01 electricity fundamentals alt405 505
TRANSCRIPT
-
8/13/2019 01 Electricity Fundamentals ALT405 505
1/87
Introduction to ElectromagneticEnergy Conversion
Devarajan Srinivasan (Srini)[email protected]
ALT 405/505
Power Conditioners for Alternative Energy
Systems
mailto:[email protected]:[email protected] -
8/13/2019 01 Electricity Fundamentals ALT405 505
2/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-2
Introduction to Electromagnetic Energy
Conversion
Fundamentals of electricity
AC circuits
Single phase
Three phase
DC machines
Synchronous machines
-
8/13/2019 01 Electricity Fundamentals ALT405 505
3/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-3
Fundamentals of Electricity
Units of electricity
Electrostatics
Electromagnetism
-
8/13/2019 01 Electricity Fundamentals ALT405 505
4/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-4
Fundamentals of Electricity
Units of Electricity
Voltage
Volt (V): The electric potential of a point
is defined as work done in bringing apositive charge of one coulomb from
infinity to that point.
Coulomb
JouleVolt
1
11
-
8/13/2019 01 Electricity Fundamentals ALT405 505
5/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-5
Fundamentals of Electricity
Units of Electricity
Current
Ampere (A): The current, which when
flowing in each of two infinitely longparallel conductors situated in vacuum
and separated 1 meter, produces on
each conductor a force of 2 x 10
-7
N permeter length.
-
8/13/2019 01 Electricity Fundamentals ALT405 505
6/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-6
Fundamentals of Electricity
Units of Electricity
Power and Energy
Joule (J): Energy required to maintain a
current of 1 Ampere through a resistanceof 1 Ohm for 1 second
Watt (W): Rate of doing work
second
JouleWatt
1
11
-
8/13/2019 01 Electricity Fundamentals ALT405 505
7/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-7
Fundamentals of Electricity
Units of Electricity
Frequency
Hz: Cycles per second
Resistance
Ohms (): A conductor is said to have a
resistance of 1 ohm if it permits a current
of 1 Ampere when 1 Volt is impressedacross it.
-
8/13/2019 01 Electricity Fundamentals ALT405 505
8/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-8
Fundamentals of Electricity
Units of Electricity
Charge
Coulomb (C): The charge of 6.242 x 1018
electrons. Hence, the charge of a singleelectron is 1.602 x 10-19Coulomb
-
8/13/2019 01 Electricity Fundamentals ALT405 505
9/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-9
Fundamentals of Electricity
Units of Electricity
Capacitance
Farad (F): The capacitance which requires
a charge of 1 Coulomb to establish apotential difference of 1 Volt
-
8/13/2019 01 Electricity Fundamentals ALT405 505
10/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-10
Fundamentals of Electricity
Units of Electricity
Flux
Weber (Wb): A unit magnetic pole of 1
Weber, placed in vacuum at a distance ofone meter from a similar and equal pole
repels it with a force of 1/4ONewton
-
8/13/2019 01 Electricity Fundamentals ALT405 505
11/87
ALT 405/505Spring 2014
Power Conditioners for Renewable Energy Systems 01-11
Fundamentals of Electricity
Units of Electricity
Inductance
Henry (H): A coil has a self-inductance of
one Henry if a current of 1 Ampereflowing through it produces flux-linkages
of 1 Weber-turn in it
-
8/13/2019 01 Electricity Fundamentals ALT405 505
12/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-12
Fundamentals of Electricity
Electrostatics
Deficiency or excess of electrons in abody is called its charge
Electrons = Negative charged accordingto convention
Surplus of electrons = Body is negativecharged
Deficit of electrons = Body is positivecharged
-
8/13/2019 01 Electricity Fundamentals ALT405 505
13/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-13
Fundamentals of Electricity
Electrostatics
Electrostatics: Science of electricity atrest
Charges are not in motionCharges exert a force on other charges
-
8/13/2019 01 Electricity Fundamentals ALT405 505
14/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-14
Fundamentals of Electricity
Electrostatics
Laws of electrostatics
Like charges repel
Unlike charges attractThe force exerted between two pointcharges is
Proportional to product of strengths
Inversely proportional to square of distance
Inversely proportional to permittivity ()
-
8/13/2019 01 Electricity Fundamentals ALT405 505
15/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-15
Fundamentals of Electricity
Electrostatics
Electric field
Consider an isolatedpoint charge in amedium
Point charge: sphere body, radiuszero
Medium (three-dimensional)
For example: air
Other examples: vacuum, gas, insulators,conductors, semi-conductors, etc.
