Chapter 6DC Machines

EET103/4

Introduction

• An electrical machine is link between an electrical system and a mechanical system.

• Conversion from mechanical to electrical: generator

• Conversion from electrical to mechanical: motor

Introduction

Machines are called

• AC machines (generators or motors) if the electrical system is AC.

• DC machines (generators or motors) if the electrical system is DC.

DC machines can be divide by:

a) DC motorb) DC Generator

DC Machines

DC Motor DC Generator

DC Machines Construction

cutaway view of a dc machine

DC Machines Construction

cutaway view of a dc machine

DC Machines Construction

Rotor of a dc machine

DC Machines Construction

Stator of a dc machine

DC Machines Fundamentals• Stator: is the stationary part of the machine. The

stator carries a field winding that is used to produce the required magnetic field by DC excitation.

• Rotor (Armature): is the rotating part of the machine. The rotor carries a distributed winding, and is the winding where the e.m.f. is induced.

• Field winding: Is wound on the stator poles to produce magnetic field (flux) in the air gap.

• Armature winding: Is composed of coils placed in the armature slots.

• Commutator: Is composed of copper bars, insulated from each other. The armature winding is connected to the commutator.

• Brush: Is placed against the commutator surface. Brush is used to connect the armature winding to external circuit through commutator

DC Machines Fundamentals In DC machines, conversion of energy from electrical to

mechanical form or vice versa results from the following two electromagnetic phenomena

1.When a conductor moves in a magnetic field, voltage is induced in the conductor.

2. When a current carrying conductor is placed in magnetic field, the conductor experiences a mechanical forces.

DC Machines Fundamentals

Generator action:An e.m.f. (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.

DC Machines Equivalent Circuit

The equivalent circuit of DC machines has two components:

Armature circuit: • It can be represented by a voltage source and a

resistance connected in series (the armature resistance). The armature winding has a resistance, RA.

The field circuit: • It is represented by a winding that generates the

magnetic field and a resistance connected in series. The field winding has resistance RF.

DC Motor

• In a dc motor, the stator poles are supplied by dc excitation current, which produces a dc magnetic field.

• The rotor is supplied by dc current through the brushes, commutator and coils.

• The interaction of the magnetic field and rotor current generates a force that drives the motor.

Basic Operation of DC Motor

• The magnetic field lines enter into the rotor from the north pole (N) and exit toward the south pole (S)

• The poles generate a magnetic field that is perpendicular to the current carrying conductors

• The interaction between the field and the current produces a Lorentz force

• The force is perpendicular to both the magnetic field and conductor

Basic Operation of DC Motor

Basic Operation of DC Motor

• The generated force turns the rotor until the coil reaches the neutral point between the poles.

• At this point, the magnetic field becomes practically zero together with the force.

• However, inertia drives the motor beyond the neutral zone where the direction of the magnetic field reverses.

• To avoid the reversal of the force direction, the commutator changes the current direction, which maintains the counter clockwise rotation.

• Before reaching the neutral zone, the current enters in segment 1 and exits from segment 2

• Therefore, current enters the coil end at slot ‘a’ and exits from slot ‘b’ during this stage

• After passing the neutral zone, the current enters segment 2 and exits from segment 1,

• This reverses the current direction through the rotor coil, when the coil passes the neutral zone

• The result of this current reversal is the maintenance of the rotation

Basic Operation of DC Motor

Basic Operation of DC Motor

Classification of DC Motor1. Separately Excited DC Motor • Field and armature windings are either connected

separate.

2. Shunt DC Motor• Field and armature windings are either connected in

parallel.

3. Series DC Motor• Field and armature windings are connected in series.

4. Compound DC Motor• Has both shunt and series field so it combines features of series and shunt motors.

Important terms

• VT – supply voltage• EA – internal generated voltage/back e.m.f.• RA – armature resistance• RF – field/shunt resistance• RS – series resistance• IL – load current• IF – field current• IA – armature current• IL – load current•

n – speed

Generated or back e.m.f. of DC Motor

• General form of back e.m.f.,

Φ = flux/pole (Weber)Z = total number of armature conductors = number of slots x number of conductor/slotP = number of polesA = number of parallel paths in armature[A = 2 (for wave winding), A = P (for lap winding)]N = armature rotation (rpm)

EA = back e.m.f.

