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00:01:13,000 --> 00:01:13,460
So, last class we introduced the sine triangle
PWM and with sine triangle PWM, how we controlled
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00:01:13,460 --> 00:01:19,660
the output voltage that is proportional to
our sine modulating wave for our converter.
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So, one leg only we talked about. So, what
we learnt from the previous class is we can
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control the output voltage, output voltage
variation that is for a converter like this,
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single leg; for the single leg, this is S1,
this is S2.
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So, we are measuring the voltage, pole voltage
A with respect to the fictitious center O.
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00:01:57,550 --> 00:02:04,550
Then we found, for a sinusoidal reference
voltage, sinusoidal reference voltage comparing
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with high frequency triangle waveform for
switch control; we found the output VA0 fundamental
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00:02:14,439 --> 00:02:21,439
or VA0 average, VA0 average is proportional
to the Vm (t), modulating wave that is our
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00:02:30,829 --> 00:02:32,590
reference wave.
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Now, we have not talked about the harmonics.
Also, I told, because of the high frequency
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triangle PWM, the next high amplitude harmonics
will be around the carrier frequency side;
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carrier frequency, triangle frequency side.
So, by going for high frequency triangle waveform,
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we can shift the high harmonic, high amplitude
harmonic to the high frequencies side correspondingly
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the ripple current drawn from the source will
be, will be controlled. It is highly reduced.
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00:03:14,719 --> 00:03:21,719
So, let us talk about the harmonics, so PWM.
See, if you really do the Fourier series and
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try to find the harmonics, it will get into
puzzle function, complicated function. Let
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00:03:26,309 --> 00:03:30,540
us take a simple thumb rule. This, I have
taken as I told before, from a very famous
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text book by Professor Ned Mohan. So, we will
be talking about the harmonics now.
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So, the harmonics order and this is amplitude
of the harmonics n and this is the frequency
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number n, harmonics number. The fundamental
happens at the frequency Vn, some amplitude.
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So, let this is the amplitude, this amplitude
we know, it is in proportional to our reference
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phase amplitude. Here, you will have the fundamental
frequency. Now, harmonics will be for a sine
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00:04:16,850 --> 00:04:23,850
triangle waveform will be the sum and difference
of the carrier frequency and the modulating
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frequency. That means the harmonics order
will be j fc plus or minus k fm. Now, for
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00:04:37,550 --> 00:04:44,550
now, from here, from this thumb rule; we can
find out the harmonics, order of harmonics
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present in the sine triangle PWM.
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So, what we have to do? For j even, we have
to substitute k all odd values. When j is
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odd; we have to substitute, we have to substitute
even values for k. Let us take J is equal
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to 1 that is here, J is equal to 1. Then,
K can have J is equal to 1 means that is odd,
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K can have all the values 0, 2, 4. So, let
us take J is equal to 1. The next harmonics
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happens at let us take K is equal to 0. So,
it will happen somewhere here, fc, this is
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fc. Then you have you get the sidebands here,
K is equal to 0. Then you have fc plus 2 and
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00:06:01,090 --> 00:06:08,090
fc minus 2, fc plus 2 fc minus 2. Then again,
you will have with decrease, as the harmonic
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order increases; the sideband amplitude will
also increase decrease. fc plus 4, fc minus
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00:06:23,480 --> 00:06:29,060
4. So, this way it goes.
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00:06:29,060 --> 00:06:36,060
Now, let us take j is equal to, j is equal
to 2. Then k will have values 1, 3, 5. Here,
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00:06:44,640 --> 00:06:51,640
I have met fc plus 2 fm, here fc plus 4 fm,
here also fc minus 2 fm, fc plus 4 fm; based
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on this equation. So, we will get some and
difference of the carrier and the modulating
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00:07:06,140 --> 00:07:12,270
frequency. Now, let us take j is equal to
2 that is 2 times the carrier frequency and
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00:07:12,270 --> 00:07:19,270
we will be taking it sidebands. Now, at 2
fc when j is equal to 2, the 2 fc; we have
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00:07:27,740 --> 00:07:31,650
sidebands at 2 fc plus fm, 2 fc minus fm.
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00:07:31,650 --> 00:07:37,790
So, if this is the point at 2 fc, we will
not have any harmonic at 2 fc from this relation;
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00:07:37,790 --> 00:07:43,310
we will have at the sidebands of 2 fc, at
the side at the sidebands of 2 fc only we
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00:07:43,310 --> 00:07:50,310
will have harmonics that is here, 2 fc plus
fm, here 2 fc minus fm. Then again here, sidebands
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00:07:59,990 --> 00:08:06,990
that is 2 fc plus 3 fm plus 3 fm and here
this one 2 fc minus 3 fm. So, this way, harmonics,
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00:08:17,900 --> 00:08:23,620
again we can give the value for j is equal
to 3, we can find out. But as the harmonic
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order that harmonic order increases, amplitude
decreases.
