth noting here
that, to get the maximum
possible power per pound
of weight out of a
machine, most motors
and generators are
designed to operate near
the saturation point on
the magnetization curve
(at the knee of the
curve).

SEPARATELY EXCITED AND SHUNT DC MOTORS:
43
 The equivalent circuit of a separately
excited and shunt dc motors is shown in
Fig a and b respectively.
 A separately excited dc motor is a motor
whose field circuit is supplied from a
separate constant-voltage power supply.
 A shunt dc motor is a motor whose field
circuit gets its power directly across the
armature terminals of the motor.

• When the supply voltage to a motor is assumed constant, there
is no practical difference in behavior between these two
machines.
• Unless otherwise specified, whenever the behavior of a shunt
motor is described, the separately excited motor is included.
• The Kirchhoff ‘s voltage law ( KVL) equation for the armature
circuit of these motors is
The Terminal Characteristic of a Shunt DC Motor:
• A terminal characteristic of a machine is a plot of the machine's
output quantities versus each other.
• For a motor, the output quantities are shaft torque and speed,
so the terminal characteristic of a motor is a plot of its output
torque versus speed.
44
T A A A
V E I R
 

How does a shunt dc motor respond to a load?
• Suppose that the load on the shaft of the motor is increased.
• Then the load torque will exceed the induced torque in
the machine, and the motor will start to slow down.
• When the motor slows down, its internal generated voltage
drops ( ), so the armature current in the shunt dc
motor increases.
• As the armature current rises, the induced torque in the motor
increases ( ), & finally the induced torque will equal
the load torque at lower mechanical speed of rotation .
• The output characteristic of a shunt dc motor can be derived
from the induced voltage and torque equations of the motor
plus Kirchhoff’s voltage law (KVL). The KVL equation for a shunt
motor is
45
 /
A T A A
I V E R
  
load ind
A
E K
 
ind A
K I
 
 


• This equation is just a straight line with a negative slope. The
resulting torque- speed characteristic is shown below a.
46
T A A A A
ind
T A A A
ind
T A
V E I R E K
V K I R I
K
V K R
K







  
  
 
 
2
A
T
ind
R
V
K K
 
 
 

• It is important to realize that, in order for the speed of the
motor to vary linearly with torque, the other terms in this
expression must be constant as the load changes.
• The terminal voltage supplied by the dc power source is
assumed to be constant - if it is not constant, then the voltage
variations will affect the shape of the torque- speed curve.
• Another effect internal to the motor that can also affect the
shape of the torque-speed curve is armature reaction.
• If a motor has armature reaction, then as its load increases, the
flux-weakening effects reduce its flux.
• The effect of a reduction in flux is to increase the motor's speed
at any given load over the speed it would run at without
armature reaction. The torque-speed characteristic with
armature reaction is shown above fig b.
47

• If a motor has compensating windings, of course there will be
no flux-weakening problems in the machine, and the flux in the
machine will be constant.
• If a shunt dc motor has compensating windings so that its flux is
constant regardless of load, and the motor's speed and
armature current are known at any one value of load, then it is
possible to calculate its speed at any other value of load, as long
as the armature current at that load is known or can be
determined.
Nonlinear Analysis of a Shunt DC Motor:
• The flux and hence the internal generated voltage , of a dc
machine is a nonlinear function of its magneto motive force.
• Therefore, anything that changes the mmf in a machine will
have a nonlinear effect on the internal generated voltage.
48
 A
E

• Since the change in cannot be calculated analytically, the
magnetization curve of the machine must be used to accurately
determine its for a given magneto motive force.
• The two principal contributors to the mmf in the machine are
its field current and its armature reaction, if present.
• Since the magnetization curve is a direct plot of versus for
a given speed ,the effect of changing machine’s field current
can be determined directly from its magnetization curve.
• If a machine has armature reaction, its flux will be reduced with
each increase in load. The total mmf is the field circuit mmf less
the mmf due to armature reaction (AR):
• We should define equivalent field current that would produce
the same output voltage as the combination of all the mmfs.
49
A
E
A
E
A
E F
I
0
net f f AR
N I
 
F F

• The resulting voltage can then be determined by locating
that equivalent field current on the magnetization curve.
• The equivalent field current of a shunt dc motor is given by
How can the effects of a given field current be determined if the
motor is turning at other than rated speed?
• The equation for the induced voltage in a dc machine when
speed is expressed in revolutions per minute is
• For a given effective field current, the flux in a machine is fixed,
so the internal generated voltage is related to speed by
50
A
E
A
E K n



* AR
F F
F
I I
N
 
F
0 0
A
A
E n
E n


• Where and represent the reference values of voltage &
speed, respectively.
• If the reference conditions are known from the magnetization
curve and the actual is known from Kirchhoff's voltage law,
then it is possible to determine the actual speed .
51
0
A
E
A
E
A
E
F
I
0
n
n
 Note that for any given load, the
speed of the motor with
armature reaction is higher than
the speed of the motor with out
armature reaction.

