WEBVTT 00:00:00.000 --> 00:00:02.880 align:middle line:90% [SQUEAKING] 00:00:02.880 --> 00:00:04.320 align:middle line:90% [RUSTLING] 00:00:04.320 --> 00:00:06.720 align:middle line:90% [CLICKING] 00:00:06.720 --> 00:00:09.420 align:middle line:90% 00:00:09.420 --> 00:00:11.640 align:middle line:84% DAVID PERREAULT: OK why don't we get started. 00:00:11.640 --> 00:00:13.660 align:middle line:90% Welcome back from spring break. 00:00:13.660 --> 00:00:16.830 align:middle line:84% I hope you guys got a little rest in. 00:00:16.830 --> 00:00:20.970 align:middle line:84% So what we're going to talk about the next few lectures 00:00:20.970 --> 00:00:26.100 align:middle line:84% is what is done when one gets to higher powers in power 00:00:26.100 --> 00:00:26.710 align:middle line:90% electronics. 00:00:26.710 --> 00:00:28.293 align:middle line:84% And in particular, we're going to talk 00:00:28.293 --> 00:00:36.840 align:middle line:84% about three-phase power, or more generally, polyphase AC systems. 00:00:36.840 --> 00:00:41.800 align:middle line:84% And let's perhaps first start by motivating it. 00:00:41.800 --> 00:00:46.960 align:middle line:84% Why would one think of wanting a polyphase system? 00:00:46.960 --> 00:00:49.780 align:middle line:90% And here's one of the notions. 00:00:49.780 --> 00:00:52.410 align:middle line:90% Suppose I had-- 00:00:52.410 --> 00:00:54.870 align:middle line:90% I was going to build a machine. 00:00:54.870 --> 00:00:58.985 align:middle line:84% So I'm going to have some rotor or some place 00:00:58.985 --> 00:01:00.360 align:middle line:84% where I'm going to make something 00:01:00.360 --> 00:01:02.490 align:middle line:90% that's going to try to spin. 00:01:02.490 --> 00:01:04.790 align:middle line:90% And so maybe I put a coil on it. 00:01:04.790 --> 00:01:07.491 align:middle line:90% 00:01:07.491 --> 00:01:10.840 align:middle line:84% And here, I'll draw some stator side coil, 00:01:10.840 --> 00:01:14.770 align:middle line:84% and I'll drive it with some voltage source. 00:01:14.770 --> 00:01:19.970 align:middle line:84% And if I do that, I can push some magnetic field here. 00:01:19.970 --> 00:01:23.630 align:middle line:84% So maybe I can create an x-directed magnetic field-- 00:01:23.630 --> 00:01:24.910 align:middle line:90% B sub x. 00:01:24.910 --> 00:01:28.540 align:middle line:90% So the notion is if I create-- 00:01:28.540 --> 00:01:30.770 align:middle line:84% in this case, I'm showing the magnetic flux density. 00:01:30.770 --> 00:01:33.010 align:middle line:84% If I create some x-directed flux density, 00:01:33.010 --> 00:01:37.870 align:middle line:84% I can cause some magnet or some piece of ferromagnetic material 00:01:37.870 --> 00:01:41.380 align:middle line:90% to align with that direction. 00:01:41.380 --> 00:01:45.310 align:middle line:84% So if this was going to give me-- 00:01:45.310 --> 00:01:49.330 align:middle line:84% I could create here, maybe B sub x 00:01:49.330 --> 00:01:55.906 align:middle line:84% is equal to B0 cosine of omega t, for example. 00:01:55.906 --> 00:01:57.370 align:middle line:84% And then if something was spinning, 00:01:57.370 --> 00:02:00.660 align:middle line:90% I could transfer energy to that. 00:02:00.660 --> 00:02:05.550 align:middle line:84% On the other hand that's only one direction. 00:02:05.550 --> 00:02:08.610 align:middle line:84% But imagine I came and said, all right. 00:02:08.610 --> 00:02:10.350 align:middle line:90% That's one phase. 00:02:10.350 --> 00:02:13.080 align:middle line:84% This could be a sinusoidal voltage I'm driving with. 00:02:13.080 --> 00:02:15.570 align:middle line:84% But perhaps I created a second one 00:02:15.570 --> 00:02:18.725 align:middle line:84% like this that's perpendicular to it. 00:02:18.725 --> 00:02:25.390 align:middle line:90% 00:02:25.390 --> 00:02:28.350 align:middle line:84% And maybe with this one, I could create 00:02:28.350 --> 00:02:35.360 align:middle line:84% some y-directed magnetic flux density. 00:02:35.360 --> 00:02:38.690 align:middle line:84% Well, maybe the orange set of coils here 00:02:38.690 --> 00:02:43.420 align:middle line:84% could create B sub y is equal to B0 sine omega t. 00:02:43.420 --> 00:02:46.160 align:middle line:90% 00:02:46.160 --> 00:02:48.200 align:middle line:84% If I did that with both of those, 00:02:48.200 --> 00:02:51.510 align:middle line:84% what would I get for a net magnetic field? 00:02:51.510 --> 00:02:54.080 align:middle line:84% I could then get a total magnetic field, 00:02:54.080 --> 00:02:56.910 align:middle line:84% or a total magnetic flux density as I'm drawing it, 00:02:56.910 --> 00:03:06.470 align:middle line:84% that B sub x is B0 cosine of omega t in the x-hat direction, 00:03:06.470 --> 00:03:13.700 align:middle line:84% plus B0 sine omega 0 t in the y-hat direction. 00:03:13.700 --> 00:03:22.190 align:middle line:84% So I'm using one coil to give me the x-directed and one coil 00:03:22.190 --> 00:03:24.200 align:middle line:90% to give me the y-directed. 