Chapter-4

DC Machines

Term-151

1

Direct Current (DC) Machines Fundamentals

Generator action: An emf (voltage) is induced in a

conductor if it moves through a magnetic field.

Motor action: A force is induced in a conductor that

has a current going through it and placed in a

magnetic field.

Any DC machine can act either as a generator or as a

motor.

2

DC Machines- Direction of Power Flow and Losses

3

DC Machines- Direction of Power Flow and Losses

4

DC Machines Analysis

Symbols that will be used.

= flux per pole

p = no. of poles

z = total number of active conductors on the armature

a = no. of parallel paths in the armature winding

n = speed of rotation of the armature in rpm

wm = speed in radians per second

5

The Internal Generated Voltage Equations

Of Real Machines

The induced voltage in any given machine depends on

three factors:

The flux Φ in the machine

The speed ω of the machine's rotor

A constant depending on the construction of the machine

The voltage out of a real machine = the number of conductors per current

path x the voltage on each conductor

6

EMF Equation

When the rotor rotates in the field a voltage is developed in the

armature.

The flux cut by one conductor

in one rotation

Therefore in n rotations, the

flux cut by one conductor

p

np

The flux cut per second by one

conductor

z

a

The number of conductors in

series

60

np

7

EMF Equation

EMF induced in the

armature windings

8

The Induce Torque Equations Of Real

Machines

The torque in any dc machine depends on three factors:

The flux Φ in the machine

The armature (or rotor) current IA in the machine

A constant depending on the construction of the machine

The torque on the armature of a real machine =the

number of conductors Z x the torque on each conductor

9

TORQUE EQUATION

EaIa=Tem - In the DC machine losses are

expressed as rotational losses

due to friction and windage (F&W).

- The torque equation can then be

rewritten as:-

SHAFT OUTPUT TORQUE = (Te -

TF&W)

10

Construction of DC Machines

11

Features of DC Machine

Field Winding

12

Construction of DC

Machines

13

Construction of DC Machines

Field system

Armature core

Armature winding

Commutator

Brushes

14

Field System

15

Field system

It is for uniform magnetic field within which the armature rotates.

Electromagnets are preferred in comparison with permanent magnets

They are cheap , smaller in size , produce greater magnetic effect and field strength can be varied

16

Field system consists of the following parts

Yoke

Pole cores

Pole shoes

Field coils

17

Armature core The armature core is cylindrical.

High permeability silicon steel stampings.

Lamination is to reduce the eddy current. loss

18

Armature winding

19

Armature winding

There are 2 types of winding

Lap and Wave winding

• A = P

• It is meant for high

current and low voltages.

• The armature windings are divided into number of sections equal to the number of poles.

• A = 2

• It is meant for low

current output and high voltages.

• 2 brushes

20

Commutator • Connect with external circuit.

• Converts ac into unidirectional current.

• Cylindrical in shape .

• Made of wedge shaped copper segments.

• Segments are insulated from each other.

• Each commutator segment is connected to armature conductors by means of a copper strip called riser.

• Number of segments equal to number of coils.

21

Carbon brush • Carbon brushes are used in DC

machines because they are soft materials.

• It does not generate spikes when they contact commutator.

• To deliver the current through armature.

• Carbon is used for brushes because it has negative temperature coefficient of resistance.

22

DC Machine Equivalent

Circuits

1. Magnetic equivalent

circuit

2. Electrical equivalent

circuit

23

1. Magnetic equivalent circuit

DC machine Cross-sectional view

DC machine Magnetic equivalent circuit

Flux-mmf relation in a dc machine

24

Electrical equivalent

circuit

DC Generator

25

DC Generator Equivalent circuit

The magnetic field produced by the stator poles induces a

voltage in the rotor (or armature) coils when the generator is

rotated.

This induced voltage is represented by a voltage source.

The stator coil has resistance, which is connected in series.

The pole flux is produced by the DC excitation/field current,

which is magnetically coupled to the rotor

The field circuit has resistance and a source

The voltage drop on the brushes represented by a battery 26

DC Generator Equivalent circuit

Equivalent circuit of a separately excited dc generator.

RfRa

Vbrush

VTEagVf

IfIag

Load

Mechanical

power in

Electrical

power out

27

DC Generator Equivalent circuit

The magnetic field produced by the stator poles induces a voltage in the rotor (or armature) coils when the generator is rotated.

The dc field current of the poles generates a magnetic flux

The flux is proportional with the field current if the iron core is not saturated:

1 fK I

The rotor conductors cut the field lines that generate voltage in the coils.

ag a mE K 28

DC Generator Equivalent circuit

When the generator is loaded, the load current produces a

voltage drop on the rotor winding resistance.

In addition, there is a more or less constant 1 to 3 V voltage

drop on the brushes.

