Predictive Control of Three Phase AC/DC Converters

4.6. CONSTANT SWITCHING FREQUENCY PREDICTIVE DIRECT POWER
CONTROL 51
which has been explained in Section 4.3. Lets rewrite power derivative equations
for two level VSC with inductive filter.
dP
dt = 3 ( )
1
2 U Lα
L (U Lα − U P α − RI Lα ) + ω L I Lβ +
( )
3 1
2 U Lβ
L (U Lβ − U P β − RI Lβ ) − ω L I Lα
(4.23)
dQ
dt = 3 (
2 U Lα ω L I Lα − 1 )
L (U Lβ − U P β − RI Lβ )
3
2 U Lβ
+
( )
1
L (U Lα − U P α − RI Lα ) + ω L I Lβ
(4.24)
If we take into consideration following assumptions:
• VSC input voltage is kept constant during U P vector application,
• line voltage vector U L does not change during that time period,
• current variations are small,
active and reactive power increments can be considered as a constant for applied
vector U P . These assumptions allow to analysis powers behavior for few applied
vectors U P during single sampling time.
Active and reactive power increments f pi , f qi caused, by voltage vector U P
application, are defined as follow:
f pi = dP
dt
f qi = dQ
dt
where i is number of applied voltage vector.
∥ (4.25)
UP =U P i
∥ (4.26)
UP =U P i
The relation between power behavior, voltage vector and application time can
be expressed as:
P P i = P + f pi t i (4.27)
Q P i = Q + f qi t i (4.28)
where P P i and Q P i are predicted powers for specified t i application time of voltage
vector U P i .