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00:08:29,340 --> 00:08:36,340
So, we are more worried about the harmonics
at fc and its sidebands and the harmonics
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at 2 times the sidebands. And, I told you
before, the sine triangle PWM, this harmonics
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00:08:48,380 --> 00:08:53,860
amplitude if you can, fc we can shift it to
high frequency side; what is the advantage?
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Its sidebands also will get shift to the high
frequency side. Then the current drawn due
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00:09:03,230 --> 00:09:08,590
to the harmonics because of the impedance
L omega increases, the ripple current amplitude
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00:09:08,590 --> 00:09:13,540
reduces and the current draw drawn will be
more close to the fundamental that is nearly
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00:09:13,540 --> 00:09:20,360
sinusoidal. So, to shift fc to the higher
frequency side, we have to increase the carrier
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00:09:20,360 --> 00:09:21,760
frequency.
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00:09:21,760 --> 00:09:28,760
To shift fc to high frequency side, side,
we have to increase the frequency of
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00:10:12,380 --> 00:10:19,380
triangle wave, the frequency of the triangle
wave. So, what is the disadvantage? If fc
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increases, the number of switching's per
fundamental cycle will increase. If fc increases,
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00:10:31,400 --> 00:10:38,400
the number of switching's that is S1 on
and then S1 off and S2 on, the number of switching's,
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00:10:51,160 --> 00:10:58,160
switching's per fundamental cycle, fundamental
cycle is the modulating wave period per fundamental
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00:11:05,320 --> 00:11:12,320
cycle
will increase. So, what will happen? The switching
losses, because we are using hard switching,
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hard voltage we have voltage and current we
are switching.
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So, for any switch, even though we have assumed
ideal condition here, the switch will have
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during a finite turn on and turn off time.
During that process, switching losses will
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be there. So, switching losses will be more
and the efficiency of the system will come
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down. So, switching losses will increase.
So, what will happen? Efficiency of the converter
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will come down, decrease, efficiency of the
power converter will decrease, will decrease,
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efficiency of the converter will decrease.
So, we cannot resort to high frequency period.
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Typically, for high power applications, the
switching frequency compared to fundamental,
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we have to limit between fc should be limit
between 500 to 600 or less than 800 hertz.
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So here, fc is not very far from the fundamental.
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So, the switching losses will increase. So,
we cannot resort to high frequency PWM. At
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the same time, we do not want high amplitude
harmonic current.
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The frequency, amplitude and the frequency
for the system, I have drawn previously; here
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we have the harmonics amplitude and here you
have the fm. Then you have the fc here, then
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00:13:32,779 --> 00:13:39,779
it sidebands here; so, fc fm. So, fc decreases,
it comes here. These sidebands becomes very
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00:13:46,250 --> 00:13:53,250
close to the fundamental. So, your low under
harmonics that is fifth, seventh will get
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boosted up. fc is still further closer; this
sidebands become lower than the fundamental
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00:14:00,560 --> 00:14:06,240
frequency. So, this is called sub harmonics.
Harmonics frequency less than the fundamental
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00:14:06,240 --> 00:14:10,980
also will introduce. We will come into system.
Harmonic current will increase; for PW if
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you draw motor drive application, torque pulsations
will increase.
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So, we do not know, we do not want to resort
to high frequency switching; at the same time,
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we want to eliminate or suppress these harmonics.
How it is done in a front end ac to dc converter?
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See previously, in the previous case, if you
see our original front end ac to dc converter;
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this is our Vin, then you have the inductor.
So, inductor will suppress the harmonic amplitudes.
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00:14:54,339 --> 00:15:01,339
Then, we have the switches, these are the
freewheeling diode. This is, this side is
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pole A, this side is leg A or pole and
you have the E0 here. So, this limb will be
connected here and this side will go here.
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00:15:48,890 --> 00:15:55,890
So, we have talked about one limb with respect
to E0, E0 and our A. So, power flow can be
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00:15:58,890 --> 00:16:04,140
according to our converter ac, this power
flow can from in the ac side to the dc side
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as well as dc side to the ac side. So, we
have analyzed the PWM with respect to the
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dc side and we found out the A pole voltage
waveform with respect to the fictitious center.