These two voltage drops reduce the terminal voltage of the

generator. The terminal voltage is;

ag T ag a brushE V I R V

29

Electrical equivalent

circuit

DC Motor

30

DC Motor Equivalent circuit

Equivalent circuit of a separately excited dc motor

Equivalent circuit is similar to the generator only the current directions are different

RfRa

Vbrush

VTEamVf

IfIam

Mechanical

power out

Electrical

power in

DC Power

supply

31

DC Motor Equivalent circuit The operation equations are:

Armature voltage equation

T am am a brushV E I R V

The induced voltage and motor speed vs angular frequency

am a mE K 2m mn

The output power and torque are:

amamout IEP out

a am

m

PT K I

32

Classification of DC

Machines

33

34

Separately Excited DC Machine

E

RaIa +

--

+

VT

a)

E

-

+Field

F F

Armature

b) Separately Excited35

Series & Shunt DC Machine

E

-

+

Field

F F

Armature

c) Series

E

-

+

Field

F F

Armature

d) Shunt

A

A

36

Cumulative & Differential DC machine

E

-

+

Field FF

Armaturee) Cummulative Compound

A

A

S S

E

-

+

Field FF

Armature

d) Differential Compound

A

A

S S

37

Long Shunt & Short Shunt DC Machine

E

-

+

Field FF

Armature

f) Long Shunt

A

A

S S

E

-

+

Field FF

Armature

g) Short Shunt

A

A

S S

38

Exercise Problems

39

Exercise-1

A four-pole dc machine has an armature of radius 12.5 cm and an

effective length of 25cm. The poles cover 75 % of the armature

periphery. The armature winding consists of 33 coils, each having

seven turns. The coils are accommodated in 33 slots. The average

flux density under each pole is 0.75 T.

A. If the armature is lap wound, then

a) Determine the armature constant Ka.

b) Determine the induced armature voltage when the armature

rotates at 1000 rpm.

c) Determine the current in the coil and the electromagnetic torque

developed when the armature current is 400 A.

d) Determine the power developed by the armature.

B. If the armature is wave-wound, repeat parts (a) to (d) above. The

current rating of the coils remains the same as in the lap-wound.

40

Exercise-2

A 12-pole dc generator has a simplex wave-wound armature

containing 144 coils of 10 turns each. The resistance of each turn is

0.011 Ω. Its flux per pole is 0.05 Wb, and the machine is running at a

speed of 200 r/min.

(a) How many current/parallel paths are there in this machine?

(b) What is the induced armature voltage of this machine?

(c) What is the effective armature resistance of this machine?

(d) If a 1 kΩ resistor is connected to the terminals of this generator,

Determine the power output and the induced counter-torque on

the shaft of this generator.

41

4.3 DC Generators

42

Separately Excited DC Generator The operation equations are:

Stator or field side:

Armature voltage equation:

Load or terminal equation:

Current equation:

f fw fc

f f f

R R R

V I R

a t a a brush

a a m

E V I R V

E K

t t LV I R

a tI I

Power developed in the armature:

Load or terminal equation:

Current equation:

a g a aP P E I

Power delivered to the load:

Load or terminal equation:

Current equation:

L t t t t LP P V I V I 43

Characteristics Performance of the DC generators

are determined by terminal output parameter IL and VT

By Kirchhoff's voltage law, the terminal voltage is,

Since the internal generated voltage is independent of armature current, the generator terminal characteristics is a straight line.

Due to the armature voltage drop, the characteristics show drooping nature.

t a a a brushV E I R V a tI ITerminal characteristics of separately

excited DC generator

44

Shunt (Self-Excited) DC Generator The operation equations are:

Stator or field side:

Armature voltage equation:

Load or terminal equation:

Current equation:

tsh

sh

VI

R

a t a a brush

a a m

E V I R V

E K

t t LV I R

a L shI I I

Power developed in the armature:

Load or terminal equation:

Current equation:

a g a aP P E I

Power delivered to the load:

Load or terminal equation:

Current equation:

L t t t t LP P V I V I 45

Characteristics By Kirchhoff's voltage law, the

terminal voltage is,

Since the internal generated voltage is independent of armature current, the generator terminal characteristics is a straight line.

Due to the armature voltage drop, the characteristics show drooping nature.

t a a a brushV E I R V

a t shI I I

Terminal characteristics of shunt DC generator

46

Series (Self-Excited) DC Generator The operation equations are:

Stator or field side:

Armature voltage equation:

Load or terminal equation:

Current equation:

se a L tI I I I

( )a t a a se brush

a a m

E V I R R V

E K

t t LV I R

a t LI I I

Power developed in the armature:

Load or terminal equation:

Current equation:

a g a aP P E I

Power delivered to the load:

Load or terminal equation:

Current equation:

L t t t t LP P V I V I 47

Characteristics By Kirchhoff's voltage law, the

terminal voltage is,

As the load increases, the field

current rises, so EA rises rapidly The

IA (RA+Rs) drop goes up too, but

at first the increase in EA goes up

more rapidly than the IA(RA+Rs)

drop rises, so Vr increases.

( )t a a a se brushV E I R R V

a t seI I I

Terminal characteristics of series DC generator

After a while, the machine approaches

saturation, and EA becomes almost

constant. At that point, the resistive

drop is the predominant effect, and VT

starts to fall.