00:03:24.200 --> 00:03:27.380 align:middle line:84% And notice that-- so these are-- the two coils 00:03:27.380 --> 00:03:32.970 align:middle line:84% are perpendicular in space or orthogonal in space. 00:03:32.970 --> 00:03:36.630 align:middle line:84% But the other thing is I'm making the two drives of them 00:03:36.630 --> 00:03:39.750 align:middle line:84% such that they're orthogonal in time as well. 00:03:39.750 --> 00:03:41.440 align:middle line:84% So they're perpendicular in time. 00:03:41.440 --> 00:03:42.540 align:middle line:90% And why would I do that? 00:03:42.540 --> 00:03:46.080 align:middle line:84% Well, let's just think about the magnitude and phase 00:03:46.080 --> 00:03:50.800 align:middle line:84% of the net flux density in this space. 00:03:50.800 --> 00:03:54.810 align:middle line:84% What I would then get is I would get the magnitude of B 00:03:54.810 --> 00:03:56.970 align:middle line:84% is the sum of the square roots of these 00:03:56.970 --> 00:04:00.930 align:middle line:84% is just going to be B0 because cosine 00:04:00.930 --> 00:04:04.200 align:middle line:90% squared plus sine squared is 1. 00:04:04.200 --> 00:04:08.370 align:middle line:84% So the net magnitude of this between x and y 00:04:08.370 --> 00:04:09.700 align:middle line:90% is just going to be 1 00:04:09.700 --> 00:04:14.070 align:middle line:84% And the angle of the net flux density 00:04:14.070 --> 00:04:18.899 align:middle line:90% is going to be the arctangent-- 00:04:18.899 --> 00:04:22.710 align:middle line:84% the angle in space is going to be the arctangent of sine 00:04:22.710 --> 00:04:27.330 align:middle line:84% of omega t over cosine of omega t, which is 00:04:27.330 --> 00:04:29.580 align:middle line:90% going to be equal to omega t. 00:04:29.580 --> 00:04:34.320 align:middle line:84% So what that says is if I play this game, what I'm going to get 00:04:34.320 --> 00:04:38.220 align:middle line:84% is a net magnetic field that has constant amplitude 00:04:38.220 --> 00:04:44.200 align:middle line:84% and rotates in space with an angular frequency omega t. 00:04:44.200 --> 00:04:49.690 align:middle line:84% So then if I put some of salient ferromagnetic material in here, 00:04:49.690 --> 00:04:52.390 align:middle line:84% or I put a magnet, a pole pair in here, 00:04:52.390 --> 00:04:56.220 align:middle line:84% I could make that rotate in space. 00:04:56.220 --> 00:04:59.360 align:middle line:84% So the concept-- and this concept 00:04:59.360 --> 00:05:04.760 align:middle line:84% of using spatially and time orthogonal 00:05:04.760 --> 00:05:07.310 align:middle line:84% signals to generate a rotating magnetic field is-- 00:05:07.310 --> 00:05:09.470 align:middle line:84% the first person who really made it practical 00:05:09.470 --> 00:05:12.210 align:middle line:84% and used it for practical purposes was Nikola Tesla. 00:05:12.210 --> 00:05:15.350 align:middle line:84% And that's the first thing that made him famous 00:05:15.350 --> 00:05:19.300 align:middle line:84% was this is how you can build AC machines. 00:05:19.300 --> 00:05:22.670 align:middle line:84% And so this is shown with two phase. 00:05:22.670 --> 00:05:28.640 align:middle line:84% And, in fact, Tesla's original systems were two phase. 00:05:28.640 --> 00:05:33.040 align:middle line:84% It turns out you can do the same thing with three phases. 00:05:33.040 --> 00:05:36.580 align:middle line:84% So you could imagine putting in-- 00:05:36.580 --> 00:05:39.400 align:middle line:84% instead of having two that are 90 degrees out of phase, 00:05:39.400 --> 00:05:50.140 align:middle line:84% you could imagine having a first one that generated something 00:05:50.140 --> 00:05:54.910 align:middle line:84% like this direction, a second one that 00:05:54.910 --> 00:05:57.950 align:middle line:90% generated a second direction-- 00:05:57.950 --> 00:06:00.660 align:middle line:90% 00:06:00.660 --> 00:06:02.750 align:middle line:84% second set of coils to generate a second direction 00:06:02.750 --> 00:06:04.730 align:middle line:90% that was this. 00:06:04.730 --> 00:06:07.650 align:middle line:90% And a third set of coils-- 00:06:07.650 --> 00:06:08.250 align:middle line:90% let's see. 00:06:08.250 --> 00:06:10.980 align:middle line:90% I've got orange, pink-- 00:06:10.980 --> 00:06:15.880 align:middle line:84% a third set of coils overlapped in space 00:06:15.880 --> 00:06:17.780 align:middle line:84% that would generate a third direction. 00:06:17.780 --> 00:06:19.480 align:middle line:84% And it turns out that if I, again, 00:06:19.480 --> 00:06:28.060 align:middle line:84% make the coils phase shifted in space and phase shifted in time, 00:06:28.060 --> 00:06:32.320 align:middle line:84% we can get a rotating magnetic field. 00:06:32.320 --> 00:06:35.230 align:middle line:84% Just to demonstrate this to you, Mansi 00:06:35.230 --> 00:06:38.710 align:middle line:84% has been very kind to set up a demonstration of this. 00:06:38.710 --> 00:06:41.470 align:middle line:84% And this is a modern version of a demonstration 00:06:41.470 --> 00:06:45.460 align:middle line:84% that Nikola Tesla himself did at the Columbian Exposition 00:06:45.460 --> 00:06:55.110 align:middle line:90% in 1893. 