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EEE 409 ELECTRICAL MACHINES II
ELECTRICAL MACHINES II
by Assoc. Prof. Dr. H. İbrahim OKUMUŞ
Karadeniz Technical University
Department of Electrical and Electronic
Engineering
E-mail : [email protected]
URL
: http://www.hiokumus.com
Doç. Dr. H. İbrahim Okumuş
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Contents
 Introduction, Basic Concepts and Definitions
 Ampere’s Law
 Magnetic Equivalent Circuit
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EEE 409 ELECTRICAL MACHINES II
 Magnetic Saturation and its effects
Transformers
 Constructional Features of Transformer
 Transformer theory
 Transformer Tests
 Transformer Performance
 Three-Phase Transformers
 Direct – Current Machine Dynamics
 Dynamic Models
 Dynamic Analysis
 Dynamic Behaviors of the Asyncronous Machines
 Dynamic Behaviors of the Syncronous Machines
 Simulation of the Electrical Machines Using MATLAB/SİMULİNK
Doç. Dr. H. İbrahim Okumuş
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References
 Lecture notes, power point presentations
Sarma, PWS Publishing Company, Boston, MA, 1996.
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EEE 409 ELECTRICAL MACHINES II
 Electric Machines: Steady-State Theory and Dynamic Performance, by Mulukutla S.
 Matrix Analysis of Electrical Machinary, by Hancock N. N., Prgamon Press 1974.
 Analysis of Electrical Machines, by Smith R. T.
 Analysis of Electrical Machinary, by Krause P. C., McGraw Hill 1986
 Unified Theory of Electrical Machines, by Jones C. V, Butterworths, 1967
 Dynamic Simulation of Electric Machinery Using MATLAB, by Ong. Chee,1998,
Printice Hall
 Electric Machinery and Transformers, by Hızıroğlu,Hüseyin,2001, Oxfort University
Press,New York
 Elektrik Makinalarının Temelleri, by Sarıoğlu,Kemal,1977,Çağlayan Kitabevi,İstanbul
 Elektrik Makinaları Dersleri, by Boduroğlu,Turgut,1976,İTÜ Yayınları,İstanbul
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EEE 409 ELECTRICAL MACHINES II
Web site of the course:
notlar12
Doç. Dr. H. İbrahim Okumuş
Line integral of magnetic field intensity H around a
closed path is equal to the total current enclosed by
the path
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EEE 409 ELECTRICAL MACHINES II
Ampere’s law
 H.dl  i
H 2i r
i
i  H
A/m
2r r
H
r
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• B exists whenever there is H
• The strength of B depends on the permeability of the medium
B   r  oH
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EEE 409 ELECTRICAL MACHINES II
B-H Relation
Wb/m2 or T
o = permeability of free space (4 10-7 H/m)
r = relative permeability of medium
 1 for air
Several hundreds to thousands for ferromagnetic materials
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Magnetic equivalent circuit
l
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EEE 409 ELECTRICAL MACHINES II
N turns
r
i
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Magnetic equivalent circuit
l
r
 H.dl  i
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EEE 409 ELECTRICAL MACHINES II
N turns
H 2r  Ni
H l  Ni = F
= magnetomotive force
A
i
Magnetic flux density inside the core,

H
Ni
B
l
The flux crossing the cross section area A of the core,
Ni
l

  BdA  BA
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Wb
8
  BA

Ni
Ni
 A 
l
l
A
F
 
R
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EEE 409 ELECTRICAL MACHINES II
Magnetic equivalent circuit
Magnetomotive force
Reluctance

F
R
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Magnetic equivalent circuit
Rc
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EEE 409 ELECTRICAL MACHINES II
lc
i
lg
N
Rg
lc
Rc 
c A c
Ni  Hc lc  Hglg
Rg 
lg
gA g
Ni  Fc  Fg
Ni  (R c  R g )
if Rg>> Rc
Ni  R g  Fg
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•
In electrical machine with ferromagnetic material, c >> o
•
It is permissible to assume that ALL MMF drop appear across the air gap
•
Since magnetic path crosses the airgap twice, half of the MMF appear at
each air gap
Ni  (R c  R g )
if Rg>> Rc
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EEE 409 ELECTRICAL MACHINES II
Magnetic equivalent circuit
Ni  R g  Fg
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Magnetic equivalent circuit

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EEE 409 ELECTRICAL MACHINES II
a
a’
Ni / 2
-
-/2
/2


-Ni / 2
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EEE 409 ELECTRICAL MACHINES II
End of the Chapter
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Notes01