PE 304 Lect 4 & 5 Uncontrolled Rectifier Circuits.pdf
PE 304 Lect 4 & 5 Uncontrolled Rectifier Circuits.pdf
PE 304 Lect 4 & 5 Uncontrolled Rectifier Circuits.pdf
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Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
<strong>Lect</strong>ures 4 & 5<br />
Diode <strong>Rectifier</strong>s<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-1
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Diode <strong>Rectifier</strong> Block Diagram<br />
• <strong>Uncontrolled</strong> utility interface (ac to dc)<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-2
• Resistive load<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
A Simple Circuit<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-3
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
A Simple Circuit (R-L Load)<br />
• Current continues to flows for a while even after the input<br />
voltage has gone negative<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-4
• From t = 0, the diode is forward biased<br />
Vs = +<br />
Ri<br />
L<br />
di<br />
dt<br />
• For 0t 1 , V L → negative, current decreases<br />
•t>t 2 ,V L → negative, but the current is still positive<br />
•at t 3 , the current goes to zero<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-5
But i(i 3 ) = i(0) = 0<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
t<br />
1<br />
∫<br />
0<br />
V<br />
L<br />
dt +<br />
1<br />
L<br />
t<br />
3<br />
∫<br />
0<br />
∫<br />
∫<br />
V<br />
V<br />
V<br />
L<br />
L<br />
L<br />
dt<br />
=<br />
dt = di<br />
=<br />
Area A − Area B =<br />
t<br />
t<br />
t<br />
3<br />
0<br />
3<br />
1<br />
V<br />
V<br />
L<br />
L<br />
dv<br />
L<br />
dt<br />
i(t<br />
3<br />
∫<br />
i(0)<br />
dt = 0<br />
dt = 0<br />
i(t<br />
)<br />
∫<br />
i(0)<br />
di<br />
3<br />
)<br />
di<br />
For t>t 3 , V R and V L are zero. So a reverse polarity voltage<br />
appears across the diode. The waveforms repeat with the time<br />
period T=1/f<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-6
A Simple Circuit (Load has a dc back-emf)<br />
• Current begins to flow when the input voltage exceeds the dc back-emf<br />
• Current continues to flows for a while even after the input voltage has<br />
gone below the dc back-emf<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-7
Single-Phase Diode <strong>Rectifier</strong> Bridge<br />
• Large capacitor at the dc output for filtering and energy<br />
storage<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-8
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Diode-<strong>Rectifier</strong> Bridge Analysis<br />
• Two simple (idealized) cases to begin with<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-9
Redrawing Diode-<strong>Rectifier</strong> Bridge<br />
• Two groups, each with two diodes<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-10
• When v s positive, D1 and D2 conduct and v d = v s and i s = i d .<br />
When v s goes negative, D3 and D4 conduct, and therefore,<br />
v d = -v s and i s = -i d . At any time, dc-side output voltage of<br />
diode rectifier expressed as<br />
• Similarly, the ac-side current can be expressed as<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
i<br />
s<br />
vd (t) = | vs<br />
⎧id<br />
if v<br />
= ⎨<br />
⎩−<br />
id<br />
if<br />
s<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
|<br />
> 0<br />
v < 0<br />
• and the transition between the two values is instantaneous<br />
due to the assumption of L s . The average value V do is<br />
2<br />
V do =<br />
2 Vs<br />
= 0.9 Vs<br />
π<br />
s<br />
5-11
•Also<br />
2<br />
Is1<br />
=<br />
2 Id<br />
= 0.9I<br />
