Direct Power and Torque Control of AC/DC/AC Converter-Fed ...

3. Vector Control Methods of AC/DC/AC Converter-Fed IM Drives – A Review
The instantaneous active power P is a scalar product between the line voltages
and currents instantaneous space vectors, whereas the instantaneous reactive power
Q is a vector product between them, and they can be expressed in complex form as:
3
P =
2
Re
* 3
3
{ ULIL
} = ( U
L
IL
+ U
L
IL
) = UL
⋅I
L
2
α α β β
(3. 43)
2
* 3
3
{ U
LIL
} = ( U
L
I
L
−U
L
I
L
) = UL
× IL
3
Q = Im
β α α β
(3. 44)
2
2
2
There is possibility to estimate the line voltages by adding the input voltage
U
p
= U dc
S 1
of the VSR to the voltages drops on the input choke U
I
. Therefore,
active and reactive power of the line can be calculated in line voltage sensorless
manner as follows:
⎛
P = ⎜U
⎝
⎛
+ ⎜U
⎝
dc
S
dc
C
S
A
dI
+ L
dt
dI
+ L
dt
LC
LA
⎞
⎟I
⎠
⎞
⎟I
⎠
LC
LA
⎛
+ ⎜U
⎝
dc
S
B
dI
+ L
dt
LB
⎞
⎟I
⎠
LB
+
(3. 45)
Q =
⎧ ⎛ dI
1 ⎪3L⎜
⎨ ⎝ dt
3 ⎪
⎩−U
dc
LA
I
LC
dI
−
dt
LC
I
LA
⎞
⎟ +
⎠
[ S ( − ) + ( − ) + ( − )] ⎪ A
ILB
I
LC
SB
I
LC
I
LA
SC
ILA
I
LB ⎭
⎫
⎪
⎬
(3. 46)
Such calculated power can be used as a feedback signals for DPC scheme. Please
consider that, power losses on the resistance of the input choke R are neglected
because they have low value in comparison to total active power.
Unfortunately, such calculation causes some problems in DSP implementation.
The differential operations of the currents are performed on the basis of finite
differences and gives very noisy signals. So, to suppress the current ripples a
relatively large inductance is needed. Moreover, calculation finite differences of the
currents should be as accurate as possible (about ten times per a switching period)
and should be avoided at the moment of the switching [105].
To avoid this problem a virtual flux – VF of the line has been introduced in [93],
[95]. The voltage in the line can be expressed with the formula:
Ψ
L = UL
(3. 47)
d
dt
After integration the VF can be expressed as:
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