Page 163 - Rashid, Power Electronics Handbook

152 Y.-S. Lee and M. Chow

The dc component of the recti®er voltage is given by Eq.
(10.5). Therefore, in addition to Eq. (10.27), the ripple factor
can also be expressed as

s 
2
P 1
RF ¼ 2 ð10:69Þ
2
n¼2;4;8 n ÿ 1
Considering only the lowest-order harmonic (n ¼ 2), the
FIGURE 10.24 Equivalent circuit for input ac ®lter.
output ripple factor of a simple inductor-input dc ®lter
(without C ) can be found, from Eqs. (10.64) and (10.69), as
f
The power factor of the circuit shown in Fig. 10.22 can be
0:4714 improved by installing an ac ®lter between the source and the
Filtered RF ¼ q  ð10:70Þ
2 recti®er, as shown in Fig. 10.24.
1 þð4pf L =RÞ
i f
Considering only the harmonic components, the equivalent
circuit of the recti®er given in Fig. 10.24 can be found as
10.5.1.4 Harmonics of the Input Current shown in Fig. 10.25. The rms value of the nth harmonic
In general, the total harmonic distortion (THD) of an input current appearing in the supply can then be obtained using the
current is de®ned as current-divider rule,
s 
2 1
I s I ¼ I ð10:75Þ
sn
2
THD ¼ ÿ1 ð10:71Þ 1 ÿð2npf Þ L C rn
I s1 i i i
where I is the rms value of the nth harmonic current of the
rn
where I is the rms value of the input current and I and the
s s1 recti®er.
rms value of the fundamental component of the input current.
Applying Eq. (10.73) and knowing I =I ¼ 1=n from Eq.
rn
r1
The THD can also be expressed as
(10.74), the THD of the recti®er with input ®lter shown in Fig.
10.24 can be found as
s 
2
P I sn
THD ¼ ð10:72Þ s 
n¼2;3;4 I s1 P 1 1 2
Filtered THD ¼ ð10:76Þ
2
n¼3;5 n 2 1 ÿð2npf Þ L C i
i
i
where I is the rms value of the nth harmonic component of
sn
the input current.
The important design parameters of typical single-phase and
Moreover, the input power factor is de®ned as
three-phase recti®ers with inductor-input dc ®lter are listed in
Table 10.5. Note that, in a single-phase half-wave recti®er, a
I s1
PF ¼ cos f ð10:73Þ freewheeling diode is required to be connected across the
I s input of the dc ®lters such that the ¯ow of load current can be
maintained during the negative half-cycle of the supply
where f is the displacement angle between the fundamental voltage.
components of the input current and voltage.
Assume that inductor L of the circuit shown in Fig. 10.22
f
has an in®nitely large inductance. The input current is then a 10.5.2 Capacitive-Input dc Filters
square wave. This input current contains undesirable higher Figure 10.26 shows a full-wave recti®er with capacitor-input
harmonics that reduce the input power factor of the system. dc ®lter. The voltage and current waveforms of this recti®er are
The input current can be easily expressed as
4I m P 1
i ¼ sin 2npf t ð10:74Þ
s i
p n¼1;3;5 n
The rms values of the input current and its fundamental
p

component are I m and 4I =ðp 2Þ, respectively. Therefore,
m
the THD of the input current of this circuit is 0.484. As the
p

displacement angle f ¼ 0, the power factor is 4=ðp 2Þ¼ 0:9. FIGURE 10.25 Equivalent circuit for input ac ®lter.