d<br />
π<br />
⎧0<br />
for even values<br />
of h<br />
Ish<br />
= ⎨<br />
⎩Is1/h<br />
for odd values of h<br />
THD = 48.43%<br />
DPF = 1.0<br />
Is<br />
PF = DPF<br />
I<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
1<br />
s<br />
=<br />
0.9<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
and<br />
5-12
Waveforms with a<br />
purely resistive load<br />
and a purely dc current<br />
at the output<br />
• In both cases, the dc-side<br />
voltage waveform is the same<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-13
Diode-<strong>Rectifier</strong> Bridge Input Current<br />
• Idealized case with a purely dc output current<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-14
Diode-<strong>Rectifier</strong> Bridge Analysis with AC-<br />
Side Inductance<br />
• Output current is assumed to be purely dc<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-15
Understanding Current Commutation<br />
• Assuming inductance in this circuit to be zero<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-16
Understanding Current Commutation (cont.)<br />
• Inductance in this circuit is included<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-17
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-18<br />
s<br />
s<br />
s<br />
s<br />
s<br />
s<br />
L<br />
di<br />
L<br />
ω<br />
t)<br />
td(ω<br />
sinω<br />
V<br />
2<br />
t<br />
ω<br />
0<br />
dt<br />
di<br />
L<br />
t<br />
sinω<br />
V<br />
2<br />
v<br />
=<br />
<<br />
<<br />
=<br />
= u<br />
s<br />
s<br />
s<br />
2<br />
0<br />
do<br />
s<br />
d<br />
s<br />
d<br />
s<br />
s<br />
u<br />
s<br />
s<br />
u<br />
0<br />
u<br />
I<br />
0<br />
d<br />
s<br />
s<br />
s<br />
s<br />
u<br />
0<br />
V<br />
0.45<br />
V<br />
π<br />
2<br />
2<br />
2<br />
t)<br />
td(ω<br />
sinω<br />
V<br />
2<br />
π<br />
2<br />
1<br />
V<br />
V<br />
2<br />
I<br />
L<br />
ω<br />
1<br />
cosu<br />
I<br />
L<br />
ω<br />
cosu)<br />
(1<br />
V<br />
2<br />
A<br />
cosu)<br />
(1<br />
V<br />
2<br />
t)<br />
td(ω<br />
sinω<br />
V<br />
2<br />
A<br />
I<br />
L<br />
ω<br />
di<br />
L<br />
ω<br />
t)<br />
td(ω<br />
sinω<br />
V<br />
2<br />
d<br />
=<br />
=<br />
=<br />
−<br />
=<br />
=<br />
−<br />
=<br />
−<br />
=<br />
=<br />
=<br />
=<br />
∫<br />
∫<br />
∫<br />
∫
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-19<br />
d<br />
s<br />
u<br />
d<br />
d<br />
s<br />
s<br />
u<br />
s<br />
d<br />
s<br />
u<br />
0<br />
s<br />
π<br />
0<br />
d<br />
I<br />
π<br />
2<br />
L<br />
ω<br />
π<br />
2<br />
A<br />
area<br />
ΔV<br />
I<br />
π<br />
2<br />
L<br />
ω<br />
V<br />
0.45<br />
π<br />
2<br />
A<br />
area<br />
V<br />
0.45<br />
V<br />
t)<br />
td(ω<br />
sinω<br />
V<br />
2<br />
π<br />
2<br />
1<br />
t)<br />
td(ω<br />
sinω<br />
V<br />
2<br />
π<br />
2<br />
1<br />
V<br />
=<br />
=<br />
−<br />
=<br />
−<br />
=<br />
−<br />
= ∫<br />
∫<br />
π<br />
I<br />
L<br />
ω<br />
2<br />
V<br />
0.9<br />
π<br />
A<br />
area<br />
V<br />
V<br />
V<br />
2<br />
I<br />
L<br />
ω<br />
2<br />
1<br />
cosu<br />
I<br />
L<br />
ω<br />
2<br />
di<br />
L<br />
ω<br />
t)<br />
ω<br />
td(<br />
sinω<br />
V<br />
2<br />
A<br />
area<br />
radian<br />
Volt<br />
i<br />
2<br />
I<br />
i<br />
i<br />
-<br />
I<br />
i<br />
i<br />
i<br />
i<br />
i<br />
d<br />
s<br />
s<br />
u<br />
do<br />
d<br />
s<br />
d<br />
s<br />
d<br />
s<br />
I<br />
I<br />
-<br />
s<br />
s<br />
u<br />
0<br />
s<br />
u<br />
u<br />
d<br />
s<br />
u<br />
d<br />
4<br />
D<br />
3<br />
D<br />
u<br />
2<br />
D<br />
1<br />
D<br />
d<br />
d<br />
−<br />
=<br />
−<br />
=<br />
−<br />
