Environmental Engineering Reference
In-Depth Information
modulation index of 0.8 (C), and an angle of 75
with the
a
-axis and modulation
depth 0.8 (D). Figure 6.12(a) shows the sample points for a 3-phase balanced set at an
angle of 20
from the phase
a
axis and for a modulation depth 0.35.
Regardless of sector, modulation depth, or vector angle, the sinusoidal syn-
chronous (regular) sampling exercises all the inverter switches during each switch-
ing cycle. This incurs higher switching losses than are necessary to synthesize the
voltage waveforms required. A more optimum switching strategy is provided by
SVPWM in which a switch is not exercised unless needed and in which only vectors
adjacent to the reference voltage vector are selected. In sinusoidal synchronous
PWM, all voltage vectors are selected regardless of the operating sector.
In SVPWM, it is convenient to represent inverter voltage vectors in the
a
-
b
plane as shown in Figure 6.13. In this figure, the six sectors of the inverter output
voltage states are listed along with a representative inverter source vector,
U
s
,in
the first sector.
I
m
-axis,
b
U
3
U
2
II
*
U
s
U
k
+1
I
III
p
/3
U
1
U
4
U
0
,
U
7
R
e
-axis,
a
VI
IV
V
U
5
U
6
Figure 6.13 Derivation of space vector PWM
As an illustration, in sector I the only available voltage vectors from which to
construct an arbitrary reference vector are
U
1
,
U
2
and either of
U
0
or
U
7
. As shown
earlier in Figure 6.12, each of these vectors is the result of a discrete switching
pattern of the inverter poles as follows:
ð
a
,
b
,
c
Þ¼ð
1, 0, 0
Þ¼
U
1
ð
a
,
b
,
c
Þ¼ð
1, 1, 0)
¼
U
2
ð
a
,
b
,
c
)
¼ð
0, 0, 0)
¼
U
0
ð
a, b, c
Þ¼ð
1, 1, 1)
¼
U
7
Each of these inverter states applies full voltage magnitude at the inverter
phase leg mid-point as discussed earlier. In order to synthesize a voltage vector of
arbitrary magnitude and of arbitrary angle within sector I (and by extension, in any