Speed Control of Shunt DC Motor:
How can the speed of a shunt dc motor be controlled?
• There are two common and one less common methods in use.
• The two common ways in which the speed of a shunt dc
machine can be controlled are by:
1. Adjusting the field resistance (and thus the field flux)
2. Adjusting the terminal voltage applied to the armature
The less common method of speed control is by:
3. Inserting a resistor in series with the armature circuit
CHANGING THE FIELD RESISTANCE:
• If the field resistance increases, then the field current decreases
( ), and as the field current decreases, the flux
decreases with it.
52
F
R
F T F
I V R
  

• A decrease in flux causes an instantaneous decrease in the
internal generated voltage ( ), which causes a large
increase in the machine’s armature current, since
• The induced torque in a motor is given by . Since the
flux in this machine decreases while the current increases,
which way does the induced torque change?
• The increase in current predominates over the decrease in flux,
and the induced torque rises :
• Since , the motor speeds up
53
A
E K 
 
T A
A
A
V E
I
R
 

 

ind A
K I
 A
I
ind A
K I
 
 

ind load
 


• However, as the motor speeds up, the internal generated
voltage rises, causing to fall. As falls, the induced torque
falls too, and finally again equals at a higher steady-
state speed than originally.
To summarize the cause-and-effect of this speed control:
1. Increasing causes to decrease.
2. Decreasing decreases
3. Decreasing lowers
4. Decreasing increases
5. Increasing increases
6. Increase in makes and the speed increases
7. Increasing 𝜔 increases again
8. Increasing decreases
54
A
E K 
 
 
A T A A
I V E R
  
A
E K
 

A
E
ind A
K I
 
  
ind

A
I A
I
ind
load
F
R F T F
I V R
 
F
I 

A
E
A
I
ind
 ind load
 

A
E

9. Decreasing decreases until at a higher speed
• The effect of increasing the field resistance on the output
characteristic of a shunt motor is shown below in Figure.
55

A
I ind
 ind load
 

 Notice that 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 would
reverse the whole process, and
the speed of the motor would
drop.
F
R

CHANGING THE ARMATURE VOLTAGE:
• The second form of speed control involves changing the voltage applied to
the armature of the motor without changing the voltage applied to the
field.
• A connection similar to that shown in figure below is necessary for this
type of control.
• In effect, the motor must be separately excited to use armature voltage
control as shown in the figure below. 56

• If the voltage is increased, then the armature current in the
motor must rise .
• As increased, the induced torque increases,
making , and the speed of the motor increases.
• But as the speed increases, the internal generated voltage
increases, causing the armature current to decrease. This
decrease in decreases the induced torque, causing at
a higher rotational speed .
To summarize the cause-and-effect:
1. An increase in increase
2. Increasing increase
3. Increasing makes increase
4. Increasing increases
5. Increasing decreases
57
 
A A A A
I V E R
  

A
V
ind A
K I
 
 
A
I
ind load
 

 A
E
A
I ind load
 


A
V  
A A A A
I V E R
  
A
I ind A
K I
 
 
ind

ind load
 


 A
E K
 
A
E  
A A A A
I V E R
  

6. Decreasing decreases until at a higher
• The effect of an increase in on the torque-speed
characteristic of a separately excited motor is shown below.
• Notice that the no-load speed of the motor is shifted by this
method of speed control , but the slope of the curve remains
constant.
58

A
V
A
I ind load
 

ind


INSERTING a RESISTOR in series with the ARMATURE CIRCUIT:
• If a resistor is inserted in series with the armature circuit , the
effect is to drastically increase the slope of the motor’s torque-
speed characteristic, making it operate more slowly if loaded.
• It will be found only in applications in which the motor spends
almost all its time operating at full speed or in applications too
inexpensive to justify a better form of speed control.
59
 The insertion of a
resistor is a very
wasteful method of
speed control, since
the losses in the
inserted resistor are
very large. For this
reason, it is rarely used
.

THE PERMANENT-MAGNET DC MOTOR:
• A permanent-magnet dc (PMDC) motor is a dc motor whose
poles are made of permanent magnets.
• These motors do not require an external field circuit, they do
not have the field circuit copper losses associated with shunt
dc motors. Therefore, they can be smaller in size. This makes
these comparatively advantageous.
• PMDC motors are especially common in smaller fractional- and
sub fractional-horsepower sizes, where the expense and space
of a separate field circuit cannot be justified.
• Permanent magnets can not produce as high a flux density as
an externally supplied shunt field, so a PMDC motor will have a
lower induced torque per ampere of armature current
than a shunt motor of the same size and construction.
60
ind A
I

• In addition, PMDC motors run the risk of demagnetization.
• The armature current in a dc machine produces an
armature magnetic field of its own.
• The armature mmf subtracts from the mmf of the poles under
some portions of the pole faces and adds to the mmf of the
poles under other portions of the pole faces reducing the
overall net flux in the machine called armature reaction effect.
• In a PMDC machine, the pole flux is just the residual flux in the
permanent magnets. If the armature current becomes very
large, there is some risk that the armature mmf may
demagnetize the poles, permanently reducing and reorienting
the residual flux in them.
• Demagnetization may also be caused by the excessive heating
which can occur during prolonged periods of overload.
61
A
I

