WEBVTT 00:00:00.000 --> 00:00:01.904 align:middle line:90% [SQUEAKING] 00:00:01.904 --> 00:00:04.284 align:middle line:90% [RUSTLING] 00:00:04.284 --> 00:00:06.664 align:middle line:90% [CLICKING] 00:00:06.664 --> 00:00:08.568 align:middle line:90% 00:00:08.568 --> 00:00:11.990 align:middle line:84% DAVID PERREAULT: OK, why don't we get started? 00:00:11.990 --> 00:00:15.620 align:middle line:84% So we're going to continue talking about three-phase power 00:00:15.620 --> 00:00:16.650 align:middle line:90% conversion systems. 00:00:16.650 --> 00:00:19.580 align:middle line:84% And I should have noted that what we're talking about 00:00:19.580 --> 00:00:23.570 align:middle line:84% is contained in Principles of Power Electronics chapter 9 00:00:23.570 --> 00:00:24.980 align:middle line:90% for reading. 00:00:24.980 --> 00:00:28.250 align:middle line:84% And just as a reminder, we talked last time 00:00:28.250 --> 00:00:31.070 align:middle line:84% about all the advantages you can get from three-phase systems, 00:00:31.070 --> 00:00:34.010 align:middle line:90% and we'll see that again today. 00:00:34.010 --> 00:00:39.830 align:middle line:84% But just to remind you, I might have three voltage sources-- 00:00:39.830 --> 00:00:48.810 align:middle line:84% Va, Vb, these are all of t, and Vc. 00:00:48.810 --> 00:00:54.000 align:middle line:90% 00:00:54.000 --> 00:00:57.810 align:middle line:84% I bring out three phases, and I may also have a neutral. 00:00:57.810 --> 00:01:08.610 align:middle line:84% And if I wrote Va of t is equal to Vs sine omega t, Vb of t 00:01:08.610 --> 00:01:14.500 align:middle line:84% is equal to Vs sine of omega t minus 2 pi over 3, 00:01:14.500 --> 00:01:20.250 align:middle line:84% so 120 degrees lagging, and then Vc of t 00:01:20.250 --> 00:01:26.970 align:middle line:84% is equal to Vs sine of omega t plus 2 pi over 3, 00:01:26.970 --> 00:01:32.520 align:middle line:84% so this might be 240 degrees lagging or 120 degrees leading, 00:01:32.520 --> 00:01:35.160 align:middle line:84% depending upon how you would like to look at it. 00:01:35.160 --> 00:01:43.810 align:middle line:84% We said we could represent any such individual signal 00:01:43.810 --> 00:01:45.070 align:middle line:90% as a phasor. 00:01:45.070 --> 00:01:51.790 align:middle line:84% So we might say Vx of t is equal to the real part of Vx hat, 00:01:51.790 --> 00:01:55.090 align:middle line:84% which is the phasor, e to the j omega t, 00:01:55.090 --> 00:01:59.920 align:middle line:84% which represents the sinusoidal nature of it. 00:01:59.920 --> 00:02:05.280 align:middle line:84% So Vx hat contains the magnitude and phase. 00:02:05.280 --> 00:02:11.170 align:middle line:84% So for example, in this example, VA hat 00:02:11.170 --> 00:02:15.910 align:middle line:84% would be equal to Vs, its magnitude, 00:02:15.910 --> 00:02:20.350 align:middle line:84% e to the minus j pi over 2, because with respect 00:02:20.350 --> 00:02:22.300 align:middle line:84% to the real part or with respect to a cosine, 00:02:22.300 --> 00:02:25.330 align:middle line:84% it's phase shifted by minus pi over 2. 00:02:25.330 --> 00:02:29.500 align:middle line:84% And I could make equivalent phase-shifted versions 00:02:29.500 --> 00:02:31.540 align:middle line:90% for VB hat and VC hat. 00:02:31.540 --> 00:02:37.360 align:middle line:84% And if we draw that on a phasor diagram, what I might get 00:02:37.360 --> 00:02:38.570 align:middle line:90% is something like this. 00:02:38.570 --> 00:02:41.470 align:middle line:84% So now I'm going to put it in the phase plane. 00:02:41.470 --> 00:02:46.440 align:middle line:84% And I'll have the real axis and the imaginary axis. 00:02:46.440 --> 00:02:50.920 align:middle line:90% So VA hat will look like this. 00:02:50.920 --> 00:02:51.540 align:middle line:90% It's a sine. 00:02:51.540 --> 00:02:55.770 align:middle line:90% 00:02:55.770 --> 00:03:01.080 align:middle line:84% VB hat would be like this, 120 degrees shifted. 00:03:01.080 --> 00:03:04.410 align:middle line:90% 00:03:04.410 --> 00:03:07.055 align:middle line:90% And VC hat would look like this. 00:03:07.055 --> 00:03:11.190 align:middle line:90% 00:03:11.190 --> 00:03:14.410 align:middle line:84% And we said, OK, these are the phasors. 00:03:14.410 --> 00:03:16.290 align:middle line:84% These represent the magnitude and phase 00:03:16.290 --> 00:03:18.010 align:middle line:90% of the individual signals. 00:03:18.010 --> 00:03:21.300 align:middle line:84% And then when I multiply by e to the j omega t, 00:03:21.300 --> 00:03:25.980 align:middle line:84% I'm essentially rotating it by an angle omega t. 00:03:25.980 --> 00:03:27.810 align:middle line:84% And to get the instantaneous time values, 00:03:27.810 --> 00:03:29.970 align:middle line:84% these guys are rotating, and I take the projection 00:03:29.970 --> 00:03:31.390 align:middle line:90% onto the real axis. 00:03:31.390 --> 00:03:36.780 align:middle line:84% So at t equals 0, sine omega t is not rotated. 00:03:36.780 --> 00:03:38.980 align:middle line:90% Sine omega t just projects to 0. 00:03:38.980 --> 00:03:43.180 align:middle line:84% If I weighted 90 degrees or omega t is equal to 90 degrees, 00:03:43.180 --> 00:03:45.740 align:middle line:84% VA hat would have rotated up here. 00:03:45.740 --> 00:03:48.850 align:middle line:84% I'd project it onto the real axis, and I'd get Vs. 00:03:48.850 --> 00:03:52.357 align:middle line:84% So we often think about three-phase systems 00:03:52.357 --> 00:03:53.440 align:middle line:90% in terms of their phasors. 00:03:53.440 --> 00:03:57.305 align:middle line:84% And the benefit is we can add and subtract phasors 00:03:57.305 --> 00:03:58.930 align:middle line:84% when we're combining signals, and we'll 00:03:58.930 --> 00:04:00.610 align:middle line:84% see that we'll do that a lot in order 00:04:00.610 --> 00:04:04.570 align:middle line:84% to figure out different combinations of things. 00:04:04.570 --> 00:04:07.990 align:middle line:84% So this is just a little bit of a review of last class. 00:04:07.990 --> 00:04:17.740 align:middle line:84% We also said that in addition to considering just the line 00:04:17.740 --> 00:04:22.029 align:middle line:84% to neutral voltages, I might also 00:04:22.029 --> 00:04:25.060 align:middle line:84% think about the line-to-line voltages. 00:04:25.060 --> 00:04:29.230 align:middle line:84% So I might think of, for example, 00:04:29.230 --> 00:04:34.690 align:middle line:84% the voltage between here and here as being VCB. 00:04:34.690 --> 00:04:38.120 align:middle line:84% If I looked at VCB, what would VCB look like? 00:04:38.120 --> 00:04:50.460 align:middle line:84% It would be VC minus VB or VC plus negative VB. 00:04:50.460 --> 00:04:51.900 align:middle line:84% So just take the opposite of that. 00:04:51.900 --> 00:04:57.495 align:middle line:90% And I would get VCB hat. 00:04:57.495 --> 00:05:01.470 align:middle line:90% 00:05:01.470 --> 00:05:06.900 align:middle line:84% And I could likewise get two other phasors, 00:05:06.900 --> 00:05:14.310 align:middle line:90% like this and like this. 00:05:14.310 --> 00:05:16.918 align:middle line:90% Actually, let me look at that. 00:05:16.918 --> 00:05:18.460 align:middle line:84% I think-- yeah, I did get that wrong. 00:05:18.460 --> 00:05:19.710 align:middle line:90% VBA goes that way. 00:05:19.710 --> 00:05:25.834 align:middle line:90% 00:05:25.834 --> 00:05:28.790 align:middle line:84% I should be careful with my angles here. 00:05:28.790 --> 00:05:29.680 align:middle line:90% It goes this way. 00:05:29.680 --> 00:05:32.210 align:middle line:90% 00:05:32.210 --> 00:05:38.270 align:middle line:84% So these guys have a 30-degree phase shift. 00:05:38.270 --> 00:05:40.163 align:middle line:90% These angles are 30 degrees. 00:05:40.163 --> 00:05:46.420 align:middle line:90% 00:05:46.420 --> 00:05:48.220 align:middle line:84% Actually, this is 30 degrees from this guy, 00:05:48.220 --> 00:05:49.260 align:middle line:90% so I should be careful. 00:05:49.260 --> 00:05:52.840 align:middle line:90% 00:05:52.840 --> 00:05:56.710 align:middle line:90% So VCB is going to be a cosine. 00:05:56.710 --> 00:06:01.390 align:middle line:84% VAC hat is going to be phase shifted here. 00:06:01.390 --> 00:06:06.210 align:middle line:84% And VBA hat is going to be phase shifted here. 00:06:06.210 --> 00:06:12.100 align:middle line:84% So what I end up with is a 30-degree phase shift. 00:06:12.100 --> 00:06:16.090 align:middle line:84% And the length of these phasors is going to be the square root 00:06:16.090 --> 00:06:17.920 align:middle line:90% of 3Vs. 00:06:17.920 --> 00:06:20.890 align:middle line:84% So if I look at the line-to-line voltages, 00:06:20.890 --> 00:06:22.720 align:middle line:84% they are square root of three larger 00:06:22.720 --> 00:06:24.370 align:middle line:84% than the line of neutral voltages, 00:06:24.370 --> 00:06:27.050 align:middle line:84% and they are phase shifted by 30 degrees. 00:06:27.050 --> 00:06:29.830 align:middle line:84% And in fact, how do we get these? 00:06:29.830 --> 00:06:34.240 align:middle line:84% We're essentially taking differences of two voltages. 00:06:34.240 --> 00:06:36.010 align:middle line:84% But if we use transformers, we can 00:06:36.010 --> 00:06:41.350 align:middle line:84% add any kind of combinations of VA and VB and VC. 00:06:41.350 --> 00:06:44.800 align:middle line:84% And we could construct arbitrarily 00:06:44.800 --> 00:06:47.450 align:middle line:84% phase-shifted versions of these waveforms. 