00:06:55.110 --> 00:06:55.860 align:middle line:90% MANSI JOISHER: OK. 00:06:55.860 --> 00:06:58.500 align:middle line:84% So today we have a demo to visualize a rotating 00:06:58.500 --> 00:07:00.000 align:middle line:90% magnetic field. 00:07:00.000 --> 00:07:02.970 align:middle line:84% The demo here is an adaption of Tesla's Egg 00:07:02.970 --> 00:07:05.470 align:middle line:90% of Columbus demo from 1893. 00:07:05.470 --> 00:07:08.310 align:middle line:84% Tesla used a two-phase inductor, but we're 00:07:08.310 --> 00:07:10.650 align:middle line:84% going to use a three-phase toroidal inductor here, 00:07:10.650 --> 00:07:12.330 align:middle line:84% and that's going to be our statehood. 00:07:12.330 --> 00:07:16.380 align:middle line:84% For our rotor, we're going to use this metal egg. 00:07:16.380 --> 00:07:19.980 align:middle line:84% And then on this side, we have our three-phase inverter 00:07:19.980 --> 00:07:21.520 align:middle line:90% with six switches. 00:07:21.520 --> 00:07:23.110 align:middle line:90% And this is our gating circuit. 00:07:23.110 --> 00:07:25.470 align:middle line:84% So what's going to happen is that we're 00:07:25.470 --> 00:07:27.720 align:middle line:84% going to create some rotating magnetic field using 00:07:27.720 --> 00:07:29.280 align:middle line:84% our statehood, and then that's going 00:07:29.280 --> 00:07:31.440 align:middle line:84% to induce some eddy currents in our rotor. 00:07:31.440 --> 00:07:32.500 align:middle line:90% That is our egg. 00:07:32.500 --> 00:07:34.930 align:middle line:84% And then it's going to force the egg to spin. 00:07:34.930 --> 00:07:38.940 align:middle line:84% So let's start by trying to slowly increase the bus voltage 00:07:38.940 --> 00:07:40.230 align:middle line:90% and see what's happen-- 00:07:40.230 --> 00:07:41.230 align:middle line:90% what's going to happen. 00:07:41.230 --> 00:07:43.780 align:middle line:84% And then I'm plotting the three-phase currents there. 00:07:43.780 --> 00:07:46.860 align:middle line:84% So they should be phase-shifted by 120 degrees. 00:07:46.860 --> 00:07:51.520 align:middle line:84% So I'm slowly increasing the bus voltage for the inverter, 00:07:51.520 --> 00:07:56.073 align:middle line:84% and we see that the phase currents slowly increase. 00:07:56.073 --> 00:07:59.090 align:middle line:90% 00:07:59.090 --> 00:08:01.670 align:middle line:84% And as I increase the voltage, we 00:08:01.670 --> 00:08:03.510 align:middle line:90% see the egg is slowly spinning. 00:08:03.510 --> 00:08:08.810 align:middle line:84% As I go higher, the egg starts spinning faster, faster. 00:08:08.810 --> 00:08:12.920 align:middle line:84% And then eventually, due to a gyroscopic action, 00:08:12.920 --> 00:08:18.380 align:middle line:84% the eggs going to start spinning at it's end, 00:08:18.380 --> 00:08:20.250 align:middle line:84% and it's going to start rotating here. 00:08:20.250 --> 00:08:24.380 align:middle line:84% So what we have here is that we have a rotating magnetic field 00:08:24.380 --> 00:08:28.200 align:middle line:84% from our stator, and it's forcing our rotor to rotate. 00:08:28.200 --> 00:08:33.651 align:middle line:84% And that's the key concept behind an induction motor. 00:08:33.651 --> 00:08:37.049 align:middle line:90% [APPLAUSE] 00:08:37.049 --> 00:08:37.549 align:middle line:90% 00:08:37.549 --> 00:08:39.007 align:middle line:84% DAVID PERREAULT: Thank you, Mansi-- 00:08:39.007 --> 00:08:41.979 align:middle line:90% 00:08:41.979 --> 00:08:45.680 align:middle line:84% a while industry founded on that demo. 00:08:45.680 --> 00:08:51.480 align:middle line:84% So let's talk about three-phase more broadly. 00:08:51.480 --> 00:08:57.410 align:middle line:84% So if I have a three-phase voltage set, 00:08:57.410 --> 00:09:07.926 align:middle line:84% maybe I could have of Va of t is equal to Vs sine omega t. 00:09:07.926 --> 00:09:16.470 align:middle line:84% Vb of t is equal to Vs sine of omega t minus 2 pi over 3. 00:09:16.470 --> 00:09:26.190 align:middle line:84% And Vc of t is equal to Vs sine of omega t plus 2 pi over 3. 00:09:26.190 --> 00:09:28.440 align:middle line:84% So we're going to have three sinusoids 00:09:28.440 --> 00:09:35.340 align:middle line:84% in time shifted by 120 degrees, or 2 pi over 3, from each other. 00:09:35.340 --> 00:09:41.760 align:middle line:84% Now, recall that we can write any of these sinusoidal time 00:09:41.760 --> 00:09:44.710 align:middle line:90% domain waveforms as phasors. 00:09:44.710 --> 00:09:55.470 align:middle line:84% So I can write Vx of t is equal to the real part of V x-hat e 00:09:55.470 --> 00:10:00.050 align:middle line:84% to the j omega t, where V x-hat is 00:10:00.050 --> 00:10:04.820 align:middle line:84% the phasor, which indicates the magnitude 00:10:04.820 --> 00:10:06.980 align:middle line:90% and phase of the sinusoid. 