• Below Fig a shows a magnetization curve for a typical
ferromagnetic material. It is a plot of flux density B versus
magnetizing intensity (or equivalently, a plot of flux versus
mmf ).
• When a strong external mmf is applied to this material and
then removed, a residual flux will remain in the material.
• To force the residual flux to zero, it is necessary to apply a
coercive magnetizing intensity with a polarity opposite to
the polarity of the magnetizing intensity that originally
established the magnetic field.
• For normal machine applications such as rotors and stators, a
ferromagnetic material should be picked which has as small a
and as possible, since such a material will have low
hysteresis losses.
62
H 
F
res
B
C
H
H
res
B C
H

• On the other hand, a good material for the poles of a PMDC motor
should have as large a residual flux density as possible, while
simultaneously having as large a coercive magnetizing intensity
as possible. The magnetization curve of such a material is shown in
above Fig b. The large produces a large flux in the machine,
while the large means that a very large current would be re-
quired to demagnetize the poles.
• In the last 40 years, a number of new magnetic materials have been
developed which have desirable characteristics for making
permanent magnets as shown in above Fig c.
• A PMDC motor is basically the same machine as a shunt dc motor,
except that the flux of a PMDC motor is fixed.
• Therefore, it is not possible to control the speed of a PMDC motor
by varying the field current or flux. The only methods of speed
control available for a PMDC motor are armature voltage control
and armature resistance control.
64
res
B
C
H
res
B
C
H

THE SERIES DC MOTOR:
• A series dc motor is a dc motor whose field windings consist of
a relatively few turns connected in series with the armature
circuit as shown in the Fig below.
65
 
T A A A S
V E I R R
  
 In a series motor, the
armature current ,
field current , and
line current are all
the same.
 The Kirchhoff’s
voltage law equation
for this motor is

Induced Torque in a Series DC Motor:
• The basic behavior of a series dc motor is due to the fact that
the flux is directly proportional to the armature current, at
least until saturation is reached.
• As the load on the motor increases, its flux increases too. An
increase in flux in the motor causes a decrease in its speed.
The result is that a series motor has a sharply drooping torque-
speed characteristic.
• The induced torque in this machine is given by Equation
• The flux in this machine is directly proportional to its armature
current (at least until the metal saturates). Therefore, the flux in
the machine can be given by
66
ind A
K I
 

A
cI
 

• where is a constant of proportionality. The induced torque is
• As a result of this relationship, it is easy to see that a series
motor gives more torque per ampere than any other dc motor.
It is therefore used in applications requiring very high torques.
• Examples of such applications are the starter motors in cars,
elevator motors, and tractor motors in locomotives.
The Terminal Characteristic of a Series DC Motor:
• To determine the terminal characteristic of a series dc motor, an
analysis will be based on the assumption of a linear
magnetization curve, and then the effects of saturation will be
considered in a graphical analysis.
• The flux in the motor is be given by Equation
67
2
ind A A
K I KcI
 
 
c
A
cI
 

• This equation will be used to derive the torque-speed
characteristic curve for the series motor.
• Kirchhoff’s voltage law
• The armature current and voltage can be expressed as
• Substituting these expressions yields
• If the flux can be eliminated from this expression, it will directly
relate the torque of a motor to its speed. To eliminate:
68
A
I
c


 
  
T A A A S
V E I R R
ind
A
I
Kc

 A
E K

 
ind
T A S
V K R R
Kc


  

• The induced torque equation can be rewritten as
• The armature current and voltage can be expressed as
• Substituting these expressions and solving for speed yields
• The resulting torque-speed relationship is 69
 
 2
ind
K
c
ind
c
K
 

 
 
 
ind
T ind A S
A S
ind T ind
A S
T
ind
c
V K R R
K Kc
R R
Kc V
Kc
R R
V
Kc
Kc

 
  


  

 

 

• That is quite an unusual relationship! This ideal torque-speed
characteristic is plotted in Fig below.
70
 
1 A S
T
ind
R R
V
Kc
Kc



 
 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.
 However, if no other load is connected to the motor, it can turn
fast enough to seriously damage it self. Never completely un-
load a series motor, and never connect one to a load by a belt
or other mechanism that could break. If that were to happen
and the motor were to become unloaded while running, the
results could be serious.

Speed Control of Series DC Motor:
• Unlike with the shunt dc motor, there is only one efficient way
to change the speed of a series dc motor. That method is to
change the terminal voltage of the motor.
• If the terminal voltage is increased, the first term of the torque-
speed Equation is increased, resulting in a higher speed for any
given torque.
• The speed of series dc motors can also be controlled 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 periods during the start up.
• Until the last 40 years or so, there was no convenient way to
change , so the only method of speed control available was
the wasteful series resistance method. That has all changed
today with the introduction of solid-state control circuits.
71
T
V

THE COMPOUNDED DC MOTOR:
• A compounded dc motor is a motor with both a shunt and a
series field as shown in the Fig below.
72
 The dots that appear on the two field coils
have the same meaning as the dots on a
transformer: Current flowing into a dot
produces a positive mmf.
 If current flows into the dots on both field
coils, the resulting mmf add to produce a
larger total mmf, known as cumulative
compounding.

