Electrical Machines I
Week 2: Magnetic circuits principles
RECALL… REMEMBER…. !!
Construction of dc machine
The Faraday laws
The EMF equation
The objective of today’s lecture
• It is required to understand the concepts of
magnetic circuits
• By making Analogy between Electric circuit and
magnetic circuit
• Learn new concepts about “Hystresis and core
losses”
3
Analogy between Magnetic and Electrical Circuits
φ
N: number of turns (T)
i= current (A)
H= magnetic field intensity (AT/m)
l= MEAN length of the core (m)
A= CROSS sectional area of core (m2)
F= Magneto motive force, (AT)
i
Toroidal core
N
Ferromagnetic core: Iron, steel
Ampere’s Law:
. THERFORE, for the
ferromagnetic core
shown
H : some people call it
the magnetizing force
l
Side view
Ferromagnetic core C core
1 turn coil
EI core
. N turn coil
The magnetic field
intensity H is in a sense
a measure of the
“effort” that a current
is putting into the
establishment of the
magnetic field.
Quantity
Electrical Circuit
Magnetic Circuit
Driving force
V (volt) EMF
F (NI) MMF
Produce
i (A)
Ф (weber)
Limited by
R (Ω)
ℜ (AT/weber)
φ
ℜ
F =MMF is analogous to Electromotive force (EMF) =E
Φ = Flux is analogous to i = Current
ℜ = Reluctance is analogous to R = Resistance
1
1
=
=
Permeance
= Analogous to conductance G =
P
ℜ
R
Since magnetic and
electrical circuits
have similar
characteristics, then
we can apply the
traditional circuits
laws to magnetic
circuits
Important Relations: Part ‘1’
OHM’s law
ℜ
R =
Resistance depends on length,
cross sectional area of cable AND
the material from which the
resistance is made
1 l
1 l
=
µ A µrµ0 A
Relative
permeability is a
way to compare the
“magnetisability” of
materials
= permeability of free space = 410 H/m
= relative permeability of material compared to free space
Steel relative permeability could
reach up to 6000!!! AND is used in
machines.
Electrical ccts
Magnetic ccts
Important Relations: Part ‘2’
Current density
(A/m2)
Flux density
(wb/m2)= Tesla
Series Magnetic ccts
Kirchoff voltage law
Kirchoff voltage law
Series resistances law
Series resistances law
Kirchoff Current law
Kirchoff Current law
Parallel resistances law
Parallel resistances law
Parallel Magnetic ccts
Electrical ccts
Magnetic ccts
Important Relations: Part ‘3’
saturation
knee
B
B
Linear
1
R
µ = µ0 µr
H
H
Electrical ccts
Current and voltage have a
“linear relationship”, the
slope of which determines
the resistance of the
electrical circuit
Magnetization curve
(linear) (Ideal)
Assume that
Magnetization curve
(actual) (non-Ideal)
A= constant
l= constant
N= constant
B is proportional to ф
H is proportional to i
Electrical ccts
Magnetic ccts
i
ф
Important Relations: Part ‘4’
Magnetization Characteristics: (BH curve)
Required to proof: proof:
Also,
The slope of the BH
curve is actually
dependent on the
permeability of the
magnetic core!!!
F = B A
∴ = B A R ,
∵ =
=
$!
∴ !"
Magnetization Characteristics
(BH curve)
WHAT DOES THAT
REALLY MEAN??!!!!!!
Check the graph to the
right. Silicon steel sheets
have higher slope than
cast iron. This means that
for the same amount of
magnetic force H, silicon
steel will produce more
magnetizing flux density B
and thus more flux ф
B2
B2 > B 1
This could be very useful
if selecting cores used in
motor and transformer
applications
B1
Magnetization Characteristics (BH curve) : A CLOSER LOOK
Part “a” : First Quad of the BH curve, CURRENT
INCREASE
B
Part “a” : First Quad of the BH curve, CURRENT
INCREASE
B
Saturation zone
Saturation
is achieved
when
dipoles are
arranged
Bsat
Br
Knee
H
Hsat
H
c
Linear zone
“Current is increased”
Flux takes
another
path when
current
decreases
Bsat
Br: Residual flux
density. It’s the
value of B when
H =0. We call it
“REMENANCE or
RETENTIVITY”
H
HHsat
c
Even through there is no
magnetizing force, the core is
still magnetized with Residual
Magnetism.