-
8/13/2019 01 Electricity Fundamentals ALT405 505
16/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-16
Fundamentals of Electricity
Electrostatics
Electric field
The isolated point charge will exert aforce on any charge that enters themedium (neighborhood of the charge)
Hence, for any external charge, themediumaround the point charge is
always under stress (under the effect of aforce)
-
8/13/2019 01 Electricity Fundamentals ALT405 505
17/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-17
Fundamentals of Electricity
Electrostatics
Electric field
At each point in space around theisolated charge
An unit positive chargeexperiences aforceof certain magnitude and direction
These lines of force in the medium
around the charge is called the electricfield
-
8/13/2019 01 Electricity Fundamentals ALT405 505
18/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-18
Fundamentals of Electricity
Electrostatics
Electric field
Electric intensity
At any point within the electric fieldThe force experienced by a unit positivecharge at that point
Hence, the unit of electric intensity (E) is
N/C
-
8/13/2019 01 Electricity Fundamentals ALT405 505
19/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-19
Fundamentals of Electricity
Electrostatics
Electric potentialConsider an electric field generated by anisolated positive charge +Q in a medium
(air).The field extends to infinity.
The force exerted on a positive charge,+q1, at infinity iszero.
-
8/13/2019 01 Electricity Fundamentals ALT405 505
20/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-20
Fundamentals of Electricity
Electrostatics
Electric potentialAs +q1 is bought closer to +Q, it isrepelled by +Q
+q1 is now under the effect of theelectric field
Workhas to be done against this force ofrepulsion to move the charge closer to+Q
-
8/13/2019 01 Electricity Fundamentals ALT405 505
21/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-21
Fundamentals of Electricity
Electrostatics
Electric potentialPerform work, by overcoming therepulsive force of the field to move
charge +q1 to an arbitrary point close to+Q
Hence, when charge +q1 is bought tosome point in the electric field, it has
some electrical potential energy
-
8/13/2019 01 Electricity Fundamentals ALT405 505
22/87
ALT 405/505Spring 2014 Power Conditioners for Renewable Energy Systems 01-22
Fundamentals of Electricity
Electrostatics
Electric potentialPotential at any point in the electric field
is equal to the work done
against the electric field
in bringing a positive charge of one coulomb
from infinity to that point
Potential is work done per unit charge
C
JV
1
11
-
8/13/2019 01 Electricity Fundamentals ALT405 505
23/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-23
Fundamentals of Electricity
Electrostatics
Electric potential
Electric field is also called
potential gradientIn other words, electric
intensity is equal to the
rate of fall of potential inthe direction of the lines
of force
m
V
C
NE
C
mN
C
J
V
-
8/13/2019 01 Electricity Fundamentals ALT405 505
24/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-24
Fundamentals of Electricity
Electrostatics
Capacitor
two conducting surfaces (plates)
separated by an insulating medium(dielectric)
-
8/13/2019 01 Electricity Fundamentals ALT405 505
25/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-25
Fundamentals of Electricity
Electrostatics
Capacitor
If anytwo conducting surfaces are notconnected, a capacitor is formed
Insulated wires in a cable or conduit
Traces on circuit boards
Device terminals
Terminal blocks, connectors
Switches
Coil windings
-
8/13/2019 01 Electricity Fundamentals ALT405 505
26/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-26
Fundamentals of Electricity
Electrostatics
Parallel plate capacitor
Battery
Negative: surplus of electronsPositive: deficit of electrons
Connect battery to capacitor plates:
there is a transient flow of electrons from
the positive plate to the negative plate
A potential difference is establishedbetween the capacitor plates
-
8/13/2019 01 Electricity Fundamentals ALT405 505
27/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-27
Fundamentals of Electricity
Electrostatics
Capacitor
An electric field exists between the plates
corresponding to this potential differenceElectric field in the insulator
Charge (electrons)
Attracted to positive plates
Repelled from negative plates