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Now, if you see here, in our converter, there
is one more leg is there; the B leg is also
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there. The net voltage, what we want across
AB is equal to VAB is equal to if you take
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the fundamental, the VA0, the average variation
due to sine triangle VA0; VA0 minus VB0, this
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is our fundamental. So, VA0 minus VB0; so
what we want the fundamental component of
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VA0 and VB0 should get added. At the same
time, this switching's of VA0 and VB0 are
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independent of each other that means VA0 will
also contain the harmonics at fc and it's
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sidebands and VB0 also conduct the harmonics
at fc and sidebands. So, we have 2 degrees
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of freedom that is one is for a phase leg,
the leg A; other one is for the leg B.
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So, VA0 and VB0, we can generate in such a
way, fundamental; fundamental of VA0 and VB0
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get added and we can choose the PWM, sine
can triangle PWM because we have two degrees
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of freedom as I told because A and B because
2 legs; the second one, we can choose the
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sine triangle PWM. The phase shift between
sine triangles, we can choose in such a way,
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00:18:16,470 --> 00:18:23,470
the harmonics
at fc and its sidebands
gets eliminated or get highly suppressed;
sidebands, the harmonics at fc and if sidebands
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are highly suppressed, highly suppressed or
eliminated.
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So, what is the advantage? So AB, we can control
independently; we do not have to resort to
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high frequency PWM so that the switching losses
can be reduced. At the same time, we do not
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have to worry that fc is very close to fm.
So, low order harmonics can boosted up because
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we can choose the PWM of A and B in such a
way, the harmonics and a fits can be highly
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suppressed. How it can be done?
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See, we are using sine triangle PWM. We are
interested it is VAB. VAB is equal to VA0
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minus VB0 and we are using sine triangle PWM
where the output fundamental is proportional
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00:19:45,390 --> 00:19:52,390
to psi. So, we will be using sine triangle
PWM such a way; the leg for A, we will use
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the VB the fundamental amplitude or a fundamental
amplitude VB0 and VA0 should be the same but
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00:20:01,490 --> 00:20:08,490
the phase angle of VB0 that means if the fundamental
is V1 angle zero here, here we want V1 angle
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180 degree. So, already VB0 fundamental is
180 degree phase shifted with respect to VA0
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fundamental. When you subtract, both will
get added. That means the output will get
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added; because of this already 180 degree,
this fundamental, fundamentals are in phase
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and get added, fundamental get added.
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So, how to get this 180 degree phase shift?
See let us draw, only the switch schematic
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of A and B; this is A, this is B, this is
S1, S2, this is S3, S4. Let us make it that
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way. So, we will be using the same triangle,
same sine wave, same sine; we will be using
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the same triangle for both the legs, same
triangle wave form, same triangle that is
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00:21:40,120 --> 00:21:47,120
fc, same triangle wave form
for both the legs. So, you use same triangle
we will be using.
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At the same time, same sine wave that is a
modulating wave that is Vm (t), it is used
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00:22:17,880 --> 00:22:24,880
for sine triangle PWM. See, if you use the
same sine and same triangle, then VA0 fundamental
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00:22:33,400 --> 00:22:39,740
and VB0 fundamental will be in phase. But
we want VB0 fundamental should be phase shifted
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00:22:39,740 --> 00:22:46,740
by 180 degree. So, to get the 180 degree,
180 degree phase shift for the B leg B; what
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we will use? The switching sequence, we will
interchange.
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That means previously we said, when sine greater
than triangle; what we say? Top switch is
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on, that was a condition we used. Then when
sine less than triangle, we will say the bottom
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00:23:37,929 --> 00:23:44,929
switch is on. So, the bottom switch is on,
it is assumed that we are switching off the
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top switch and switching on the bottom instantaneously
and we will assume the switching transitions
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are instantaneous. Now, this is for leg A,
this is the condition.
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Now, to get the 180 degree phase shift, we
will change a switching sequence for leg B.
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For the leg B the conditions are different.
For the leg B, say I will write it here, leg
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00:24:16,190 --> 00:24:23,190
B, the condition; we are using the same sine
wave, same modulating wave for both the cases.
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00:24:26,480 --> 00:24:33,480
Sine greater than triangle that is our carrier
wave Vc, Vc (t). What we are doing? Here,
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00:24:36,789 --> 00:24:43,789
according to this figure, not the top switch
is on; S4, bottom switch is on. Then, sine
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00:24:57,450 --> 00:25:04,450
less than triangle that comparison, we will
do the top that is S3 on.