48

Short Shunt DC Generator The operation equations are:

Series field side:

Shunt field current

Armature voltage equation:

Load or terminal equation:

Current equation:

se L tI I I

a t a a se se brush

a a m

E V I R I R V

E K

t t LV I R

a L shI I I

Power developed in the armature:

Load or terminal equation:

Current equation:

a g a aP P E I

Power delivered to the load:

Load or terminal equation:

Current equation:

L t t t t LP P V I V I

t se sesh

sh

V I RI

R

49

Long Shunt DC Generator The operation equations are:

Series field side:

Shunt field current

Armature voltage equation:

Load or terminal equation:

Current equation:

se aI I

( )a t a a se brush

a a m

E V I R R V

E K

t t LV I R

a L shI I I

Power developed in the armature:

Load or terminal equation:

Current equation:

a g a aP P E I

Power delivered to the load:

Load or terminal equation:

Current equation:

L t t t t LP P V I V I

tsh

sh

VI

R

50

Characteristics

51

4.4 DC Motors

52

HW-3

Draw the equivalent circuits of

various DC motors & derive

their voltage, current and

power equations. Draw their

performance characteristics.

Due Date: Monday, November 16, 2015

53

Performance of DC

Machines

54

DC Generator A DC generator is a machine that takes in mechanical input

power to produce electrical power output.

The performance of a dc generator is assessed by means of the following:

Generator Efficiency:

Voltage Regulation:

100 100 100out in out

in in out

P P Losses P

P P P Losses

, ,

,

100t NL t FL

t FL

V VVR

V

55

DC Motor: A DC motor is a machine that produces mechanical output

power from the applied electrical input.

The performance of a dc motor is assessed by means of the following:

Motor Efficiency:

Speed Regulation:

100 100 100out in out

in in out

P P Losses P

P P P Losses

, ,

,

100m NL m FL

m FL

n nSR

n

56

Power Flow & Losses in

a DC Machine

57

Efficiency Calculations

Losses in DC Machines

58

All these losses appear as heat and thus raise the temperature of the machine. They

also lower the efficiency of the machine.

Constant Losses

Variable Losses

Electrical or Copper Losses (I2R Losses)

Armature copper loss:

59

These losses occur due to currents in the armature and field windings of the dc machine.

Brush Losses:

There is also brush contact loss due to brush contact resistance (i.e., resistance between the surface of brush and surface of commutator). This loss is generally included in armature copper loss.

It can also be calculated explicitly by the following relation.

2

A a aP I R

2

sh sh shP I R

2

se se seP I R

Shunt field copper loss:

Series field copper loss:

BD BD aP V I

Core or Iron Losses

60

As iron core of the armature is continuously rotating in a magnetic field, there are some losses taking place in the core. This loss consists of Hysteresis loss and Eddy current loss.

When the armature core rotates in the magnetic field, an emf is also induced in the core (just like it induces in armature conductors), according to the Faraday's law of electromagnetic induction. Though this induced emf is small, it causes a large current to flow in the body due to low resistance of the core. This current is known as eddy current. The power loss due to this current is known as eddy current loss.

Hysteresis loss is due to reversal of magnetization of the armature core. When the core passes under one pair of poles, it undergoes one complete cycle of magnetic reversal. The frequency of magnetic reversal if given by, f=PN/120. The loss that takes place due to repeated magnetization & demagnetization of the iron core contributes to the hysteresis loss.

Hysteresis loss:

Eddy current loss:

Mechanical Losses

61

The mechanical losses in a dc machine are the losses associated with

mechanical effects.

These losses are due to friction and windage.

(i) friction loss e.g., bearing friction, brush friction etc.

(ii) windage loss i.e., air friction of rotating armature.

These losses depend upon the speed of the machine. But for a given speed,

they are practically constant.

Mechanical and core losses are together considered as rotational losses .

The Power-Flow Diagram of DC Generator

62

The Power-Flow Diagram of DC Motor

63

Exercise Problems

64

Exercise-1

A separately excited dc generator running at 1200 rpm & delivers

12kW at 240 V as terminal voltage. The armature resistance is 0.3

ohms. Each brush takes 1 V drop. Pmech=600 W, Pcore=300 W and

Pstray=200 W. The field circuit resistance is 200 ohms and DC field

voltage is 250 V.

65

a) Draw the equivalent circuit and the corresponding power

flow diagram.

b) Find the induced voltage.

c) Determine the converted or developed power and the

induced torque.

d) Find the efficiency of the machine.

Exercise-2

A 220 V shunt DC motor has an armature resistance of 0.2 ohms and

a field resistance of 110 ohms. At no-load the motor runs at 1000

rpm and it draws a line current of 7 A. At full-load, the input to the

motor is 11 kW.

66

a) Draw the equivalent circuit.

b) Find the rotational losses.

c) Find the speed, speed regulation and developed torque at full

load.

d) Find the efficiency of the motor.

HW-4

67

Questions #:

4.2, 4.16, 4.17, 4.18, 4.25, 4.26,4.39,

4.40 found on pages 192-198 of the

text book.