SYLLABUS(EE-205-F)
SECTION-A
MAGNETIC CIRCUITS AND INDUCTION:
Magnetic Circuits, Magnetic Materials and their properties, static and
d
dynamic
i emfs
f andd force
f
on currentt carrying
i conductor,
d t AC operation
ti
of Magnetic Circuits, Hysteresis and Eddy current losses.
SECTION B
SECTION-B
DC MACHINES :
Basic theory of DC generator, brief idea of construction, emf
equation, load characteristics, basic theory of DC motor, concept of
back emf, torque and power equations, load characteristics,
starting and speed control of DC motors, applications.
1
SECTION -C
Synchronous Machine
Constructional features, Armature winding, EMF Equation, Winding
coefficients, equivalent circuit and phasor diagram, Armature reaction, O. C.
& S. C. tests, Voltage Regulation
• Synchronous Motor: Starting methods, Effect of varying field current at
different loads, V- Curves.
SECTION-D
Three phase Transformer & Induction Machine
Three Phase Transformer: Review of Single phase transformer. Three Phase
transformer: Basics & operation
Induction Machine: Constructional features,
features Rotating magnetic field,
field
Principle of operation Phasor diagram, equivalent circuit, torque and power
equations, Torque- slip characteristics, no load & blocked rotor tests,
efficiency, Induction generator & its applications. Introduction of Single
phase Induction Motor, Repulsion motor. AC Commutator
Motors:Universal
i
l motor, Single
Si l phase
h
a.c. series
i compensatedd motor, stepper
motors
2
Hans Christian Oersted (1777 –
1851)
In 1820 he showed that a current produces a
magnetic
g
field.
X
3
4
Electric Current and Magnetic Field
5
Terminology
1.
2.
3.
4.
5
5.
6.
7
7.
Flux density (Φ)
Magnetic flux Density (B)
Magnetic
g
field Intensityy ((H))
MMF (Magneto Motive Force)
Reluctance (S=L/µa)
(S L/µa)
Permeability (B/H=µ)
Relative permeability (Bi/Ba=µr)
6
Magnetic Flux (Φ)
• Total number of line of force in a magnetic
field
• Unit is Weber (Wb)
• 1 weber = 108 line
of force
7
Magnetic flux density (B)
• Flux per unit area
• B = Φ/A
• Unit is Tesla
8
Magnetic field Intensity/strength (H)
• Force experience by a unit North pole placed in a magnetic
field of another magnet (m2).
•
F1= F2 = Km
K 1m2/r
/2
m1
m2
• Unit N-pole is the N-pole with the pole strength of 1 Wb
/
• H = F/m1 = Km1m2/r2 m1 = Km2/r2
9
Reluctance and Permeability
y
• Reluctance S = Kℓ/a (like resistance(R=ρℓ/a))
• Permanence = 1/S ( like conductance(G)
= 1/resistance(R))
• K = 1/μ (like resistivity(ρ = 1/ σ))
• K = constant
t t
• μ = permeability (like conductivity( σ))
•
μ = B/H = Φ/a/F/m = Φr2/aKm
1
2
• Means S = ℓ/μa and S = mmf/Φ = N X I/ Φ
10
•
•
•
•
•
•
•
S = N X I/ Φ
=> Φ = N X I/ S
But B = Φ/a
Therefore, B = N X I/ Sa
H = B/
B/µ => N X I/ µSa
S
But S = ℓ/μa
=> H = N X I/ ℓ
This is the magnetic field intensity inside
the solenoid.
11
MMF
• Magneto motive force
• Force responsible
for the flow of flux
12
Electromagnets
• Whenever current passes through a conductor or a
coil, magnetic field gets developed
across it.
• The magnetic material piece in
between the piece will start acting
g
as a magnet
• IMP: when the current stop passing through, the
electromagnetic stop loses its magnetic property.
13
Ri ht hand
Right
h d rule
l
• An electric current passes through a straight
wire. Here, the thumb points in the direction
of the conventional current
(from positive to negative),
and the fingers point in the
direction of the magnetic
g
lines
of flux.
14
Flemings left hand rule
15
• When an electric current flows in a wire,,
and an external magnetic field is applied
across that flow,, the wire experiences
p
a
force perpendicular both to that field and to
the direction of the current flow.
• Used in Motors
• Fleming right hand rule used in generators
• F=BIℓ
16
Why force produce?
•
17
Properties of lines of force
• They all have the same strength.
strength
• The lines never cross one another.
• They
Th form
f
closed
l d curve which
hi h outside
t id the
th
magnet is directed from north pole to south
pole
l & inside
i id the
th magnett from
f
south
th pole
l to
t
north pole.
