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# ABSTRACT

Document source : repository.lib.ncsu.edu

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52
+
+
+
+
=
r
s
dr
s
qr
s
s
ds
s
qs
lr
m
lr
m
m
lr
m
ls
m
m
ls
m
m
ls
b
r
s
dr
s
qr
s
s
ds
s
qs
i
i
i
i
i
i
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0
0
'
'
'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
(4.3)

where
b
= 2
f
rated
and f
rated
is the power supply system frequency.
The electromagnetic torque developed by the induction motor is expressed as:
(
)
s
ds
s
qs
s
qs
s
ds
em
i
i
P
T
-
=
2
2
3
(4.4)

where P is the number of poles.
The standard load model assumes a single inertia for the rotor and load and hence the rotor
dynamics become
em
damp
mech
T
T
T
dt
d
J
=
+
+
(4.5)
Eq (4.5) is the equation of motion of the rotor with torques T
em
, T
mech
, and T
damp
acting on a
single inertia, J. T
mech
is the mechanical torque produced by the load and T
damp
is the torque
produced due to friction and windage. Inertia J is the sum of all inertias connected to the
motor shaft and includes the rotor inertia, couplings, and load inertia.
4.2 NON-LINEAR MOTOR MODEL
The standard motor model neglects the following factors: line impedance, stator leakage
reactance saturation, rotor resistance variations with slip, and rotor leakage reactance
variations with slip, mutual flux path saturation, and stray load losses. These factors are
often critical in induction motor behavior during large transient such as start-up and therefore
need to be taken into account.

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Summary :

## 52 And the flux linkages are: + + + + = r s dr s qr s s ds s qs lr m lr m m lr m ls m m ls m m ls b r s dr s qr s s ds s qs i i i i i i x x x x x x x x x x x x x x 0 0 ' ' ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 (4.3) where b = 2 f rated and f rated is the power supply system frequency.

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