00:10:06.980 --> 00:10:12.830 align:middle line:84% So in this case, I could write Vs sine omega t 00:10:12.830 --> 00:10:18.290 align:middle line:84% as being equal to the real part of Vs e 00:10:18.290 --> 00:10:24.570 align:middle line:84% to the minus j pi over 2, e to the j omega t. 00:10:24.570 --> 00:10:27.570 align:middle line:90% 00:10:27.570 --> 00:10:31.320 align:middle line:90% And in this case, if I plotted-- 00:10:31.320 --> 00:10:39.540 align:middle line:84% this is my-- this could be my phasor VA hat, 00:10:39.540 --> 00:10:43.290 align:middle line:84% which says it has a magnitude of Vs 00:10:43.290 --> 00:10:45.510 align:middle line:90% and a phase of minus pi over 2. 00:10:45.510 --> 00:10:49.860 align:middle line:84% So on the real and imaginary plane, on the complex plane, 00:10:49.860 --> 00:10:53.400 align:middle line:84% it might look like this, where it 00:10:53.400 --> 00:10:56.580 align:middle line:84% has an angle of minus 90 degrees with respect to 0 00:10:56.580 --> 00:11:00.995 align:middle line:90% and an amplitude of Vs. 00:11:00.995 --> 00:11:06.530 align:middle line:84% And if I then said if this was VA hat, then I could have, 00:11:06.530 --> 00:11:16.990 align:middle line:84% say, VB hat would be here, and VC hat would be here. 00:11:16.990 --> 00:11:20.800 align:middle line:90% 00:11:20.800 --> 00:11:25.660 align:middle line:84% And so that's a snapshot of the magnitude and phase 00:11:25.660 --> 00:11:26.810 align:middle line:90% of each of these. 00:11:26.810 --> 00:11:29.980 align:middle line:84% When I'm multiplying by e to the g omega t, 00:11:29.980 --> 00:11:33.010 align:middle line:84% that means I'm taking this set of elements 00:11:33.010 --> 00:11:36.590 align:middle line:84% and rotating it by an angle omega t. 00:11:36.590 --> 00:11:40.340 align:middle line:84% So I could think of these phasors as spinning in time. 00:11:40.340 --> 00:11:42.670 align:middle line:84% And the real part, which is the projection 00:11:42.670 --> 00:11:44.260 align:middle line:84% to give me the time domain waveform, 00:11:44.260 --> 00:11:48.610 align:middle line:84% is really the instantaneous projection onto the real axis. 00:11:48.610 --> 00:11:51.700 align:middle line:84% So at time equals 0, VA is Vs sine omega 00:11:51.700 --> 00:11:57.160 align:middle line:84% t has 0 value because sine wave is 0 at time equals 0. 00:11:57.160 --> 00:12:00.570 align:middle line:84% If I waited until omega t equals 90, it would rotate up, 00:12:00.570 --> 00:12:06.990 align:middle line:84% and it would have a value Vs. So we often draw-- 00:12:06.990 --> 00:12:14.670 align:middle line:84% we often express our time domain waveforms as a set of phasors. 00:12:14.670 --> 00:12:17.490 align:middle line:90% Any questions about that? 00:12:17.490 --> 00:12:24.180 align:middle line:84% AUDIENCE: So the phase on sine omega t of pi over 2-- 00:12:24.180 --> 00:12:25.110 align:middle line:90% that's just-- 00:12:25.110 --> 00:12:26.893 align:middle line:90% that make it so it's 0 equals 0? 00:12:26.893 --> 00:12:27.810 align:middle line:90% DAVID PERREAULT: Yeah. 00:12:27.810 --> 00:12:31.380 align:middle line:84% This minus pi over 2 is just saying that if I'm a sine wave, 00:12:31.380 --> 00:12:36.000 align:middle line:84% a sine has 0 projection at t equals 0. 00:12:36.000 --> 00:12:39.540 align:middle line:84% And as I wait and omega t gets bigger, 00:12:39.540 --> 00:12:43.668 align:middle line:84% this kind of rotates around and becomes larger, 00:12:43.668 --> 00:12:44.960 align:middle line:90% which is what a sine wave does. 00:12:44.960 --> 00:12:48.440 align:middle line:90% 00:12:48.440 --> 00:12:56.720 align:middle line:84% So I can create a set of three phases that way 00:12:56.720 --> 00:12:59.480 align:middle line:84% and represent them with a phasor. 00:12:59.480 --> 00:13:01.850 align:middle line:84% So I can talk only about this component 00:13:01.850 --> 00:13:06.290 align:middle line:84% if I desire, understanding that the instantaneous waveform is 00:13:06.290 --> 00:13:11.480 align:middle line:84% rotated and projected to get the instantaneous time domain value. 00:13:11.480 --> 00:13:14.800 align:middle line:84% There's different ways we might connect these three voltage 00:13:14.800 --> 00:13:15.300 align:middle line:90% sources. 00:13:15.300 --> 00:13:19.200 align:middle line:84% So suppose I create three voltage sources this way. 00:13:19.200 --> 00:13:22.280 align:middle line:84% The most typical way you see a source connected 00:13:22.280 --> 00:13:28.610 align:middle line:84% is in a so-called y connection, also 00:13:28.610 --> 00:13:30.870 align:middle line:84% historically sometimes called a star connection. 