dc machines electrical machines – i

Electrical Machines – I

DC machines

General Idea

Electrical Machine

Electrical Energy Mechanical Energy

Losses – I2R, friction, etc

Types of electrical machines

Types of electrical machines

Rotating type Stationary type

Transformers

Motors and generators

AC motors and generators

DC motors and Generators

Magnets and field

Permanent Magnet

Electromagnet

The magnetic field can be controlled by regulating the amount of current flowing

Faraday’s Coil and Magnet Experiment - Deflection

The amount of deflection

is proportion

al to the amount of

voltage induced

Faraday’s Experiment – Effect of speed of movement of the magnet


is proportional

to the amount of

voltage induced

(electromotive force)

Faraday’s Experiment – effect of number of turns of the coil


is proportion

al to the amount of

voltage induced

Faraday’s Law• Faraday’s law of electromagnetic induction: - – The induced electromotive force (EMF or voltage) in any closed

circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit. For a coil of wire of N turns EMF is given as: -

– The negative sign indicates that the direction of EMF is opposite to the source that produces it

– is the number of magnetic field lines that a conductor intersects per unit time

dtdNe

dtd

dtde

DC Generators

Lorentz’s Single conductor Experiment in a magnetic field – a generator point of view

I

Conductor

N

W

S

E

F

B

F

B

I

Lorentz force law - generators

•When a conductor is moved in a magnetic field, the electrons experience a force which causes current to flow in the conductor and this current is mutually perpendicular to the direction of the field and the force applied. [For Generators]

•Where θ is the angle between the wire and the magnetic field.• q = charge• v = velocity of electrons •B = magnetic field strength

F = qvBsinθ

Lorentz’s Single conductor Experiment in a magnetic field – a generator point of view

I

Rotational direction

Conductor

N

W

S

E

F

B

F

B

I

Flux distribution at different positions

NS

B

C

D

A

dφ/dt = 0

dφ/dt = 0

dφ/dt = max dφ/dt = max

•dφ/dt = number of lines that the conductor intersects (passes through) per unit time•dφ/dt = 0 because the direction of conductor movement is parallel to the direction of flux

Single loop in a magnetic field – position A

N S

V

a

b

c

d

N

W

S

E

R1

R2

Single loop in a magnetic field – position B

N S

V

-ve

+ve

F

I

F

I

a

bc

d

N

W

S

E

R1

R2

Single loop in a magnetic field – position C

N S

V

a

b

c

dN

W

S

E

R1

R2

Single loop in a magnetic field – position D

N S

V-ve

+ve

a

cb

d

N

W

S

E

R1

R2

I

F

I

F


N S

V

a

b

c

d

N

W

S

E

R1

R2

DC from AC

AC waveform

DC waveform

The Idea of commutation

POSITION B

POSITION D

R1+veR2-ve

R1-veR2+ve

Slip rings and Commutator segments

Slip Rings

Commutator Segments

Left Brush Right Brush


N S

V

N

W

S

Ea

b

c

d

CA

CB

1 2

Single loop in a magnetic field – position B

N S

V

+ve-ve

N

W

S

E

d

bc

aCB

CA

1 2

I

I

F

F

Single loop in a magnetic field – position C

N S

V

N

W

S

Ed

c

b

a1 2

CB

CA

Single loop in a magnetic field – position D

N S

V

+ve -ve

N

W

S

E

a

cb

d

1 2

CA

CB

I

I

F

F


N S

V

N

W

S

Ea

b

c

d

CA

CB

1 2

Converting Impure DC to Pure DC

Effect of number of poles

N S

S

S

N

N

polesofnumberppE

__

Eavg1

Eavg2Eavg2 > Eavg1

Effect of number of conductorsN S

N S

Eavg2

Eavg1Eavg2>Eavg1

zE z = total number of conductors

Effect of field strength and Electromagnets

• Another factor effecting the EMF is the field strength. The strength of Permanent magnets depend upon the material with which it is made. However, the strength of an electromagnet depends upon the amount of current passing through it.

• Ampere’s Law– The magnetic field in space around an electric

current is proportional to the electric current.