00:06:47.450 --> 00:06:49.910 align:middle line:84% And that's kind of a neat trick that gets used a lot. 00:06:49.910 --> 00:06:53.580 align:middle line:84% And we'll see one little step of how you might do that today. 00:06:53.580 --> 00:06:57.470 align:middle line:90% 00:06:57.470 --> 00:07:04.010 align:middle line:84% So that's a quick summary of, OK, 00:07:04.010 --> 00:07:07.760 align:middle line:84% what do these three-phase waveforms look like? 00:07:07.760 --> 00:07:09.800 align:middle line:84% And we're going to see that now I have lots 00:07:09.800 --> 00:07:11.880 align:middle line:90% of wires, lots of voltages. 00:07:11.880 --> 00:07:13.490 align:middle line:84% It becomes a little bit complicated 00:07:13.490 --> 00:07:14.837 align:middle line:90% to keep track of everything. 00:07:14.837 --> 00:07:16.670 align:middle line:84% And so what we'll see is people have come up 00:07:16.670 --> 00:07:19.670 align:middle line:84% with means of keeping track of what's 00:07:19.670 --> 00:07:22.920 align:middle line:84% going on with the different phase voltages. 00:07:22.920 --> 00:07:26.360 align:middle line:84% So why don't we start talking about power electronics using 00:07:26.360 --> 00:07:27.600 align:middle line:90% three phase? 00:07:27.600 --> 00:07:29.210 align:middle line:84% And I thought a nice place to start 00:07:29.210 --> 00:07:32.060 align:middle line:84% would be to start with simple rectifiers. 00:07:32.060 --> 00:07:34.760 align:middle line:84% At the beginning of class, we talked about AC, 00:07:34.760 --> 00:07:37.560 align:middle line:84% and we had single-phase rectifiers. 00:07:37.560 --> 00:07:41.000 align:middle line:84% Let's compare and contrast a three-phase rectifier 00:07:41.000 --> 00:07:44.000 align:middle line:90% to a single-phase rectifier. 00:07:44.000 --> 00:07:49.370 align:middle line:84% So we want something that's going to convert AC to DC. 00:07:49.370 --> 00:07:53.240 align:middle line:90% So what might that look like? 00:07:53.240 --> 00:07:58.590 align:middle line:84% Perhaps I could construct something that looked like this. 00:07:58.590 --> 00:08:00.370 align:middle line:90% Here's the simplest notion. 00:08:00.370 --> 00:08:10.760 align:middle line:84% Suppose I took Va with respect to the neutral, Vb with respect 00:08:10.760 --> 00:08:12.200 align:middle line:90% to the neutral-- 00:08:12.200 --> 00:08:14.030 align:middle line:84% and maybe I won't mark it as ground, 00:08:14.030 --> 00:08:15.570 align:middle line:90% but I'll mark it with an x-- 00:08:15.570 --> 00:08:20.700 align:middle line:84% Vc with respect to the neutral, and Vc with respect 00:08:20.700 --> 00:08:21.325 align:middle line:90% to the neutral. 00:08:21.325 --> 00:08:25.430 align:middle line:90% 00:08:25.430 --> 00:08:29.050 align:middle line:84% And why don't I just put a diode from each? 00:08:29.050 --> 00:08:32.675 align:middle line:90% 00:08:32.675 --> 00:08:35.840 align:middle line:84% This would be the equivalent, the three-phase equivalent 00:08:35.840 --> 00:08:37.789 align:middle line:90% of a half-wave rectifier. 00:08:37.789 --> 00:08:40.429 align:middle line:84% And now I'll connect this up and maybe I 00:08:40.429 --> 00:08:42.950 align:middle line:84% connect it to a big inductor LD, so I 00:08:42.950 --> 00:08:46.830 align:middle line:90% get an almost DC current Id. 00:08:46.830 --> 00:08:49.375 align:middle line:84% And we'll connect that back to here. 00:08:49.375 --> 00:08:53.940 align:middle line:90% 00:08:53.940 --> 00:08:58.220 align:middle line:84% And clearly I have my load resistor here, RL. 00:08:58.220 --> 00:09:02.220 align:middle line:84% So what would this thing do ideally? 00:09:02.220 --> 00:09:06.360 align:middle line:84% Well, basically, whichever diode is going to be on 00:09:06.360 --> 00:09:11.460 align:middle line:84% is going to be the maximum of Va, Vb, and Vc. 00:09:11.460 --> 00:09:14.040 align:middle line:90% So if I call this-- 00:09:14.040 --> 00:09:19.000 align:middle line:84% let me call this just for nomenclature Vd1-- 00:09:19.000 --> 00:09:32.080 align:middle line:84% Vd1 is simply equal to the maximum of Va, Vb, and Vc, 00:09:32.080 --> 00:09:34.770 align:middle line:84% because this diode is going to or things. 00:09:34.770 --> 00:09:40.140 align:middle line:84% The method of assumed states with diodes would tell you that. 00:09:40.140 --> 00:09:42.940 align:middle line:84% So what are these things-- what do these waveforms look like? 00:09:42.940 --> 00:09:46.350 align:middle line:84% What would that output Vd1 look like? 00:09:46.350 --> 00:09:48.690 align:middle line:90% So let me plot these things. 00:09:48.690 --> 00:09:54.090 align:middle line:90% If I said Va was a sine wave-- 00:09:54.090 --> 00:09:55.570 align:middle line:84% so the sine wave looks like this. 00:09:55.570 --> 00:09:58.020 align:middle line:84% And just for reference, when I plot these things 00:09:58.020 --> 00:10:00.720 align:middle line:84% for three-phase stuff, it's often convenient to break things 00:10:00.720 --> 00:10:05.047 align:middle line:84% up into pi over 6 integrals, 30-degree intervals, 00:10:05.047 --> 00:10:06.880 align:middle line:84% just because it becomes easy to plot things. 00:10:06.880 --> 00:10:09.900 align:middle line:84% So if I took Va, it would look like something like this. 00:10:09.900 --> 00:10:20.210 align:middle line:90% 00:10:20.210 --> 00:10:24.440 align:middle line:84% And here's the pain of dealing with three-phase systems is 00:10:24.440 --> 00:10:28.000 align:middle line:84% you've got lots of waveforms to plot. 00:10:28.000 --> 00:10:30.130 align:middle line:90% So forth. 00:10:30.130 --> 00:10:37.900 align:middle line:84% Vb would just be Va lagged by 120 degrees or 4 pi over 6-- 00:10:37.900 --> 00:10:40.000 align:middle line:90% 1, 2, 3, 4 units here. 00:10:40.000 --> 00:10:41.985 align:middle line:84% So it would be doing something like this. 00:10:41.985 --> 00:10:58.920 align:middle line:90% 00:10:58.920 --> 00:11:00.700 align:middle line:90% So Vb would look like this. 00:11:00.700 --> 00:11:04.360 align:middle line:90% 00:11:04.360 --> 00:11:10.170 align:middle line:84% And then Vc would be, again, a log-- another 1, 2, 3, 4. 00:11:10.170 --> 00:11:12.125 align:middle line:84% So it would look something like this. 00:11:12.125 --> 00:11:31.000 align:middle line:90% 00:11:31.000 --> 00:11:33.760 align:middle line:84% And what this equivalent to the half-wave rectifier-- what 00:11:33.760 --> 00:11:34.880 align:middle line:90% would it do? 00:11:34.880 --> 00:11:45.760 align:middle line:84% So if this is Va, this is Vb, and this is Vc, 00:11:45.760 --> 00:11:49.780 align:middle line:84% all this half-wave rectifier would 00:11:49.780 --> 00:11:53.170 align:middle line:84% do would be to pick off a Vd1 that's 00:11:53.170 --> 00:11:57.320 align:middle line:84% just the maximum, whichever voltage is the maximum. 00:11:57.320 --> 00:12:07.620 align:middle line:84% So Vd1 would look like this and so forth. 00:12:07.620 --> 00:12:11.010 align:middle line:90% So this is Vd1. 00:12:11.010 --> 00:12:14.890 align:middle line:84% OK, does that make sense to everybody? 00:12:14.890 --> 00:12:22.210 align:middle line:84% Now, this kind of equivalent to a half-wave rectifier 00:12:22.210 --> 00:12:26.860 align:middle line:84% is maybe one step of what you could do. 00:12:26.860 --> 00:12:30.250 align:middle line:84% But what would happen if I then said, 00:12:30.250 --> 00:12:34.390 align:middle line:84% well, let me not connect it this way, 00:12:34.390 --> 00:12:38.470 align:middle line:84% but let me just connect it differentially. 00:12:38.470 --> 00:12:42.190 align:middle line:84% So I'll connect my inductor here, 00:12:42.190 --> 00:12:49.570 align:middle line:84% and then I'll go to another set of diodes like this 00:12:49.570 --> 00:12:58.120 align:middle line:84% and connect this to Va, Vb, and Vc. 00:12:58.120 --> 00:13:02.641 align:middle line:90% 00:13:02.641 --> 00:13:04.790 align:middle line:84% And now I'm going to make my output-- 00:13:04.790 --> 00:13:09.290 align:middle line:84% I'll make this VD2, and I'll make this voltage VD. 00:13:09.290 --> 00:13:12.964 align:middle line:90% 00:13:12.964 --> 00:13:15.740 align:middle line:84% So if this set of diodes made Vd1 00:13:15.740 --> 00:13:20.930 align:middle line:84% the maximum of Va, Vb, and Vc, what would this set of diodes 00:13:20.930 --> 00:13:21.430 align:middle line:90% do? 00:13:21.430 --> 00:13:28.440 align:middle line:90% 00:13:28.440 --> 00:13:30.630 align:middle line:84% This is making-- this one will forward 00:13:30.630 --> 00:13:34.320 align:middle line:90% bias with whoever's largest. 00:13:34.320 --> 00:13:37.440 align:middle line:84% Can anybody see what this is going to do? 00:13:37.440 --> 00:13:40.402 align:middle line:90% Which diode is going to turn on? 00:13:40.402 --> 00:13:41.770 align:middle line:90% AUDIENCE: Minimum. 00:13:41.770 --> 00:13:43.978 align:middle line:84% DAVID PERREAULT: It's going to be the minimum, right. 00:13:43.978 --> 00:13:46.150 align:middle line:84% Whichever voltage is lowest between Va, Vb, 00:13:46.150 --> 00:13:47.980 align:middle line:90% and Vc is going to turn on. 00:13:47.980 --> 00:13:56.470 align:middle line:84% So Vd2 is going to equal the minimum of Va, Vb, and Vc. 00:13:56.470 --> 00:14:00.160 align:middle line:90% 00:14:00.160 --> 00:14:05.860 align:middle line:84% So this guy over here would come off and pick off 00:14:05.860 --> 00:14:08.440 align:middle line:90% the bottom of these guys. 00:14:08.440 --> 00:14:10.570 align:middle line:84% So it might come off and say I'm going to-- 00:14:10.570 --> 00:14:17.230 align:middle line:84% I'm going to select this and this and this. 00:14:17.230 --> 00:14:18.160 align:middle line:90% So here's Vd2. 