A

PZNEA

60

Torque Equation of a DC Motor

• The armature torque of a DC motor is given by

Φ = flux/pole (Weber)Z = total number of armature conductors = number of slots x number of conductor/slotP = number of polesA = number of parallel paths in armature

IA = armature current

Ta = armature torque

)(2

meterNewtonA

PZIT A

a

Equivalent Circuit of DC Motor

F

TF R

VI

AAAT RIEV

F

FF R

VI

AAAT RIEV

AL II

Separately Excited DC Motor

Shunt DC Motor

FAL III

)( SAAAT RRIEV

LSA III

Series DC Motor

)( SAAAT RRIEV

F

TF R

VI FLA III

Compound DC Motor

Speed of a DC Motor

• For shunt motor

• For series motor

1

2

1

212

2

1

1

2

1

2 ,A

A

A

A

E

E

n

nthenIf

E

E

n

n

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1

1

2

2

1

1

2

1

2

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A

A

A

A

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I

I

E

E

E

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n

n

Example 1

A 250 V, DC shunt motor takes a line current of 20 A. Resistance of shunt field winding is 200 Ω and resistance of the armature is 0.3 Ω. Find the armature current, IA and the back e.m.f., EA.

SolutionGiven quantities:• Terminal voltage, VT = 250 V• Field resistance, RF = 200 Ω• Armature resistance, RA = 0.3 Ω• Line current, IL = 20 A

Figure 1

Solution (cont..)

the field current,

the armature current,

VT = EA + IARA

the back e.m.f.,

EA = VT – IARA = 250 V – (18.75)(0.3) = 244.375 V

A25.1200

V250

F

TF

FAL

R

VI

III

18.75A

A25.1A20

FLA III

Example 2

A 50hp, 250 V, 1200 r/min dc shunt motor with compensating windings has an armature resistance (including the brushes, compensating windings, and interpoles) of 0.06 Ω. Its field circuit has a total resistance Radj + RF of 50 Ω, which produces a no-load speed of 1200 r/min. There are 1200 turns per pole on the shunt field winding.

Example 2 (cont..)

a) Find the speed of this motor when its input current is 100 A.

b) Find the speed of this motor when its input current is 200 A.

c) Find the speed of this motor when its input current is 300 A.

SolutionGiven quantities:• Terminal voltage, VT = 250 V• Field resistance, RF = 50 Ω• Armature resistance, RA = 0.06 Ω• Initial speed, n1 = 1200 r/min

Figure 2

Solution (cont..) (a) When the input current is 100A, the armature

current in the motor is

Therefore, EA at the load will be A95A5A100

50

V250A100

F

TLFLA R

VIIII

V3.244

V7.5V250

)06.0)(A95(V250

AATA RIVE

Solution (cont..)

• The resulting speed of this motor is

min/r1173

min/r1200250

3.244

11

22

1

2

1

2

V

V

nE

En

E

E

n

n

A

A

A

A

Solution (cont..)(b) When the input current is 200A, the armature

current in the motor is

Therefore, EA at the load will be A195A5A200

50

V250A200

F

TLFLA R

VIIII

V3.238

V7.11V250

)06.0)(195(V250

A

RIVE AATA

Solution (cont..)

• The resulting speed of this motor is

min/r1144

min/r1200250

3.238

11

22

1

2

1

2

V

V

nE

En

E

E

n

n

A

A

A

A

Solution (cont..)(c) When the input current is 300A, the armature

current in the motor is

Therefore, EA at the load will be A295A5A300

50

V250A300

F

TLFLA R

VIIII

V3.232

V7.17V250

)06.0)(295(V250

A

RIVE AATA

Solution (cont..)

• The resulting speed of this motor is

min/r1115

min/r1200V250

V3.232

11

22

1

2

1

2

nE

En

E

E

n

n

A

A

A

A

Example 3

The motor in Example 2 is now connected in separately excited circuit as shown in Figure 3. The motor is initially running at speed, n = 1103 r/min with VA = 250 V and IA = 120 A, while supplying a constant-torque load. If VA is reduced to 200 V, determine

i). the internal generated voltage, EA

ii). the final speed of this motor, n2

Example 3 (cont..)

