Page 243 - Rashid, Power Electronics Handbook

232 J. Espinoza

14.2.2.1 Bipolar PWM Technique around twice the normalized carrier frequency m and its
f
States 1 and 2 (Table 14.2) are used to generate the ac output multiples. Speci®cally,
voltage in this approach. Thus, the ac output voltage wave-
h ¼ lm k l ¼ 2; 4; ... ð14:17Þ
form features only two values, which are v and ÿv .To f
i
i
generate the states, a carrier-based technique can be used as
in half-bridge con®gurations (Fig. 14.3), where only one where k ¼ 1; 3; 5; ... and the harmonics in the dc link current
sinusoidal modulating signal has been used. It should be appear at normalized frequencies f centered around twice the
p
noted that the on state in switch S þ in the half-bridge normalized carrier frequency m and its multiples. Speci®cally,
f
corresponds to both switches S 1þ and S 2ÿ being in the on
state in the full-bridge con®guration. Similarly, S in the on p ¼ lm k 1 l ¼ 2; 4; .. . ð14:18Þ
f
ÿ
state in the half-bridge corresponds to both switches S and
1ÿ
S being in the on state in the full-bridge con®guration. This where k ¼ 1; 3; 5; .... This feature is considered to be an
2þ
is called bipolar carrier-based SPWM. The ac output voltage advantage because it allows the use of smaller ®ltering
waveform in a full-bridge VSI is basically a sinusoidal wave- components to obtain high-quality voltage and current wave-
form that features a fundamental component of amplitude ^ v forms while using the same switching frequency as in VSIs
o1
that satis®es the expression modulated by the bipolar approach.
^ v ¼ ^ v ab1 ¼ v m a ð14:15Þ 14.2.2.3 Selective Harmonic Elimination
o1
i
In contrast to half-bridge VSIs, this approach is applied in a
in the linear region of the modulating technique (m 1), per-line fashion for full-bridge VSIs. The ac output voltage
a
which is twice that obtained in the half-bridge VSI. Identical features odd half- and quarter-wave symmetry; therefore, even
conclusions can be drawn for the frequencies and amplitudes harmonics are not present (^ v oh ¼ 0, h ¼ 2; 4; 6; ...). More-
of the harmonics in the ac output voltage and dc link current, over, the ac output voltage waveform (v ¼ v ab in Fig. 14.8),
o
and for operations at smaller and larger values of odd m f should feature N pulses per half-cycle in order to adjust the
(including the overmodulation region (m > 1)), than in half- fundamental component and eliminate N ÿ 1 harmonics. For
a
bridge VSIs, but considering that the maximum ac output instance, to eliminate the third, ®fth and seventh harmonics
voltage is the dc link voltage v . Thus, in the overmodulation and to perform fundamental magnitude control (N ¼ 4), the
i
region the fundamental component of amplitude ^ v o1 satis®es equations to be solved are:
the expression
cosð1a Þÿ cosð1a Þþ cosð1a Þÿ cosð1a Þ¼ p^ v =ðv 4Þ
2
4
o1
i
3
1
4
v < ^ v ¼ ^ v ab1 < v i ð14:16Þ cosð3a Þÿ cosð3a Þþ cosð3a Þÿ cosð3a Þ¼ 0
4
2
3
1
o1
i
p
cosð5a Þÿ cosð5a Þþ cosð5a Þÿ cosð5a Þ¼ 0
1 2 3 4
cosð7a Þÿ cosð7a Þþ cosð7a Þÿ cosð7a Þ¼ 0
1 2 3 4
14.2.2.2 Unipolar PWM Technique
ð14:19Þ
In contrast to the bipolar approach, the unipolar PWM
technique uses the states 1, 2, 3, and 4 (Table 14.2) to generate where the angles a ; a ; a , and a are de®ned as shown in Fig.
3
4
2
1
the ac output voltage. Thus, the ac output voltage waveform 14.10(a). The angles a ; a ; a , and a are plotted for different
2
4
3
1
can instantaneously take one of three values, namely, v ; ÿv , values of ^ v =v in Fig. 14.11a. The general expressions to
i
o1
i
i
and 0. To generate the states, a carrier-based technique can be eliminate an arbitrary N ÿ 1(N ÿ 1 ¼ 3; 5; 7; ...) number of
used as shown in Fig. 14.9, where two sinusoidal modulating harmonics are given by
signals (v and ÿv ) are used. The signal v is used to generate
c
c
c
N
v ,and ÿv is used to generate v ; thus v bN1 ¼ÿv aN1 . P k p ^ v o1
c
aN
bN
k
On the other hand, v ¼ v aN1 ÿ v bN1 ¼ 2 v aN1 ; thus ÿ k¼1 ðÿ1Þ cosðna Þ¼ 4 v i
o1
^ v ¼ 2 ^ v aN1 ¼ m v . This is called unipolar carrier-based N
i
o1
a
SPWM. ÿ P ðÿ1Þ cosðna Þ¼ 0 for n ¼ 3; 5; ... ; 2N ÿ 1
k
k
Identical conclusions can be drawn for the amplitude of the k¼1
fundamental component and harmonics in the ac output ð14:20Þ
voltage and dc link current, and for operations at smaller
and larger values of m , (including the overmodulation region where a ; a ; ... ; a N should satisfy a < a < < a <
1
2
f
N
2
1
(m > 1)), than in full-bridge VSIs modulated by the bipolar p=2.
a
SPWM. However, because the phase voltages (v aN and v ) are Figure 14.10c shows a special case where only the funda-
bN
identical but 180 out of phase, the output voltage mental ac output voltage is controlled. This is known as
(v ¼ v ab ¼ v aN ÿ v ) will not contain even harmonics. output control by voltage cancellation, which derives from
bN
o
Thus, if m is taken even, the harmonics in the ac output the fact that its implementation is easily attainable by using
f
voltage appear at normalized odd frequencies f centered two phase-shifted square-wave switching signals as shown in
h