00:14:18.160 --> 00:14:20.890 align:middle line:90% 00:14:20.890 --> 00:14:23.950 align:middle line:84% And sorry, I know that's not a very visible color. 00:14:23.950 --> 00:14:26.950 align:middle line:84% So I got one set of three diodes picking off 00:14:26.950 --> 00:14:30.010 align:middle line:84% the maximum, the other set of diodes picking off the minimum. 00:14:30.010 --> 00:14:32.800 align:middle line:84% And the voltage across my filter inductor 00:14:32.800 --> 00:14:36.220 align:middle line:84% LD, which is going to give me my approximate-- 00:14:36.220 --> 00:14:39.130 align:middle line:84% this is LD here, and I'm going to get an approximately 00:14:39.130 --> 00:14:42.040 align:middle line:84% constant current that I'm going to call ID-- 00:14:42.040 --> 00:14:47.080 align:middle line:84% is really driven by the difference between Vd1 and Vd2. 00:14:47.080 --> 00:14:58.060 align:middle line:84% So VD is equal to the max of Va, Vb, and Vc 00:14:58.060 --> 00:15:07.960 align:middle line:84% minus the minimum of Va, Vb, and Vc. 00:15:07.960 --> 00:15:10.810 align:middle line:84% Now, clearly I'm not using different voltage sources, Va, 00:15:10.810 --> 00:15:11.840 align:middle line:90% Vb, and Vc. 00:15:11.840 --> 00:15:16.000 align:middle line:84% I'm just connecting this back over to here, for example. 00:15:16.000 --> 00:15:19.230 align:middle line:84% Does that make sense to everybody? 00:15:19.230 --> 00:15:23.700 align:middle line:84% So if I did that, it turns out that this 00:15:23.700 --> 00:15:31.920 align:middle line:84% is the same thing as the maximum of the line-to-line voltages 00:15:31.920 --> 00:15:33.580 align:middle line:90% and their negatives. 00:15:33.580 --> 00:15:36.924 align:middle line:90% 00:15:36.924 --> 00:15:40.320 align:middle line:84% So let's take a look at that, and let me just 00:15:40.320 --> 00:15:44.790 align:middle line:84% express that slightly differently just 00:15:44.790 --> 00:15:48.390 align:middle line:90% so you can see it. 00:15:48.390 --> 00:15:51.280 align:middle line:84% I'm going to draw a little bit differently. 00:15:51.280 --> 00:15:54.780 align:middle line:84% I'm going to draw this same circuit. 00:15:54.780 --> 00:15:57.120 align:middle line:90% It's got six diodes in it. 00:15:57.120 --> 00:16:01.690 align:middle line:84% And let me draw that over here just so we can see it. 00:16:01.690 --> 00:16:04.950 align:middle line:84% So here I have-- it's going to look a little less messy now. 00:16:04.950 --> 00:16:07.410 align:middle line:90% Here's my neutral connection. 00:16:07.410 --> 00:16:15.870 align:middle line:84% I'm going to have Va and then two diodes, 00:16:15.870 --> 00:16:20.430 align:middle line:84% one picking the positive, one picking the negative; 00:16:20.430 --> 00:16:28.140 align:middle line:84% Vb, one picking the positive, one picking the negative; 00:16:28.140 --> 00:16:33.090 align:middle line:90% and Vc, one picking-- 00:16:33.090 --> 00:16:36.090 align:middle line:84% this is Vc, one picking the positive and one picking 00:16:36.090 --> 00:16:38.856 align:middle line:90% the negative. 00:16:38.856 --> 00:16:44.130 align:middle line:84% And now I'm going to have my filter inductor, Ld, 00:16:44.130 --> 00:16:48.420 align:middle line:84% my almost DC current Id, and then my output voltage. 00:16:48.420 --> 00:16:51.710 align:middle line:84% And this is the voltage that we've been calling V sub d. 00:16:51.710 --> 00:16:54.561 align:middle line:90% 00:16:54.561 --> 00:16:57.410 align:middle line:84% So that's just a different way to draw the same thing. 00:16:57.410 --> 00:17:00.294 align:middle line:90% 00:17:00.294 --> 00:17:06.400 align:middle line:84% But what we can see is this voltage Vd 00:17:06.400 --> 00:17:13.140 align:middle line:84% is going to be whichever is the maximum of Va, Vb, Vc goes here. 00:17:13.140 --> 00:17:18.690 align:middle line:84% And the minimum of Va, Vb, and Vc is here. 00:17:18.690 --> 00:17:27.920 align:middle line:84% So I'm really driving this thing with the line-to-line voltages. 00:17:27.920 --> 00:17:32.810 align:middle line:84% In other words, the differences between Va, Vb, and Vc 00:17:32.810 --> 00:17:38.660 align:middle line:84% are what are driving this rectifier. 00:17:38.660 --> 00:17:45.830 align:middle line:84% And so we could actually draw this as something 00:17:45.830 --> 00:17:46.840 align:middle line:90% slightly different. 00:17:46.840 --> 00:17:49.230 align:middle line:84% We could rewrite how this is done. 00:17:49.230 --> 00:17:51.920 align:middle line:84% And let me add a little bit of context 00:17:51.920 --> 00:17:53.550 align:middle line:84% on this that'll make sense in a second. 00:17:53.550 --> 00:17:55.420 align:middle line:84% Let me give these diodes numbers. 00:17:55.420 --> 00:18:07.170 align:middle line:84% This is D1, D4, D3, D6, and D5, and D2. 00:18:07.170 --> 00:18:11.430 align:middle line:84% And I'm picking these numbers for a very specific reason. 00:18:11.430 --> 00:18:14.230 align:middle line:84% And we're going to see this in a minute. 00:18:14.230 --> 00:18:18.070 align:middle line:84% But basically, this is going to pick off 00:18:18.070 --> 00:18:20.350 align:middle line:84% the maximum of the line-to-line voltages 00:18:20.350 --> 00:18:24.010 align:middle line:84% and the maximum of the negative of the line-to-line voltages. 00:18:24.010 --> 00:18:31.000 align:middle line:84% So that's essentially the same as this characteristic here. 00:18:31.000 --> 00:18:34.030 align:middle line:84% So let me draw what that would look like, 00:18:34.030 --> 00:18:36.720 align:middle line:84% and maybe this thing will become a little bit more clear. 00:18:36.720 --> 00:18:39.640 align:middle line:90% 00:18:39.640 --> 00:18:42.413 align:middle line:84% So let me now plot the line-to-line voltages. 00:18:42.413 --> 00:19:07.024 align:middle line:90% 00:19:07.024 --> 00:19:10.290 align:middle line:84% And again, I apologize for lots of sketching here, 00:19:10.290 --> 00:19:12.650 align:middle line:84% but that's just the way it is with three-phase systems. 00:19:12.650 --> 00:19:21.380 align:middle line:90% 00:19:21.380 --> 00:19:25.580 align:middle line:84% OK, let's come back and look at our line-to-line voltages. 00:19:25.580 --> 00:19:29.600 align:middle line:90% OK, here we go. 00:19:29.600 --> 00:19:34.390 align:middle line:84% At t equals 0, VCB is at a maximum. 00:19:34.390 --> 00:19:37.823 align:middle line:84% So VCB is going to look like this. 00:19:37.823 --> 00:20:01.470 align:middle line:90% 00:20:01.470 --> 00:20:03.215 align:middle line:90% And so VCB looks like this. 00:20:03.215 --> 00:20:13.850 align:middle line:90% 00:20:13.850 --> 00:20:14.965 align:middle line:90% So this is VCB. 00:20:14.965 --> 00:20:19.520 align:middle line:90% 00:20:19.520 --> 00:20:25.180 align:middle line:84% The next line-to-line voltage phase that rolls around is VAC. 00:20:25.180 --> 00:20:32.690 align:middle line:90% And he's delayed by 2 pi over 3. 00:20:32.690 --> 00:20:34.510 align:middle line:90% So 1, 2, 3, 4. 00:20:34.510 --> 00:20:36.705 align:middle line:84% He's going to be his maximums here. 00:20:36.705 --> 00:21:01.436 align:middle line:90% 00:21:01.436 --> 00:21:03.490 align:middle line:84% So he's going to do something like this. 00:21:03.490 --> 00:21:08.900 align:middle line:90% 00:21:08.900 --> 00:21:10.720 align:middle line:84% And we said this was going to be VAC. 00:21:10.720 --> 00:21:15.830 align:middle line:90% 00:21:15.830 --> 00:21:19.430 align:middle line:84% And then the next one to rotate around is VBA. 00:21:19.430 --> 00:21:21.000 align:middle line:90% So let me put him on. 00:21:21.000 --> 00:21:26.030 align:middle line:84% VBA is going to be delayed by another four units, 1, 2, 3, 4. 00:21:26.030 --> 00:21:27.600 align:middle line:90% 1, 2, 3, 4. 00:21:27.600 --> 00:21:29.440 align:middle line:84% And he's going to be at maximum here, 00:21:29.440 --> 00:21:31.210 align:middle line:84% so he's going to do something like this. 00:21:31.210 --> 00:21:50.480 align:middle line:90% 00:21:50.480 --> 00:21:52.170 align:middle line:90% And we said that was VBA. 00:21:52.170 --> 00:21:57.860 align:middle line:90% 00:21:57.860 --> 00:22:01.780 align:middle line:84% Now, what is this rectifier going to do? 00:22:01.780 --> 00:22:04.040 align:middle line:84% I said it was going to pick off the maximum 00:22:04.040 --> 00:22:07.880 align:middle line:84% of the line-to-line voltages and the maximum of the negatives 00:22:07.880 --> 00:22:11.356 align:middle line:90% of the line-to-line voltages. 00:22:11.356 --> 00:22:18.040 align:middle line:84% So if you wanted to look at it as things rotating around, 00:22:18.040 --> 00:22:21.960 align:middle line:84% we had our line-to-line set that looked like this. 00:22:21.960 --> 00:22:24.550 align:middle line:90% 00:22:24.550 --> 00:22:26.385 align:middle line:90% Here's our line-to-line set. 00:22:26.385 --> 00:22:30.610 align:middle line:90% 00:22:30.610 --> 00:22:32.180 align:middle line:90% So this is-- right? 00:22:32.180 --> 00:22:34.540 align:middle line:90% This is VCB. 00:22:34.540 --> 00:22:36.010 align:middle line:90% This is VBA hat. 00:22:36.010 --> 00:22:38.710 align:middle line:90% 00:22:38.710 --> 00:22:41.530 align:middle line:90% And this is VAC hat. 00:22:41.530 --> 00:22:43.570 align:middle line:90% But I also have his negatives. 