• If current flows into the dot on one field coil and out of the dot
on the other field coil , the resulting mmf subtract.
• In the above Fig, the round dots correspond to cumulative
compounding of the motor, and the squares correspond to
differential compounding.
• Kirchhoff’s voltage law equation for a compounded dc motor is
• The currents in the compounded motor are related by
• The net mmf and the effective shunt field current in the
compounded motor are given by
73
 
  
T A A A S
V E I R R
A L F
T
F
F
I I I
V
I
R
 


where the positive sign in the equations is associated with a
cumulatively compounded motor and the negative sign is
associated with a differentially compounded motor.
Torque-Speed Characteristic of a Cumulatively Compounded :
• In this dc motor, there is a component of flux which is constant
and another component which is proportional to its armature
current (and thus to its load).
• Therefore, 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).
74
*
net F SE AR
SE AR
F F A
F F
N
I I I
N N
  
  
F F F F
F

• In a sense, the cumulatively compounded dc motor 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.
75
 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.
 A comparison of the torque-speed
characteristics of each of these types of
machines is shown in Fig a and b.
(b)The torque-speed characteristic of a
cumulatively compounded dc motor compared
to a shunt motor with the same no-load speed.
(a) The torque-speed
characteristic of a cumulatively
compounded dc motor
compared to series and shunt
motors with the same full-load
rating.

Torque-Speed Characteristic of a Differentially Compounded :
• In this dc motor, the shunt mmf and series mmf subtract from each other. This
means that as the load on the motor increases, increases and the flux in the motor
decreases. But as the flux decreases, the speed of the motor increases.
• This speed increase causes another increase in load, which further increases ,
further decreasing the flux, and increasing the speed again.
• The result is that a differentially compounded motor is unstable and tends to run
away.
• This instability is much worse than that of a shunt motor with armature reaction. It is
so bad that a differentially compounded motor is unsuitable for any application.
• To make matters worse, it is impossible to start such a motor.
76
A
I
A
I

• At starting conditions the armature current and the series field current are
very high. Since the series flux subtracts from the shunt flux, the series
field can actually reverse the magnetic polarity of the machine’s poles.
The motor will typically remain still or turn slowly in the wrong direction
while burning up, because of the excessive armature current.
77
 When this type of motor is to be started, its
series field must be short circuited, so that it
behaves as an ordinary shunt motor during the
starting period.
 A typical terminal characteristic for a
differentially compounded dc motor is shown
in Fig.

Speed Control in the Cumulatively Compounded DC Motor:
• The techniques available for the control of speed in a
cumulatively compounded dc motor are the same as those
available for a shunt motor:
1. Change the field resistance
2. Change the armature voltage
3. Change the armature resistance
• The arguments describing the effects of changing or are
very similar to the arguments given for the shunt motor.
• Theoretically, the differentially compounded dc motor could be
controlled in a similar manner. Since the differentially
compounded motor is almost never used, that fact hardly
matters.
78
F
R
A
R
A
V
A
V
F
R

DC MOTOR EFFICIENCY CALCULATIONS :
• To calculate the efficiency of a dc motor, the following losses
must be determined::
1. Copper losses
2. Brush drop losses
3. Mechanical losses
4. Core losses
5. Stray losses
• The efficiency of the motor is:
79
*100%
*100%
out
in
in brush cu core mech stray
in
P
P
P P P P P P
P
 
    


DC Generators
INTRODUCTION TO DC GENERATORS:
• As previously mentioned, there is no real difference between a
generator and a motor except for the direction of power flow.
• There are five major types of dc generators, classified according
to the manner in which their field flux is produced:
1. Separately excited generator
2. Shunt generator
3. Series generator
4. Cumulatively compounded generator
5. Differentially compounded generator
• These various types of dc generators differ in their terminal
(voltage-current) characteristics, and therefore in the
applications to which they are suited.
80

• DC generators are compared by their voltages, power ratings,
efficiencies, and voltage regulations. VR is defined as:
• It is a rough measure of the shape of the generator‘s voltage-
current characteristic - a positive VR means a drooping
characteristic, and a negative VR means a rising characteristic.
• All generators are driven by a source of mechanical power,
which is usually called the prime mover of the generator.
• A prime mover for a dc generator may be a steam turbine, a
diesel engine, or even an electric motor. Since the speed of the
prime mover affects the output voltage, and since prime movers
can vary widely in their speed characteristics, it is customary to
compare the VR and output characteristics of different
generators, assuming constant speed prime movers.
81
*100%
nl fl
fl
V V
VR
V



• DC generators are quite rare in modern power systems. Even dc
power systems such as those in automobiles now use ac
generators plus rectifiers to produce dc power.
• The equivalent circuit and a simplified version of the equivalent
circuit is shown below in Fig a and b respectively.
• They look similar to the equivalent circuits of a dc motor, except
that the direction of current flow and the brush loss are
reversed.
82