00:13:30.870 --> 00:13:32.850 align:middle line:90% And one might do that this way. 00:13:32.850 --> 00:13:46.030 align:middle line:84% Maybe I would have VA, VB of t, and VC of t. 00:13:46.030 --> 00:13:49.320 align:middle line:90% 00:13:49.320 --> 00:13:52.380 align:middle line:84% And you notice that what I do is I-- 00:13:52.380 --> 00:13:54.330 align:middle line:84% for illustrative purposes, sometimes I 00:13:54.330 --> 00:13:58.260 align:middle line:84% draw the voltages' directions in my schematic 00:13:58.260 --> 00:14:01.050 align:middle line:84% in the way they're reflected in terms of their phasor diagram, 00:14:01.050 --> 00:14:03.240 align:middle line:84% just to show their relations to one another. 00:14:03.240 --> 00:14:05.620 align:middle line:84% That's kind of a convention that people follow. 00:14:05.620 --> 00:14:07.140 align:middle line:84% But what I'm doing is I'm connecting 00:14:07.140 --> 00:14:09.540 align:middle line:84% one terminal of each source to one node 00:14:09.540 --> 00:14:13.200 align:middle line:84% that we're going to call the neutral. 00:14:13.200 --> 00:14:14.860 align:middle line:90% And that's the neutral point. 00:14:14.860 --> 00:14:17.430 align:middle line:84% And then I have three voltages that I 00:14:17.430 --> 00:14:20.220 align:middle line:84% can play with, each with respect to this neutral voltage. 00:14:20.220 --> 00:14:26.300 align:middle line:84% So something where I brought out of this wire, this wire, 00:14:26.300 --> 00:14:28.050 align:middle line:84% and this wire are my three phase voltages. 00:14:28.050 --> 00:14:31.380 align:middle line:84% And the neutral would be called three-phase four wire. 00:14:31.380 --> 00:14:35.020 align:middle line:84% And that's a very common way to connect a source. 00:14:35.020 --> 00:14:36.730 align:middle line:84% You can also connect a load that way. 00:14:36.730 --> 00:14:39.780 align:middle line:90% And we'll talk about why. 00:14:39.780 --> 00:14:46.270 align:middle line:84% Another way one could connect it is to have a delta connection. 00:14:46.270 --> 00:14:50.200 align:middle line:84% So I could have-- for example, I could 00:14:50.200 --> 00:14:51.590 align:middle line:90% connect something this way. 00:14:51.590 --> 00:14:56.530 align:middle line:84% I could have a voltage VBC connected this way, 00:14:56.530 --> 00:15:05.310 align:middle line:90% a voltage VAB connected here. 00:15:05.310 --> 00:15:11.520 align:middle line:90% And a voltage VCB-- 00:15:11.520 --> 00:15:15.360 align:middle line:90% I'm sorry-- VCA connected here. 00:15:15.360 --> 00:15:22.600 align:middle line:84% And if I did that, then I could bring out these three leads. 00:15:22.600 --> 00:15:28.410 align:middle line:84% Now I have no neutral, but I still have A, B, and C, 00:15:28.410 --> 00:15:31.020 align:middle line:84% and I can just do the differential connections. 00:15:31.020 --> 00:15:36.810 align:middle line:84% So this is-- this is node A. This is still node B, 00:15:36.810 --> 00:15:39.090 align:middle line:90% and this is still node C. 00:15:39.090 --> 00:15:43.260 align:middle line:84% Now, this is a less common way to connect a set of sources 00:15:43.260 --> 00:15:46.020 align:middle line:84% because if there's any imbalance between these, 00:15:46.020 --> 00:15:48.300 align:middle line:84% I would get circulating currents around this loop, 00:15:48.300 --> 00:15:51.330 align:middle line:84% So people tend not to connect generators this way. 00:15:51.330 --> 00:15:53.230 align:middle line:84% But sometimes you see it done that way. 00:15:53.230 --> 00:15:54.790 align:middle line:84% I've seen it done that way before. 00:15:54.790 --> 00:15:58.500 align:middle line:84% It's not uncommon to connect loads that way. 00:15:58.500 --> 00:16:00.870 align:middle line:84% So these are two basic-- and this 00:16:00.870 --> 00:16:03.780 align:middle line:84% is called a delta connection, for obvious reasons. 00:16:03.780 --> 00:16:07.720 align:middle line:90% 00:16:07.720 --> 00:16:10.500 align:middle line:84% So you can either have your sources or your loads connected 00:16:10.500 --> 00:16:12.512 align:middle line:90% in delta or y. 00:16:12.512 --> 00:16:14.220 align:middle line:84% The only difference with delta connection 00:16:14.220 --> 00:16:17.040 align:middle line:84% is you have no neutral to trans-- 00:16:17.040 --> 00:16:20.820 align:middle line:90% to connect up to other things. 00:16:20.820 --> 00:16:22.270 align:middle line:90% Any questions about that? 00:16:22.270 --> 00:16:25.830 align:middle line:90% 00:16:25.830 --> 00:16:30.090 align:middle line:90% So why would we do this? 00:16:30.090 --> 00:16:32.220 align:middle line:84% Why bother with three-phase systems? 00:16:32.220 --> 00:16:34.460 align:middle line:84% And I said people almost exclusively 00:16:34.460 --> 00:16:36.110 align:middle line:90% do this at higher power levels. 00:16:36.110 --> 00:16:37.350 align:middle line:90% What is the advantage? 00:16:37.350 --> 00:16:39.800 align:middle line:84% Well, it turns out there's a lot of advantages 00:16:39.800 --> 00:16:41.960 align:middle line:84% of doing a three-phase system instead 00:16:41.960 --> 00:16:43.610 align:middle line:90% of a single-phase system. 00:16:43.610 --> 00:16:47.030 align:middle line:84% And let's go through those advantages. 