
Three-Phase AC–DC Converters 11-11
Based on the measured DC link voltage u
dc
and the duty cycles of modulator D
a
, D
b
, D
c
, the virtual ux
Ψ
–
L
components are calculated in stationary (α-β) coordinates system as follows:
Ψ
L dc a b c L
u D D D dt Li
α α
= − +
+
∫
2
3
1
2
( )
(
11.25a)
Ψ
L dc b c L
u D D dt Li
β β
= −
+
∫
1
2
( )
(
11.25b)
11.2.3.3
I
nstantaneous Power Calculation Based on Voltage Estimation
e
i
nstantaneous
v
alues
o
f
a
ctive
(p) a
nd
r
eactive
p
ower
(q) i
n
A
C
v
oltage
s
ensorless
s
ystem
a
re
e
stimated
b
y
E
quations
1
1.26.
F
irst
p
art
o
f
b
oth
e
quations
r
epresents
p
ower
i
n
t
he
i
nductance
a
nd
t
he
s
econd
p
art
i
s
t
he
p
ower
o
f
t
he
P
WM
A
C–DC
c
onver ...