Chapter 4

Chapter Four
DC Machines
Contents
 Introduction
 Construction
 Armature reaction and Commutation
 Characteristics of DC Generator
By: Yimam A.(MSc.)

Introduction
 DC machines are generators that convert mechanical energy to dc electric
energy and motors that convert dc electric energy to mechanical energy.
 Most DC machines are similar to AC machines: i.e. they have AC voltages
and currents within them.
 DC machines have DC outputs just because they have a mechanism
converting AC voltages to DC voltages at their terminals. This mechanism
is called a commutator; therefore, DC machines are also called
commutating machines.
 DC generators are not as common as they used to be, because direct
current, when required, is mainly produced by electronic rectifiers.
2

Cont.…..
 While dc motors are widely used, such as automobile, aircraft, and portable
electronics, in speed control applications.
 Generator action: An emf (voltage) is induced in a conductor if it moves
through a magnetic field.
 Motor action: A force is induced in a conductor that has a current going
through it and placed in a magnetic field.
 Any DC machine can act either as a generator or as a motor.
3

Generator Principle
 An electric generator is based on the principle that whenever flux is cut by a
conductor, an e.m.f. is induced which will cause a current to flow if the
conductor circuit is closed.
𝑒𝑖𝑛𝑑 = 𝑣 × 𝐵 𝑙
 The direction of induced e.m.f. (and hence current) is given by Fleming’s
right hand rule. Therefore, the essential components of a generator are:
(a) a magnetic flux
(b) conductor or a group of conductors
(c) motion of conductor w.r.t. magnetic flux.
4

Fleming’s right hand rule
► If three fingers of a right hand, namely thumb,
index finger and middle finger are outstretched
so that every one of them is at right angles
with the remaining two, and if this position
index finger is made to point in the direction
of lines of flux, thumb in the direction of the
relative motion of the conductor with respect
to flux then the outstretched middle finger
gives the direction of the e.m.f. induced in the
conductor.
5

Simplest rotating dc machine
6
Fig: e.m.f generated in the loop

Cont.…..
1. When the loop is in position no. 1, the generated e.m.f. is zero because the
coil sides (AB and CD) are cutting no flux but are moving parallel to it.
2. When the loop is in position no. 2, the coil sides are moving at an angle to
the flux and, therefore, a low e.m.f. is generated as indicated by point 2.
3. When the loop is in position no. 3, the coil sides (AB and CD) are at right
angle to the flux and are, therefore, cutting the flux at a maximum rate. Hence
at this instant, the generated e.m.f. is maximum as indicated by point 3.
4. At position 4, the generated e.m.f. is less because the coil sides are cutting
the flux at an angle.
7

Cont.…..
5. At position 5, no magnetic lines are cut and hence induced e.m.f. is zero as
indicated by point 5.
6. At position 6, the coil sides move under a pole of opposite polarity and
hence the direction of generated e.m.f. is reversed. The maximum e.m.f. in
this direction (i.e., reverse direction) will be when the loop is at position 7 and
zero when at position 1. This cycle repeats with each revolution of the coil.
8

Constructional Details of DC Machine
9

A Cut Away View of Practical DC Generator
10

A DC machine has the following parts
 Yoke
 Pole
 Field winding
 Armature
 Commutator
 Brushes
 Shaft
 Bearings
12

Yoke
The outer frame or yoke serves purpose of
◘ It provides mechanical support for the poles & acts as a protecting cover
for the whole machine.
◘ It carries the magnetic flux produced by the poles (it provides a path of
low reluctance for magnetic flux.)
 It acts as protective cover to other parts. Viz field pole, field winding,
armature core etc.
 Have high permeability
 For Small machines -- Cast iron—low cost
 For Large Machines -- Cast Steel (Rolled steel)
13

Poles
Functions of pole core and pole shoe :
◘ Pole core basically carries a field winding which is necessary to produce
the flux.
◘ It directs the flux produced through air gap to armature core, to the next
pole.
◘ Pole shoe enlarges the area of armature core to come across the flux,
which is necessary to produce larger induced e.m.f. To achieve this, pole
shoe has been given a particular shape.
 It is made up of magnetic material like cast iron or cast steel. As it requires a definite
shape and size, laminated construction is used. The laminations of required size and
shape are stamped together to get a pole which is then bolted to the yoke. 14

Field Winding
 The field winding is wound on the pole core with a definite direction.
◘ To carry current due to which pole core, on which the field winding is
placed behaves as an electromagnet, producing necessary flux.
 As it helps in producing the magnetic field i.e. exciting the pole as an
electromagnet it is called Field winding or Exciting winding.
 It has to carry current hence obviously made up of some conducting
material. So aluminum or copper is the choice.
 Field coils are former wound and placed on each pole and are connected in
series.
16

Commutator
 It actually takes alternating current from armature and converts it to direct
current and then send it to external load.
 Each segment is insulated from the shaft by means of insulated
commutator segment.
 Each commutator segment is connected with corresponding armature
conductor through segment riser or lug.
 Hard drawn copper bars segments insulated from each other by mica
segments (insulation)
 It is made up of hard drawn copper(cu-99.7% and c-0.3%).
17

Cont.…..
Functions:
◘ To facilitate the collection of current
from the armature conductors.
◘ To convert internally developed
alternating e.m.f. to unidirectional (d.c.)
e.m.f.
◘ To produce unidirectional torque in case
of motors.
 As it collects current from armature, it is
also made up of copper segments.
18