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00:25:08,520 --> 00:25:15,520
So, the switching sequence is reverse, that
we will ensure that the VB1 is 180 degree
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00:25:16,530 --> 00:25:23,530
phase. This will ensure that the VB0 fundamental,
it will have the same amplitude we are using
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00:25:30,990 --> 00:25:37,990
the sine triangle amplitude. The VB0 fundamental
will be phase shifted by 180 degree with respect
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00:25:46,820 --> 00:25:53,820
to VA0 fundamental, with respect to VA0 fundamental
that is this condition, we want this condition.
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00:26:08,429 --> 00:26:15,429
So, what is the advantage? When you subtract,
this will get added. Fundamental VA0 and we
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00:26:16,450 --> 00:26:23,260
are more interested the fundamental; so fundamental,
we can control by controlling the Vm (t) for
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00:26:23,260 --> 00:26:26,460
both cases. So, fundamental we can adjust,
control it.
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00:26:26,460 --> 00:26:33,460
Now, how about the harmonics? As I told, the
harmonics, harmonics at fc and its sidebands,
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00:26:50,320 --> 00:26:57,320
we should suppress it or the harmonics, individual
harmonics from the A0 and VB0 should, we should,
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00:27:03,720 --> 00:27:10,720
both we should suppress or it should be highly
reduced. We have to suppress it or we want
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to eliminate it, suppress or eliminate. If
you see in the previous figure, the fc has
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00:27:25,400 --> 00:27:30,659
the maximum amplitude; the sine triangle PWM
fc has the maximum amplitude. So, how do let
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00:27:30,659 --> 00:27:36,190
us look at how fc can be cancelled? And, if
we can suppress the other sidebands, that
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00:27:36,190 --> 00:27:38,240
also it is okay.
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00:27:38,240 --> 00:27:45,169
So, fundamental, we should get added and how
to get the fundamental, it should get added;
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00:27:45,169 --> 00:27:52,169
we know it. Now, how to get the harmonics?
So, what we will choose? fc here, fc we will
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00:27:55,600 --> 00:28:02,600
choose as 11 times fm. That is fm is the frequency
of the sine wave, the triangular frequency
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00:28:06,350 --> 00:28:13,350
11 times that is an odd multiple. See, there
is a why odd multiple?
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00:28:14,559 --> 00:28:21,559
See, we want our output wave form proportional
to our Vm (t), sinusoidal wave form. Sinusoidal,
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00:28:22,130 --> 00:28:26,990
sinusoidal is an odd function. So, to get
the odd symmetry, the triangle wave form also
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00:28:26,990 --> 00:28:32,270
for the PWM wave form; odd symmetry means
that upper half should be exactly symmetrical
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with respect to the lower after 180 degree.
So, to get that odd symmetry, we are using
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00:28:38,870 --> 00:28:45,870
11 times. So, this is typically used. So,
fm is for a 50 hertz mains or 60 hertz mains;
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00:28:46,530 --> 00:28:53,530
11 into 50. So, around 55 so that as I told
before, the switching frequency less than
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00:28:53,820 --> 00:29:00,820
6 700 hertz is a ensured here. So, 11 times
we are using, triangle wave form and we are
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00:29:03,840 --> 00:29:10,840
using the sine triangle, VA0 the sine triangle
is like this. So, if it is this is our Vm
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00:29:14,950 --> 00:29:21,950
(t); Vm (t) both, Vm (t) is the same for both
VA0 and VB0.
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00:29:22,270 --> 00:29:29,270
So, triangle wave form, let us say, this is
the triangle wave form for the, if this is
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00:29:40,090 --> 00:29:47,090
the triangle wave form we are using for VC
(t) for phase leg A; what we will use? We
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00:29:55,620 --> 00:30:02,620
will use 180 degree phase shifted, degree,
180 degree phase shifted, 180 degree phase
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00:30:11,490 --> 00:30:18,490
shifted triangle wave that is VC (t) for leg
B. So, what is the advantage? See, this is
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00:30:27,640 --> 00:30:34,640
the wave form, that wave form will typically,
typically look like this. See, exact wave
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00:30:34,809 --> 00:30:41,809
form, 180 degree phase shifted. So, this is
for, this is the wave form for leg B and this
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00:30:52,140 --> 00:30:57,270
is the one for leg A.
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00:30:57,270 --> 00:31:04,270
Now, what will happen to the harmonics because
harmonics already, fc we said, already it
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is 11 times fm. So, the harmonic, the phase
angle, the phase relation of fc, the phase
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00:31:15,169 --> 00:31:22,120
relation of fc with respect to A and with
respect to V will be 180 degree phase shifted.