-
8/13/2019 01 Electricity Fundamentals ALT405 505
28/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-28
Fundamentals of Electricity
Electrostatics
Capacitor charging
Increase electric potential between
platesAdd electrons to negative plate
Remove electrons from positive plate
As the capacitor is charged, work is doneagainst the repulsion force of the plates
to strengthen the field
-
8/13/2019 01 Electricity Fundamentals ALT405 505
29/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-29
Fundamentals of Electricity
Electrostatics
Capacitor discharging
Decrease electric potential between
platesRemove electrons from negative plate
Add electrons to positive plate
As the capacitor is discharged, work isderived from the attraction force of the
plates to collapse the field
-
8/13/2019 01 Electricity Fundamentals ALT405 505
30/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-30
Fundamentals of Electricity
Electrostatics
Capacitor
Hence, electric energy is stored in the
electric field of a capacitorCharge capacitor to add to the storage by
strengthening the field
Discharge capacitor to remove from thestorage by collapsing the field
-
8/13/2019 01 Electricity Fundamentals ALT405 505
31/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-31
Fundamentals of Electricity
Electrostatics
Capacitance
The property of a capacitor to store
electricityThe capacity of a capacitor
Defined as the charge required per unit
potential difference
V
QC
-
8/13/2019 01 Electricity Fundamentals ALT405 505
32/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-32
Fundamentals of Electricity
Electrostatics
Capacitance
Q Coulomb of charge is required
To establish a potential difference of VVolts between its plates
then capacitance is:V
QC
-
8/13/2019 01 Electricity Fundamentals ALT405 505
33/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-33
Fundamentals of Electricity
Electrostatics
Capacitance
The unit of capacitance is Farad
One Farad is the capacitance whichrequires a charge of one Coulomb to
establish a potential of one Volt between
its platesV
QC
-
8/13/2019 01 Electricity Fundamentals ALT405 505
34/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-34
Fundamentals of Electricity
Electrostatics
Capacitors in series
C1, C2, C3 = capacitance of
three capacitors
V1, V2, V3 = voltage across
each capacitorV = voltage across
combination
C = combined capacitance
In series combination, the
charge on all capacitors is
the same
CVVCVCVCQ
CCCC
C
Q
C
Q
C
Q
C
Q
VVVV
332211
321
321
321
1111
-
8/13/2019 01 Electricity Fundamentals ALT405 505
35/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-35
Fundamentals of Electricity
Electrostatics
Capacitors in parallel
C1, C2, C3 = capacitance of
three capacitors
Q1, Q2, Q3 = charge on
each capacitor
V = voltage across
combination
C = combined capacitance
In parallel combination,
the voltage on all
capacitors is the same
321
321
321
CCCC
VCVCVCCV
QQQQ
-
8/13/2019 01 Electricity Fundamentals ALT405 505
36/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-36
Fundamentals of Electricity
Electrostatics
Energy stored in a capacitor
Charging of a capacitor requires energy
from the charging sourceThis energy is stored in the electric field
set up in the dielectric
-
8/13/2019 01 Electricity Fundamentals ALT405 505
37/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-37
Fundamentals of Electricity
Electrostatics
Energy stored in a capacitor
Discharging the capacitor recovers this
energy and collapses the field
C
QQVCVW
JCVW
22
2
2
1
2
1
2
1
2
1
-
8/13/2019 01 Electricity Fundamentals ALT405 505
38/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-38
Fundamentals of Electricity
Electrostatics
Current in a capacitor
Current is the rate of change of charge
tdiCv
dt
dvCCv
dt
d
dt
dQi
t
0
1
)(
-
8/13/2019 01 Electricity Fundamentals ALT405 505
39/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-39
Fundamentals of Electricity
Electrostatics
A capacitor has the ability to store charge
Voltage across a capacitor is proportional tocharge, NOTcurrent
A capacitor can have voltage across it evenwhen there is no current flowing
-
8/13/2019 01 Electricity Fundamentals ALT405 505
40/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-40
Fundamentals of Electricity
Electrostatics
Current flows through a capacitor, onlywhen the voltage across it is changing.