Brushes
 Brushes are stationary and resting on the surface of the commutator.
◘ To collect current from commutator and make it available to the
stationary external circuit.
 They are usually made of carbon or graphite and are in the shape of a
rectangular block.
 Brushes are rectangular in shape. They are housed in brush holders, which
are usually of box type.
 The brushes are made to press on the commutator surface by means of a
spring, whose tension can be adjusted with the help of lever. A flexible
copper conductor called pig tail is used to connect the brush to the external
circuit. 20

Shaft and bearings
 Shaft-- Mechanical link between prime mover and armature
 Bearings– For free rotation
 For small machine, ball bearing is used and for heavy duty dc generator,
roller bearing is used.
 The bearing must always be lubricated properly for smooth operation
and long life of generator.
21

Armature
Armature Core
 Armature core provides house for the armature winding and
 provide low reluctance path for the flux through the armature.
 It is made up of magnetic material like cast iron and cast steel.
 It is made up of laminated construction to keep eddy current loss as low as
possible.
 Although a DC generator provides direct current but induced current in the
armature is alternating in nature.
22

Armature Winding
 Armature winding is the interconnection of the armature conductors,
placed in the slots provided on the armature core periphery.
 When the armature is rotated, in case of generator, magnetic flux gets cut
by armature conductors and e.m.f. gets induced in them.
◘ Generation of e.m.f takes place in the armature winding in case of
generators.
◘ To carry the current supplied in case of d.c motors.
◘ To do the useful work in the external circuit.
 As armature winding carries entire current which depends on external load,
it has to be made up of conducting material, which is copper.
24

Cont.…..
 Armature winding is generally former wound.
 The conductors are placed in the armature slots which are lined with tough
insulating material.
 Depending upon the manner in which the armature conductors are
connected to the commutator segments, there are two types of armature
winding in a dc machine.
Lap winding
Wave winding
25

Armature reaction
 When a load is connected to the terminals of the machine, a current will
flow in its armature windings. This current flow will produce a magnetic
field of its own, which will distort the original magnetic field from the
machine's poles. This distortion of the flux in a machine as the load is
increased is called armature reaction.
 Armature reaction is the effect of magnetic field set up by armature current
on the distribution of flux under main poles of a dc machine.
 The armature reaction has two effects:
1. The armature flux distorts the main flux (cross-magnetization)
2. The armature flux weakens the main flux (demagnetization)
26

Cont.….
 Armature field: is the field which is produced by the armature conductors
due to current flowing through them.
 Main field: is the field which is produced by the poles which is necessary for
the operation.
 MNA(Magnetically Neutral Axis): It is the axis along which no E.M.F is
produced, hence brushes are kept on this axis.
 GNA(Geometrically Neutral Axis): It is the axis which divides the armature
core in to two equal parts.
 Polar Axis: It is the imaginary line which joins the center of NS poles.
27

Case I: When no load is connected to the machines
 Consider a two pole DC Generator.
 For the sake of simplicity, the brushes
are shown directly touching the
armature conductors, but practically
they touch commutator segments.
 Assuming that the generator is not
driving any load, so that there is no
current in the armature conductors.
 The distribution of main field flux is
as shown in the fig.
28

Cont.….
29
 The flux is distributed symmetrically with respect to polar axis.
 The M.N.A coincides the G.NA.
 The vector o𝐹𝑚 represents the mmf producing the main flux both in
magnitude and direction.
 MNA is perpendicular to vector o𝐹𝑚.

Case II: Armature conductors carrying current and no field current flows
 Consider that the field coils are unexcited
whereas the armature conductors are
carrying current.
 The direction of current in the armature
conductors can be found by Fleming’s
RHR
 According to Fleming’s right hand rule,
the direction of this flux is clock-wise in
conductors which are influence of N pole
and Anti-clock wise in conductors which
are influence of s pole. 30

Cont.….
31
 Under N pole the current is flowing in downward direction, whereas under
S pole the current is flowing in upward direction.
 The vector o𝐹𝐴 represents the armature mmf both in magnitude and
direction.
 This mmf depends on the magnitude of the armature current.

Case III: Field current and armature current acting simultaneously
 In practice the two mmfs exist simultaneously
in the generator under load conditions.
 The flux through the armature is not uniform
and symmetrical. The flux gets distorted.
 Due to interaction of two fluxes the resultant
flux distribution is changed as shown in the
fig.
 The flux is concentrated at the top corners of
poles and weakened out at the bottom
corners of the pole tips.
 The new position of MNA is perpendicular
to the resultant mmf vector o𝐹𝑅.
32

Cont.….
 The armature conductors which were earlier
under the influence of S pole come under the
influence of N pole and vice versa.
 The conductors on the left of new position of
MNA carry current downwards and those to
the right carry current upwards.
 The armature mmf is now along new position
of MNA represented by vector o𝐹𝑅 . It is
inclined to an angle 𝜃 to the left.
33

Cont.….
 The armature mmf represented by vector o𝐹𝑅 can be resolved into two
components
 o𝐹𝑑 parallel to the polar axis and
 o𝐹𝑐 perpendicular to the axis
 The component o𝐹𝑑 is in direct opposition with field mmf vector
o𝐹𝑚.This will tend to reduce the total flux.
 This component is called demagnetizing component of the armature
reaction
 The other component o𝐹𝑐 is at right angles to vector o𝐹𝑚.
 This will produce distortion in the main field .This component is called
cross magnetizing component of the armature reaction
34

