Revision: Basic Principles - Cairo University Revision: Basic Principles. Electromagnetic Force. For a current carrying conductor: where dl is taken in the direction of current. If

Revision: Basic Principles

AC Circuits Three-phase Circuits Magnetic Fields Time-varying Fields: Faraday’s Law Magnetic Circuits

1


Sources Of Magnetic Fields

2


Direction Of Magnetic Fields:Ampere’s Right Hand Rule

Ampere’s Law

. enc

H dl I

3


B Magnetic flux density (Tesla) H Magnetic field intensity (A/m)μo permeability of free space µr relative permeability of a mediumφ Magnetic Flux (Weber – Lines)

B H o r B A

4


Magnetic Materials

5


Faraday’s Experiment (1831)6

Revision: Basic Principles7


E N

dEdt

8


Lenz’s Law

0ddt

0ddt

9


Faraday’s Law for Induction

dinduced emf Ndt

10


Transformer EMF

de Ndt

dBe NAdt

11


For a moving conductor:

If the magnetic field is perpendicular to the conductor:

mF qv B

mind

F v B Eq

2

211

.e v B dl

-

+

e Blv

12


Electromagnetic ForceFor a current carrying conductor:

where dl is taken in the direction of current

If the magnetic field is perpendicular to the conductor:

mF I dl B

mF BIL

13

Concept of Magnetic Circuits

What’s a magnetic circuit ?

They are basically ferromagneticstructures (mostly iron) with coils wound around them. Because of the material high permeability, most of the magnetic flux is confined inside themagnetic circuit. Examples: Transformers, Actuators, Electromagnets and Electric machines.

14


It’s an approximate technique to compute magnetic flux.

2NIH

a

2NIB

a

2( )2NI b

a

BA

22( )

NIab

15


VIR

lRA

2

2( )

aRb

22( )

VI ab

16


22( )

VI ab

22( )

NIab

17


I

( )V EMF ( )NI MMF

lRA

mclA

Mean core

length

Reluctance

18


V IR NI

V RI

NI

19


DC Magnetic Circuits: the supply is DC, magnetic circuit laws can be used directly.

1DC

coil

ViR

2DC

coil

ViR

20


DC Magnetic Circuits

1 2i i

1 21 2

mc mc

c c

l lA A

1 2Ni Ni

1 1

2 2

1Ni1

12Ni

2

2

1 1 2 2

21


AC Magnetic Circuits: the supply is AC, Faraday’s law must be considered first.

22


AC Magnetic Circuits:

ACv e zero

ACv e

(Neglecting Coil Resistance)

V zero

de Ndt

23


AC Magnetic Circuits

ACdv Ndt

sin( )mdV t Ndt

By Integrationcos( ) sin( )

2m mV Vt tN N

Ф is dependent on V and f

24



1 2

1 2

2 1

ii

11

mc

c

lNiA

22

mc

c

lNiA

1 1 2 2c c

mc mc

Ni A Ni Al l

1Ni1

12Ni

2

2

25


AC Magnetic CircuitsTo get the current

sin( )2

mc m

c

l Vi tN A N

mc

c

liN A

2sin( )

2m

c

mc

Vi tN A

l

26



2c

mc

VIN Aj

l

core

VIj L

2

coremc

c

NL lA

mcc

lA

2NL

Self Inductance

27



ACdv Ndt

From magnetic circuits:

Ni

( )ACd Niv Ndt

2

ACN div

dt

AC

div Ldt

28

Example

Find the value of the current that will produce a flux of 0.0025 Wb.

5000r NI

mc

c

lA

4(30 2 2.5) 140mcl cm

50N

10cm

25*10 50cA cm

Example

Find the value of the current that will produce a flux of 0.0025 Wb.

5000r 7 41.4

(5000)(4 10 )(50 10 )

50N

10cm

144563.38 H

NI

2.228I A

Example

Find the inductance of the coil.

5000r

50N

10cm144563.38 H

2NL

0.056L H

Magnetic Circuits: Electric Machines

An electrical machine is a device which converts mechanical energy into electrical energy or vice versa.

e BlvmF BIL

32


Electrical machines have generally two basic parts named "Stator" and "Rotor". The stator is the stationary member. The rotor is the rotating member. A small air gap exists between the two member.

33

Magnetic Circuits: Electric Machines34


Salient Poles Stator

NS

35

Magnetic Circuits: Electric Machines36


NS

. enc

H dl I

. 2 f fc

H dl N I

g g 2 f fH H N I Neglecting the reluctance of the steel parts

gg f f fH N I MMF M

f go

gM B

fg o

MBg

37


NS

fI gB

,f gM B

38


Single-phase machines

S N

39

Magnetic Field Production & Distribution


. enc

H dl I

.c

H dl Ni

g2g

NiH M gfo

BM g

g gH H Ni

S N

40



NS S

M

S N

cos( )m ei I ti

et

2e f 1,3,5,..

4 1( ) cos( )2 hNiM h

p h

41



i

et

cos( )m ei I t

M

4 cos2fund

NiM

42


Three-phase machines

43


Three-phase machines

cos( )a m ei I t

cos( 120)b m ei I t

cos( 120)c m ei I t

44

Revision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesRevision: Basic PrinciplesConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsConcept of Magnetic CircuitsExampleExampleExampleMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Field Production & DistributionMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric MachinesMagnetic Circuits: Electric Machines

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Revision: Basic Principles - Cairo University Revision: Basic Principles. Electromagnetic Force. For a current carrying conductor: where dl is taken in the direction of current. If