00:22:43.570 --> 00:22:49.990 align:middle line:84% So I have the opposite here that looks like this. 00:22:49.990 --> 00:22:54.310 align:middle line:90% So this is V hat CA. 00:22:54.310 --> 00:22:55.880 align:middle line:90% This is V hat BA. 00:22:55.880 --> 00:23:00.220 align:middle line:90% 00:23:00.220 --> 00:23:02.610 align:middle line:90% And this is V hat BC. 00:23:02.610 --> 00:23:05.890 align:middle line:90% 00:23:05.890 --> 00:23:10.510 align:middle line:84% So essentially I could think of this thing rotating in time, 00:23:10.510 --> 00:23:12.970 align:middle line:84% both the orange and yellow, that the line-to-line 00:23:12.970 --> 00:23:15.310 align:middle line:84% and its negatives, and the rectifier 00:23:15.310 --> 00:23:16.780 align:middle line:84% is just going to pick off whichever 00:23:16.780 --> 00:23:20.540 align:middle line:90% is maximum at any given time. 00:23:20.540 --> 00:23:27.770 align:middle line:84% So if I have, for example, here is VBA, 00:23:27.770 --> 00:23:29.995 align:middle line:90% VAB does something like this. 00:23:29.995 --> 00:23:35.800 align:middle line:90% 00:23:35.800 --> 00:23:42.045 align:middle line:84% If I have VCB, VBC does something like this. 00:23:42.045 --> 00:23:45.160 align:middle line:90% 00:23:45.160 --> 00:23:52.650 align:middle line:84% And if I have VAC, I have VCA does something like this. 00:23:52.650 --> 00:23:57.820 align:middle line:90% 00:23:57.820 --> 00:24:00.700 align:middle line:84% And what this rectifier is going to do 00:24:00.700 --> 00:24:12.830 align:middle line:84% if I want to now come get Vd, this voltage Vd 00:24:12.830 --> 00:24:16.132 align:middle line:84% is going to just be the maximum of all the line 00:24:16.132 --> 00:24:17.340 align:middle line:90% to lines and their negatives. 00:24:17.340 --> 00:24:19.090 align:middle line:84% So it's going to do something like this. 00:24:19.090 --> 00:24:27.620 align:middle line:90% 00:24:27.620 --> 00:24:29.640 align:middle line:90% And here's out to 2 pi. 00:24:29.640 --> 00:24:33.140 align:middle line:90% So this is Vd. 00:24:33.140 --> 00:24:37.150 align:middle line:84% OK, does that make sense to everybody? 00:24:37.150 --> 00:24:39.490 align:middle line:84% I apologize for the lots of drawing, 00:24:39.490 --> 00:24:41.890 align:middle line:84% but I wanted you to get convinced 00:24:41.890 --> 00:24:45.040 align:middle line:84% that the whole point of having these six diodes 00:24:45.040 --> 00:24:52.480 align:middle line:84% is that Vd, as I've written it over here, 00:24:52.480 --> 00:24:59.920 align:middle line:84% is the maximum of Va, Vb, Vc minus the minimum of Va, Vb, Vc. 00:24:59.920 --> 00:25:05.432 align:middle line:84% But this could also be written as the maximum of the line 00:25:05.432 --> 00:25:06.640 align:middle line:90% to lines and their negatives. 00:25:06.640 --> 00:25:30.225 align:middle line:84% So VCB, VAB, VAC, VBC, VBA, and VCA. 00:25:30.225 --> 00:25:32.880 align:middle line:90% 00:25:32.880 --> 00:25:35.310 align:middle line:90% VCA. 00:25:35.310 --> 00:25:39.260 align:middle line:84% That's all the line to lines and their negatives. 00:25:39.260 --> 00:25:44.300 align:middle line:84% And that's what I'm getting with this right here. 00:25:44.300 --> 00:25:46.820 align:middle line:90% 00:25:46.820 --> 00:25:49.880 align:middle line:90% Now, why am I harping on this? 00:25:49.880 --> 00:25:51.560 align:middle line:90% A few reasons. 00:25:51.560 --> 00:25:56.420 align:middle line:84% Let's start to think about this as compared to-- 00:25:56.420 --> 00:25:58.880 align:middle line:84% oh, before I do that, let me just 00:25:58.880 --> 00:26:03.260 align:middle line:84% tell you a couple of things, just for bookkeeping. 00:26:03.260 --> 00:26:07.610 align:middle line:84% We've named our phases A, B, and C, 00:26:07.610 --> 00:26:11.580 align:middle line:90% originally, such that A rotates. 00:26:11.580 --> 00:26:14.720 align:middle line:84% Then after A maximums, B maximums, 00:26:14.720 --> 00:26:17.100 align:middle line:84% and C maximums, and so forth as we're going around. 00:26:17.100 --> 00:26:21.492 align:middle line:84% So it goes A B, C, A, B, C, right? 00:26:21.492 --> 00:26:25.230 align:middle line:84% When I start to do this and I do the rectifier, 00:26:25.230 --> 00:26:26.235 align:middle line:90% I get two effects. 00:26:26.235 --> 00:26:29.100 align:middle line:90% 00:26:29.100 --> 00:26:32.070 align:middle line:84% The way these maxima rotates between 00:26:32.070 --> 00:26:35.730 align:middle line:84% the positive and negative line, the line maximums, C becomes 00:26:35.730 --> 00:26:39.750 align:middle line:90% A, then B-- 00:26:39.750 --> 00:26:42.120 align:middle line:90% and B stays constant. 00:26:42.120 --> 00:26:46.080 align:middle line:84% Then B goes to C, and A stays constant. 00:26:46.080 --> 00:26:52.050 align:middle line:84% And then A goes to B, and C stays constant. 00:26:52.050 --> 00:26:54.620 align:middle line:84% Then C goes to A, and B stays constant. 00:26:54.620 --> 00:26:57.420 align:middle line:84% And then B goes to C, and A stays constant and so forth. 00:26:57.420 --> 00:27:00.140 align:middle line:84% So I'm either changing this letter or this letter 00:27:00.140 --> 00:27:02.770 align:middle line:90% as I go along. 00:27:02.770 --> 00:27:06.400 align:middle line:84% So that's how we know what's going to maximize. 00:27:06.400 --> 00:27:08.680 align:middle line:84% And then the other thing that's happening 00:27:08.680 --> 00:27:12.550 align:middle line:84% is these diodes are numbered so that they go sequentially. 00:27:12.550 --> 00:27:16.670 align:middle line:84% And you say, well, why do I focus on this? 00:27:16.670 --> 00:27:19.870 align:middle line:84% It's because if you're suddenly poking scope probes into one 00:27:19.870 --> 00:27:22.240 align:middle line:84% of these circuits, you really want 00:27:22.240 --> 00:27:24.430 align:middle line:84% to know what one's going to conduct next, 00:27:24.430 --> 00:27:26.270 align:middle line:90% like, how is it going to run? 00:27:26.270 --> 00:27:28.090 align:middle line:90% And so you number your diodes-- 00:27:28.090 --> 00:27:29.590 align:middle line:84% and in different circuits, you might 00:27:29.590 --> 00:27:33.290 align:middle line:84% number your switches-- such that they conduct sequentially. 00:27:33.290 --> 00:27:41.320 align:middle line:84% So for example, when VAB is at a maximum right here, 00:27:41.320 --> 00:27:48.790 align:middle line:90% I have D1 and D6 conducting. 00:27:48.790 --> 00:27:51.280 align:middle line:84% What's the next one that's going to conduct? 00:27:51.280 --> 00:27:57.860 align:middle line:90% Its D1, D6, then D6. 00:27:57.860 --> 00:28:00.390 align:middle line:90% Then it's going to be D1, D2. 00:28:00.390 --> 00:28:05.630 align:middle line:84% It's going to be VAC is going to be next. 00:28:05.630 --> 00:28:11.250 align:middle line:84% So it's going to go 6, 1; 1, 2; 2, 3. 00:28:11.250 --> 00:28:13.740 align:middle line:84% So then it's going to be VBC max. 00:28:13.740 --> 00:28:20.990 align:middle line:84% And the conduction order is 1 2; 2, 3; 3, 4; 4, 5; 5, 6; 6, 00:28:20.990 --> 00:28:22.430 align:middle line:90% 1, so forth. 00:28:22.430 --> 00:28:26.690 align:middle line:84% So we sequentially number our devices 00:28:26.690 --> 00:28:31.080 align:middle line:84% so that you get consecutive segments conducted. 00:28:31.080 --> 00:28:32.092 align:middle line:90% Why do I focus on that? 00:28:32.092 --> 00:28:33.800 align:middle line:84% Just because it's a real pain in the butt 00:28:33.800 --> 00:28:38.473 align:middle line:84% to keep things straight if you don't be smart about 00:28:38.473 --> 00:28:39.390 align:middle line:90% how you number things. 00:28:39.390 --> 00:28:41.760 align:middle line:84% And so I wanted to bring the convention to your attention. 00:28:41.760 --> 00:28:43.177 align:middle line:84% So let me stop there and just say, 00:28:43.177 --> 00:28:45.230 align:middle line:84% are there any questions so far about 00:28:45.230 --> 00:28:47.440 align:middle line:90% what this rectifier is doing? 00:28:47.440 --> 00:28:51.390 align:middle line:90% 00:28:51.390 --> 00:28:55.740 align:middle line:84% OK, so now let's come back to why I care about three phase 00:28:55.740 --> 00:28:56.380 align:middle line:90% to begin with. 00:28:56.380 --> 00:28:59.250 align:middle line:84% What's wonderful about three phase? 00:28:59.250 --> 00:29:03.090 align:middle line:84% Well, let's just compare this rectifier to the rectifier 00:29:03.090 --> 00:29:06.610 align:middle line:84% we considered at the beginning of the term. 00:29:06.610 --> 00:29:13.530 align:middle line:84% This is a three-phase bridge rectifier. 00:29:13.530 --> 00:29:16.920 align:middle line:84% How would that compare to a single-phase rectifier? 00:29:16.920 --> 00:29:19.090 align:middle line:84% What would a single-phase rectifier look like? 00:29:19.090 --> 00:29:22.700 align:middle line:84% A single-phase full bridge would have four devices, like this. 00:29:22.700 --> 00:29:26.580 align:middle line:90% 00:29:26.580 --> 00:29:32.130 align:middle line:84% It would have an inductive filter. 