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00:31:22,120 --> 00:31:29,070
See, this how do you, how do you say 180 degree
phase shifted? Because the triangle waveform
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00:31:29,070 --> 00:31:36,070
is 180 degree phase shifted and is an odd
multiple. So, if you if you see the comparison
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00:31:37,200 --> 00:31:44,200
here, what is happening for phase A during
this period? This is what is happening. Phase
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00:31:48,539 --> 00:31:54,750
A during this period will appear; for phase
B, the final PWM waveform, it will here. So
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00:31:54,750 --> 00:32:01,750
phase, if the phase A here will be exactly
matching to phase B here because of the 180
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00:32:03,690 --> 00:32:08,870
degree phase shift. So, from the PWM waveform
we can say that the because of the triangle,
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00:32:08,870 --> 00:32:15,870
the harmonics at fc will also be 180 degree
phase shifted. So, 180 degree phase shifted
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00:32:16,340 --> 00:32:18,070
here.
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00:32:18,070 --> 00:32:25,070
So, the phase angle of the carrier wave form,
fc its 180 degree phase shifted. Then for
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00:32:26,970 --> 00:32:32,620
the phase B, there is one more phase shift
180 degree because the logic is interchanged
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00:32:32,620 --> 00:32:37,220
not the top switch when sine is greater. So,
there is one more 180 degree. So, carrier
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00:32:37,220 --> 00:32:43,679
wave form, fundamental gets 180 degree wave
form, the carrier wave form fc have a phase
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00:32:43,679 --> 00:32:50,679
shift of 180 plus 180, 360. So, the PWM, the
fc, the phase angle of fc, fc A will be equal
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00:32:56,559 --> 00:33:03,559
to fc B will also be will be equal to at the
same phase because 2 times; one is one is
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00:33:06,120 --> 00:33:08,650
triangle phase shifted.
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00:33:08,650 --> 00:33:15,650
See, we will show the simulation study of
this one later than we will verify this one.
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Triangle phase shifted by 180 degree and then
one more, the sequence of operation is also
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changed because of that is not the B phase,
not the top switch; bottom switch is on when
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sine is greater than the triangle because
of the inversion of the sequence of operation
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00:33:38,760 --> 00:33:45,760
of the switch sequence. This will also introduce
one more phase shift for the carrier frequency
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00:33:56,770 --> 00:34:02,400
wave form. So, carrier frequency for the A
phase as well as B phase will be in phase.
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00:34:02,400 --> 00:34:04,059
So, what is the advantage here?
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00:34:04,059 --> 00:34:11,059
If you see here, the fundamental component
of leg A and leg B, fundamental leg B, leg
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00:34:31,550 --> 00:34:38,550
A and leg B have a phase shift of, phase shift
of 180 degree with respect to each other.
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00:34:46,070 --> 00:34:53,070
Then but the, but the harmonics at fc will
be will not have any phase shift or that means
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00:35:10,560 --> 00:35:17,420
they are in, the phase relation between the
harmonics fc at VA0 VB0 will be the, will
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00:35:17,420 --> 00:35:24,420
be in the in same phase. The phase, the phase
difference is 0. We will not have any phase
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difference.
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00:35:28,890 --> 00:35:35,890
So, when you take the VAB wave form, that
VAB, the harmonics of the VAB wave form; we
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00:35:37,599 --> 00:35:44,599
will have the amplitude of the fundamental
will be two times the fundamental component
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00:35:46,050 --> 00:35:53,050
of the VA0 or so 2 times VA0 fundamental plus
VA0 at fc. VAB is equal to VA0 minus VB0;
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00:36:03,380 --> 00:36:09,510
so it will have fundamental will be there,
VA0 at fc will be 0 because we are subtracting.
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00:36:09,510 --> 00:36:15,930
Because of the subtraction, both have both
the fc have that the same phase, it will get
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00:36:15,930 --> 00:36:22,930
cancelled. So, fc will get cancelled. Then
what will happen to fc plus 2 fm?
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00:36:24,470 --> 00:36:31,470
See, fc is already an odd function. fc plus
2 fm will also odd. So, it will also have
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00:36:34,690 --> 00:36:41,580
the phase difference as closest 180 degree.
So, for fc, the phase difference will be exactly
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00:36:41,580 --> 00:36:46,339
like this; for other one if we can multiply
by the number and see, it may be very close,
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00:36:46,339 --> 00:36:51,869
here it will come. So, the net value will
be highly suppressed and already the sidebands
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00:36:51,869 --> 00:36:56,589
amplitudes are suppressed; so, in the VAB
wave form again because of the subtraction,
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00:36:56,589 --> 00:37:01,070
opposite effect, with a small phase difference,
it will get suppressed. This is true with
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00:37:01,070 --> 00:37:08,010
fc plus for m for fm also because it has that
is also an odd function.
