Page 241 - Rashid, Power Electronics Handbook

230 J. Espinoza

FIGURE 14.6 The half-bridge VSI. Ideal waveforms for the SHE technique: (a) ac output voltage for third and ®fth harmonic elimination; (b)
spectrum of (a); (c) ac output voltage for third, ®fth, and seventh harmonic elimination; (d) spectrum of (c).

a are plotted for different values of ^ v =v in Fig. 14.7a. The fundamental magnitude control (N ÿ 1 ¼ 3), the equations
o1
i
3
general expressions to eliminate an even N ÿ 1 to be solved are:
ðN ÿ 1 ¼ 2; 4; 6; ...) number of harmonics are
cosð1a Þÿ cosð1a Þþ cosð1a Þÿ cosð1a Þ¼ð2 ÿ p^ v =v Þ=4
N 1 2 3 4 o1 i
o1
P k 2 þ p^ v =v i
ÿ ðÿ1Þ cosða Þ¼
k cosð3a Þÿ cosð3a Þþ cosð3a Þÿ cosð3a Þ¼ 1=2
3
4
1
2
k¼1 4
cosð5a Þÿ cosð5a Þþ cosð5a Þÿ cosð5a Þ¼ 1=2
2
1
4
3
N
P k 1
ÿ ðÿ1Þ cosðna Þ¼ for n ¼ 3; 5; ... ; 2N ÿ 1 cosð7a Þÿ cosð7a Þþ cosð7a Þÿ cosð7a Þ¼ 1=2
k 1 2 3 4
k¼1 2
ð14:10Þ
ð14:9Þ
where a , a ; ... ; a N should satisfy a < a < < a < where the angles a ; a ; a , and a are de®ned as shown in Fig.
1
N
4
1
2
2
1
3
2
p=2. Similarly, to eliminate an odd number of harmonics, 14.6b. The angles a ; a , a and a are plotted for different
1 2 3 4
for instance, the third, ®fth and seventh, and to perform values of ^ v =v in Fig. 14.7b. The general expressions to
o1 i
100° 100°
90° 90°
80° a 4
70°
a 3
60°
a 2
50°
40°
30°
a 1
20°
10°
v ˆ v / v ˆ o1 v /
0° 0 0.1 0.2 0.3 0.4 0.5 o1 i i
a) b)
FIGURE 14.7 Chopping angles for SHE and fundamental voltage control in half-bridge VSIs: (a) third and ®fth harmonic elimination; (b) third,
®fth, and seventh harmonic elimination.