If dv/dt=0 (dc voltage), the current is zero.
Hence for dc circuits, the capacitor is anopen circuit
-
8/13/2019 01 Electricity Fundamentals ALT405 505
41/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-41
Fundamentals of Electricity
Electrostatics
dv/dt = i/C
For a given current, the rate of change ofvoltage is inversely proportional to
capacitance.
Larger the C, the more difficult it is tochange V.
The voltage across a capacitor cannotchange instantaneously (dt = 0)
-
8/13/2019 01 Electricity Fundamentals ALT405 505
42/87
-
8/13/2019 01 Electricity Fundamentals ALT405 505
43/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-43
Fundamentals of Electricity
Electromagnetism
Magnets (medium, body) always havea pair (two) of magnetic poles:
North pole
South pole
Electromagnetism: science of
electricity and magnetism
-
8/13/2019 01 Electricity Fundamentals ALT405 505
44/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-44
Fundamentals of Electricity
Electromagnetism
Laws of magnetic force
Like poles repel
Unlike poles attractThe force between two magnetic poles ina medium is
Proportional to pole strengths
Inversely proportional to square of distance
Inversely proportional to the permeability
-
8/13/2019 01 Electricity Fundamentals ALT405 505
45/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-45
Fundamentals of Electricity
Electromagnetism
Magnetic flux
The strength of a magnetic pole
The strength of a magnetic pole can bedefined by the force it exerts on
another pole
-
8/13/2019 01 Electricity Fundamentals ALT405 505
46/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-46
Fundamentals of Electricity
Electromagnetism
Magnetic flux
Unit of magnetic flux is called Weber
One Weberthe strength of a magnetic pole
which when placed in vacuum
at a distance of 1 meterfrom a similar and equal pole
repels it with a force of 1/4O
-
8/13/2019 01 Electricity Fundamentals ALT405 505
47/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-47
Fundamentals of Electricity
Electromagnetism
Magnetic field
Consider an isolatedpoint pole in amedium
Point pole: sphere magnet, radiuszero
Medium (three-dimensional)
For example: air
Other examples: vacuum, gas, ferrousmetals
-
8/13/2019 01 Electricity Fundamentals ALT405 505
48/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-48
Fundamentals of Electricity
Electromagnetism
Magnetic field
The isolated point magnetic pole willexert a force on any pole that enters themedium (neighborhood of the pole)
Hence, for any external pole, the mediumaround the pole is always under stress
(under the effect of a force)
-
8/13/2019 01 Electricity Fundamentals ALT405 505
49/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-49
Fundamentals of Electricity
Electromagnetism
Magnetic field
At each point in space around theisolated pole
A North-pole of one Wbexperiences aforceof certain magnitude and direction
These lines of force in the medium
around the pole charge is called themagnetic field
-
8/13/2019 01 Electricity Fundamentals ALT405 505
50/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-50
Fundamentals of Electricity
Electromagnetism
Magnetic field
Magnetic field intensity
At any point within the magnetic fieldThe force experienced by a unit North-pole at that point
Hence, the unit of magnetic fieldintensity (H) is N/Wb
-
8/13/2019 01 Electricity Fundamentals ALT405 505
51/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-51
Fundamentals of Electricity
Electromagnetism
Flux density (B)
The amount of flux (Wb)
passing per unit area through a planeat right angles to the flux
The unit of flux density is Tesla
T = Wb/m2
-
8/13/2019 01 Electricity Fundamentals ALT405 505
52/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-52
Fundamentals of Electricity
Electromagnetism
Magnetic induction
Consider a magnetic field around a
magnetPlace a bar of zero-strength (zero Wb)
magnetic material in the magnetic field
The bar gets magnetized by aphenomenon called magnetic induction
-
8/13/2019 01 Electricity Fundamentals ALT405 505
53/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-53
Fundamentals of Electricity
Electromagnetism
Permeability ()
A bar of magnetic material is placed in a
uniform fieldthe bar is magnetized