00:29:32.130 --> 00:29:34.440 align:middle line:90% And here would be Vd. 00:29:34.440 --> 00:29:38.110 align:middle line:90% And here would be Vac. 00:29:38.110 --> 00:29:40.910 align:middle line:90% 00:29:40.910 --> 00:29:43.590 align:middle line:84% So what would Vd look like in this? 00:29:43.590 --> 00:29:52.670 align:middle line:84% When Vac is positive, Vac looked like this. 00:29:52.670 --> 00:29:55.070 align:middle line:90% Here's Vac. 00:29:55.070 --> 00:29:58.470 align:middle line:84% What would Vd look like in this circuit? 00:29:58.470 --> 00:30:01.490 align:middle line:84% Vd would give me the full wave rectification of this. 00:30:01.490 --> 00:30:03.840 align:middle line:90% So Vd would look like this. 00:30:03.840 --> 00:30:07.860 align:middle line:84% It would look like this bump and then the negative of it. 00:30:07.860 --> 00:30:12.776 align:middle line:90% 00:30:12.776 --> 00:30:16.510 align:middle line:84% Well, OK, what's the fundamental ripple frequency? 00:30:16.510 --> 00:30:18.910 align:middle line:84% If, for example, Vac was 60 hertz, 00:30:18.910 --> 00:30:20.650 align:middle line:84% what's the fundamental ripple frequency 00:30:20.650 --> 00:30:24.820 align:middle line:90% in the rectified output? 00:30:24.820 --> 00:30:26.920 align:middle line:90% 120 hertz, right? 00:30:26.920 --> 00:30:32.380 align:middle line:84% So I got to size this inductor to filter a full-scale ripple 00:30:32.380 --> 00:30:33.284 align:middle line:90% at 120 hertz. 00:30:33.284 --> 00:30:36.520 align:middle line:90% 00:30:36.520 --> 00:30:37.850 align:middle line:90% OK, well, I can do that. 00:30:37.850 --> 00:30:39.850 align:middle line:84% I can get a big inductor and go do that. 00:30:39.850 --> 00:30:42.850 align:middle line:90% What happens over here? 00:30:42.850 --> 00:30:46.110 align:middle line:84% Well, if I counted it, this is a half a pulse. 00:30:46.110 --> 00:30:51.250 align:middle line:84% 1, 2, 3, 4, 5, 5 and 1/2, 6 pulses per line cycle. 00:30:51.250 --> 00:30:54.310 align:middle line:84% So that means that the fundamental ripple frequency 00:30:54.310 --> 00:31:00.710 align:middle line:84% of the three-phase bridge is at 360 hertz, three times as high. 00:31:00.710 --> 00:31:05.280 align:middle line:90% Yeah, three times as high. 00:31:05.280 --> 00:31:07.490 align:middle line:90% I can multiply. 00:31:07.490 --> 00:31:11.250 align:middle line:84% And keep in mind, how big is the amplitude on this? 00:31:11.250 --> 00:31:12.860 align:middle line:90% This is the full ripple. 00:31:12.860 --> 00:31:15.080 align:middle line:84% On the other hand, look how big the ripple 00:31:15.080 --> 00:31:17.450 align:middle line:84% is, the voltage ripple, that has to be 00:31:17.450 --> 00:31:21.770 align:middle line:84% filtered by the inductor in the three-phase bridge. 00:31:21.770 --> 00:31:25.640 align:middle line:84% If I go look at the Ld up there, it 00:31:25.640 --> 00:31:28.370 align:middle line:84% has to only take three times the frequency, which 00:31:28.370 --> 00:31:29.750 align:middle line:90% means it's smaller. 00:31:29.750 --> 00:31:31.210 align:middle line:90% And the ripple is far smaller. 00:31:31.210 --> 00:31:32.460 align:middle line:90% The ripple voltage is smaller. 00:31:32.460 --> 00:31:35.180 align:middle line:84% So the inductor that I need for my three-phase bridge 00:31:35.180 --> 00:31:37.370 align:middle line:84% is teensy tiny compared to the inductor 00:31:37.370 --> 00:31:39.170 align:middle line:84% that I need for my single-phase bridge. 00:31:39.170 --> 00:31:41.960 align:middle line:84% So I'll be much happier building a three phase instead 00:31:41.960 --> 00:31:45.600 align:middle line:90% of a single-phase rectifier. 00:31:45.600 --> 00:31:47.940 align:middle line:84% What did it cost me in terms of devices? 00:31:47.940 --> 00:31:50.520 align:middle line:84% Now, it's risky just counting components 00:31:50.520 --> 00:31:52.630 align:middle line:84% because not all components are created equal. 00:31:52.630 --> 00:31:58.800 align:middle line:84% But roughly speaking, to do this beastie, I needed four diodes. 00:31:58.800 --> 00:32:02.590 align:middle line:84% To do the three-phase beastie, I only needed six diodes. 00:32:02.590 --> 00:32:06.250 align:middle line:84% So I swapped six devices for four devices, admittedly 00:32:06.250 --> 00:32:07.960 align:middle line:90% of slightly different scale. 00:32:07.960 --> 00:32:12.040 align:middle line:84% But suddenly, I get much, much nicer performance. 00:32:12.040 --> 00:32:15.170 align:middle line:84% Everything becomes good in terms of the output filter. 00:32:15.170 --> 00:32:17.290 align:middle line:90% And that inductor is really big. 00:32:17.290 --> 00:32:18.790 align:middle line:90% It's low frequency. 00:32:18.790 --> 00:32:21.520 align:middle line:84% I would usually need a really big single-phase inductor. 00:32:21.520 --> 00:32:25.390 align:middle line:84% For a three-phase system, I need a very small inductor. 00:32:25.390 --> 00:32:28.730 align:middle line:90% Any questions about that? 00:32:28.730 --> 00:32:29.400 align:middle line:90% Yeah. 00:32:29.400 --> 00:32:32.400 align:middle line:84% AUDIENCE: What's an application of the three-phase rectifier? 00:32:32.400 --> 00:32:33.840 align:middle line:90% DAVID PERREAULT: OK, sure. 00:32:33.840 --> 00:32:39.560 align:middle line:84% Do you guys remember I brought in an alternator earlier 00:32:39.560 --> 00:32:42.170 align:middle line:84% in the term when we're talking about power factor? 00:32:42.170 --> 00:32:45.830 align:middle line:84% That's actually a three-phase-- an alternator means an AC 00:32:45.830 --> 00:32:47.630 align:middle line:90% generator, essentially. 00:32:47.630 --> 00:32:48.990 align:middle line:90% So that's a three phase. 00:32:48.990 --> 00:32:50.700 align:middle line:90% It came out with three phases. 00:32:50.700 --> 00:32:54.710 align:middle line:84% You run into six diodes and, boom, suddenly you have DC. 00:32:54.710 --> 00:32:57.710 align:middle line:84% And they control the amplitude of which they 00:32:57.710 --> 00:32:59.522 align:middle line:90% generate by a field control. 00:32:59.522 --> 00:33:00.980 align:middle line:84% They use an electromagnet that they 00:33:00.980 --> 00:33:03.530 align:middle line:84% change the strength of the electromagnet that basically 00:33:03.530 --> 00:33:06.920 align:middle line:84% controls how big the AC voltage that you're 00:33:06.920 --> 00:33:08.220 align:middle line:90% sending it through is. 00:33:08.220 --> 00:33:11.330 align:middle line:84% So one application of a three-phase rectifier 00:33:11.330 --> 00:33:12.440 align:middle line:90% would just be in your car. 00:33:12.440 --> 00:33:15.560 align:middle line:90% Every car has one. 00:33:15.560 --> 00:33:18.500 align:middle line:84% More to the point, though, anywhere I'm 00:33:18.500 --> 00:33:20.820 align:middle line:90% going to go from AC to DC-- 00:33:20.820 --> 00:33:23.180 align:middle line:84% so if I want to run a three-phase drive-- 00:33:23.180 --> 00:33:24.210 align:middle line:90% now, it depends. 00:33:24.210 --> 00:33:26.460 align:middle line:84% I may want to invert back into the line in some cases. 00:33:26.460 --> 00:33:29.430 align:middle line:84% But if all I want to do is take power from AC line 00:33:29.430 --> 00:33:33.270 align:middle line:84% and then use it for something, when I'm at high power, 00:33:33.270 --> 00:33:36.600 align:middle line:84% I come in with three phase, I put a three-phase rectifier 00:33:36.600 --> 00:33:38.055 align:middle line:90% in there, and I get DC out. 00:33:38.055 --> 00:33:39.930 align:middle line:84% So if I'm at the front end of my data center, 00:33:39.930 --> 00:33:42.840 align:middle line:84% that's probably what I have is a big three-phase rectifier 00:33:42.840 --> 00:33:44.950 align:middle line:84% to take that AC and turn it into DC. 00:33:44.950 --> 00:33:47.160 align:middle line:84% And this is probably the simplest version 00:33:47.160 --> 00:33:50.020 align:middle line:84% of a three-phase rectifier that you'd actually use. 00:33:50.020 --> 00:33:52.680 align:middle line:84% People tend not to use halfwave rectifiers 00:33:52.680 --> 00:33:54.300 align:middle line:90% because they inject DC back. 00:33:54.300 --> 00:33:59.880 align:middle line:84% And likewise, they tend not to use this simple rectifier, 00:33:59.880 --> 00:34:01.080 align:middle line:90% the half-- 00:34:01.080 --> 00:34:03.100 align:middle line:84% the three-diode version, they tend not to use. 00:34:03.100 --> 00:34:04.860 align:middle line:84% So this is kind of the simplest rectifier 00:34:04.860 --> 00:34:08.250 align:middle line:90% you'd use for three phase. 00:34:08.250 --> 00:34:11.550 align:middle line:90% Other questions? 00:34:11.550 --> 00:34:15.610 align:middle line:84% OK, what's another advantage of this thing? 00:34:15.610 --> 00:34:19.090 align:middle line:84% Well, we talked-- we actually talked about this last class 00:34:19.090 --> 00:34:21.699 align:middle line:90% in abstract terms. 00:34:21.699 --> 00:34:25.190 align:middle line:84% What would be my line current in this case? 00:34:25.190 --> 00:34:28.810 align:middle line:90% What would be Iac? 00:34:28.810 --> 00:34:32.510 align:middle line:90% My Vac looks like a sine wave. 00:34:32.510 --> 00:34:38.050 align:middle line:84% Well, if this Id is constant, approximately, 00:34:38.050 --> 00:34:40.130 align:middle line:84% because I've done a good job filtering, 00:34:40.130 --> 00:34:43.480 align:middle line:84% I see when Vac is positive, it looks like Id. 00:34:43.480 --> 00:34:47.560 align:middle line:84% And when Vac is negative, it looks like minus Id. 00:34:47.560 --> 00:34:49.680 align:middle line:84% Iac would look like a square wave. 00:34:49.680 --> 00:34:54.638 align:middle line:90% 00:34:54.638 --> 00:34:58.120 align:middle line:84% So I get some kind of power factor out of that. 00:34:58.120 --> 00:35:00.920 align:middle line:84% If I calculated the power factor of this thing, 00:35:00.920 --> 00:35:03.980 align:middle line:90% it would be about 0.91. 