THE SEPARATEL EXCITED GENERATOR :
• A separately excited dc generator is a generator whose field
current is supplied by a separate external dc voltage source.
• The equivalent circuit is shown in Fig below.
• The voltage represents the actual voltage measured at the
terminals, and the current represents the current flowing in
the lines connected to the terminals of the generator. 83
T
V
A
I

• The internal generated voltage is , and the armature current
is . It is clear that the armature current is equal to the line
current in a separately excited generator:
The Terminal Characteristic of Separately Excited DC Generator:
• The terminal characteristic of a separately excited generator is a
plot of versus for a constant speed .
• By Kirchhoff’s voltage law, the terminal voltage is
84
T A A A
V E I R
 
A
I
A
E
A L
I I

T
V L
I 
A
I
 Since the internal generated
voltage is independent of ,
the terminal characteristic of the
separately excited generator is
straight line, as shown in Fig.

What happens in this generator when the load is increased?
• When the load supplied by the generator is increased, (and
therefore ) increases. As the armature current increases, the
drop increases, so the terminal voltage of the generator falls.
• This terminal characteristic is not always entirely accurate.
• In generators without compensating windings, an increase in
causes an increase in armature reaction, & armature reaction
causes flux weakening.
85
A
I
L
I
A A
I R
A
I
 This flux weakening causes a
decrease which further
decreases the terminal voltage
of the generator.
 The resulting terminal
characteristic is shown.
A
E K 
 

Control of Terminal Voltage:
• The terminal voltage of a separately excited dc generator can be
controlled by changing the internal generated voltage .
• By Kirchhoff’s voltage law , so if increases,
will increase, and if decreases, will decrease.
• Since the internal generated voltage is given by the equation
, there are two possible ways to control the voltage of this
generator:
1. Change the speed of rotation: If increases, then
increases, so increases too.
2. Change the field current: If is decreased, then the field
current increases ( ) Therefore, the flux in the
machine increases . As the flux rises, must rise
too, so increases.
86
A
E
A
E
T A A A
V E I R
  T
V
A
E T
V
A
E
A
E K

 A
E K
 
T A A A
V E I R
  
F
R
F F F
I V R
  
A
E K 
 
T A A A
V E I R
  

• In many applications, the speed range of the prime mover is
quite limited, so the terminal voltage is most commonly
controlled by changing the field current.
• A separately excited generator driving a resistive load is shown
below in Fig a and Fig b shows the effect of a decrease in field
resistance on the terminal voltage of the generator when it is
operating under a load.
87

THE 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.
88
A F L
I I I
 
 The equivalent circuit is
shown in Fig below.
 In this circuit, the ar-
mature current of the
machine supplies both the
field circuit & the load
attached to the machine:
 The Kirchhoff’s voltage law
equation for the armature
circuit is:

• This type of generator has a distinct advantage over the
separately excited dc generator in that no external power supply
is required for the field circuit. But that leaves an important
question unanswered:
If the generator supplies its own field current, how does it get the
initial field flux to start when it is first turned on?
Voltage Build up in a Shunt Generator:
• Assume that the generator in above Fig has no load connected
to it and that the prime mover starts to turn the shaft of the
generator.
How does an initial voltage appear at the terminals?
• The voltage buildup in a dc generator depends on the presence
of a residual flux in the poles of the generator.
89
T A A A
V E I R
 

• When a generator first starts to turn, an internal voltage will be
generated which is given by
• This voltage appears at the terminals of the generator (it may
only be a volt or two).
• But when that voltage appears at the terminals, it causes a
current to flow in the generator’s field coil ( ).
• This field current produces a mmf in the poles, which increases
the flux in them.
• The increase in flux causes an increase in , which
increases the terminal voltage .
• When rises, increases further, increasing the flux more,
which increases , etc.
• This voltage buildup behavior is shown in Fig below.
90
A res
E K 

F T F
I V R
 
A
E K 
 
T
V
T
V F
I 
A
E

• Notice that it is the effect of magnetic saturation in the pole
faces which eventually limits the terminal voltage of the
generator.
91
 These steps are drawn in to
make obvious the positive
feedback between the
generator’s internal voltage and
its field current. In a real
generator, the voltage does not
build up in discrete steps:
Instead both & increase
simultaneously until steady-
state conditions are reached,
A
E F
I
What if a shunt generator is started and no voltage builds up?
 There are several possible causes for the voltage to fail to build
up during starting, Among them are:

1. There may be no residual magnetic flux in the generator to
start the process going.
• If the residual , then , & the voltage never builds
up. If this problem occurs, disconnect the field from the
armature circuit and connect it directly to an external dc source
such as a battery, the current flow from this external dc source
will leave a residual flux in the poles, which will then allow
normal starting known as “flashing the field”.
2. The direction of rotation of the generator may have been
reversed, or the connections of the field.
• In either case, the residual flux produces an internal generated
voltage , The voltage produces a field current which
produces a flux opposing the residual flux, instead of adding to
it. Under these circumstances, the flux actually decreases below
and no voltage can ever build up.
92
0
res
  0
A
E 
A
E A
E
res