Conclusion
 With brushes located along G.N.A. (i.e., 𝜃= 0°), there is no demagnetizing component
of armature reaction (𝐹𝑑 = 0). There is only distorting or cross magnetizing effect of
armature reaction.
 With the brushes shifted from G.N.A., armature reaction will have both demagnetizing
and distorting effects. Their relative magnitudes depend on the amount of shift. This
shift is directly proportional to the armature current.
 The demagnetizing component of armature reaction weakens the main flux. On the
other hand, the distorting component of armature reaction distorts the main flux.
 The demagnetizing effect leads to reduced generated voltage while cross magnetizing
effect leads to sparking at the brushes.
35

Commutation
 The armature conductors carry current in one direction when they are
under the influence of N-pole and in opposite direction when they are
under S-pole. So when the conductors come under the influence of the S-
pole from the influence of N-pole, the direction of flow of current in them
is reversed.
 This reversal of current in a coil will take place when the two commutator
segments to which the coil is connected are being short circuited by brush.
 The process of reversal of current in a coil is termed as commutation.
 The period during which the coil remains short-circuited is called
commutation period(Tc). This commutation period is very small of the
order of 0.001 to 0.003s. 36

Cont.…
♦ Commutation is the process of converting the ac voltages and currents in
the rotor of a dc machine to dc voltages and currents at its terminals.
♦ The process of reversal of current in a coil when it passes through M.N.A
is known as commutation.
Let us consider a DC machine
 Having an armature wound with ring winding
 The width of the commutator bar is equal to the width of the brush and
current flowing through the conductor is 𝐼 𝐶.
 Let the commutator is moving from left to right. Then the brush will
move from right to left.
37

Cont.…
 At the first position, the brush is connected the commutator bar b (as
shown in fig 1). Then the total current conducted by the commutator bar b
into the brush is 2𝐼 𝐶.
 When the armature starts to move right, then the brush comes to contact
of bar a. Then the armature current flows through two paths and through
the bars a and b (as shown in fig 2). The total current (2𝐼 𝐶) collected by the
brush remain same.
38

Cont.…
 As the contact area of the bar a with the brush increases and the contact
area of the bar b decreases, the current flow through the bars increases and
decreases simultaneously. When the contact area become same for both the
commutator bar then same current flows through both the bars (as shown
in fig 3).
 When the brush contact area with the bar b decreases further, then the
current flowing through the coil B changes its direction and starts to flow
counter-clockwise (as shown in fig 4).
 When the brush totally comes under the bar a (as shown in fig 5) and
disconnected with the bar b then current 𝐼 𝐶 flows through the coil B in the
counter-clockwise direction and the short circuit is removed. 39

Cont.…
 If the commutation process or the
reversal of current is completed by the
end of the short circuit time or the
commutation period the commutation
is called ideal commutation(Linear
commutation).
 If the reversal of current is not
completed during the short circuit
time then there is sparking occurs at
the brush contacts and the
commutator surface is damaged due to
overheating and the machine is called
non ideal commutation(poorly
commutated).
42

Methods of Improving Commutation
 Improving commutation means to make current reversal in the short-
circuited coil as sparkless as possible.
 The following are the two principal methods of improving commutation:
I. Resistance Commutation
II. E.M.F Commutation
43

I. Resistance Commutation
 The reversal of current in a coil (i.e., commutation) takes place while the
coil is short-circuited by the brush.
 Therefore, there are two parallel paths for the current as long as the short
circuit exists.
 If the contact resistance between the brush and the commutator is made
large, then current would divide in the inverse ratio of contact resistances
(as for any two resistances in parallel). This is the key point in improving
commutation. This is achieved by using carbon brushes (instead of Cu
brushes) which have high contact resistance.
 This method of improving commutation is called resistance commutation.
44

II. emf commutation
 By the help of inter poles, neutralize the self- reactance voltage by
producing reversing emf.
 In this method, arrangement is made to neutralize the reactance voltage by
producing a reversing emf in the short-circuited coil under commutation.
 This reversing emf, as the name shows, is an emf in opposition to the
reactance voltage and if its value is made up equal to the latter, it will
completely wipe it off, thereby producing quick reversal of current in short
circuited coil which will result in sparkles commutation.
45

How to Reduce Armature Reaction?
 The armature reaction is due to the presence of armature flux.
 Armature flux is produced due to the current flowing in armature
conductors.
 Now, if we place another winding in close proximity of the armature
winding and if it carries the same current but in the opposite direction as
that of the armature current, then this will nullify the armature field. Such
an additional winding is called as compensating winding and it is placed
on the pole faces.
 Compensating winding is connected in series with the armature winding
in such a way that it carries the current in opposite direction.
46

Compensating Winding
 In order to neutralize the cross
magnetizing effect of armature reaction,
a compensating winding is used.
 A compensating winding is an auxiliary
winding embedded in slots in the pole
faces.
 It is connected in series with armature in
a manner so that the direction of current
through the compensating conductors in
any one pole face will be opposite to the
direction of the current through the
adjacent armature conductors.
47

Cont.…
Drawbacks:
 There is only one disadvantage of compensating winding and that is it is
costly.
Advantages:
 It is used in large machines having heavy fluctuation.
 It is used when same output is required at low voltage.
48