00:16:47.030 --> 00:16:50.240 align:middle line:84% I've already shown you one, actually, 00:16:50.240 --> 00:16:54.890 align:middle line:84% and that is this one, in the sense that because I can create 00:16:54.890 --> 00:16:58.370 align:middle line:84% a rotating magnetic field, if I only had a single phase, 00:16:58.370 --> 00:17:02.060 align:middle line:84% if I started misaligned with my rotor, 00:17:02.060 --> 00:17:05.359 align:middle line:84% then I could get it going, and it would generate-- it would 00:17:05.359 --> 00:17:06.180 align:middle line:90% it would spin. 00:17:06.180 --> 00:17:07.760 align:middle line:90% I can transfer energy that way. 00:17:07.760 --> 00:17:11.630 align:middle line:84% But if I started out aligned, it just would never start. 00:17:11.630 --> 00:17:13.040 align:middle line:90% It would just sit there. 00:17:13.040 --> 00:17:15.240 align:middle line:84% Because I can only generate-- with single-phase, 00:17:15.240 --> 00:17:19.220 align:middle line:84% I can only generate one physical direction. 00:17:19.220 --> 00:17:21.835 align:middle line:84% Whereas, with polyphase I can generate multiple directions. 00:17:21.835 --> 00:17:22.710 align:middle line:90% So that's one reason. 00:17:22.710 --> 00:17:25.099 align:middle line:84% That's a zeroth reason I might do it. 00:17:25.099 --> 00:17:27.200 align:middle line:90% But what's another reason? 00:17:27.200 --> 00:17:30.230 align:middle line:90% Let's consider power transfer. 00:17:30.230 --> 00:17:36.800 align:middle line:84% If I just came up, and I gave you a single phase-- 00:17:36.800 --> 00:17:41.600 align:middle line:84% here we go, VS sine omega t, and I hook it 00:17:41.600 --> 00:17:48.380 align:middle line:84% to a load, R, what is the power that I transfer? 00:17:48.380 --> 00:17:52.890 align:middle line:90% Well, this is VA of t. 00:17:52.890 --> 00:17:57.110 align:middle line:84% So power would be equal to V squared over R. 00:17:57.110 --> 00:18:04.890 align:middle line:84% So it'd be just VS squared over R, sine squared of omega t, 00:18:04.890 --> 00:18:10.520 align:middle line:84% which through trigonometry I could rewrite as VS squared over 00:18:10.520 --> 00:18:17.030 align:middle line:84% 2R times 1 minus the cosine of 2 omega t. 00:18:17.030 --> 00:18:19.260 align:middle line:84% So what would that look like in time? 00:18:19.260 --> 00:18:24.480 align:middle line:84% If I plotted the power transfer to the resistor in time, 00:18:24.480 --> 00:18:25.660 align:middle line:90% that would look like this. 00:18:25.660 --> 00:18:34.130 align:middle line:84% I'd have an average value of VS squared over 2R, 00:18:34.130 --> 00:18:38.780 align:middle line:84% but it would pulsate because it pulsates because of this cosine 00:18:38.780 --> 00:18:40.400 align:middle line:90% of 2 omega t. 00:18:40.400 --> 00:18:41.480 align:middle line:90% And it would do this. 00:18:41.480 --> 00:18:45.290 align:middle line:84% It would pulsate between 0 and twice the average value 00:18:45.290 --> 00:18:47.180 align:middle line:90% like this. 00:18:47.180 --> 00:18:53.210 align:middle line:84% Every 0 crossing-- this is at twice the line frequency 00:18:53.210 --> 00:18:54.440 align:middle line:90% at 2 omega t. 00:18:54.440 --> 00:18:57.510 align:middle line:84% Every 0 crossing is because the voltage went through 0. 00:18:57.510 --> 00:19:00.000 align:middle line:84% When I got 0 voltage, I'm not getting any power transfer. 00:19:00.000 --> 00:19:02.270 align:middle line:84% So no matter what I do, I'm going 00:19:02.270 --> 00:19:05.290 align:middle line:90% to have this pulsating power. 00:19:05.290 --> 00:19:08.450 align:middle line:84% The way that reflects itself is even if I do have a single-phase 00:19:08.450 --> 00:19:11.203 align:middle line:84% motor and I'm doing that, I'm going to have torque ripple-- 00:19:11.203 --> 00:19:12.620 align:middle line:84% if it's running at constant speed, 00:19:12.620 --> 00:19:16.930 align:middle line:84% I'm going to have torque ripple at twice the line frequency. 00:19:16.930 --> 00:19:19.000 align:middle line:90% Or I'm going to have-- 00:19:19.000 --> 00:19:21.220 align:middle line:84% if I'm going to have a rectifier, 00:19:21.220 --> 00:19:23.770 align:middle line:84% and I want to deliver constant power to somewhere else, 00:19:23.770 --> 00:19:27.820 align:middle line:84% I'm going to have to buffer these energy pulsations. 00:19:27.820 --> 00:19:30.160 align:middle line:84% And so I'm going to have to put energy storage out there 00:19:30.160 --> 00:19:30.770 align:middle line:90% to do that. 00:19:30.770 --> 00:19:31.270 align:middle line:90% Yeah? 00:19:31.270 --> 00:19:36.640 align:middle line:84% AUDIENCE: So VS squared over 2R is the average? 00:19:36.640 --> 00:19:39.200 align:middle line:84% DAVID PERREAULT: VS squared over 2R is the average 00:19:39.200 --> 00:19:43.310 align:middle line:84% because the average of the cosine 2 omega t is 0. 