=<br />
=<br />
=<br />
=<br />
−<br />
+<br />
−<br />
=<br />
=<br />
=<br />
=<br />
=<br />
∫<br />
∫
Current Commutation Waveforms<br />
• Shows the volt-seconds needed to commutate current<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-20
Current Commutation in Full-Bridge <strong>Rectifier</strong><br />
• Shows the necessary volt-seconds<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-21
Understanding Current Commutation<br />
• Note the current loops for analysis<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-22
<strong>Rectifier</strong> with a dcside<br />
voltage<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-23
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-24<br />
s<br />
s<br />
circuit<br />
short<br />
θ<br />
θ<br />
d<br />
d<br />
θ<br />
θ<br />
d<br />
s<br />
θ<br />
θ<br />
d<br />
s<br />
s<br />
d<br />
b<br />
θ<br />
θ<br />
d<br />
s<br />
θ<br />
θ<br />
d<br />
s<br />
d<br />
s<br />
d<br />
s<br />
L<br />
b<br />
p<br />
b<br />
s<br />
d<br />
L<br />
ω<br />
V<br />
I<br />
π<br />
dθ<br />
)<br />
(θ<br />
i<br />
I<br />
t)<br />
d(ω<br />
)<br />
V<br />
-<br />
t)<br />
sin(ω<br />
V<br />
2<br />
(<br />
0<br />
t)<br />
d(ω<br />
)<br />
V<br />
-<br />
t)<br />
sin(ω<br />
V<br />
2<br />
(<br />
L<br />
ω<br />
1<br />
θ)<br />
(<br />
i<br />
θ<br />
θ<br />
where<br />
t)<br />
d(ω<br />
)<br />
V<br />
-<br />
t)<br />
sin(ω<br />
V<br />
2<br />
(<br />
di<br />
L<br />
ω<br />
V<br />
-<br />
t)<br />
sin(ω<br />
V<br />
2<br />
dt<br />
di<br />
L<br />
v<br />
θ<br />
π<br />
θ<br />
sinθ<br />
V<br />
2<br />
V<br />
b<br />
b<br />
b<br />
b<br />
b<br />
=<br />
=<br />
=<br />
=<br />
><br />
=<br />
=<br />
−<br />
=<br />
=<br />
∫<br />
∫<br />
∫<br />
∫<br />
∫
DC-Side Voltage and Current Relationship<br />
• Zero current corresponds to dc voltage equal to the peak of<br />
the input ac voltage<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-25
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Effect of DC-Side Current on<br />
THD, PF and DPF<br />
• Very high THD at low current values<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-26
Crest Factor versus the Current Loading<br />
• The Crest Factor is very high at low values of current<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-27
Diode-<strong>Rectifier</strong> with a Capacitor Filter<br />
• Power electronics load is represented by an equivalent load<br />
resistance<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-28
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Diode <strong>Rectifier</strong> Bridge<br />
• Equivalent circuit for analysis on one-half cycle basis<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-29
Diode-Bridge <strong>Rectifier</strong>: Waveforms<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-30
Diode-Bridge <strong>Rectifier</strong>: Waveforms<br />
• Analysis using PSpice- You may repeat with PSim<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-31
• Analysis using PSpice-<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Input Line-Current Distortion<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-32
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Line-Voltage Distortion<br />
• PCC is the point of common coupling<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-33
(v<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
(v<br />
pcc<br />
v<br />
v<br />
pcc<br />
)<br />
pcc<br />
pcc<br />
)<br />
1<br />
dis<br />
=<br />
=<br />
=<br />
v<br />
v<br />
v<br />
s<br />
s<br />
s<br />
= − L<br />
− L<br />
− L<br />
− L<br />
s1<br />
s1<br />
s1<br />
s1<br />
∑<br />
h≠1<br />
dis<br />
