Page 196 - Rashid, Power Electronics Handbook

12 Three-Phase Controlled Recti®ers 185

and voltage is higher than that from the half-wave recti®er, and its
average value is given by
rms
V ¼ 1:17 a V ðprimÞf ÿN ð12:4Þ
D
ð p=6þa
V max
V ¼ cos ot dðotÞ
D
where a is the secondary to primary turn relation of the p=3 ÿp=6þa
transformer. On the other hand, a relation between the sin p=6 rms cos a
currents is also possible to obtain. With the help of Fig. 12.5, ¼ V max p=6 cos a 1:35 V f ÿN ð12:8Þ
I D
rms
I ¼ p ð12:5Þ The dc voltage ripple is also smaller than the one generated by
sec 
3 the half-wave recti®er, due to the absence of the third
p 
I D 2 harmonic with its inherently high amplitude. The smoothing
rms
I ¼ a ð12:6Þ
prim reactor L is also considerably smaller than the one needed for
3 D
a 3-pulse (half-wave) recti®er.
The ac currents of the 6-pulse recti®er are shown in Fig.
Combining Eqs. (12.2) to (12.6), it yields
12.7. The currents in the secondary windings present a dc
component, but the magnetic ¯ux is compensated by the
VA prim ¼ 1:21 P D double star. As can be observed, only one valve is ®red at a
ð12:7Þ
VA ¼ 1:48 P time, and then this connection in no way corresponds to a
sec D
parallel connection. The currents inside the delta show a

symmetrical waveform, with 60 conduction. Finally, due to
Equation (12.7) shows that the power transformer has to be the particular transformer connection shown in Fig. 12.6, the
oversized 21% at the primary side, and 48% at the secondary source currents also show a symmetrical waveform, but with

side. Then a special transformer has to be built for this 120 conduction.
recti®er. In terms of average VA, the transformer needs to be Evaluation of the rating of the transformer is done in
35% larger that the rating of the dc load. The larger rating of similar fashion to the way the half-wave recti®er is evaluated:
the secondary respect to primary is because the secondary
carries a dc component inside the windings. Furthermore, the
VA ¼ 1:28 P
transformer is oversized because the circulation of current prim D ð12:9Þ
harmonics does not generate active power. Core saturation, VA sec ¼ 1:81 P D
due to the dc components inside the secondary windings, also
needs to be taken into account for iron oversizing.
Thus, the transformer must be oversized 28% at the primary
side, and 81% at the secondary side. In terms of size it has an
average apparent power of 1.55 times the power P (55%
12.2.2 Six-Pulse or Double Star Rectifier D
oversized). Because of the short conducting period of the
The thyristor side windings of the transformer shown in Fig. valves, the transformer is not particularly well utilized.
12.6 form a six-phase system, resulting in a 6-pulse starpoint
(midpoint connection). Disregarding commutation overlap, a

each valve conducts only during 60 per period. The direct
I D
w
v a v 3 v b v 1 v c
i a
i b
D
i A
v A i A

FIGURE 12.6 Six-pulse recti®er. FIGURE 12.7 AC current waveforms for the 6-pulse recti®er.