00:35:03.980 --> 00:35:06.920 align:middle line:84% Now, the square wave, the fundamentals 00:35:06.920 --> 00:35:09.500 align:middle line:84% in phase-- of the currents in phase with the voltage, so it's 00:35:09.500 --> 00:35:14.180 align:middle line:84% 0.91 basically because the square wave has 00:35:14.180 --> 00:35:19.010 align:middle line:84% third, fifth, seventh, et cetera, harmonics in it. 00:35:19.010 --> 00:35:25.180 align:middle line:84% What would the line currents in this thing look like? 00:35:25.180 --> 00:35:29.530 align:middle line:84% Well, let's just go figure out one line current. 00:35:29.530 --> 00:35:34.240 align:middle line:84% Why don't I come back and do the line current in-- 00:35:34.240 --> 00:35:36.160 align:middle line:84% let's see, what color haven't I used? 00:35:36.160 --> 00:35:39.520 align:middle line:90% Let me pick this color. 00:35:39.520 --> 00:35:43.345 align:middle line:84% Let's look at the line current here for just-- 00:35:43.345 --> 00:35:46.150 align:middle line:90% 00:35:46.150 --> 00:35:47.640 align:middle line:90% let me think about this. 00:35:47.640 --> 00:35:50.980 align:middle line:90% 00:35:50.980 --> 00:35:55.270 align:middle line:84% Let's pick the line current for phase A. 00:35:55.270 --> 00:35:58.680 align:middle line:84% So let's figure out what I sub A looks like. 00:35:58.680 --> 00:36:01.450 align:middle line:90% 00:36:01.450 --> 00:36:06.580 align:middle line:84% If I come back over here, A is conducting in this interval 00:36:06.580 --> 00:36:09.010 align:middle line:90% and in this interval, AB and AC. 00:36:09.010 --> 00:36:15.790 align:middle line:84% When AB and AC are maximum, this diode 1 is conducting. 00:36:15.790 --> 00:36:19.430 align:middle line:84% And when he's conducting, he's carrying a constant current Id. 00:36:19.430 --> 00:36:22.350 align:middle line:84% So IA would look something like this. 00:36:22.350 --> 00:36:24.470 align:middle line:90% It would conduct here. 00:36:24.470 --> 00:36:27.680 align:middle line:84% It would start conducting at 30 degrees, 00:36:27.680 --> 00:36:32.340 align:middle line:84% continue conducting until here, 150 degrees. 00:36:32.340 --> 00:36:34.950 align:middle line:84% Then he would go quiet for a little while. 00:36:34.950 --> 00:36:37.138 align:middle line:84% And then when he's conducting negative, 00:36:37.138 --> 00:36:38.680 align:middle line:84% he's going to carry negative current. 00:36:38.680 --> 00:36:43.785 align:middle line:90% 00:36:43.785 --> 00:36:46.740 align:middle line:84% Does that waveform pattern look familiar to anybody? 00:36:46.740 --> 00:36:49.334 align:middle line:90% 00:36:49.334 --> 00:36:52.200 align:middle line:84% So this is essentially the current pattern 00:36:52.200 --> 00:36:59.880 align:middle line:84% I'm going to conduct for I sub A of t. 00:36:59.880 --> 00:37:03.480 align:middle line:84% And keep in mind, I didn't draw it well. 00:37:03.480 --> 00:37:06.300 align:middle line:90% Let me draw it-- 00:37:06.300 --> 00:37:10.500 align:middle line:84% let me draw it back on my line to neutral waveforms 00:37:10.500 --> 00:37:11.920 align:middle line:90% because this has Va. 00:37:11.920 --> 00:37:13.560 align:middle line:90% Va is in red. 00:37:13.560 --> 00:37:14.750 align:middle line:90% So here's Va. 00:37:14.750 --> 00:37:22.340 align:middle line:90% 00:37:22.340 --> 00:37:23.880 align:middle line:90% What does IA look like? 00:37:23.880 --> 00:37:25.640 align:middle line:90% IA looks like this. 00:37:25.640 --> 00:37:29.670 align:middle line:90% It conducts after 30 degrees. 00:37:29.670 --> 00:37:34.170 align:middle line:84% It stops conducting at 150 and then conducts negatively 00:37:34.170 --> 00:37:36.770 align:middle line:90% like this. 00:37:36.770 --> 00:37:40.920 align:middle line:84% So I can match the red and pink waveforms between the line 00:37:40.920 --> 00:37:44.160 align:middle line:84% voltage and the line current, the current 00:37:44.160 --> 00:37:45.990 align:middle line:90% in that voltage source. 00:37:45.990 --> 00:37:49.150 align:middle line:84% Does that make sense to everybody? 00:37:49.150 --> 00:37:52.900 align:middle line:84% So what does that say about his power factor? 00:37:52.900 --> 00:37:56.320 align:middle line:90% OK, well, we can calculate that. 00:37:56.320 --> 00:37:59.340 align:middle line:84% And let's just do that for some good exercise here. 00:37:59.340 --> 00:38:03.810 align:middle line:90% 00:38:03.810 --> 00:38:07.470 align:middle line:84% First of all, what's the average power? 00:38:07.470 --> 00:38:11.790 align:middle line:84% I would argue that the average power in this thing could be-- 00:38:11.790 --> 00:38:15.120 align:middle line:84% is essentially the product of the red and the pink, 00:38:15.120 --> 00:38:20.445 align:middle line:84% which I could write as 1 over pi, the integral from 0 to pi-- 00:38:20.445 --> 00:38:23.070 align:middle line:84% and I can do it in a half cycle because the other half cycle is 00:38:23.070 --> 00:38:24.360 align:middle line:90% symmetric-- 00:38:24.360 --> 00:38:31.110 align:middle line:90% of Vs sine omega t times ID. 00:38:31.110 --> 00:38:37.280 align:middle line:84% But its only ID between pi over 6 and 5 pi over 6. 00:38:37.280 --> 00:38:39.960 align:middle line:90% 00:38:39.960 --> 00:38:41.940 align:middle line:90% That's the average power. 00:38:41.940 --> 00:38:50.760 align:middle line:84% So this is going to give me Vs ID times the cosine of pi over 6 00:38:50.760 --> 00:38:53.320 align:middle line:84% minus the cosine of 5 pi over six, 00:38:53.320 --> 00:38:55.070 align:middle line:84% which is going to be the square root of 3. 00:38:55.070 --> 00:39:00.668 align:middle line:90% 00:39:00.668 --> 00:39:04.020 align:middle line:90% And this is 1 over pi. 00:39:04.020 --> 00:39:06.380 align:middle line:90% OK, so that's the average power. 00:39:06.380 --> 00:39:11.615 align:middle line:90% What's the RMS of phase A? 00:39:11.615 --> 00:39:14.190 align:middle line:90% 00:39:14.190 --> 00:39:19.190 align:middle line:84% If this has a amplitude Vs, what would 00:39:19.190 --> 00:39:21.862 align:middle line:90% be the RMS of single phase? 00:39:21.862 --> 00:39:23.570 align:middle line:84% AUDIENCE: Vs divided by square root of 2. 00:39:23.570 --> 00:39:25.695 align:middle line:84% DAVID PERREAULT: Yes, Vs over the square root of 2. 00:39:25.695 --> 00:39:28.220 align:middle line:90% 00:39:28.220 --> 00:39:32.990 align:middle line:90% What's I RMS of phase A? 00:39:32.990 --> 00:39:36.170 align:middle line:84% OK well, it's the square root of the average 00:39:36.170 --> 00:39:37.860 align:middle line:90% of the square of this thing. 00:39:37.860 --> 00:39:39.770 align:middle line:84% So if I squared the pink waveform-- 00:39:39.770 --> 00:39:42.920 align:middle line:90% and this amplitude here is ID-- 00:39:42.920 --> 00:39:47.360 align:middle line:84% I would take this thing, I would square it, I'd have ID squared. 00:39:47.360 --> 00:39:50.540 align:middle line:84% And then it's at ID squared for 2/3 of the time, 00:39:50.540 --> 00:39:52.850 align:middle line:90% 4/6 of the time. 00:39:52.850 --> 00:39:58.490 align:middle line:84% So this would just be equal to ID times the square root 00:39:58.490 --> 00:39:59.430 align:middle line:90% of 2 over 3. 00:39:59.430 --> 00:40:02.430 align:middle line:90% You could just take the RMS. 00:40:02.430 --> 00:40:06.930 align:middle line:84% That gives me a power factor equal to what? 00:40:06.930 --> 00:40:14.010 align:middle line:84% It's the average power divided by V MRS I RMS. 00:40:14.010 --> 00:40:21.900 align:middle line:84% And that's going to be Vs ID square root of 3 over pi divided 00:40:21.900 --> 00:40:32.070 align:middle line:84% by Vs over the square root of 2 divided by ID square root of 2 00:40:32.070 --> 00:40:36.900 align:middle line:84% over the square root of 3 which is just equal to 3 over pi. 00:40:36.900 --> 00:40:45.300 align:middle line:84% And 3 over pi, if you want to calculate it, it's about 0.96. 00:40:45.300 --> 00:40:48.078 align:middle line:84% So whereas having a single-phase bridge-- 00:40:48.078 --> 00:40:49.620 align:middle line:84% and if I did it for the other phases, 00:40:49.620 --> 00:40:51.245 align:middle line:84% the other phases are just time shifted. 00:40:51.245 --> 00:40:53.970 align:middle line:84% So all the phases have the same power factor. 00:40:53.970 --> 00:40:58.140 align:middle line:84% So the beauty of this three-phase piece compared 00:40:58.140 --> 00:41:00.060 align:middle line:84% to a single-phase piece is instead 00:41:00.060 --> 00:41:02.970 align:middle line:84% of getting a power factor of about 0.91, 00:41:02.970 --> 00:41:07.760 align:middle line:84% I've got automatically a power factor of 0.96. 00:41:07.760 --> 00:41:09.540 align:middle line:90% Why is the power factor higher? 00:41:09.540 --> 00:41:11.070 align:middle line:90% Because look at this waveform. 00:41:11.070 --> 00:41:14.480 align:middle line:84% You can see just by eye or by recollection 00:41:14.480 --> 00:41:16.550 align:middle line:84% of our harmonic cancellation discussion 00:41:16.550 --> 00:41:20.000 align:middle line:84% that this thing has no triple-N harmonics. 