00:19:43.310 --> 00:19:45.580 align:middle line:84% So if I took a time average of this, 00:19:45.580 --> 00:19:48.940 align:middle line:84% this term goes away and I get VS squared over 2R. 00:19:48.940 --> 00:19:52.760 align:middle line:84% And then I get this equal size pulsation. 00:19:52.760 --> 00:19:58.030 align:middle line:84% So the peak pulsation is equal to the average value. 00:19:58.030 --> 00:20:01.060 align:middle line:84% So what happens-- what would happen if I walked out and I 00:20:01.060 --> 00:20:03.310 align:middle line:90% said, OK, well, let me go-- 00:20:03.310 --> 00:20:07.990 align:middle line:84% instead of having one load, suppose I had three. 00:20:07.990 --> 00:20:10.810 align:middle line:84% And I come up here and I'd say, OK, 00:20:10.810 --> 00:20:16.820 align:middle line:84% let me connect one resistor to here, one resistor to here, 00:20:16.820 --> 00:20:18.830 align:middle line:90% and one resistor to here. 00:20:18.830 --> 00:20:20.190 align:middle line:90% What would that do? 00:20:20.190 --> 00:20:25.790 align:middle line:84% What would that net transfer to those three loads do? 00:20:25.790 --> 00:20:29.000 align:middle line:84% And we can write that the same way. 00:20:29.000 --> 00:20:30.560 align:middle line:90% So we could say, all right. 00:20:30.560 --> 00:20:37.160 align:middle line:84% Well, the power in this case is going 00:20:37.160 --> 00:20:46.790 align:middle line:84% to be equal to VS squared over R times sine squared of omega t, 00:20:46.790 --> 00:20:54.050 align:middle line:84% plus sine squared of omega t minus 2 pi over 3, 00:20:54.050 --> 00:20:59.065 align:middle line:84% plus sine squared of omega t plus 2 pi over 3. 00:20:59.065 --> 00:21:02.495 align:middle line:90% 00:21:02.495 --> 00:21:07.640 align:middle line:84% I can then rewrite these again as being equal to VS squared 00:21:07.640 --> 00:21:16.340 align:middle line:84% over 2R times 3 minus cosine of 2 omega t, 00:21:16.340 --> 00:21:25.040 align:middle line:84% minus cosine of 2 omega t, minus 4 pi over 3, 00:21:25.040 --> 00:21:32.030 align:middle line:84% minus cosine of omega t, plus 4 pi over 3. 00:21:32.030 --> 00:21:35.050 align:middle line:84% Now, why am I interested in that? 00:21:35.050 --> 00:21:39.360 align:middle line:84% If I look at these three terms, these things 00:21:39.360 --> 00:21:46.190 align:middle line:84% form a three-phase set at twice the line frequency. 00:21:46.190 --> 00:21:48.790 align:middle line:90% This should have been 2 omega t. 00:21:48.790 --> 00:21:52.030 align:middle line:84% So in other words, if I looked at the phasors 00:21:52.030 --> 00:21:55.000 align:middle line:84% for these three terms, they're at 2 omega t, 00:21:55.000 --> 00:22:00.630 align:middle line:84% but they are adding up the same way that those three signals add 00:22:00.630 --> 00:22:01.130 align:middle line:90% up. 00:22:01.130 --> 00:22:04.000 align:middle line:84% In other words, they add up to 0. 00:22:04.000 --> 00:22:09.830 align:middle line:84% So these three things net to 0 all the time. 00:22:09.830 --> 00:22:14.860 align:middle line:84% And then I just get a pure DC power transfer of three VS 00:22:14.860 --> 00:22:21.300 align:middle line:90% squared over 2R constant power. 00:22:21.300 --> 00:22:25.590 align:middle line:84% So in principle, then, if I had a three-phase rectifier that 00:22:25.590 --> 00:22:30.390 align:middle line:84% treated each line the same, it could draw constant power 00:22:30.390 --> 00:22:33.450 align:middle line:84% from those three phases and need no energy storage 00:22:33.450 --> 00:22:35.520 align:middle line:84% to deliver constant power to the output. 00:22:35.520 --> 00:22:37.440 align:middle line:84% Or I would need to have no torque 00:22:37.440 --> 00:22:42.270 align:middle line:84% ripple in principle, at least, for power transfer reasons. 00:22:42.270 --> 00:22:46.260 align:middle line:84% So this kind of constant power transfer capability 00:22:46.260 --> 00:22:47.830 align:middle line:84% of three-phase is a huge advantage. 00:22:47.830 --> 00:22:53.190 align:middle line:84% And the way to think about that intuitively 00:22:53.190 --> 00:22:58.890 align:middle line:84% is just that, OK, if I have three-phase shift in sinusoids, 00:22:58.890 --> 00:23:01.400 align:middle line:84% when one of them is crossing 0 and isn't delivering power, 00:23:01.400 --> 00:23:03.150 align:middle line:84% the other two can deliver power to make up 00:23:03.150 --> 00:23:04.268 align:middle line:90% for it and vice versa. 00:23:04.268 --> 00:23:06.060 align:middle line:84% So there's always somebody-- there's always 00:23:06.060 --> 00:23:08.790 align:middle line:84% a phase that can deliver power and make 00:23:08.790 --> 00:23:10.085 align:middle line:90% the power transfer constant. 00:23:10.085 --> 00:23:13.690 align:middle line:90% 00:23:13.690 --> 00:23:16.390 align:middle line:84% Now, I should say, by the way, you 00:23:16.390 --> 00:23:17.950 align:middle line:90% can do this with two-phase, too. 00:23:17.950 --> 00:23:21.610 align:middle line:84% Because if I thought about it, if I had a sine and a cosine, 00:23:21.610 --> 00:23:24.370 align:middle line:84% I'd have power as being sine squared plus cosine squared, 00:23:24.370 --> 00:23:25.850 align:middle line:90% which also adds to 1. 