Page 236 - Power Electronic Control in Electrical Systems

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224 Power electronic equipment

where
^
A s is the amplitude of the sinusoidal signal and
^
A c is the amplitude of the triangular signal.
The PWM method shown in Figure 6.47 is presented for an amplitude modulation
^
^
ratio of 0.8 (A s ˆ 0:8p:u:, A c ˆ 1p:u:). When the harmonic content of the resultant
voltage waveform is considered, the following observations can be made. The wave-
form v AO contains a fundamental component with amplitude equal to M a on a per
unit basis as shown in Figure 6.47(c). The harmonics are positioned as sidebands as
follows

f h ˆ k f c m f 1 (6:33)
where

k ˆ 1, 3, 5, ... when m ˆ 0, 2, 4, 6, ...
and
k ˆ 2, 4, 6, ... when m ˆ 1, 3, 5, ...

When the two-level PWM method is used with a single-phase full-bridge VSC (Figure
6.26), the waveforms are shown in Figure 6.48. When comparing the waveforms of
Figure 6.48 with the ones presented earlier in Figure 6.47 for a half-bridge leg, the

Fig. 6.48 Two-level sinusoidal PWM with a single-phase full-bridge VSC. (a) reference (sinusoidal) and carrier
(triangular) signals (f c ˆ 15 f 1 and M a ˆ 0:8); (b) voltage waveform AB ; and (c) normalized harmonic
amplitude of the voltage waveform v AB .