Inter-poles
 As the compensating windings are too costly, inter-poles are used to
neutralize the Cross-magnetizing effect of armature reaction.
 These are small poles fixed to the yoke and spaced in between the main
poles.
 They are wound with comparatively few heavy gauge copper wire turns and
are connected in series with the armature so that they carry full armature
current.
 Their polarity, in the case of a generator, is the same as that of the main
pole ahead in the direction of rotation.
 For a motor, the polarity of the inter pole must be the same as that of the
main pole behind it in the direction of rotation. 49

Cont.…
 Interpoles are the small auxiliary
poles placed between the main
field poles. Winding on the
interpoles is connected in series
with the armature.
 Each interpole is wound in such a
way that its magnetic polarity is
same as that of the main pole
ahead of it.
50

Cont.…
There are mainly two functions of inter-poles:
1. As their polarity is the same as that of the leading pole, they induce an
e.m.f in the coil(under commutation) which helps the reversal of current. The
e.m.f induced by the inter-poles is known as reversing-commutating e.m.f.
This e.m.f neutralizes the reactance e.m.f and makes commutation sparkless.
2. Another function of the inter-poles is to neutralize the cross-magnetizing
effect of armature reaction. Hence, brushes are not be shifted from the
original position.
51

EMF equation of DC machines
52
Let, Ø= Flux per pole in weber
Z = Total number of armature conductors
=Number of slots × Number of conductors per slot
P = Number of poles
A = Number of parallel paths=2 for wave winding and
=P for lap winding
N =armature speed in rpm
𝐸𝑔 = emf generated in any one of the parallel path=e.m.f/parallel path

Cont.…
 Flux cut by 1 conductor in one revolution of the armature
𝑑∅ = 𝑃∅ webers
 Time taken to complete one revolution
𝑑𝑡 = Τ60 𝑁 𝑠𝑒𝑐𝑜𝑛𝑑
 e.m.f generated/conductor =
𝑑∅
𝑑𝑡
=
𝑃∅
Τ60 𝑁
=
𝑃∅𝑁
60
𝑣𝑜𝑙𝑡𝑠
 e.m.f. of generator
𝐸𝑔 = 𝑒. 𝑚. 𝑓 𝑝𝑒𝑟 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑝𝑎𝑡ℎ
= e.m.f/parallel path × number of conductors in series per parallel path
𝐸𝑔 =
𝑃∅𝑁
60
×
𝑍
𝐴
=
𝑃∅𝑍𝑁
60𝐴
53

Cont.…
𝐸𝑔 =
∅𝑍𝑁
60
𝑃
𝐴
𝐸𝑔 =
∅𝑍𝑁𝑃
120
for wave winding dc machine
𝐸𝑔 =
∅𝑍𝑁
60
for simplex lap winding dc machine
𝐸𝑔 =
𝐾∅𝑁
60
where K=
𝑃𝑍
𝐴
 When the machine is operating as a generator this induced emf is called
the generated emf (𝐸𝑔).
 When the machine is operating as a motor this induced emf is called a
counter or back emf (𝐸 𝑏)
54

The Internal Generated Voltage and Induced Torque
Equations of Dc Machines
Induced Voltage
 The voltage in any single conductor under the pole faces is
𝑒𝑖𝑛𝑑 = 𝑒 = 𝑣𝐵𝑙
 The voltage out of the armature of a real machine is thus
𝐸𝐴 =
𝑍𝑣𝐵𝑙
𝑎
where Z is the total number of conductors and
a is the number of current paths.
55

Cont.…
 The velocity of each conductor in the rotor can be expressed as 𝑣 = 𝑟𝜔,
where r is the radius of the rotor, so
𝐸𝐴 =
𝑍𝑟𝜔𝐵𝑙
𝑎
 This voltage can be re-expressed in a more convenient form by noting that
the flux of the pole is equal to the flux density under the pole times the
pole’s area
∅ = 𝐵𝐴 𝑝
 The rotor of the machine is shaped like a cylinder, so its area is
A = 2𝜋𝑟𝑙
56

Cont.…
 If there are P poles on the machine, then the portion of the area associated
with each pole is the total area A divided by the number of poles P.
𝐴 𝑃 =
𝐴
𝑃
=
2𝜋𝑟𝑙
𝑃
 The total flux per pole in the machine is thus
∅ = 𝐵𝐴 𝑃 =
𝐵(2𝜋𝑟𝑙)
𝑃
=
2𝜋𝑟𝑙𝐵
𝑃
 Therefore, the internal generated voltage in the machine can be expressed
as
𝐸𝐴 =
𝑍𝑟𝜔 𝑚 𝐵𝑙
𝑎 57

Cont.…
 Therefore
𝐸𝐴 =
𝑍𝑟𝜔 𝑚 𝐵𝑙
𝑎
=
𝑍𝑃
2𝜋𝑎
2𝜋𝑟𝑙𝐵
𝑃
𝜔 𝑚
=
𝑍𝑃
2𝜋𝑎
∅𝜔 𝑚
Finally
𝐸𝐴 = 𝐾∅𝜔 𝑚 or 𝐸𝐴 = 𝐾′∅𝑛
Where K =
𝑍𝑃
2𝜋𝑎
and K′ =
𝑍𝑃
60𝑎
58

Cont.…
 Therefore, The induced voltage in any given dc machine depends on three
factors:
1. The flux ∅ in the machine
2. The speed 𝜔 of the machine's rotor
3. A constant depending on the construction of the machine
59

