EE321 Spring 2008
Homework 13
Problem 56 – Rotating MMF
Using the configuration we studied in class (Figure 5.21 in text), the stator currents of a 4 pole
machine are given by
)
200
cos(
50
)
200
sin(
50
t
i
t
i
bs
as
−
=
=
The speed of the machine is 500 rpm in the CW direction.
What is the physical speed and direction of the
stator MMF as viewed from the rotor.
Problem 57 – Phase Inductance
Suppose the winding function of aphase of the stator is given by
⎟
⎠
⎞
⎜
⎝
⎛
=
sm
s
as
P
N
P
w
φ
2
cos
2
and the winding function of the bphase of the rotor is given by
⎟
⎠
⎞
⎜
⎝
⎛
=
rm
r
br
P
N
P
w
φ
2
sin
2
Express the mutual inductance between the aphase stator and bphase rotor windings in terms of
s
N
,
r
N
,
P
,
the rotor radius
r
, the rotor length
L
, the airgap
g
, the permeability of free space
0
μ
and electrical
rotor position
r
θ
.
Problem 58 – QD Transformation
Show in detail that
ms
s
s
T
sr
s
r
L
K
L
K
=
−
1
'
where
'
sr
L
is given by (5.348) and
ms
L
is given by (5.5
23).
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 Spring '08
 Staff
 Frequency, Trigraph, Physical quantities, Inductor, Electric motor

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