00:41:20.000 --> 00:41:22.010 align:middle line:84% We said one of the benefits of three phase 00:41:22.010 --> 00:41:23.820 align:middle line:84% is because everything is time shifted. 00:41:23.820 --> 00:41:27.260 align:middle line:90% Even if your currents-- 00:41:27.260 --> 00:41:29.600 align:middle line:84% even if you draw an individual current, 00:41:29.600 --> 00:41:32.150 align:middle line:84% all the triple-N's have to cancel because 00:41:32.150 --> 00:41:33.420 align:middle line:90% of the three-phase nature. 00:41:33.420 --> 00:41:35.390 align:middle line:84% And you're seeing it right here in the line 00:41:35.390 --> 00:41:37.460 align:middle line:90% current of the rectifier, 00:41:37.460 --> 00:41:41.360 align:middle line:84% So whereas the single phase will have fundamental 00:41:41.360 --> 00:41:46.010 align:middle line:84% third, fifth, seventh, ninth, et cetera, 00:41:46.010 --> 00:41:49.310 align:middle line:84% this thing gets rid of the third, sixth, and ninth. 00:41:49.310 --> 00:41:52.370 align:middle line:84% And the lowest harmonic content of this 00:41:52.370 --> 00:41:55.160 align:middle line:90% is the fifth and the seventh. 00:41:55.160 --> 00:41:56.815 align:middle line:90% Any questions about that? 00:41:56.815 --> 00:41:59.360 align:middle line:90% 00:41:59.360 --> 00:42:01.550 align:middle line:84% AUDIENCE: I wanted to know about the power factor-- 00:42:01.550 --> 00:42:03.890 align:middle line:84% the power factor and the phases are different. 00:42:03.890 --> 00:42:07.370 align:middle line:84% Is there a notion of [INAUDIBLE] power factor? 00:42:07.370 --> 00:42:10.110 align:middle line:84% DAVID PERREAULT: Well, everything's-- if the phases are 00:42:10.110 --> 00:42:11.610 align:middle line:84% balanced, then they're all the same. 00:42:11.610 --> 00:42:14.310 align:middle line:90% And that's the idealized case. 00:42:14.310 --> 00:42:16.040 align:middle line:84% When you're talking about power factor, 00:42:16.040 --> 00:42:20.800 align:middle line:84% you really only talk about one port of the circuit. 00:42:20.800 --> 00:42:23.005 align:middle line:84% So I suppose if you had an unbalanced situation 00:42:23.005 --> 00:42:25.010 align:middle line:84% and it's a more complicated situation, 00:42:25.010 --> 00:42:26.510 align:middle line:84% you could start looking at the power 00:42:26.510 --> 00:42:31.400 align:middle line:84% factor of the different phases being different. 00:42:31.400 --> 00:42:33.433 align:middle line:84% But generally, let's just keep it simple 00:42:33.433 --> 00:42:35.350 align:middle line:84% and say everything's balanced, which it should 00:42:35.350 --> 00:42:38.230 align:middle line:90% be if it's working right. 00:42:38.230 --> 00:42:39.260 align:middle line:90% Other questions? 00:42:39.260 --> 00:42:42.470 align:middle line:90% 00:42:42.470 --> 00:42:47.120 align:middle line:84% So we've seen what you can do with just basically throwing 00:42:47.120 --> 00:42:48.125 align:middle line:90% two more devices at it. 00:42:48.125 --> 00:42:50.000 align:middle line:84% Suddenly, three-phase is looking pretty good, 00:42:50.000 --> 00:42:53.760 align:middle line:84% especially at high power because more complex, 00:42:53.760 --> 00:42:54.620 align:middle line:90% I got more devices. 00:42:54.620 --> 00:42:56.250 align:middle line:90% I got 50% more devices. 00:42:56.250 --> 00:42:57.980 align:middle line:84% On the other hand, my inductor just 00:42:57.980 --> 00:43:00.460 align:middle line:90% got a heck of a lot smaller. 00:43:00.460 --> 00:43:03.610 align:middle line:84% And we said that's related to the notion 00:43:03.610 --> 00:43:09.860 align:middle line:84% of with three-phase power, if I were drawing ideal sine waves, 00:43:09.860 --> 00:43:11.387 align:middle line:90% I'd be drawing continuous power. 00:43:11.387 --> 00:43:12.720 align:middle line:90% Now, I'm not drawing sine waves. 00:43:12.720 --> 00:43:15.050 align:middle line:90% I'm drawing this funny waveform. 00:43:15.050 --> 00:43:16.910 align:middle line:84% But it's just basically much easier 00:43:16.910 --> 00:43:18.750 align:middle line:84% to get close to continuous power. 00:43:18.750 --> 00:43:22.520 align:middle line:84% I need much less filtering to give me kind of constant power 00:43:22.520 --> 00:43:26.340 align:middle line:84% at the output because I have three phases at my disposal. 00:43:26.340 --> 00:43:30.920 align:middle line:84% Whereas in the case of the single phase, 00:43:30.920 --> 00:43:33.260 align:middle line:84% basically that inductor is serving 00:43:33.260 --> 00:43:35.817 align:middle line:84% to ride through the twice line frequency ripple. 00:43:35.817 --> 00:43:37.900 align:middle line:84% I don't need to do that in the three-phase system. 00:43:37.900 --> 00:43:40.530 align:middle line:90% 00:43:40.530 --> 00:43:42.300 align:middle line:84% I'm of running out of time, but I 00:43:42.300 --> 00:43:48.240 align:middle line:84% did want to give you one more kind of notion of what 00:43:48.240 --> 00:43:51.740 align:middle line:90% you can do with three phase. 00:43:51.740 --> 00:43:58.200 align:middle line:84% I mentioned that naturally, if I compared the line to neutral 00:43:58.200 --> 00:44:03.390 align:middle line:84% and the line-to-line waveforms, I get a 30-degree phase shift. 00:44:03.390 --> 00:44:09.150 align:middle line:84% Well, we often use that kind of 30-degree phase shift 00:44:09.150 --> 00:44:10.620 align:middle line:90% to our advantage. 00:44:10.620 --> 00:44:13.440 align:middle line:84% Or I can build a transformer set that 00:44:13.440 --> 00:44:16.680 align:middle line:84% can grab pieces of Va and Vb and Vc 00:44:16.680 --> 00:44:20.190 align:middle line:84% and add them up symmetrically with a symmetrical 00:44:20.190 --> 00:44:23.550 align:middle line:84% set of transforms to generate some new set of waveforms 00:44:23.550 --> 00:44:26.670 align:middle line:84% with an arbitrary phase shift to it. 00:44:26.670 --> 00:44:29.100 align:middle line:84% And because I have these three phases, 00:44:29.100 --> 00:44:30.870 align:middle line:84% I can get new three-phase sets that 00:44:30.870 --> 00:44:34.110 align:middle line:84% also add to 0 with this arbitrary phase shift. 00:44:34.110 --> 00:44:36.990 align:middle line:90% OK, how would we use that? 00:44:36.990 --> 00:44:44.250 align:middle line:84% Well, when people get to high powers, first of all, 00:44:44.250 --> 00:44:47.850 align:middle line:84% you can't go out and buy a diode with either enough 00:44:47.850 --> 00:44:50.870 align:middle line:84% voltage or enough current for what you want to do. 00:44:50.870 --> 00:44:54.650 align:middle line:84% So if you think about trying to build 00:44:54.650 --> 00:44:57.860 align:middle line:84% a tokamak for fusion or something and you're going to-- 00:44:57.860 --> 00:45:01.400 align:middle line:84% you need serious amounts of power, tens of thousands 00:45:01.400 --> 00:45:02.450 align:middle line:90% of amps. 00:45:02.450 --> 00:45:05.270 align:middle line:84% Maybe you can't go buy individual diodes 00:45:05.270 --> 00:45:06.650 align:middle line:90% with tens of thousands of amps. 00:45:06.650 --> 00:45:08.150 align:middle line:84% Now, you get some help because now I 00:45:08.150 --> 00:45:11.040 align:middle line:84% have six devices to help me process that power. 00:45:11.040 --> 00:45:12.810 align:middle line:90% But maybe I would need more. 00:45:12.810 --> 00:45:15.380 align:middle line:84% Or maybe what I really want is really high 00:45:15.380 --> 00:45:19.610 align:middle line:84% voltage that I can't do with individual diode voltages. 00:45:19.610 --> 00:45:21.850 align:middle line:84% So here's the kind of trick you can play. 00:45:21.850 --> 00:45:26.810 align:middle line:90% 00:45:26.810 --> 00:45:29.510 align:middle line:90% You can go and say-- 00:45:29.510 --> 00:45:31.680 align:middle line:84% and I can do this with yy or delta y. 00:45:31.680 --> 00:45:36.140 align:middle line:84% But let's imagine that I come in with my waveforms. 00:45:36.140 --> 00:45:43.460 align:middle line:84% And I'll build one set of transformers that maybe take 00:45:43.460 --> 00:45:51.800 align:middle line:84% the line-to-line voltages and generate a new set of waveforms 00:45:51.800 --> 00:45:55.580 align:middle line:84% that are in phase with that and maybe another set 00:45:55.580 --> 00:46:00.040 align:middle line:84% of transformers that generate the 30-degree phase shift. 00:46:00.040 --> 00:46:01.350 align:middle line:90% How could I do that? 00:46:01.350 --> 00:46:10.640 align:middle line:84% Well, for example, suppose I took Va, Vb and-- 00:46:10.640 --> 00:46:13.640 align:middle line:90% Va, Vb and Vc. 00:46:13.640 --> 00:46:18.230 align:middle line:90% 00:46:18.230 --> 00:46:21.890 align:middle line:84% And I will just go build a transformer that says says, OK, 00:46:21.890 --> 00:46:26.900 align:middle line:84% let me take the line-to-line voltages, 00:46:26.900 --> 00:46:29.210 align:middle line:84% which are square root of 3 bigger, 00:46:29.210 --> 00:46:33.995 align:middle line:84% and then I will go generate a new set, a new y set of-- 00:46:33.995 --> 00:46:36.780 align:middle line:84% I'll connect the primaries and delta and the secondaries and y. 00:46:36.780 --> 00:46:41.000 align:middle line:84% So I'll make a delta to y transformation. 