Induced Torque
 The torque on the armature of a DC machine is equal to the number of
conductors Z times the torque on each conductor.
 The torque in any single conductor under the pole faces is
𝜏 𝑐𝑜𝑛𝑑 = 𝑟𝐼𝑐𝑜𝑛𝑑 𝑙𝐵
 If there are a current paths in the machine, then the total armature current
𝐼𝐴 is split among the a current paths, so the current in a single conductor is
given by
𝐼𝑐𝑜𝑛𝑑 =
𝐼𝐴
𝑎
and the torque in a single conductor on the motor may be expressed as
60

Cont.…
and
𝜏 𝑐𝑜𝑛𝑑 =
𝑟𝐼𝐴 𝑙𝐵
𝑎
 Since there are Z conductors, the total induced torque in a dc machine
rotor is
𝜏𝑖𝑛𝑑 =
𝑍𝑟𝑙𝐵𝐼𝐴
𝑎
 The flux per pole in this machine can be expressed as
∅ = 𝐵𝐴 𝑃 =
𝐵(2𝜋𝑟𝑙)
𝑃
=
2𝜋𝑟𝑙𝐵
𝑃
61

Cont.…
 So the total induced torque can be re-expressed as
𝜏𝑖𝑛𝑑 =
𝑍𝑃
2𝜋𝑎
∅𝐼𝐴
 Finally
𝜏𝑖𝑛𝑑 = 𝐾∅𝐼𝐴
Where K =
𝑍𝑃
2𝜋𝑎
62

Cont.…
The torque in any dc machine depends on three factors:
1. The flux ∅ in the machine
2. The armature (or rotor) current 𝐼𝐴 in the machine
3. A constant depending on the construction of the machine
63

Power Flow and Losses in Dc Machines
The Losses in DC Machines
 The losses that occur in dc machines can be divided into five basic
categories:
1. Electrical or copper losses (𝐼2 𝑅 losses)
2. Brush losses
3. Core losses
4. Mechanical losses
5. Stray load losses
64

1. Electrical or Copper Losses
 Copper losses are the losses that occur in the armature and field windings
of the machine.
𝐴𝑟𝑚𝑎𝑡𝑢𝑟𝑒 𝑙𝑜𝑠𝑠: 𝑃𝐴 = 𝐼𝐴
2
𝑅 𝐴
𝐹𝑖𝑒𝑙𝑑 𝐿𝑜𝑠𝑠: 𝑃𝐹 = 𝐼 𝐹
2
𝑅 𝐹
Where 𝑃𝐴 =Armature loss 𝑃𝐹 =Field circuit loss
𝐼𝐴 =Armature current 𝐼 𝐹 =Field current
𝑅 𝐴 =Armature resistance 𝑅 𝐹 =Field resistance
65

2. Brush Losses
 The brush drop loss is the power lost across the contact potential at the
brushes of the machine.
 Unless otherwise specified the brush voltage drop is usually assumed to be
about 2 V.
𝑃𝐵𝐷 = 𝑉𝐵𝐷 𝐼𝐴
Where 𝑃𝐵𝐷 = brush drop loss
𝑉𝐵𝐷 = brush voltage drop
𝐼𝐴 = Armature current
66

Cont.…
3. Core Losses: The core losses are the hysteresis losses and eddy current
losses occurring in the metal of the motor. These losses vary as the square of
the flux density (𝐵2) and for the rotor, as the 1.5 𝑡ℎ power of the speed of
rotation (𝑛1.5
) .
4. Mechanical Losses: The friction and windage losses are the mechanical
losses. Friction losses are losses caused by the friction of the bearings in the
machine, while windage losses are caused by the friction between the moving
parts of the machine and the air inside the motor's casing. These losses vary
as the cube of the speed of rotation of the machine.
5. Stray Losses (Or Miscellaneous Losses): Stray losses are losses that cannot
be placed in one of the previous categories. For most machines, stray losses are taken by
convention to be 1 percent of full load.
67

The Power-Flow Diagram
68
Fig 4a : Power-flow diagram of a dc generator
𝝉𝝉

Cont.…
69
Fig 4b : Power-flow diagrams of a dc motor
𝝉

Cont.…
 For a dc generator, mechanical power is input into the machine, and then
the stray losses, mechanical losses, and core losses are subtracted.
 After they have been subtracted, the remaining power is ideally converted
from mechanical to electrical form at the point labeled 𝑃𝑐𝑜𝑛𝑣.
 The mechanical power that is converted is given by
𝑃𝑐𝑜𝑛𝑣 = 𝜏𝑖𝑛𝑑 𝜔 𝑚
and the resulting electric power produced is given by
𝑃𝑐𝑜𝑛𝑣 = 𝐸𝐴 𝐼𝐴
 This is not the power that appears at the machine 's terminals. Before the
terminals are reached, the electrical(𝐼2 𝑅) losses and the brush losses must
be subtracted. 70

Efficiency of a DC machine
 DC generators take in mechanical power and produce electric power, while
dc motors take in electric power and produce mechanical power.
 There is always some loss associated with the process.
 The efficiency of a dc machine is defined by the equation
𝜂 =
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
× 100%
 The difference between the input power and the output power of a
machine is the losses that occur inside it. Therefore,
𝜂 =
𝑃𝑖𝑛 − 𝑃𝑙𝑜𝑠𝑠
𝑃𝑖𝑛
× 100%
71