Figure 3

Solution

Given quantities

• Initial line current, IL = IA = 120 A

• Initial armature voltage, VA = 250 V

• Armature resistance, RA = 0.06 Ω

• Initial speed, n1 = 1103 r/min

Solution (cont..)

i) The internal generated voltage

EA = VT - IARA

= 250 V – (120 A)(0.06 Ω)

= 250 V – 7.2 V

= 242.8 V

Solution (cont..)

ii) Use KVL to find EA2

EA2 = VT - IA2RA

Since the torque is constant ant he flux is constant, IA is constant. This yields a voltage of

EA2 = 200 V – (120 A)(0.06 Ω) = 200 V – 7.2 V = 192.8 V

Solution (cont..)

• The final speed of this motor

min/r876

min/r1103V8.242

V8.192

11

22

1

2

1

2

nE

En

E

E

n

n

A

A

A

A

Example 4

A DC series motor is running with a speed of 800 r/min while taking a current of 20 A from the supply. If the load is changed such that the current drawn by the motor is increased to 50 A, calculate the speed of the motor on new load. The armature and series field winding resistances are 0.2 Ω and 0.3 Ω respectively. Assume the flux produced is proportional to the current. Assume supply voltage as 250 V.

SolutionGiven quantities• Supply voltage, VT = 250 V• Armature resistance, RA = 0.2 Ω• Series resistance, RS = 0.3 Ω• Initial speed, n1 = 800 r/min• Initial armature current, Ia1 = IL1 = 20 A

Figure 4

Solution (cont..)

For initial load, the armature current, Ia1 = 20 A and the speed n1 = 800 r/min

V = EA1 + Ia1 (RA + RS)

The back e.m.f. at initial speed

EA1 = V - Ia1 (RA + RS) = 250 – 20(0.2 + 0.3) = 240 V

Solution (cont..) When the armature current increased, Ia2 = 50 A, the back emf

EA2 = V – Ia2 (RA + RS) = 250 – 50(0.2 + 0.3) = 225 V

min/r30050

20

240

225800

2

1

1

212

2

1

1

2

1

2

2

1

1

2

1

2

I

I

E

Enn

I

I

E

E

n

n

E

E

n

n

A

A

A

A

A

A

The speed of the motor on new load

DC Generator

Generating of an AC Voltage

• The voltage generated in any dc generator inherently alternating and only becomes dc after it has been rectified by the commutator

Generation of an AC Voltage

Armature windings

• The armature windings are usually former-wound. This are first wound in the form of flat rectangular coils and are then puller.

• Various conductors of the coils are insulated each other. The conductors are placed in the armature slots which are lined with tough insulating material.

• This slot insulation is folded over above the armature conductors placed in the slot and is secured in place by special hard wooden or fiber wedges.

Lap and wave Windings

There are two types of windings mostly employed:• Lap winding• Wave winding

The difference between the two is merely due to the different arrangement of the end connection at the front or commutator end of armature.

Generated or back e.m.f. of DC Generator

• General form of generated e.m.f.,

Φ = flux/pole (Weber)Z = total number of armature conductors = number of slots x number of conductor/slotP = number of polesA = number of parallel paths in armature[A = 2 (for wave winding), A = P (for lap winding)]N = armature rotation (rpm)E = e.m.f. induced in any parallel path in armature

A

PZNE

60

Classification of DC Generator1. Separately Excited DC Generator• Field and armature windings are either connected

separate.

2. Shunt DC Generator• Field and armature windings are either connected in

parallel.

3. Series DC Generator• Field and armature windings are connected in series.

4. Compound DC Generator• Has both shunt and series field so it combines features of series and shunt motors.

Equivalent circuit of DC generator

FAL III

AL II

Separately excited DC generator

F

FF R

VI

AAAT RIEV

Shunt DC generator

F

TF R

VI

AAAT RIEV

FAL III

ASL III

Series DC generator

)( SAAAT RRIEV

Compound DC generator

F

TF R

VI

AAAT RIEV

Example

• A DC shunt generator has shunt field winding resistance of 100Ω. It is supplying a load of 5kW at a voltage of 250V. If its armature resistance is 0.02Ω, calculate the induced e.m.f. of the generator.

Solution

Given quantities

• Terminal voltage, VT = 250V

• Field resistance, RF = 100Ω

• Armature resistance, RA = 0.22Ω

• Power at the load, P = 5kW

Solution (cont..)

A5.2100

V250

F

TF

FLA

R

VI

III

The field current,

A20V250

W5000

TL V

PIThe load current,

The armature current, IA = IL + IF = 20A + 2.5A = 22.5A

The induced e.m.f.,

EA = VT + IA RA = 250V + (22.5)(0.22) = 254.95V