00:46:41.000 --> 00:46:45.510 align:middle line:84% So what's that going to mean is if I have my fundamental-- 00:46:45.510 --> 00:46:47.810 align:middle line:90% [ALARM SOUNDS] 00:46:47.810 --> 00:46:51.765 align:middle line:84% If I have my fundamental of this set, 00:46:51.765 --> 00:46:54.140 align:middle line:84% when I run it through the transformer and I can get the 1 00:46:54.140 --> 00:46:56.075 align:middle line:84% over square root of 3 scaling I want, 00:46:56.075 --> 00:46:57.450 align:middle line:84% I run it through the transformer, 00:46:57.450 --> 00:47:00.200 align:middle line:84% I get another set of three-phase voltages that are 30-degree 00:47:00.200 --> 00:47:02.160 align:middle line:90% shifted. 00:47:02.160 --> 00:47:04.980 align:middle line:84% So now I have two sets of waveforms 00:47:04.980 --> 00:47:06.900 align:middle line:90% that are 30 degrees apart. 00:47:06.900 --> 00:47:10.560 align:middle line:84% So if I had a first diode rectifier up here, 00:47:10.560 --> 00:47:12.810 align:middle line:84% maybe it would just look like that one. 00:47:12.810 --> 00:47:16.600 align:middle line:90% That's this diode rectifier. 00:47:16.600 --> 00:47:17.100 align:middle line:90% Oops. 00:47:17.100 --> 00:47:18.550 align:middle line:90% This is a transformer. 00:47:18.550 --> 00:47:21.180 align:middle line:84% I'll run it into a first diode rectifier. 00:47:21.180 --> 00:47:23.220 align:middle line:90% So this is-- so this is like-- 00:47:23.220 --> 00:47:26.280 align:middle line:84% maybe this is delta to delta and this is delta to y. 00:47:26.280 --> 00:47:30.030 align:middle line:90% 00:47:30.030 --> 00:47:33.750 align:middle line:90% I'll do a first diode rectifier. 00:47:33.750 --> 00:47:37.200 align:middle line:84% And his output voltage looks exactly 00:47:37.200 --> 00:47:38.560 align:middle line:90% like this purple waveform. 00:47:38.560 --> 00:47:40.300 align:middle line:84% I guess I should use the correct color. 00:47:40.300 --> 00:47:46.880 align:middle line:90% This is Vd up there. 00:47:46.880 --> 00:47:51.830 align:middle line:84% And now I'll build a second rectifier. 00:47:51.830 --> 00:47:53.730 align:middle line:90% There's another six devices. 00:47:53.730 --> 00:47:55.610 align:middle line:90% Now I've got 12 devices. 00:47:55.610 --> 00:48:00.980 align:middle line:90% And let me make him-- 00:48:00.980 --> 00:48:05.420 align:middle line:90% I'll call this Vd prime. 00:48:05.420 --> 00:48:10.440 align:middle line:84% Well, if I've shifted the phase of the inputs by 30 degrees, 00:48:10.440 --> 00:48:15.530 align:middle line:84% all I'm going to do is shift the phase of the rectified output 00:48:15.530 --> 00:48:16.860 align:middle line:90% ripple by 30 degrees. 00:48:16.860 --> 00:48:20.630 align:middle line:90% So the second one, Vd prime-- 00:48:20.630 --> 00:48:37.830 align:middle line:84% if this is Vd, Vd prime is just going to do this and so forth. 00:48:37.830 --> 00:48:39.900 align:middle line:90% See where I'm going with this? 00:48:39.900 --> 00:48:44.880 align:middle line:84% And so now I connect these guys in series, 00:48:44.880 --> 00:48:47.100 align:middle line:84% and I hook them up to this inductor 00:48:47.100 --> 00:48:48.930 align:middle line:90% and then my load resistor. 00:48:48.930 --> 00:48:53.880 align:middle line:90% And this is Vd plus Vd prime. 00:48:53.880 --> 00:48:58.020 align:middle line:84% First of all, I've got much more voltage, which I might want, 00:48:58.020 --> 00:48:59.970 align:middle line:84% because each of these volt diodes 00:48:59.970 --> 00:49:03.030 align:middle line:84% only blocks half the total output voltage. 00:49:03.030 --> 00:49:06.290 align:middle line:90% Secondly, the ripples cancel. 00:49:06.290 --> 00:49:10.200 align:middle line:84% So if I had six pulses per line cycle, 360 hertz, 00:49:10.200 --> 00:49:11.360 align:middle line:90% now I'm going to have-- 00:49:11.360 --> 00:49:14.720 align:middle line:84% the lowest ripple content's going to be at 12 times 00:49:14.720 --> 00:49:15.540 align:middle line:90% the line frequency. 00:49:15.540 --> 00:49:17.576 align:middle line:84% This would be called a 12-pulse rectifier. 00:49:17.576 --> 00:49:20.330 align:middle line:90% 00:49:20.330 --> 00:49:22.610 align:middle line:84% So first of all, I have higher frequency again. 00:49:22.610 --> 00:49:24.780 align:middle line:84% 720 hertz is the fundamental ripple. 00:49:24.780 --> 00:49:28.440 align:middle line:84% And by the way, the amplitude of that ripple is again smaller. 00:49:28.440 --> 00:49:31.700 align:middle line:84% So this inductor again gets smaller. 00:49:31.700 --> 00:49:34.325 align:middle line:90% [ALARM SOUNDS] 00:49:34.325 --> 00:49:35.690 align:middle line:90% 00:49:35.690 --> 00:49:38.630 align:middle line:84% And the net result of that is that we 00:49:38.630 --> 00:49:42.090 align:middle line:90% get really small filtering. 00:49:42.090 --> 00:49:45.020 align:middle line:84% I'm trading numbers of devices and complexity 00:49:45.020 --> 00:49:49.370 align:middle line:84% for really good output ripple at higher powers, 00:49:49.370 --> 00:49:51.210 align:middle line:90% in this case, higher voltages. 00:49:51.210 --> 00:49:53.125 align:middle line:84% I can play the same game with what's 00:49:53.125 --> 00:49:54.500 align:middle line:84% known as an interface transformer 00:49:54.500 --> 00:49:58.140 align:middle line:84% and get much higher currents if I prefer to set higher voltages. 00:49:58.140 --> 00:50:00.410 align:middle line:84% The other thing I can do, and while this makes a great 00:50:00.410 --> 00:50:02.090 align:middle line:84% homework problem and I'm out of time, 00:50:02.090 --> 00:50:06.860 align:middle line:84% if you track back and look at the line harmonics for this 00:50:06.860 --> 00:50:10.740 align:middle line:84% thing, and you do it right, instead of having fifth 00:50:10.740 --> 00:50:13.890 align:middle line:84% and seventh as being the lowest harmonic you can have 11th 00:50:13.890 --> 00:50:16.500 align:middle line:84% and 13th be the lowest harmonic or the lowest significant 00:50:16.500 --> 00:50:18.000 align:middle line:90% harmonic. 00:50:18.000 --> 00:50:21.960 align:middle line:84% So not only do I make the ripple smaller and my filter smaller, 00:50:21.960 --> 00:50:26.220 align:middle line:84% but I make the line current waveform more sinusoidal, 00:50:26.220 --> 00:50:29.280 align:middle line:84% and I get a higher power factor again. 00:50:29.280 --> 00:50:32.230 align:middle line:84% If you don't like that, fine, do three of them. 00:50:32.230 --> 00:50:33.660 align:middle line:90% Get an 18-pulse rectifier. 00:50:33.660 --> 00:50:34.800 align:middle line:90% People do that. 00:50:34.800 --> 00:50:36.700 align:middle line:90% You want a 24-pulse rectifier? 00:50:36.700 --> 00:50:37.655 align:middle line:90% It exists. 00:50:37.655 --> 00:50:39.030 align:middle line:84% And what they do is they just use 00:50:39.030 --> 00:50:42.750 align:middle line:84% these phase-shifting transformer sets, stack it up in series 00:50:42.750 --> 00:50:45.330 align:middle line:84% or parallel with the right technique, 00:50:45.330 --> 00:50:47.170 align:middle line:84% and you can get to really high powers. 00:50:47.170 --> 00:50:50.640 align:middle line:84% And suddenly, even though an individual diode is a nonlinear 00:50:50.640 --> 00:50:53.310 align:middle line:84% thing and it draws harmonics, you murder all the harmonics, 00:50:53.310 --> 00:50:55.710 align:middle line:84% and you get something that just acts beautifully. 00:50:55.710 --> 00:51:00.660 align:middle line:84% And that's the game you play at really high powers with lower 00:51:00.660 --> 00:51:02.400 align:middle line:84% voltage and lower current devices 00:51:02.400 --> 00:51:04.350 align:middle line:90% than you could otherwise do. 00:51:04.350 --> 00:51:08.857 align:middle line:84% So we've talked about three-phase rectifiers, 00:51:08.857 --> 00:51:10.690 align:middle line:84% and I tried to use this lecture both to show 00:51:10.690 --> 00:51:13.120 align:middle line:84% what you do in terms of numbering devices 00:51:13.120 --> 00:51:18.580 align:middle line:84% and in terms of what are some of-- how some of the advantages 00:51:18.580 --> 00:51:21.140 align:middle line:84% play in a very simple case when you just have diodes. 00:51:21.140 --> 00:51:25.000 align:middle line:84% Next time we'll start to look at more active kinds 00:51:25.000 --> 00:51:27.222 align:middle line:84% of power electronic circuits in three phase. 00:51:27.222 --> 00:51:27.805 align:middle line:90% Last question. 00:51:27.805 --> 00:51:32.340 align:middle line:84% AUDIENCE: Is it the transformer or is it the delta-y connection 00:51:32.340 --> 00:51:34.515 align:middle line:84% that helps with the 30-degree phase shift? 00:51:34.515 --> 00:51:37.520 align:middle line:84% DAVID PERREAULT: Well, it's how you do the transformers. 00:51:37.520 --> 00:51:41.380 align:middle line:84% In this case, it's just because I'm taking the line to line, 00:51:41.380 --> 00:51:44.480 align:middle line:84% and I'm using that to make a new line to neutral. 00:51:44.480 --> 00:51:47.050 align:middle line:90% That's how I get my phase shift. 00:51:47.050 --> 00:51:48.220 align:middle line:90% But I could do-- 00:51:48.220 --> 00:51:50.230 align:middle line:84% I could do something more sophisticated 00:51:50.230 --> 00:51:53.650 align:middle line:84% and get different phase shifts if I wanted. 00:51:53.650 --> 00:51:54.590 align:middle line:90% OK, we're out of time. 00:51:54.590 --> 00:51:56.460 align:middle line:90% Have a great day. 00:51:56.460 --> 00:52:00.000 align:middle line:90%