E

The EMF equation

zpaEn

aznpE

b

b

6060

Eb= generated EMF (volts) (back EMF - motors)p = number of polesn = speed (RPM)z = total number of conductorsa = total number of parallel paths

1 parallel path

2 parallel path

Electromagnet

I

I

NS

II

NS

Electromagnet

• Metals offer an easier path for the flow of magnetic flux

Stator frame

Field coils

Physical structure of DC machines

DC Motors

Lorentz’s Single conductor Experiment in a magnetic field – a motors point of view

F

B

I

F

B

I

Rotational direction

Conductor

N

W

S

E

Lorentz’s force law - Motors

• Lorentz force: - If a current carrying conductor (with current I A) is placed in a magnetic field (with field B T), it experiences a force (F N) in a direction mutually perpendicular to the magnetic field and the current. [For Motors]

sinBILF

• B = Magnetic field intensity• I = current in the conductor• L = length of the conductor• θ = angle between the current (or conductor) and the field


N S N

W

S

Ea

b

c

d

CA

CB

1 2 • Two brushes are shorted, hence no current flows through the conductors. +

DC motors

+

N S

+N S

N S

N S

A

B

B

A

A

B

A

B

F

FF

F

Electrical circuit of a DC machine

AIPZT

TIETPalso

IEPRIIEVI

RIEVRIEVRIEV

am

maa

mm

aam

aaaaa

aaa

aab

aab

2

_

2

•It is quite evident that the torque of the motor is directly proportional to the flux produced by magnets and the armature current.

V

Eb = Ea = armature voltage

atm IkT

Steady state characteristics – No load

apzk

kVn

nkVnkEaznpE

e

e

e

ea

a

60

60

VERIVERIEV

a

aaa

aaa

volts

250 500

speed

500

1000

RPM

Ke = 2

• current drawn is very small under no-load or Ia is 0 or of the order of 1e-3• no-load current basically supplies the frictional losses of the machine• We can also say that the no-load speed is directly proportional to the applied voltage

Torque under no-load is the torque required to overcome the frictional losses which are extremely small

Steady state characteristics – When loaded

lma

t

ma

atm

am

TTTkTI

IkTAIPZT

2 Torque

speedRPM

load

motor

900

X

• Acceleration and deceleration is governed by the sign of the accelerating torque• Under steady-state conditions the armature current is constant and the motor torque is equal to the load torque as there is no acceleration

ltee

aaa

aaa

TkkR

kVn

RIVERIEV

900time

Transient characteristics

lm TT

Steady state characteristics – When loaded - Droop

lte

a

e

TkkR

kVn

125V 250V 375V 500V

RPM

500 1000

Torque

Slope = Droop

• Droop is the fall in speed as load is applied• Droop is directly proportional to the armature resistance•Machines with least amount of droop are chosen so that expensive controls can be avoidedΔn

ΔT

Full Load

No-load Δn = 5 to 10%

Connections

Stator frame

Field coils

Types of Electric circuit of a DC machine

• Permanent magnet excited• Separately excited• Shunt Excited

– Constant Speed applications

• Series Excited– Heavy torque

Shunt motors used for constant speed applications. Why?

increasesTIkTincreasesI

increasesEVaznpEE

RVI

m

atm

a

a

ab

shsh

60

V

• This increase in torque causes the machine to accelerate and hence prevent the speed from falling.

• armature current control• armature current becomes extremely high

Series motors used for constant high torque applications. Why?

current

Flux lines

Load added

ase II Φ α Ia

• The Series motor is able to overcome high load torque as the flux is proportional to the load current.

• armature current and flux increase• flux and current control• poor speed regulation due to high series resistance and saturation• higher voltage required due to voltage division

Speed control of DC motors

Control System

DC motorPID Controller-

Reference Speed (1750

RPM) +

Load or Disturbances

Δω

ω

Separately Excited machine rated 5Hp

Ki/sΔω

Kp

sKd

+

V

lte

a

e

TkkR

kVn

Proportional control

Integral control

Derivative control

PID control

dttdeku

dtteku

teku

dd

t

ii

pp

)(

)(

)(

0

Proportional control sets the voltage proportional to the

current value of error in speed

integral control sets the voltage proportional to the accumulated error in speed over a certain time period

Derivative controller sets the voltage proportional to the rate at which the error in speed is approaching zero

Over many time steps the error accumulates and sums up. Seeking

action.

di

p skskksu )(

Reduction of oscillations and snappy response but amplifies

noise.

PID Control

Parameter: Rise Time Overshoot Settling Time S.S.Error Kp Decrease Increase Small Change Decrease Ki Decrease Increase Increase Eliminate Kd Small Change Decrease Decrease None

The End

dc machines electrical machines – i

Engineering