1
DEPARTMENT OF ELECTRICAL AND COMPUTING ENGINEERING
FINAL EXAMINATION
ELECTROMECHANICAL ENERGY CONVERSION
ECSE462B
Examiner:
Professor B.T.Ooi
Associate Examiner: Professor F.D.Galiana
Date:
December 10, 2004
Time
: AM (3 hours)
INSTRUCTIONS:
•
OPEN BOOK EXAMINATION
•
Answer all
six
questions.
Trigonometric Identities
cos(A+B)=cosAcosBsinAsinB
cos(AB)=cosAcosB+sinAsinB
sin(A+B)=sinAcosB+cosAsinB
sin(AB)=sinAcosBcosAsinB
[
Systeme Internationale
or MKS units are used. Field vectors are represented by bold
letters, for example
B
and
K
. The directional vectors in cylindrical coordinates are:
u
r
,
u
ϕ
and
u
z
. The superscript
T
denotes “transpose”. State vectors are also represented in
bold, for example
v
dq
,
λ
dq
,
i
dq
.]
Questions #1 & #2
refer to an electric machine consisting of a cylindrical rotor inside an
annular stator. They are separated by an airgap “g” at a mean radius “R”. The stack
length is “L”. The permeability of the iron is infinite and the permeability of the airgap is
μ
o
.
Question 1
An electric machine has only one 4pole stator winding carrying current i
S
α
which
produces a sheet current
K
S
α
=
u
z
i
S
α
B
S
sin(
2
ϕ
) where B
S
is the Fourier coefficient of the
fundamental space harmonic and where the position
ϕ
=0
0
is
fixed to the stator
.
(a)
What is the magnetic field density distribution
B
S
α
around the airgap?
The rotor has two 4pole windings carrying currents i
R
α
and i
R
β
which produce sheet
currents
K
R
α
=
u
z
i
R
α
B
R
sin(2
ϕ
1
+
δ
) and
K
R
β
=
u
z
i
R
β
B
R
sin(2
ϕ
1
+
δ
+90
0
), where B
R
is the
Fourier coefficient of the fundamental space harmonic and where the position
ϕ
1
=0
0
is
fixed to the rotor
.
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(b) What are the magnetic field density distributions
B
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 Spring '09
 BonTekOoi
 Magnetism, Magnetic Field, magnetic field density

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