“Current is decreased”
Linear zone: i increases, H increases, B increases sharply AND VICE VERSA
Saturation zone: i increases, H increases, B increases slightly till any further increase in H will NOT
allow any change in B AND VICE VERSA
Magnetization Characteristics (BH curve) : A CLOSER LOOK
Part “b” : Second and Third Quad of the BH curve,
CURRENT INCREASE
Part “b” : Third and Fourth Quad) of the BH curve,
CURRENT DECREASE
B
This represents the
amount of magnetizing
force needed to
“demagnetize” the core
completely. It is called
“COERCIVITY”
Br
“Hystresis” is the true
name of the BH
characteristics
H
-Hc
Hc
Hc
-Bsat
“Current is increased”
“Current is decreased”
In Part ‘b’, the polarity of the supply has been reversed
The magnet keeps traveling along the “hystresis curve” over and over everytime the magnetization changes
its magnitude OR direction
Magnetization Characteristics (BH curve) : SUMMARY
Magnetization Characteristics (BH curve) : A CLOSER LOOK
This means that the
magnet goes
through the process
of magnetization
and
demagnetization 4
times in 1 cycle of
the ac supply
We have seen what happens to a core
when magnetized and de magnetized by dc
current, SO WHAT WILL HAPPEN IF THE
EXCITING CURRENT IS
ALTERNATING???
Decrease magnetization
(demagnetization) in
forward direction
Decrease magnetization
(demagnetization) in
reverse direction
increase magnetization
in forward direction
increase magnetization
in reverse direction
Magnetization Characteristics (BH curve) : USES
It has been concluded
that “turning the atoms”
will require ENERGY!! This
energy must be taken
from the source, which
will lead to LOSSES!!
Magnetization Characteristics: LOSSES
Core Losses (also
known as Magnetic
or Iron Losses)
Hystresis Losses %
'
Eddy Current
Losses
%&
Magnetization Characteristics: LOSSES
1- Hystresis Losses:
• The fact that turning the dipoles (atoms of magnet) require energy, leads to
the FIRST type of losses occurring in magnetic cores which is called
HYSTRESIS LOSSES
• HYSTRESIS LOSSES= The energy required to accomplish orientation of
domains during each cycle of the applied ac current to the core
The area enclosed in the hystresis loop formed by applying an AC
current to the core is directly proportional to the energy lost in a
given ac cycle. The smaller the applied MMF on the core, the smaller
the area of the resulting hystresis loop and so the smaller the
resulting losses
we can't eliminate the loss but we can reduce it to some extent by using
appropriate cores for each type of application as mentioned in the previous
slide materials with thin hysteresis have minimum hystresis losses
Losses cause
heating of
core and
may cause
fatigue to
material
Magnetization Characteristics: LOSSES
2- Eddy Current:
• Eddy currents are created when a conductor experiences
changes in the magnetic field.
• EDDY CURRENT LOSSES= Induced currents in the core will
cause current to circulate in the core causing heat to the
magnetic core
e = −N
∆Φ
∆t
Faraday law 1 states that if a flux passes through a turn of a coil of a wire, a
voltage will be induced in the wire that is directly proportional to the rate of
change of flux with respect to time. This “time changing flux” induces voltage
WITHIN a ferromagnetic core in just the same manner as it does in a wire
wrapped around the core !!!! They act exactly like when current passes through a
resistance and causes heat losses and they depend on the resistivity of material in
which the current swirls and the size of the swirl.
we reduce eddy currents by making the core of thin laminations OR use high
resistivity material. Thin laminations will cause current swirl to be reduced, thus lower
emf induced and lower current will circulate.
Questions
• Demonstrate the analogy between electrical and magnetic circuits
• Explain the theory of hystresis curve
• Describe and define what is meant by the following terms used in
magnetic cores “Saturation- Remenance- Permeability- ReluctanceCoercivity”
• Explain the types of losses occurring in magnetic cores and how can
you reduce them