Environmental Engineering Reference
In-Depth Information
Because we know the inverter phase leg voltages, it is a straightforward cal-
culation to arrive at the line-to-line voltages at the inverter output. These are the
voltages that will be applied to the electric machine as a load:
4
p
6
U
ab
¼
p
m
i
U
dc
sin
w
t
þ
p
2
4
U
bc
¼
p
m
i
U
dc
sin
w
t
ð
6
:
22
Þ
4
3
7
p
6
U
ca
¼
p
m
i
U
dc
sin
w
t
The line-to-line voltages are sinusoidal but the modulating function that will
produce these output voltages is not sinusoidal. First, to clarify the amplitudes of
the line-to-line,
U
1-1
, phase to negative bus,
U
1
, and peak of the modulating
function,
U
m
, one finds
4
j
U
1
1
j¼
p
m
i
4
3
m
i
ð
6
:
23
Þ
j
U
1
j¼
m
i
2
< j
U
m
j <
m
i
p
The double-valued nature of the SVPWM modulating function is characteristic
and due to the fact that harmonics of triple order may be added to phase voltages
without affecting the Park transformation from stationary to synchronous reference
frames. Therefore, there is an infinite variety of modulating functions that generate
a sinusoidal line-to-line voltage but in themselves are not sinusoidal. To illustrate
this fact it is necessary to generate such an SVPWM modulating function. This
function, if applied to the sinusoidal synchronous modulator discussed earlier, will
in fact generate SVPWM gating waveforms.
If the synchronous sampling process described in Figure 6.11 is applied here
but with the SVPWM modulating function shown in Figure 6.15 for phases
U
,
V
,
W
1.732051
2
e
U
(
i
)
1
e
W
(
i
)
e
V
(
i
)
0
0
0
50
100
150
200
250
300
350
400
i
0
359
Figure 6.15 SVPWM modulating functions