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00:37:08,010 --> 00:37:15,010
So what, so what is the final conclusion from
this one, from this PWM wave form? We have
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00:37:16,700 --> 00:37:23,700
fundamental with 2 leg, 2 leg; leg A and B.
If you see here, this is Vn and fn will have
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00:37:28,089 --> 00:37:35,089
high amplitude, fundamental at fm. All the
sidebands here get cancelled. Then the next
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00:37:36,820 --> 00:37:43,820
harmonic is happens at 2 fc plus fm and 2
fc minus fm. So, next harmonic amplitudes
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00:37:51,859 --> 00:37:58,430
appearing in the current or voltage wave form
will be at the sidebands of 2 times fc. So,
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00:37:58,430 --> 00:38:05,430
there the amplitude as you go, the harmonic
order increases, the amplitude gets reduced.
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00:38:05,950 --> 00:38:12,950
So this way, properly choosing the 2 degrees
of freedom, we can have a control of the harmonics.
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00:38:15,460 --> 00:38:22,460
Now, so in that case can we suppress this
2 fc and 2 fc plus fm and 2 fc minus fm?
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00:38:23,640 --> 00:38:30,640
See, one more thing I want to tell you here;
see, if you see the harmonics, harmonic spectrum,
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00:38:36,589 --> 00:38:43,589
the Vn and the fn you have the fundamental
at fm, then the all the sidebands at fc we
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00:38:49,040 --> 00:38:56,040
got cancelled, then we said, you have the
next harmonics at happens at 2 fc plus fm
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00:38:57,440 --> 00:39:04,440
and 2 fc minus fm, then the next harmonics
at 3 fc, this is also an odd function. So,
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00:39:05,760 --> 00:39:11,520
its sidebands also get suppressed. So, all
the harmonics at fc and its odd multiple and
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00:39:11,520 --> 00:39:18,520
it sidebands get cancelled or get suppressed
from this configuration. Then we have harmonics
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00:39:20,440 --> 00:39:26,109
at the even multiple and its side sidebands
that 2 fc. So, that means again from here,
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00:39:26,109 --> 00:39:33,109
4 fc plus fm and 4 fc minus fm. Then only
we will have all other.
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00:39:35,560 --> 00:39:42,560
Here, if you see, all these harmonics get
cancelled. That is all these odd multiple
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00:39:42,890 --> 00:39:49,890
and its sidebands. That means odd multiple
and its sidebands get suppressed, highly suppressed
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00:40:06,990 --> 00:40:13,990
when we use this triangle frequency and odd
multiple of sine wave and at the same time,
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00:40:15,410 --> 00:40:22,410
the triangle wave form for B phase is 180
degree phase shifted with respect to the A
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00:40:22,630 --> 00:40:27,359
leg and the switching sequence, we are using
same fundamental but the switching sequence
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00:40:27,359 --> 00:40:31,990
is as a 180 degree phase shift for the second
phase.
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00:40:31,990 --> 00:40:36,820
So, that will make sure that the fundamental
get added and 180 degree phase shift along
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00:40:36,820 --> 00:40:40,950
with the switching sequence 180 degree, we
will see to that odd multiple and all its
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00:40:40,950 --> 00:40:47,660
sidebands have a phase difference with have
zero phase difference. So, when you subtract,
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00:40:47,660 --> 00:40:54,660
both will get from the, both legs get cancelled.
Then is there any way we can suppress or eliminate
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00:40:57,760 --> 00:41:04,760
this part? Then we require one more degree
of freedom. See, for that we should use a
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00:41:05,300 --> 00:41:11,920
configuration like this. See, let us say,
these are used for high power applications.
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00:41:11,920 --> 00:41:18,920
So, you have single phase mains here, the
configuration will be like this; this is
the transformer, this is our main, single
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00:41:25,900 --> 00:41:32,900
phase. Then we will have the one secondary
here, another secondary here. Then you have
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00:41:41,290 --> 00:41:48,290
the inductance here that is L, L here. Then
you have one converter here. Here to suppress
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00:41:51,109 --> 00:41:56,720
the next harmonics, second, harmonics at the
sidebands of second fc, we will use one more
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00:41:56,720 --> 00:42:01,020
converter in series and parallel configuration.