Uniform external field intensity = H (N/Wb)
Bar induced flux density = B (Wb/m2)
theAbsolute Permeabilityof the bar is defined
as
H
B
-
8/13/2019 01 Electricity Fundamentals ALT405 505
54/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-54
Fundamentals of Electricity
Electromagnetism
Electric current and magnetismAny current carrying conductor sets up amagnetic field
The magnetic field is created in the mediumsurrounding the conductor (wire)
The strength of the magnetic field depends onthe current magnitude and permeability of themedium
The direction of the field depends on thecurrent direction
-
8/13/2019 01 Electricity Fundamentals ALT405 505
55/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-55
Fundamentals of Electricity
Electromagnetism
Work law of magnetismConsider N (e.g. N = 5) straight parallelwires
In a medium (e.g. air)Each carrying constant I (e.g. I = 10 A)
A magnetic field is set up by the current
This field will exert a force on anymagnetic pole
-
8/13/2019 01 Electricity Fundamentals ALT405 505
56/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-56
Fundamentals of Electricity
Electromagnetism
Work law of magnetismMove a magnetic pole in a closed path inthe magnetic field set up by the current
carrying conductorsWork is done, along this closed path
On the pole if moving against the fielddirection or
By the pole if moving in the field direction
-
8/13/2019 01 Electricity Fundamentals ALT405 505
57/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-57
Fundamentals of Electricity
Electromagnetism
Work law of magnetismThe net work in Joules done on or by aunit North pole
in moving around any completed path inthe magnetic field
is equal to the ampere-turns linked withthe path
If the path includes all N conductors, theampere-turns = NI (e.g. 5*10 = 50 J)
-
8/13/2019 01 Electricity Fundamentals ALT405 505
58/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-58
Fundamentals of Electricity
Electromagnetism
Force on two parallel conductorsConsider two parallel conductors carryingcurrents
Each conductor sets up a magnetic fieldThe magnetic fields set up by the twoconductors exerts a force between them
The work law can be used to determinethe force between the two conductors
-
8/13/2019 01 Electricity Fundamentals ALT405 505
59/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-59
Fundamentals of Electricity
Electromagnetism
Force on two parallel conductorsTwo parallel conductors
attract each other if the currents flow in
the same directionrepeleach other if the currents flow inthe opposite direction
-
8/13/2019 01 Electricity Fundamentals ALT405 505
60/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-60
Fundamentals of Electricity
Electromagnetism
Force on two parallel conductorsThe force between two such parallelconductors is
Proportional to the product of the currentstrengths
Proportional to the length of the conductors
Inversely proportional to the distance
between them
-
8/13/2019 01 Electricity Fundamentals ALT405 505
61/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-61
Fundamentals of Electricity
Electromagnetism
One Amperethe current which when flowing in eachof
two infinitely longparallel conductorssituated in vacuum
separated by 1 meterbetween centers
produces on each conductor a force of 2x 10-7Newtonper meter length
-
8/13/2019 01 Electricity Fundamentals ALT405 505
62/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-62
Fundamentals of Electricity
Electromagnetism
Magneto-motive force (mmf)mmf is the work done in joules
in carrying a unit magnetic pole
once around a magnetic path
Magnetic path is also called magneticcircuit
m
AT
Wb
NH
ATWb
mN
Wb
Jmmf
-
8/13/2019 01 Electricity Fundamentals ALT405 505
63/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-63
Fundamentals of Electricity
Electromagnetism
Magneto-motive force (mmf)The unit of mmf is ampere-turns
It is the product of
the number of turns in a magnetic circuitand the current in A through those turns
m
AT
Wb
NH
ATWb
mN
Wb
Jmmf
-
8/13/2019 01 Electricity Fundamentals ALT405 505
64/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-64
Fundamentals of Electricity
Electromagnetism
Magneto-motive force (mmf)Drives or tends to drive a flux through amagnetic circuit