dt<br />
di<br />
dt<br />
s1<br />
dis1<br />
dt<br />
di<br />
dt<br />
sh<br />
− L<br />
s1<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
∑<br />
h≠1<br />
di<br />
dt<br />
sh<br />
5-34
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Line-Voltage Distortion<br />
• Distortion in voltage supplied to other loads<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-35
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Voltage Doubler <strong>Rectifier</strong><br />
• In 115-V position, one capacitor at-a-time is charged from the<br />
input.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-36
A Three-Phase, Four-Wire System<br />
• A common neutral wire is assumed<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-37
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-38<br />
line<br />
n<br />
3<br />
s<br />
n<br />
2<br />
1)<br />
k<br />
3(2<br />
h<br />
2<br />
sh<br />
n<br />
1)<br />
k<br />
3(2<br />
h<br />
h<br />
h<br />
sh<br />
n<br />
c<br />
b<br />
a<br />
n<br />
1<br />
k<br />
2<br />
h<br />
h<br />
h<br />
sh<br />
1<br />
1<br />
1<br />
s<br />
c<br />
1<br />
k<br />
2<br />
h<br />
h<br />
h<br />
sh<br />
1<br />
1<br />
1<br />
s<br />
b<br />
1<br />
k<br />
2<br />
h<br />
h<br />
h<br />
sh<br />
1<br />
1<br />
1<br />
s<br />
1<br />
k<br />
2<br />
h<br />
ah<br />
1<br />
a<br />
a<br />
I<br />
3<br />
I<br />
I<br />
3<br />
I<br />
I<br />
3<br />
I<br />
)<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
2<br />
3<br />
i<br />
i<br />
i<br />
i<br />
i<br />
h)<br />
240<br />
-<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
240)<br />
-<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
2<br />
i<br />
and<br />
h)<br />
120<br />
-<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
2<br />
120)<br />
-<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
2<br />
i<br />
1,2,3.....<br />
k<br />
where<br />
)<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
)<br />
Φ<br />
-<br />
t<br />
sin(ω<br />
I<br />
2<br />
i<br />
i<br />
i<br />
=<br />
≅<br />
⎟<br />
⎟<br />
⎠<br />
⎞<br />
⎜<br />
⎜<br />
⎝<br />
⎛<br />
=<br />
=<br />
+<br />
+<br />
=<br />
+<br />
=<br />
+<br />
=<br />
=<br />
+<br />
=<br />
+<br />
=<br />
∑<br />
∑<br />
∑<br />
∑<br />
∑<br />
∑<br />
∞<br />
−<br />
=<br />
∞<br />
−<br />
=<br />
∞<br />
+<br />
=<br />
∞<br />
+<br />
=<br />
∞<br />
+<br />
=<br />
∞<br />
+<br />
=
Current in A Three-Phase, Four-Wire<br />
System<br />
• The current in the neutral wire can be very high<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-39
• Commonly used<br />
Three-Phase, Full-Bridge <strong>Rectifier</strong><br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-40
Three-Phase, Full-Bridge <strong>Rectifier</strong>: Redrawn<br />
• Two groups with three diodes each<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-41
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-42<br />
LL<br />
LL<br />
6<br />
π<br />
6<br />
π<br />
LL<br />
do<br />
LL<br />
6<br />
π<br />
6<br />
π<br />
LL<br />
LL<br />
ab<br />
d<br />
d<br />
d<br />
a<br />
v<br />
1.35<br />
v<br />
2<br />
π<br />
3<br />
t)<br />
ω<br />
td(<br />
cosω<br />
v<br />
2<br />
3<br />
π/<br />
1<br />
V<br />
v<br />
2<br />
t)<br />
ω<br />
td(<br />
cosω<br />
v<br />
2<br />
A<br />
π<br />
6<br />
1<br />
t<br />
ω<br />
π<br />
6<br />
1<br />
-<br />
t<br />
cosω<br />
v<br />
2<br />
v<br />
v<br />
conducting<br />
is<br />
4<br />
or<br />
1<br />
diode<br />
neither<br />
when<br />
0<br />
conducting<br />
is<br />
4<br />
diode<br />
when<br />
I<br />
-<br />
conducting<br />
is<br />
1<br />
diode<br />
when<br />