• If this problem occurs, it can be fixed by reversing the direction
of rotation, by reversing the field connections, or by flashing the
field with the opposite magnetic polarity.
3. The field resistance may be adjusted to a value greater than
the critical resistance.
A
I
F
R
 To realize this problem, refer to Fig.
 Normally, the shunt generator will
build up to the point where the
magnetization curve intersects the
field resistance line.
 If the field resistance has the value shown at in the fig, its
line is nearly parallel to the magnetization curve. At that point,
the voltage of the generator can fluctuate very widely with
only tiny changes in or . This value of the resistance is
called the critical resistance.
2
R

• If exceeds the critical resistance (as at in the Fig), then the
steady-state operating voltage is essentially at the residual level,
and it never builds up.
• The solution to this problem is to reduce .
• Since the voltage of the magnetization curve varies as a function
of shaft speed, the critical resistance also varies with speed. In
general, the lower the shaft speed, the lower the critical
resistance.
The Terminal Characteristic of a Shunt DC Generator:
• The terminal characteristic of a shunt differs from that of a
separately excited dc generator, because the amount of field
current in the machine depends on its terminal voltage.
• To understand the terminal characteristic of a shunt, start with
the machine unloaded & add loads, observing what happens.
F
R
F
R 3
R

• As the load on the generator is increased, increases and so
also increases.
• An increase in increases the armature resistance voltage drop
, causing to decrease. This is precisely the same
behavior observed in a separately excited generator.
• However, when decreases, the field current in the machine
decreases with it. This causes the flux in the machine to
decrease, decreasing . This causes a further decrease in the
terminal voltage .
L
I
A F L
I I I
  
A
I
A A
I R T A A A
V E I R
  
T
V
A
E
T A A A
V E I R
  
 Notice that the voltage drop-off is
steeper than just the drop in a
separately excited. Thus, the VR of
this generator is worse than the VR
of the same piece of equipment
connected separately excited.
A A
I R

Voltage Control for a Shunt DC Generator:
• As with the separately excited generator, there are two ways to
control the voltage of a shunt generator:
1. Change the shaft speed of the generator.
2. Change the field resistor, thus changing the field current.
• Changing the field resistor is the principal method used to
control terminal voltage in real shunt generators.
• If is decreased, then the increases.
• When increases, the machine’s flux increases, causing
the internal generated voltage to increase.
• The increase in causes the terminal voltage of the
generator to increase as well.
m

F
R F T F
I V R
 
F
I 
A
E
A
E

The Analysis of Shunt DC Generators:
• The analysis of a shunt dc generator is somewhat more
complicated than the analysis of a separately excited generator,
because the field current in the machine depends directly on the
machine’s own output voltage.
F
R T F
V I
T A
V E

 Fig shows a magnetization curve for
a shunt dc generator drawn at the
actual operating speed.
 The which is just equal to
is shown by a straight line laid over
the magnetization curve.
 At no load & generator operates at the voltage where the
magnetization curve intersects the field resistance line.
 The key to understanding the graphical analysis of shunt
generators is to remember Kirchhoff's voltage law ( KVL) :

or
• The difference between the internal generated voltage and the
terminal voltage is just the drop in the machine.
• The line of all possible values of is the magnetization curve,
and the line of all possible terminal voltages is the resistor line (
).
• Therefore, to find the terminal voltage for a given load, just
determine the drop and locate the place on the graph
where that drop fits exactly between the and the lines.
• There are at most two places on the curve where the drop
will fit exactly.
• If there are two possible positions, the one nearer the no-load
voltage will represent a normal operating point.

F T F
R V I
A
E
A
E
T A A A
A T A A
V E I R
E V I R
 
 
A A
I R
A A
I R
T
V
A A
I R

• A detailed plot showing several different points on a shunt
generator’s characteristic as shown in Fig a. Note the dashed
line in Fig b.
• This line is the terminal characteristic when the load is being
reduced. The reason that it does not coincide with the line of
increasing load is the hysteresis in the stator poles.

• If armature reaction is present in a shunt generator, this process
becomes a little more complicated.
• The armature reaction produces a demagnetizing mmf at the
same time that the drop occurs in the machine.
• To analyze a generator with armature reaction present, assume
that its armature current is known.
• Then the resistive voltage drop is known, and the
demagnetizing mmf of the armature current is known.
• The terminal voltage of this generator must be large enough to
supply the generator’s flux after the demagnetizing effects of
armature reaction have been subtracted.
• To meet this requirement both the armature reaction mmf and
the drop must fit between the line and the
line.
A A
I R
A A
I R
A A
I R A
E
T
V

• To determine the output voltage for a given magneto motive
force, simply locate the place under the magnetization curve
where the triangle formed by the armature reaction and
effects exactly fits between the line of possible values and
the line of possible values as shown in Fig below.
A A
I R
A
E
T
V

THE SERIES DC GENERATOR:
• A series dc generator is a generator whose field is connected in
series with its armature.
• Since the armature has a much higher current than a shunt
field, the series field in a generator of this sort will have only a
very few turns of wire, and the wire used will be much thicker
than the wire in a shunt field.
NI

F
 Because mmf is given by the
equation , exactly the
same mmf can be produced
from a few turns with high
current as can be produced
from many turns with low
current.