Corresponds to emf in an electric circuitHence, mmf between two points can bemeasured
by the work done in Joules
in carrying a unit magnetic pole
from one point to the other
-
8/13/2019 01 Electricity Fundamentals ALT405 505
65/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-65
Fundamentals of Electricity
Electromagnetism
Electromagnetic interaction
When a current carrying conductor
is placed in a magnetic fieldit experiences a force
which acts in a direction perpendicular to
both the direction of the current and thefield
-
8/13/2019 01 Electricity Fundamentals ALT405 505
66/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-66
Fundamentals of Electricity
Electromagnetism
Electromagnetic interaction
If a conductor of length Lm
lies in a magnetic field of flux density BWb/m2
carries a current IA
the force on the conductor is F = BIL N
-
8/13/2019 01 Electricity Fundamentals ALT405 505
67/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-67
Fundamentals of Electricity
Electromagnetism
Electromagnetic induction
Consider an electrical circuit (branch, one
loop) in a magnetic fieldThis circuit (loop) has some magnetic flux
linked to it
Within the area of the loopPerpendicular to the loop
d l f l
-
8/13/2019 01 Electricity Fundamentals ALT405 505
68/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-68
Fundamentals of Electricity
Electromagnetism
Electromagnetic induction
Flux-linkages of a coil is the product
the number of turns of the coilAnd the flux linked with the coil (Wb-turns)
d l f l i i
-
8/13/2019 01 Electricity Fundamentals ALT405 505
69/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-69
Fundamentals of Electricity
Electromagnetism
Electromagnetic induction
Whenever the magnetic flux linked with
a circuitChanges
an emf is always induced in it
dt
dNN
dt
de
)(
F d l f El i i
-
8/13/2019 01 Electricity Fundamentals ALT405 505
70/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-70
Fundamentals of Electricity
Electromagnetism
Electromagnetic induction
The magnitude of the induced emf is
equal to the rate of change of flux-linkages
dt
dNN
dt
de
)(
F d l f El i i
-
8/13/2019 01 Electricity Fundamentals ALT405 505
71/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-71
Fundamentals of Electricity
Electromagnetism
Electromagnetic induction
Lenzs law
The induced emf sets up a current
in such a direction
that magnetic effect produced by the current
opposes the very cause producing it
dt
dNN
dt
de
)(
F d t l f El t i it
-
8/13/2019 01 Electricity Fundamentals ALT405 505
72/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-72
Fundamentals of Electricity
Electromagnetism
Inductance
Consider a coil
N turns wound on a magnetic material
carrying a constant dc current of I A
This produces an mmf of NI AT in themagnetic material
F d t l f El t i it
-
8/13/2019 01 Electricity Fundamentals ALT405 505
73/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-73
Fundamentals of Electricity
Electromagnetism
Inductance
This mmf drives a flux of Wb in themagnetic circuit
NI produces flux density B (Wb/m2)depending on of the magnet
B = *A, where A is the cross sectional areaof the magnet
Hence, the coil has a flux-linkage of NWb-turns
F d t l f El t i it
-
8/13/2019 01 Electricity Fundamentals ALT405 505
74/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-74
Fundamentals of Electricity
Electromagnetism
Inductance
If the current through is slowly changed:
The flux-linkages associated with the coil
changes
An emf is induced in the coil
The emf opposes the changein flux-linkage
and hence the changein current (Lenzs law)
F d t l f El t i it
-
8/13/2019 01 Electricity Fundamentals ALT405 505
75/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-75
Fundamentals of Electricity
Electromagnetism
Inductance
The property of the coil to resist thechange of current through it is called self-
inductance
Inductance is defined as the flux-linkageper ampere in the coil
Inductance is a function of the magneticmaterial and dimensions of the coil
F ndamentals of Electricit
-
8/13/2019 01 Electricity Fundamentals ALT405 505
76/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-76
Fundamentals of Electricity