I<br />
i<br />
=<br />
=<br />
=<br />
=<br />
=<br />
<<br />
<<br />
=<br />
=<br />
⎪<br />
⎩<br />
⎪<br />
⎨<br />
⎧<br />
=<br />
∫<br />
∫<br />
−<br />
−
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Is<br />
=<br />
2<br />
Id<br />
3<br />
= 0.816 I<br />
1<br />
Is1<br />
=<br />
π<br />
Is1<br />
Ish<br />
=<br />
h<br />
6 Id<br />
= 0.78I<br />
where h = 5.7.11.13, .....<br />
DPF = 1.0<br />
PF<br />
=<br />
3<br />
π<br />
=<br />
0.955<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
d<br />
d<br />
5-43
Three-Phase, Full-Bridge <strong>Rectifier</strong> Waveforms<br />
• Output current is<br />
assumed to be dc<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-44
Three-Phase, Full-Bridge <strong>Rectifier</strong>: Input<br />
Line-Current<br />
• Assuming output current to be purely dc and zero ac-side<br />
inductance<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-45
Three-Phase, Full-Bridge <strong>Rectifier</strong><br />
• Including the ac-side inductance<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-46
3-Phase <strong>Rectifier</strong>: Current Commutation<br />
• output<br />
current is<br />
assumed to be<br />
purely dc<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-47
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-48<br />
LL<br />
d<br />
s<br />
LL<br />
d<br />
s<br />
I<br />
0<br />
Ls<br />
LL<br />
cn<br />
an<br />
u<br />
0<br />
cn<br />
an<br />
I<br />
0<br />
s<br />
cn<br />
an<br />
s<br />
Ls<br />
Lc<br />
La<br />
cn<br />
an<br />
comm<br />
s<br />
c<br />
s<br />
Lc<br />
s<br />
a<br />
s<br />
La<br />
u<br />
d<br />
c<br />
u<br />
a<br />
v<br />
2<br />
I<br />
L<br />
ω<br />
2<br />
1<br />
cosu<br />
2<br />
cosu)<br />
(1<br />
v<br />
2<br />
I<br />
L<br />
ω<br />
diu<br />
ω<br />
t<br />
sinω<br />
v<br />
2<br />
v<br />
-<br />
v<br />
t)<br />
d(ω<br />
2<br />
v<br />
v<br />
diu<br />
L<br />
ω<br />
2<br />
v<br />
v<br />
dt<br />
diu<br />
L<br />
dt<br />
diu<br />
2<br />
v<br />
v<br />
v<br />
v<br />
v<br />
dt<br />
diu<br />
L<br />
dt<br />
di<br />
L<br />
v<br />
dt<br />
diu<br />
L<br />
dt<br />
di<br />
L<br />
v<br />
i<br />
I<br />
i<br />
i<br />
i<br />
d<br />
d<br />
−<br />
=<br />
−<br />
=<br />
=<br />
=<br />
−<br />
=<br />
−<br />
=<br />
=<br />
−<br />
=<br />
−<br />
=<br />
−<br />
=<br />
=<br />
=<br />
=<br />
−<br />
=<br />
=<br />
∫<br />
∫<br />
∫
v<br />
A<br />
Pn<br />
ΔV<br />
V<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
u<br />
d<br />
d<br />
=<br />
v<br />
V<br />
an<br />
do<br />
− L<br />
= ω LsI<br />
ω LsI<br />
=<br />
π/ 3<br />
=<br />
d<br />
d<br />
s<br />
- ΔV<br />
diu<br />
dt<br />
=<br />
d<br />
3<br />
π<br />
=<br />
ω<br />
v<br />
L<br />
LL<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
s<br />
an<br />
I<br />
d<br />
= 1.35V<br />
− v<br />
2<br />
-<br />
cn<br />
3<br />
π<br />
ω<br />
L<br />
s<br />
I<br />
d<br />
5-49
<strong>Rectifier</strong> with a Large Filter Capacitor<br />
• Output voltage is assumed to be purely dc<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-50
Three-Phase, Full-Bridge <strong>Rectifier</strong><br />
• THD, PF and DPF as functions of load current<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-51
Crest Factor versus the Current Loading<br />
• The Crest Factor is very high at low values of current<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-52
Three-Phase <strong>Rectifier</strong> Waveforms<br />
• Can be simulated using PSpice or PSim<br />
Copyright © 2003<br />
by John Wiley & Sons, Inc.<br />
Chapter 5 Line-Frequency Diode<br />
<strong>Rectifier</strong>s<br />
5-53