
AC-to-DC Three-Phase/Switch/Level PWM Boost Converter 12-21
v
0
=
v
0,h
− v
0,l
, and I
3
is the third-order identity matrix. d
1
, d
2
, and d
3
are the duty cycles of switches
Q
1
,Q
2
, and Q
3
respectively. Note that system (12.59) is a time-varying model that depends on the sign
of the line currents i
s,1
, i
s,2
, and i
s,3
. erefore, it is not suitable for a stationary control design process. In
order to overcome this drawback, the following input transformation is proposed:
′
= − +
∀ ∈
{ }
d d i
v
v
k , ,
k k s k
( ) sgn( )
,
1 1 2 3
0
0
∆
,
(
12.60)
Adding Equation 12.60 to system (12.59) yields
v
i
d
s
s
= +
′
L
d
dt
v
0
2
G ,
(12.61)
where
v
s
= [v
s,1n
, v
s,2n
, v
s,3n
]
T
is t ...