Types of DC Machines
According to method of excitation dc machines
 Separately excited dc machine
 Self excited dc machine
Shunt dc machine
Series dc machine
Compound dc machine
 Cumulatively compounded machine
 Differentially compounded machine
72

DC Generators
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 a separately excited generator, the field flux
is derived from a separate 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 generator.
3. Series generator. In a series generator, the field flux is produced by
connecting the field circuit in series with the armature of the generator.
73

Cont.…
4. Cumulatively compounded generator. In a cumulatively compounded
generator, both a shunt and a series field are present, and their effects are
additive.
5. Differentially compounded generator. In a differentially compounded
generator, both a shunt and a series field are present, but their effects are
subtractive. .
74

The Equivalent Circuit of a DC Generator
 Two circuits are involved in DC generators
►Armature Circuit
►Field Circuit
 Armature circuit represents Thevenin equivalent of the entire rotor.
 It contains an ideal voltage source 𝐸𝐴 and a resistor 𝑅 𝐴.
 Brush voltage drop is represented by a small battery
 The field coils, which produce the magnetic flux
◘ Inductor 𝐿 𝐹 and resistor 𝑅 𝐹.
◘ 𝑅 𝑎𝑑𝑗 for field current control
75

Cont.…
76
Fig a: The equivalent circuit of a dc generator.
Fig b: A simplified equivalent circuit of a dc
generator with 𝐑 𝐅 combining the resistances of the
field coils and the variable control resistor.

Characteristics of DC generators
The three most important characteristic curves of a dc generator are:
1. Magnetization or open-circuit characteristic (O.C.C.): shows the
relationship between the field current 𝐼 𝐹 and the generated emf 𝐸𝑔 at no load
and at constant given speed.
2. External characteristic: shows the relationship between the terminal
voltage V across the load and the current 𝐼𝐿 flowing in the external load
circuit.
3. Internal or total characteristic: shows the relationship between the emf
generated E (after allowing for demagnetizing effect of armature reaction)
at load and the armature current 𝐼 𝑎.
77

1.Magnetization characteristic or open-circuit characteristic (O.C.C.)
 This characteristic shows the relation between
generated emf at no load (E0) and the field
current (If) at a given fixed speed.
 The O.C.C. curve is just the magnetization
curve and it is practically similar for all type
of generators.
 The data for O.C.C. curve is obtained by
operating the generator at no load and
keeping a constant speed. Field current is
gradually increased and the corresponding
terminal voltage is recorded.
78

Cont.…
 From the emf equation of dc generator,
we know that 𝐸𝑔 = 𝑘∅𝜔.
 However, even when the field current is
zero, some amount of emf is generated.
 This initially induced emf is due to the
fact that there exists some residual
magnetism in the field poles.
 Due to the residual magnetism, a small
initial emf is induced in the armature.
79

2. Internal or Total Characteristic (𝑬 𝒈/𝑰 𝒂)
 It gives the relation between the e.m.f. E actually induces in the armature
(after allowing for the demagnetising effect of armature reaction) and the
armature current 𝐼 𝑎.
 An internal characteristic curve shows the relation between the on-load
generated emf (𝐸𝑔) and the armature current (𝐼 𝑎).
 The on-load generated emf 𝐸𝑔 is always less than 𝐸 𝑜 due to the armature
reaction.
 𝐸𝑔 can be determined by subtracting the drop due to demagnetizing effect
of armature reaction from no-load voltage 𝐸 𝑜.
80

3. External characteristic
 It is also referred to as performance characteristic or load characteristic or
sometimes voltage-regulating curve.
 It gives relation between terminal voltage (V) and the load current (𝐼𝐿).
 Terminal voltage V is less than the generated emf 𝐸𝑔 due to voltage drop in
the armature circuit. Therefore, external characteristic curve lies below the
internal characteristic curve.
 External characteristic are very important to determine the suitability of a
generator for a given purpose.
81

1. Separately Excited Generator.
 A separately excited dc generator is
a generator whose field current is
supplied by a separate external dc
voltage source.
 In this circuit, the voltage 𝑉𝑇
represents the actual voltage
measured at the terminals of the
generator, and
 The current 𝐼𝐿 represents the
current flowing in the lines
connected to the terminals. 82

Terminal Characteristic of a Separately Excited DC Generator
 The terminal characteristic of a device is a plot of the output quantities of
the device versus each other.
 For a dc generator, the output quantities are its terminal voltage and line
current.
 The terminal characteristic of a separately excited generator is thus a plot
of 𝑉𝑇 versus 𝐼𝐿 for a constant speed 𝜔. By Kirchhoff's voltage law, the
terminal voltage is
 Since the internal generated voltage is independent of 𝐼𝐴, the terminal
characteristic of the separately excited generator is a straight line.
83

Cont.…
 When the load supplied by the
generator is increased, 𝐼𝐿 (and
therefore 𝐼𝐴) increases.
 As the armature current increases,
the 𝐼𝐴 𝑅 𝐴 drop increases, so the
terminal voltage of the generator
falls.
84
Fig :The terminal characteristic of a separately excited dc
generator with compensating windings.

Cont.…
 In generators without compensating
windings, an increase in 𝐼𝐴 causes an
increase in armature reaction, and
armature reaction causes flux
weakening.
 This flux weakening causes a decrease
in 𝐸𝐴 = 𝐾∅ ↓ 𝜔 which further
decreases the terminal voltage of the
generator.
85
Fig :The terminal characteristic of a separately
excited dc generator without compensating windings.

