Predictive Control of Three Phase AC/DC Converters

PP1
fp1 fp2 fp3
PP2 t3
t2 t1
QP2 QP3
fq1 fq2 fq3
QP1
PP3
52 CHAPTER 4. PREDICTIVE DIRECT POWER CONTROL
4.6.2 Voltage Vectors Sequence
Lets consider situation when three voltage vectors are selected within sampling
time, then (4.27), (4.28) can be rewritten:
P P 1 = P + f p1 t 1
P P 2 = P P 1 + f p2 t 2
P P 3 = P P 2 + f p3 t 3
(4.29)
Q P 1 = Q + f q1 t 1
Q P 2 = Q P 1 + f q2 t 2
Q P 3 = Q P 2 + f q3 t 3
(4.30)
T s = t 1 + t 2 + t 3 (4.31)
where t 1 , t 2 , t 3 are voltage vectors application times. Figure 4.7 shows graphical
representation of (4.29), (4.30) and (4.31). Relations (4.29) – (4.31) can be
P
(a)
P
Q
(b)
Q
Figure 4.7: Active (a) and reactive (b) power changes under three U P i voltage
vectors application during one sampling time T s
t2 t3
Ts
t1
simplified to:
P P 3 = P + f p1 t 1 + f p2 t 2 + f p3 t 3
Q P 3 = Q + f q1 t 1 + f q2 t 2 + f q3 t 3
T s = t 1 + t 2 + t 3
(4.32)