• Always try to contract its length.
• So,, exert a force on a conductor
downwards.
18
Electric Circuit
Magnetic Circ
Circuit
it
19
A Few Definitions Related to
Electromagnetic Field
Φ (Unit is Weber (Wb)) = No. of lines of force in the magnetic field
B (Unit is Tesla (T)) = Magnetic Flux Density = Φ/A=wb/m2
H (Unit is Amp/m) = Magnetic Field Intensity=NI/l
μ = permeability = μo μr = B/H
μo = 4π*10
4 *10-77 H/m
H/ (H ⇒Henry)
H
)=P
Permeability
bilit off free
f space (air)
( i)
μr = Relative Permeability
μr >> 1 for Magnetic Material
20
Magnetic Circuits (2)
F =NI= Magneto Motive Force or MMF = # of turns *
Current passing through it
or
F = NI = Hl (why!)
B
Φ
l = NI
l = NI
or
μ
μA
NI
or Φ =
l /((μ
μA)
NI
or Φ =
ℜ
ℜ = Reluctance of magnetic path
21
Analogy Between Magnetic and Electric
Circuits
F =MMF is analogous to Electromotive force (EMF) =E
Φ = Flux is analogous to I = Current
e ucta ce iss analogous
a a ogous to R = Resistance
es sta ce
ℜ = Reluctance
1
1
P = Permeance =
= Analogous to conductance G =
ℜ
R
22
Analogy between 'magnetic circuits' and electrical
circuits
1.Drivingg force
2.Response
3.Field intensityy
4.Density
6 Impedance
6.Impedance
Magnetic ckt.
mmf
flux
g
field int.
Magnetic
Flux density
Reluctance
(i)Series
(ii) Parallel
Electric ckt
emf
current
Electric field int.
Current density
Resistance
(i)Series
(ii) parallel
23
Magnetic materials
• Diamagnetic materials =µr< 1
e.g. Zinc, Mercury, lead, silver, copper (orbital and axial
rotation are opposite
pp
to each other))
• Paramagnetic materials = µr > 1
e g Aluminium(1.00000065),
e.g.
Aluminium(1 00000065) tin,
tin platinum,
platinum magnesium,
magnesium
manganese
• Ferromagnetic materials =µ
µr >>> 1 ( they are in same
direction)varying from hundreds to thousands.
e.g. iron, steel, nickel, cobalt and some other alloys
24
Ferromagnetic
g
materials
1. Soft Ferromagnetic material
High permeability, easily magnetized and demagnetized, extremely
small hysteresis, iron and its alloys with nickel, cobalt tungsten and
aluminium
suitable for transformers, inductors, generators telephone
recievers.
recievers
2. Hard
Ferromagnetic
material
relatively
low
permeability, difficult to magnetize and demagnetize, relatively high
hysteresis loss, high coercive force, cobalt steel and various alloys
of nickel, aluminium and cobalt.(cobalt steel)
Permanent magnets in loud speakers
25
26
Permanent Magnets
• Alloys of Iron, Cobalt and Nickle
•Have large B-H loops, with large Br and –Hc
•Due
D tto hheatt treatment
t t
t becomes
b
mechanically
h i ll hard
h d andd are thus
th
called HARD IRON
•Field intensity is determined by the coercive field required to
demagnetize it
27
Magnetization Curves
saturation
B
knee
B
Linear
H
Magnetization curve
(linear) (Ideal) Air
H
Magnetization curve
(non-linear) iron,etc.
28
Magnetization Curves (for examples)
29
Magnetization Curves(2)
•One can linearize magnetic circuits by including air-gaps
•However that would cause a large increase in ampere-turn
requirements.
Ex: Transformers don’t have air-gaps. They have very little
magnetizing current (5% of full load)
Induction motors have air-gaps. They have large magnetizing
current (30-50%)
Question: why induction motors have air –gap and
transformers don’t?
don t?