Electromagnetism
Inductance
A coil is said to have a self-
inductance of one Henryif a current of 1 A
produces flux-linkage of 1
Wb-turn in it
t
dteL
i
dt
diLN
dt
de
L IN
HI
NL
0
1
)(
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
77/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-77
Fundamentals of Electricity
Electromagnetism
Inductance
A coil is said to have a self-
inductance of one Henryif 1 V is induced in it
when current through it
changes at the rate of 1A/s
t
dteL
i
dt
diLN
dt
de
L IN
HI
NL
0
1
)(
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
78/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-78
Fundamentals of Electricity
Electromagnetism
Inductors in series
L1, L2, L3 = Inductance of
three coils
V1, V2, V3 = voltage induced
across each coil
V = voltage across
combination
L = combined inductance
In series combination, thecurrent through each coil is
the same
321
321
321
LLLL
dt
diL
dt
diL
dt
diL
dt
diL
VVVV
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
79/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-79
Fundamentals of Electricity
Electromagnetism
Inductors in parallel
L1, L2, L3 = Inductance of
three coils
V1, V2, V3 = voltage
induced across each coilV = voltage across
combination
L = combined inductance
In parallel combination,
the induced emf acrosseach coil is the same
321
321
3
3
2
2
1
1
1111
LLLL
dtdi
dtdi
dtdi
dtdi
dt
diL
dt
diL
dt
diL
dt
diLV
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
80/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-80
Fundamentals of Electricity
Electromagnetism
Inductor charging
Coil with N turns and zero current
Slowly increase current from zero to Ithe self-induced emf opposes this change
Work must be done to overcome this
opposition and strengthen the magneticfield
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
81/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-81
Fundamentals of Electricity
Electromagnetism
Inductor discharging
Coil with N turns and current I A
Slowly decrease current from I to zerothe self-induced emf opposes this change
and slows the collapse of flux (and flux-
linkages) till current is zero
Work is derived from the coil to collapse
the magnetic field
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
82/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-82
Fundamentals of Electricity
Electromagnetism
Energy stored in magnetic field
Charge inductor to add to the storage
by strengthening the fieldDischarge inductor to remove from the
storage by collapsing the field
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
83/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-83
Fundamentals of Electricity
Electromagnetism
Energy stored in magnetic field
Charging the inductor requires energy
from the charging sourceThis energy is stored in the magnetic field
of the inductor
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
84/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-84
Fundamentals of Electricity
Electromagnetism
Energy stored in magnetic field
Discharging the inductor recovers this
energy and collapses the field
L
N
INLIW
JL IW
2
2
2
)(
2
1
2
1
2
1
2
1
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
85/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-85
Fundamentals of Electricity
Electromagnetism
An inductor has the ability to store energy
Current through a coil is proportional to V-s(Wb-turn), NOTvoltage
An inductor can have current through it,even when there is no voltageacross it
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
86/87
ALT 405/505
Spring 2014
Power Conditioners for Renewable Energy Systems 01-86
Fundamentals of Electricity
Electromagnetism
Voltage is induced across an inductor onlywhen the current through it is changing.
If di/dt = 0, the voltage is zero.
Hence for dc circuits, the inductor is a shortcircuit.
Fundamentals of Electricity
-
8/13/2019 01 Electricity Fundamentals ALT405 505
87/87
Fundamentals of Electricity
Electromagnetism
di/dt = v/L
For a given induced voltage, the rate ofchange of current is inversely proportional
to inductance. Larger the L, the more difficult it is to
change i.
The current through an inductance cannotchange instantaneously (dt = 0)