Environmental Engineering Reference
In-Depth Information
5.7 Exercises
Q1:
Repeat example 2 by reversing any two of the phase currents and show that
the rotor will reverse its rotation direction. In this exercise the currents are
defined as
i
a
¼
I
0
sin
w
t
;
i
b
¼
I
0
sin
ðw
t
þ
120
Þ
;
i
c
¼
I
0
sin
ðw
t
120
Þ
Normal Connections in Block Mode
AAAB
B
C
C
B
C
CCAAB
A1:
reverse phase B and C connections
AAAC
CCB
B
CCB
B
AAC
Q2:
The following exercises are meant to expand on the topic of IPM machines
and their torque production via magnet and reluctance components. Exam-
ple 2 should also be used as reference. In the following exercises, the IPM
torque expression will be needed:
3
2
P
2
½
m
IPM
¼
y
m
I
d
þð
L
d
L
q
Þ
I
d
I
q
Given that a stator max current,
I
s
¼
450 A, and a current angle
d ¼
35
compute the
I
d
and
I
q
components of stator current at maximum loading.
A2:
I
d
¼
258 A and
I
q
¼
369 A
Q3:
For the IPM of Q2 and given that its phase winding flux linkage,
k
m
¼
0.058 Wb-t, and the fact that this is a 3-phase, 8-pole machine, compute the
magnet torque at maximum load.
A3:
m
mag
¼
129.5 Nm (note, the first term in the equation given in Q2)
Q4:
Given that the total torque,
m
IPM
, of (Q2) is 270 Nm at 450 A
dc
and for
the stated current angle of maximum torque production compute the quan-
tity (
L
d
L
q
).
A4:
L
d
L
q
¼
246
m
H
Q5:
At maximum loading the inductance ratio of an IPM decreases significantly
from its unexcited value. Taking the ratio,
L
d
/
L
q
¼
2.7 at maximum loading
and using the result of Q4, compute the values of
L
d
and
L
q
.
A5:
L
d
¼
391
m
H and
L
q
¼
145
m
H.
Q6:
Apply (5.22) from this chapter and calculate the characteristic current of this
IPM.
A6:
148 A
Q7:
Compute the quantity (
L
d
L
q
) for the Synchronous Reluctance machine of
section 5.5.2 if the same torque target (
m
SyncRel
¼
270 Nm) is imposed
