an investigation of dual stator winding induction machines

{ k [ ˆ*
( i iˆ
) ] ( k)
[ ˆ*
Im λ ⋅ − + 1−
Re ⋅ ( i − iˆ
) ] }
⎛ K i ⎞
ˆ ω r = ⎜ K p + ⎟ ⋅
qdr qds qds
λqdr
qds qds
(1.15)
⎝ S ⎠
By minimizing the squared error
been proposed in [10.30].
2
i ˆ
s − is
, a voltage error-based speed estimator has
The instability problem at low speed is the main limitation of MRAS schemes
especially when the machine is working under generating mode or braking mode. To
overcome the problem, different error functions have been proposed [10.23-10.24, 10.29,
10.33, 10.36]. The design methodologies of properly choosing the observer gain and
speed estimation controller parameters become another way to solve the instability issue
such that the instability region can be reduced or even eliminated by using the right
observer parameters [10.20-10.21, 10.25-10.32, 10.38]. The approach that the observer
poles are placed proportionally to the poles of induction machine has been reported in
[10.20-10.21]. In [10.25], a different pole-placement technique was proposed in which
the observer poles correspond to the induction machine poles shifted to the left in the s
plane by an amount k s , which is a machine parameters dependent constant. Similar
approach has been adopted in [10.34]. Speed-adaptive gains have been proposed in
[10.27] to give enough damping at high speed. The expression of observer gain in
complex form is given as:
where,
⎡ 1+
j ⋅ sign
K = λ⎢
⎣−1
+ j ⋅ sign
⎧ ' ˆ ωm
⎪λ
,
λ = ⎨ ωλ
⎪ '
⎩λ
,
( )
( ) ⎥ ˆ ωm
⎤
ˆ ωm
⎦
m
λ
37
(1.16)
if ˆ ωm
< ωλ
, ωˆ m is estimated rotor speed,
if ˆ ω ≥ ω
'
λ and ω λ are positive
constants. The instability of sensorless control under low speed generating condition has