• Since the full-load current flows through it, a series field is
designed to have the lowest possible resistance.
• Here , the armature current, field current , and line current all
have the same value. The Kirchhoff ‘s voltage law is:
The Terminal Characteristic of a Series Generator:
• 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 is reduced to
a small level given by the residual flux in the machine.
• As the load increases, the field current rises, so rises rapidly.
• The drop goes up too, but at first the increase in
goes up more rapidly than the drop rises, so
increases.
 
A A S
I R R

T
V
A
E
 
T A A A S
V E I R R
  
A
E
 
A A S
I R R
 T
V

• After a while, machine approaches saturation, becomes
almost constant. At that point, the resistive drop is the
predominant effect, and starts to fall as shown below.
• It is obvious that this machine would make a bad constant-
voltage source. In fact, its VR is a large negative number.
• Series generators are used only in a few specialized applications,
where the steep voltage characteristic of the device can be
exploited. One such application is arc welding.
T
V
A
E
T
V

• Series generators used in arc welding are deliberately designed
to have a large armature reaction, which gives them a terminal
characteristic like the one shown below.
 Notice that when
the welding
electrodes make
contact with each
other before welding
commences, a very
large current flows.
 As the operator separates the welding electrodes, there is a
very steep rise in the generator’s voltage, while the current
remains high. This voltage ensures that a welding arc is
maintained through the air between the electrodes.

THE CUMULATIVELY COMPOUNDED DC GENERATOR:
• A cumulatively compounded dc generator is a dc generator with
both series and shunt fields, connected so that the magneto
motive forces from the two fields are additive.
F
I
A
I
er
X
 The Fig shows the
equivalent circuit of a
cumulatively compounded
dc generator in the “long-
shunt” connection.
 Current flowing into a dot
produces a positive mmf,
and out of a dot produce
negative mmf as of .
 Notice that flows into the dotted end of the series field coil
and that flows into the dotted end of the shunt field coil.

• There is another way to look up a cumulatively compounded
generator. It is the “short-shunt” connection, where the series
field is out side the shunt field circuit and has current flowing
through it instead of . Short- shunt cumulatively
compounded dc generator is shown in Fig above.
A F L
I I I
 
 
T A A A S
V E I R R
  
T
F
F
V
I
R

*
net F SE AR
SE AR
F F A
F F
N
I I I
N N
  
  
F F F F
F
 Therefore, the total mmf on this machine is given by:
 The other hand:
A
I
L
I

The Terminal Characteristic of a Cumulatively Compounded:
• Suppose that the load on the generator is increased.
• Then as the load increases, the load current increases. Since (
), the armature current increases too. At this point two
effects occur in the generator:
1. As increases, the voltage drop increases as
well. This tends to cause a decrease in .
2. As increases, the series field mmf increases.
This increases the total mmf increases the
flux in the generator. This increases , which in turn tends to
make rise.
• The two effects oppose each other, with one tend to increase
the other one decreases .
Which effect predominates in a given machine?
A F L
I I I
  
L
I
A
I
 
T A A A S
V E I R R
   
A
E
 
A A S
I R R

A
I
A
I SE SE A
N I

F
tot F F SE A
N I N I
  
F
 
T A A A S
V E I R R
   
T
V

• It all depends on just how many series turns were placed on the
poles of the machine. The question can be answered by taking
several individual cases:
1. Few series turns ( small): If there are only a few series turns,
the resistive voltage drop effect wins hands down. The voltage
falls off just as in a shunt generator, but not quite as steeply
as shown.
SE
N
 This type of
construction, where the
full-load terminal
voltage is less than the
no-load terminal
voltage, is called under-
compounded.

2. More series turns ( large): If there are a few more series
turns of wire on the poles, then at first the flux- strengthening
effect wins, and the terminal voltage rises with the load.
However, as the load continues to increase, magnetic
saturation sets in , and the resistive drop becomes stronger
than the flux increase effect. In such a machine, the terminal
voltage first rises and then falls as the load increases. If at
no load is equal to at full load, the generator is called flat-
compounded.
3. Even more series turns are added ( large): If even more
series turns are added to the generator, the flux-
strengthening effect predominates for a longer time before
the resistive drop takes over. The result is a characteristic
with the full-load actually higher than the no-load .
This is called over-compounded.
SE
N
T
V T
V
SE
N
T
V T
V

• It is also possible to realize all these voltage characteristics in a
single generator if a diverter resistor is used.
SE
N
div
R
 Fig shows a cumulatively com
pounded dc generator with a
relatively large number of
series turns . A diverter
resistor is connected around
the series field.
 If the resistor is adjusted to a large value, most of the
armature current flows through the series field coil, and the
generator is over-compounded. On the other hand, if the
resistor is adjusted to a small value, most of the current
flows around the series field through , and the generator
is under-compounded. It can be smoothly adjusted with the
resistor to have any desired amount of compounding.
div
R
div
R