30
Iron Losses in Magnetic Circuit
There are two types of iron losses
a) Hysteresis losses
b) Eddy Current Losses
Total iron loss is the sum of these two losses
31
Hysteresis losses
1
f=
T
f =frequency
of sine source
i
B
Br
B-H or Hysteresis loop
saturation
3
i
knee point
1
Hc
4
0
2
5
4
0
1
2
t
3
H
5
Br = Retentive flux density (due to property of retentivity)
Hc= Coercive
Coerci e field intensity
intensit (due
(d e to property
propert of coercivity)
coerci it )
32
33
34
Hysteresis losses (2)
•The lagging phenomenon of B behind H is called hysteresis
•In each of the current cycle
y the energy
gy lost in the core is
proportional to the area of the B-H loop
•Energy lost/cycle = Vcore ∫ HdB
n
• Ph = Hysteresis
ys e es s loss
oss = f Vcore
HdB
d
=
k
B
h
maxf
∫
kh = Constant,
Constant n = 1.5-2.5,
1 5 2 5 Bmax= Peak flux density
35
Eddy current loss
flux
Current
Laminations
flux
Because off time
B
i variation
i i off flux
fl flowing
fl i through
h
h the
h magnetic
i
material as shown, current is induced in the magnetic material,
followingg Faraday’s
y law. This current is called eddyy current.
The direction of the current is determined by Lenz’s law. This current
can be reduced by using laminated (thin sheet) iron structure, with
Insulation between the laminations
laminations.
• Pe = Eddy current loss = keB2maxf
ke = Constant
C t t
, Bmax= Peak
P k fl
flux density
d it
36
37
Magnetic Circuits (1)
w
I
N
l= mean length
d
38
39
Magnetization Circuits with Air-gap
lc
i
w
lg
N
lc
ℜc =
μ c Ac
ℜg =
Ni = H c lc + H g l g
lg
μ g Ag
Ni
Φ=
ℜc + ℜ g
d
Ac = Ag = wd ( Neglecting fringing )
40
Fringing
i
lc
w
N
With large air-gaps, flux tends to leak outside the air –gap. This is
called fringing which increases the effective flux area. One way to
approximate this increase is:
wn = w + l g ; d n = d + l g ; Agn = wn d n
41
Find Exciting current if B=1.2T and µr=6000
with and without fringing
g g
42
A Magnetic Circuit with Reluctances in
Series and Parallel ( Find I )
43
44
Static emf Dynamic emf
When the conductor in which the emf is
induced is stationary then the emf is called
static emf .
- Eg . Transformer
- When the conductor in which the emf is
induced is moving one then the emf is
called dynamic emf.
- eg. D.C. generator
45
Faraday’s law of Electromagnetic
Induction
The EMF ((Electromotive Force)) induced in a magnetic
g
circuit is
Equal to the rate of change of flux linked with the circuit and is
opposite to the cause which produces it.
Ni
φ
=
dλ
d ( NΦ
Φ))
dΦ
l / μA
e=−
=−
= −N
dt
dt
dt
d ⎡ Ni ⎤
e = −N ⎢
dt ⎣ l / μA ⎥⎦
N2μA
L=
l
N 2μA di
e=−
l dt
dLi
di
=L
∴e =
dt
dt
46
Dynamically induced emf
47
Flemings right hand rule
48
Fleming’s Right Hand Rule Or
G
Generator
Rule
l
FORE FINGER = MAGNETIC FIELD
900
900
900
MIDDLE FINGER = INDUCED
VOLTAGE
VOLTAGE = B l u
49
50
51
Electromagnetic Force, f
f=Bli, where B,
f=Bli
B f and i are mutually perpendicular.
perpendicular Turn
the current vector i towards the flux vector B. If a right
hand screw is turned in the same way, the direction in
which
hi h the
h screw will
ill move represents the
h direction
di i off the
h
force f.
52
Flemings left hand rule
53
EMEC TEST
Q.1 Explain
Q
p
the Magnemotive
g
force,reluctance,magnetic
,
, g
flux
density
(6)
Q.2 Differentiate between magnetic
Q
g
and electric circuits ((4))
Q.3A wrought iron bar 30 cm long and 2 cm in diameter is
bent into a circular shape .It is then wound with 600 turns of
wire . Calculate the current required to produce a flux of .5
mWb in magnetic circuit in the following cases:
i) no air-gap
ii) With an air gap of 1mm and µ=4000 and (10)
54
iii)With an air gap of 1mm ; assume the
following
g data for the magnetization
g
of iron:
H
2500
3000
3500
4000
B
1.55
1 55
11.59
59
11.6
6
11.615
615
55
ANSWERS
•
•
•
•
•
•
I =0.158 (with no air gap)
II=2
2.258
258 (with air gap)
ATg = Hglg =1260
H = 3000AT/
Hc
3000AT/m
AT =2160
I=2160/600 =3.6 A
56
Inductance(L)
Definition: Flux Linkage(λ) per unit of current(I) in a magnetic circuit
Φ
λ NΦ
L= =
I
I
NI
Φ=
ℜ
Ι
Ν
N2
∴L =
ℜ
Thus inductance depends on the geometry of construction
57