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.
 By Kirchhoff's voltage law 𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴 𝑅 𝐴, so if 𝐸𝐴 increases, 𝑉𝑇 will
increase, and if 𝐸𝐴 decreases, 𝑉𝑇 will decrease. Since the internal generated
voltage 𝐸𝐴 is given by the equation 𝐸𝐴 = 𝐾∅𝜔, there are two possible ways
to control the voltage of this generator:
1. Change the speed of rotation: If 𝜔 increases, then 𝐸𝐴 = 𝐾∅𝜔 ↑increases,
so 𝑉𝑇 = 𝐸𝐴 ↑ −𝐼𝐴 𝑅 𝐴 increases too.
2. Change the field current: If 𝑅 𝐹 is decreased, then the field current increases
(𝐼 𝐹 = Τ𝑉𝐹 𝑅 𝐹). Therefore, the flux ∅ in the machine increases. As the flux
rises, 𝐸𝐴 = 𝐾∅ ↑ 𝜔 must rise too, so 𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴 𝑅 𝐴 increases. 86

Nonlinear Analysis of a Separately Excited DC Generator
 Because the internal generated voltage of a generator is a nonlinear
function of its magnetomotive force, it is not possible to calculate simply
the value of 𝐸𝐴 to be expected from a given field current.
 The magnetization curve of the generator must be used to accurately
calculate its output voltage for a given input voltage.
 In addition, if a machine has armature reaction, its flux will be reduced with
each increase in load, causing 𝐸𝐴 to decrease. The only way to accurately
determine the output voltage in a machine with armature reaction is to use
graphical analysis.
87

Cont.…
 The total magnetomotive force in a separately excited generator is the field
circuit magnetomotive force less the magnetomotive force due to armature
reaction (AR):
 The equivalent field current of a separately excited dc generator is given by
 Also, the difference between the speed of the magnetization curve and the
real speed of the generator must be taken into account using Equation
88

Cont.…
89
(a) A separately excited dc generator with a resistive load.
(b) The effect of a decrease in field resistance on the
output voltage of the generator

2. Shunt DC Generator
 It is a dc generator that supplies its own
field current by having its field
connected directly across the terminals
of the machine.
 The armature current of the machine
supplies both the field circuit and the
load attached to the machine:
 It has a distinct advantage over the
separately excited dc generator in that no
external power supply is required for the
field circuit.
90

Voltage Build up in a Shunt DC Generator
 The voltage buildup in a dc generator depends on the presence of a
residual flux in the poles of the generator. 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. But when that
voltage appears at the terminals, it causes a current to flow in the
generator's field coil (𝐼 𝐹 = Τ𝑉𝑇 ↑ 𝑅 𝐹).
 This field current produces a magnetomotive force in the poles, which
increases the flux in them. The increase in flux causes an increase in
𝐸𝐴 = 𝐾∅ ↑ 𝜔, which increases the terminal voltage 𝑉𝑇. When 𝑉𝑇 rises, 𝐼 𝐹
increases further, increasing the flux ∅ more, which increases 𝐸𝐴 , etc 91

Cont.…
92Fig. Voltage buildup on starting in a shunt dc generator

Cont.…
 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 flux ∅ 𝑟𝑒𝑠 = 0, then 𝐸𝐴 = 0, and 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, this procedure is known as "flashing
the field." 93

Cont.…
2. 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 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 ∅ 𝑟𝑒𝑠 and no
voltage can ever build up, 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.
94

Cont.…
3. The field resistance may be adjusted to
a value greater than the critical
resistance.
 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 𝑅2
in the figure, its line is nearly parallel to
the magnetization curve.
 If 𝑅 𝐹 exceeds the critical resistance (as at
𝑅3 in the figure), then the steady-state
operating voltage is essentially at the
residual level, and it never builds up.
 The solution is to reduce 𝑹 .
95
The effect of shunt field resistance on no-load terminal
voltage in a dc generator. If 𝑅 𝐹 > 𝑅2 (the critical resistance).
then the generator's voltage will never build up.

Terminal Characteristic of a Shunt DC Generator
 To understand the terminal characteristic of a shunt generator, start with
the machine unloaded and add loads.
 As the load on the generator is increased, 𝐼𝐿- increases and so 𝐼𝐴 = 𝐼 𝐹 + 𝐼𝐿
also increases. An increase in 𝐼𝐴 increases the armature resistance voltage
drop 𝐼𝐴 𝑅 𝐴, causing 𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴 𝑅 𝐴 to decrease.
 However, when 𝑉𝑇 decreases, the field current 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 terminal voltage 𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴 𝑅 𝐴
 The voltage regulation of this generator is worse than the voltage regulation
of the same piece of equipment connected separately excited.
96

Cont.…
97
Fig : The terminal characteristic of a shunt dc generator

Voltage Control of a Shunt DC Generator
 There are two ways to control the voltage of a shunt generator:
1. Change the shaft speed 𝜔 𝑚 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 𝑅 𝐹 is decreased, then
the field current 𝐼 𝐹 = Τ𝑉𝑇 𝑅 𝐹 ↓ increases.
 When 𝐼 𝐹 increases, the machine's flux ∅ increases, causing the internal
generated voltage 𝐸𝐴 to increase. The increase in 𝐸𝐴 causes the terminal
voltage of the generator to increase as well.
98

3. 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.
 Since the full-load current flows through it, a series field is designed to have
the lowest possible resistance.
99

Cont.…
◘ The armature current, field
current, and line current all have
the same value.
◘ The Kirchhoff's voltage law
equation for this machine is
100
Figure :The equivalent circuit of a
series dc generator.