Voltage Control of Cumulatively Compounded DC Generators:
• The techniques available for controlling the terminal voltage of
a cumulatively compounded dc generator are exactly the same
as that of controlling the voltage of a shunt dc generator.
1. Change the speed of rotation: An increase in causes to
increase, increasing the
2. Change the field current: A decrease in causes to
increase, which increases the total magneto motive force in
the generator. As increases, the flux in the machine
increases, and increases. This increases .
Analysis of Cumulatively Compounded DC Generators:
• The equivalent shunt field current due to the effects of the
series field and armature reaction is given by
F
R

 
T A A A S
V E I R R
   
A
E K
 
F T F
I V R
 
tot
F 
A
E K 
  T
V
SE AR
eq A
F F
N
I I
N N
 
F
eq
I

• Therefore, the total effective shunt field current is:
• This equivalent current represents a horizontal distance to
the left or right of the field resistance line ( ) along the
axes of the magnetization curve.
• The resistive drop in the generator is given , which is
a length along the vertical axis on the magnetization curve.
• Both the equivalent current and the resistive voltage drop
depend on the strength of the armature current
• Therefore, they form the two sides of a triangle whose
magnitude is a function of .
• To find the output voltage for a given load , determine the size
of the triangle and find the one point where it exactly fits
between the field current line and the magnetization curve.
F T F
R V I

*
F F eq
I I I
 
eq
I
 
A A S
I R R

eq
I
 
A A S
I R R
 A
I
A
I

• The terminal
voltage at no-
load con-
ditions will be
the point at
which the
resistor line
and the
magnetization
curve
intersect, as
before.
eq
I
 
A A S
I R R

 As load is added to the generator, the series field mmf increases,
increasing the equivalent shunt field current & the resistive
voltage drop .

• To find the new
output voltage in this
generator, slide the
left most edge of the
resulting triangle
along the shunt field
current line until the
upper tip of the
triangle touches the
magnetization curve.
 The upper tip of the triangle then represents the internal
generated voltage, while the lower line represents the terminal
voltage of the machine.
 Fig shows this process repeated several times to construct a
complete terminal characteristic for the generator.

THE DIFFERENTIALLY COMPOUNDED DC GENERATOR :
• A differentially compounded dc generator is a generator with
both shunt and series fields, but this time their mmf subtract
from each other.
• Notice that the armature current is now flowing out of a dotted
coil end, while the shunt field current is flowing into a dotted
coil end. In this machine, the net mmf is:

• The equivalent shunt field current due to the series field and
armature reaction is given by
• The total effective shunt field current in this machine is
or
• Like the cumulatively compounded generator, the differentially
compounded generator can be connected in either long-shunt
or short-shunt fashion.
net F SE AR
net F F SE A AR
N I N I
  
  
F F F F
F F
*
F F eq
I I I
 
* SE AR
F F A
F F
N
I I I
N N
  
F
SE AR
eq A
F F
N
I I
N N
  
F

The Terminal Characteristic of a Differentially Compounded:
• In the differentially compounded dc generator, the same two
effects occur that were present in the cumulatively
compounded dc generator. This time, though, the effects both
act in the same direction. They are
1. As increases, the voltage drop increases as
well. This tends to cause a decrease in .
2. As increases, the series field mmf increases.
This increases in series field the total mmf on the generator
( ), which in turn reduces the net flux. A
decrease in flux decreases , which in turn decreases .
• Since both these effects tend to decrease the voltage drops
drastically as the load is increased on the generator. A typical
terminal characteristic for a differentially compounded dc
generator is shown in Fig below.
 
T A A A S
V E I R R
   
A
E
 
A A S
I R R

A
I
A
I SE SE A
N I

F
tot F F SE A
N I N I
  
F
T
V
T
V

Voltage Control of a Differentially Compounded:
• Even though the voltage drop characteristics of a differentially
compounded dc generator are quite bad, it is still possible to
adjust the terminal voltage at any given load setting.
• The techniques available for adjusting are exactly the same
as those for shunt & cumulatively compounded dc generators:
1. Change the speed of rotation
2. Change the field current
T
V
m

F
I

Graphical Analysis of a Differentially Compounded:
• The voltage characteristic of a differentially compounded is
graphically determined in precisely the same manner as that
used for the cumulatively compounded as shown below.
T F
V R
eq
I
 The portion of the effective
shunt field current due to
the actual shunt field is
always equal , since
that much current is
present in the shunt field.
 The remainder of the
effective field current is
given by and is the sum
of the series field and
armature reaction effects .

• This equivalent current represents a negative horizontal
distance along the axes of the magnetization curve, since both
the series field and the armature reaction are subtractive.
• The resistive drop is given by , which is a length
along the vertical axis on the magnetization curve.
eq
I
 
A A S
I R R

 To find the output
voltage for a given
load, determine the
size of the triangle
formed by the resistive
voltage drop
and find the one point
where it exactly fits
between the field
current line and the
magnetization curve.
 
A A S
I R R


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