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00:42:01,020 --> 00:42:08,020
So, let us see, how it can be done? I think
this configuration originally done by Siemens
254
00:42:09,970 --> 00:42:16,640
for the attraction drive applications front
end ac to dc converter. So here, this front
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00:42:16,640 --> 00:42:23,640
ends mains will be around 25 KV line. This
will go here, so we have two converters. Both
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00:42:33,670 --> 00:42:40,670
will be feeding to our output dc that means
this will also go here, this will come here
257
00:42:42,750 --> 00:42:49,750
and from the other side, this will go here
and this will come here.
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00:42:55,630 --> 00:43:02,609
So, what we want? The harmonics we said, suppressed.
What do you mean by harmonics with respect
259
00:43:02,609 --> 00:43:09,359
to the first converter harmonic suppressed?
The current drawn by the first converter,
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00:43:09,359 --> 00:43:14,050
the harmonics at fc and its sidebands will
get cancelled. That means the reflected current
261
00:43:14,050 --> 00:43:21,050
from the mains, that suppressed harmonics
will be there. Now, through this converter
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00:43:21,240 --> 00:43:27,520
and interaction between these two converter
if we can suppress the second and its sidebands,
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00:43:27,520 --> 00:43:34,410
then that will if we the if the second harmonics
produced by this converter and this converter
264
00:43:34,410 --> 00:43:39,920
has a 180 degree phase difference, then this
will not reflect here. It will get cancelled
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00:43:39,920 --> 00:43:45,310
here in the transformer minty circuit and
it will and it will not reflect here and the
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00:43:45,310 --> 00:43:51,450
current drawn here will be as close as to
a sinusoidal with small ripple.
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00:43:51,450 --> 00:43:56,650
So, mains will not get corrupted and the mains
will have and we are controlling the close
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00:43:56,650 --> 00:44:01,109
loop control such that we are getting a unity
power factor also. That is a best way to drop
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00:44:01,109 --> 00:44:08,109
power from the mains. Now, the question is
how do you suppress the harmonics current?
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00:44:08,430 --> 00:44:14,960
We do not want the second harmonics because
of this one more converter is added, the second
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00:44:14,960 --> 00:44:20,210
harmonics and its sidebands, we should not
get reflected here in the primary.
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00:44:20,210 --> 00:44:24,760
So here, what we are doing; the same principle,
identical principle what we used for here,
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00:44:24,760 --> 00:44:30,270
we will be using here as far as the sine triangle
is concerned, individual phase leg A; this
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00:44:30,270 --> 00:44:37,270
is AB, this is let us say A1 B1, this is A2
B2. Same technique we will use, same modulating
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00:44:43,230 --> 00:44:49,490
wave will use. As for as the B2 switch sequence
is concerned compared to A2 that triangle
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00:44:49,490 --> 00:44:54,599
will be 90 180 degree phase shifted and the
switching sequence will be reversed. But what
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00:44:54,599 --> 00:44:56,400
we will do here?
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00:44:56,400 --> 00:45:03,400
The triangle waveform this one to this one,
second converter that is converter one, this
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00:45:04,589 --> 00:45:11,589
is we will say converter 1, this we will say
converter 2. The triangle waveform here, we
280
00:45:30,859 --> 00:45:37,859
will say, the triangle wave form of converter
2 is phase shifted by 90 degree with respect
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00:45:50,040 --> 00:45:56,560
to the converter 1. So, what you mean by 90
degree? We will draw the wave form slowly
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00:45:56,560 --> 00:46:03,500
and then find out. What is the advantage?
So, both converter, we will have fc, we will
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00:46:03,500 --> 00:46:10,500
have 2 fc plus fm and 2 fc minus fm. See,
2 fc plus fm 2 fc minus fm, here also this
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00:46:17,310 --> 00:46:24,310
converter also has sidebands at 2 fc plus
fm and 2 fc minus fm. So, 90 degree means
285
00:46:31,460 --> 00:46:38,460
what will happen? So, it is 90 degree phase
shifted with respect to the converter 1. So,
286
00:46:40,450 --> 00:46:41,690
what happens?
287
00:46:41,690 --> 00:46:48,690
The harmonics at 2 times the carrier frequency,
the harmonics at 2 fc will have 180 degree
288
00:47:05,670 --> 00:47:12,670
phase shift because it is 90 degree phase
shifted triangle, so 2 into 90 phase shifted.
289
00:47:19,660 --> 00:47:26,510
The harmonics at 2 fc will have 180 degree,
180 degree phase shifted; the harmonics at
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00:47:26,510 --> 00:47:33,510
2 fc of converter 2. Converter 2 will phase
shifted 180 with respect to converter 1. But
291
00:47:45,890 --> 00:47:52,890
so 180 degree, so 2 fc plus fm that also very
close, very close to 180 degree. That means
292
00:47:53,369 --> 00:47:57,010
as I told because if you do the harmonic,
so it will be very close, slight phase shift
293
00:47:57,010 --> 00:48:01,680
will be there because it is not exactly 2
fc, 2 fc plus fm.