The Terminal Characteristic of a Series Generator
 At no load, there is no field current , so 𝑉𝑇 is reduced to a small level given
by the residual flux in the machine.
 As the load increases, the field current rises, so 𝐸𝐴 rises rapidly.
 The 𝐼𝐴(𝑅 𝐴 + 𝑅 𝑆) drop goes up too, but at first the increase in 𝐸𝐴 goes up
more rapidly than the 𝐼𝐴(𝑅 𝐴 + 𝑅 𝑆) 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 effect, and 𝑉𝑇
starts to fall.
101

Cont.…
 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. Series generators used in
arc welding are deliberately
designed to have a large armature
reaction.
102
Figure: Derivation of the terminal
characteristic for a series dc generator

Cont.…
 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.
103
Figure: A series generator terminal
characteristic with large armature reaction
effects. suitable for electric welders.

4. Cumulatively Compounded DC Generator
 It is a dc generator with both series and shunt fields, connected so that the
magneto motive forces from the two fields are additive.
104
Figure: equivalent circuit of
a cumulatively compounded
dc generator in the "long-
shunt" connection.

Cont.…
 The total magneto motive force on this machine is given by
 where is the shunt field magnetomotive force,
is the series field magnetomotive force, and
is the armature reaction magnetomotive force.
The equivalent effective shunt field current for this machine is given by
105
 voltage and current relationships for this
generator are

Cont.…
 Another way to hook up a
cumulatively compounded
generator is the "short-shunt"
connection, where the series
field is outside the shunt field
circuit and has current 𝐼𝐿
flowing through it instead of
𝐼𝐴.
106
Figure :Equivalent circuit of a cumulatively compounded
dc generator with a short-shunt connection.

Terminal Characteristic of a Cumulatively Compounded DC Generator
 Suppose that the load on the generator is increased. Then as the load
increases, the load current 𝐼𝐿 increases. Since 𝐼𝐴 = 𝐼 𝐹 + 𝐼𝐿, the armature
current 𝐼𝐴 increases too. At this point two effects occur in the generator:
1. As 𝐼𝐴 increases, the 𝐼𝐴(𝑅 𝐴+𝑅 𝑆) voltage drop increases as well. This tends to
cause a decrease in the terminal voltage 𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴(𝑅 𝐴+𝑅 𝑆).
2. As 𝐼𝐴 increases, the series field magnetomotive force 𝑓𝑆𝐸 = 𝑁𝑆𝐸 𝐼𝐴
increases too. This increases the total magnetomotive force
𝑓𝑡𝑜𝑡 = 𝑁𝐹 𝐼 𝐹+𝑁𝑆𝐸 𝐼𝐴 which increases the flux in the generator. The increased
flux in the generator increases 𝐸𝐴, which in turn tends to make
𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴(𝑅 𝐴+𝑅 𝑆) rise.
107

Cont.…
 These two effects oppose each other, with one tending to increase 𝑉𝑇 and
the other tending to decrease 𝑉𝑇. Which effect predominates in a given
machine?
 It all depends on just how many series turns were placed on the poles of
the machine.
1. Few series turns (𝑵 𝑺𝑬 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. This type of construction, where the
full-load terminal voltage is less than the no-load terminal voltage, is called
undercompounded.
108

Cont.…
2. More series turns (𝑵 𝑺𝑬 larger). 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 𝑉𝑇 at no load is equal to 𝑉𝑇at full load,
the generator is called flat-compounded.
3. Even more series turns are added (𝑵 𝑺𝑬 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.
109

Cont.…
 The result is a characteristic with the
full-load terminal voltage actually
higher than the no-load terminal
voltage. If 𝑉𝑇 at a full load exceeds
𝑉𝑇 at no load, the generator is called
overcompounded
110
Figure :Terminal characteristics of cumulatively
compounded dc generators.

Voltage Control of Cumulatively Compounded DC Generators
 There are two ways to control the voltage of cumulatively compounded
Generators:
1. Change the speed of rotation: An in crease in 𝜔 causes 𝐸𝐴 = 𝐾∅𝜔 to
increase, increasing the terminal voltage 𝑉𝑇 = 𝐸𝐴 − 𝐼𝐴(𝑅 𝐴+𝑅 𝑆) .
2. Change the field current: A decrease in 𝑅 𝐹 causes 𝐼 𝐹 = Τ𝑉𝑇 𝑅 𝐹 to increase,
which increases the total magnetomotive force in the generator. As 𝑓𝑡𝑜𝑡
increases, the flux ∅ in the machine increases, and 𝐸𝐴 = 𝐾∅𝜔 increases .
Finally, an increase in 𝐸𝐴raises 𝑉𝑇.
111

5. Differentially Compounded DC Generator
 It is a generator with both shunt and series fields, but this time their
magnetomotive forces subtract from each other.
112

Cont.…
 In this machine, the net
magnetomotive force 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
 Like the cumulatively compounded
generator, the differentially
compounded generator can be
connected in either long-shunt or
short-shunt fashion.
113

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