294
00:48:01,680 --> 00:48:08,680
But because fc is very high, so this 2 fc
plus fm also very close to 180 degree phase
295
00:48:10,359 --> 00:48:17,359
shift; 2 fc and its sidebands will be will
be 180 degree, close to 180 degree phase shift
296
00:48:18,130 --> 00:48:25,130
as for as converter 1 and converter 2 and
the flux due to this transformer 1 and transformer
297
00:48:28,190 --> 00:48:34,220
2 will cancel here. That means it will not
get reflected here. So, the harmonics at sidebands
298
00:48:34,220 --> 00:48:41,220
of 2 fc plus fm and 2 fc minus fm and the
sidebands will get highly suppressed here.
299
00:48:41,859 --> 00:48:47,560
But not at the 4 fc, 4 fc means again 4 into
90, 360; that are in phase. But if you see
300
00:48:47,560 --> 00:48:52,810
here, 4 fc is very far away. So, that will
not have much effect. So, the fundamental
301
00:48:52,810 --> 00:48:59,810
will be very close to a sinusoidal with harmonics
due to the harmonic amplitude at 4 fc and
302
00:49:02,520 --> 00:49:09,520
its sidebands. That means what it shows? All
the harmonics at fc and sidebands and 2 fc
303
00:49:09,970 --> 00:49:16,970
and sidebands, 3 fc and 3 fc sidebands that
means what it shows because of this one, we
304
00:49:17,400 --> 00:49:21,920
can finally summarize. Now, so what are the
advantages here?
305
00:49:21,920 --> 00:49:28,920
So, we will conclude. So, we have two converters
connected parallel to the load and the sine
306
00:49:29,829 --> 00:49:35,640
triangle PWM we are using and the triangle
wave form, we are properly phase shifting
307
00:49:35,640 --> 00:49:40,810
and the sequence of operation with respect
to one converter; the leg for A and B, we
308
00:49:40,810 --> 00:49:45,170
are interchanging. So, what happens, this
conclusion?
309
00:49:45,170 --> 00:49:52,170
Fundamental
get added and all harmonics; harmonics at
fc, fc plus or minus fm, then 3 fc plus or
310
00:50:15,440 --> 00:50:22,440
minus fm, fm, 3 fm, all that bands, then?
sorry fc plus 2 fm and fc plus? Plus or minus
311
00:50:33,260 --> 00:50:40,260
2 fm that is because when this is odd, this
has to be even. Here, two fc minus fm plus
312
00:50:47,380 --> 00:50:54,380
or minus fm and all other odd multiple of
fm plus minus 2 fc get cancelled and the current
313
00:51:08,460 --> 00:51:15,460
drawn from the mains that is our single phase
line from the mains will be sinusoidal, close
314
00:51:28,280 --> 00:51:35,280
to a sinusoid with harmonic amplitudes, with
harmonics at 4 fc plus or minus fm. This very
315
00:51:43,300 --> 00:51:49,980
far away also with control that is close loop
control, we are also trying to get unity power
316
00:51:49,980 --> 00:51:56,980
factor. That means the fundamental current
is in phase with the mains force, unity power
317
00:51:58,630 --> 00:52:03,000
factor also.
318
00:52:03,000 --> 00:52:08,980
This is a standard ac t, very ac to dc converter
used for traction drive application. I think
319
00:52:08,980 --> 00:52:14,960
originally it is used by the Siemens for attraction
drive application where they used 11 times
320
00:52:14,960 --> 00:52:21,960
fm; fm is 50 hertz, 11 times fm used for the
carrier frequency and they suppress and suppressed
321
00:52:23,000 --> 00:52:23,900
all these harmonics.
322
00:52:23,900 --> 00:52:30,609
Now, you have close loop control of this one
to get unity power factor and how to form
323
00:52:30,609 --> 00:52:34,680
like the close loop control. Before coming
to the close loop control, how we design the
324
00:52:34,680 --> 00:52:40,220
C value and L value. We will study in the
next class. Then once the design part is over;
325
00:52:40,220 --> 00:52:45,160
what are the basis for designing the L value
and C. Then for then close loop control, how
326
00:52:45,160 --> 00:52:50,000
do you form the close loop and how do you
design the close loop parameter in the subsequent
327
00:52:50,000 --> 00:52:53,900
classes.
328
00:52:53,900 --> 00:53:00,900
Thank you.