00:23:25.850 --> 00:23:30.220 align:middle line:84% So you can do the constant power transfer trick and the rotating 00:23:30.220 --> 00:23:32.320 align:middle line:84% magnetic field trick with two-phase as well 00:23:32.320 --> 00:23:35.290 align:middle line:90% as three-phase. 00:23:35.290 --> 00:23:37.940 align:middle line:90% So why might we do three-phase? 00:23:37.940 --> 00:23:41.830 align:middle line:84% And here's a very, very valuable reason why you might do it. 00:23:41.830 --> 00:23:46.660 align:middle line:84% Let's just think about suppose I go 00:23:46.660 --> 00:23:49.870 align:middle line:84% and I want to transfer power over some distance, 00:23:49.870 --> 00:23:51.220 align:middle line:90% So I have a generator. 00:23:51.220 --> 00:23:55.960 align:middle line:84% I want to send some power some distance, 00:23:55.960 --> 00:23:58.660 align:middle line:84% and then I want to throw it into a load. 00:23:58.660 --> 00:24:02.500 align:middle line:90% So here's my sources. 00:24:02.500 --> 00:24:04.070 align:middle line:90% Here's my three-phase. 00:24:04.070 --> 00:24:07.093 align:middle line:84% I'll make it a y-connected system. 00:24:07.093 --> 00:24:12.907 align:middle line:90% 00:24:12.907 --> 00:24:19.330 align:middle line:84% And now suppose I wanted to go send this single-phase. 00:24:19.330 --> 00:24:22.520 align:middle line:90% Here's my wires. 00:24:22.520 --> 00:24:23.950 align:middle line:90% Here's my first wire. 00:24:23.950 --> 00:24:27.910 align:middle line:90% 00:24:27.910 --> 00:24:31.500 align:middle line:90% And I'll hook my load here. 00:24:31.500 --> 00:24:36.940 align:middle line:84% And keep in mind, these wires have some resistance to them. 00:24:36.940 --> 00:24:38.620 align:middle line:84% So if I want to keep my loss down, 00:24:38.620 --> 00:24:40.810 align:middle line:84% I need to use a certain amount of size of wire 00:24:40.810 --> 00:24:43.430 align:middle line:84% to carry the current that I want to carry. 00:24:43.430 --> 00:24:47.080 align:middle line:84% So that's the single-phase system right there. 00:24:47.080 --> 00:24:48.060 align:middle line:90% I deliver the wire. 00:24:48.060 --> 00:24:50.750 align:middle line:84% I got to buy so much copper to deliver the wire 00:24:50.750 --> 00:24:53.540 align:middle line:90% within an allowed loss limit. 00:24:53.540 --> 00:24:55.400 align:middle line:84% But suppose I go out and say, OK, 00:24:55.400 --> 00:24:58.520 align:middle line:90% let me go use two other phases. 00:24:58.520 --> 00:25:02.980 align:middle line:84% So I'll make-- here's my other conductor here. 00:25:02.980 --> 00:25:06.940 align:middle line:84% And maybe I'll connect them on this side as well. 00:25:06.940 --> 00:25:09.830 align:middle line:84% Here's another one, and I'll do my third one. 00:25:09.830 --> 00:25:14.770 align:middle line:84% So I'm sending current out this wire and back this wire. 00:25:14.770 --> 00:25:16.700 align:middle line:90% And then I'll go do my last one. 00:25:16.700 --> 00:25:20.050 align:middle line:90% I'll send current out this wire. 00:25:20.050 --> 00:25:27.440 align:middle line:84% I'll connect, and I'll send current back through this wire 00:25:27.440 --> 00:25:29.510 align:middle line:90% as well. 00:25:29.510 --> 00:25:34.010 align:middle line:84% So now I'm transferring three times as much power, 00:25:34.010 --> 00:25:36.590 align:middle line:84% if all the resistors were the same. 00:25:36.590 --> 00:25:41.930 align:middle line:84% But notice that I said all these three voltages and the resulting 00:25:41.930 --> 00:25:43.800 align:middle line:84% all these three currents add to 0. 00:25:43.800 --> 00:25:52.010 align:middle line:84% And that means that the net current in these center 00:25:52.010 --> 00:25:55.240 align:middle line:90% conductors is what? 00:25:55.240 --> 00:25:56.660 align:middle line:90% 0. 00:25:56.660 --> 00:25:59.810 align:middle line:84% So suddenly, if what I cared about 00:25:59.810 --> 00:26:04.640 align:middle line:84% was the copper loss to send power down the line, 00:26:04.640 --> 00:26:07.987 align:middle line:84% I can basically throw away half of my conductors 00:26:07.987 --> 00:26:10.320 align:middle line:84% for a three-phase system instead of single-phase system. 00:26:10.320 --> 00:26:14.240 align:middle line:84% I need half the copper to carry that much current. 00:26:14.240 --> 00:26:19.250 align:middle line:84% And that is a huge advantage if your goal is to transfer power 00:26:19.250 --> 00:26:20.310 align:middle line:90% over long distances. 00:26:20.310 --> 00:26:24.758 align:middle line:84% So three-- in fact, AC distribution, if you see what-- 00:26:24.758 --> 00:26:26.300 align:middle line:84% you look up, what you're going to see 00:26:26.300 --> 00:26:29.520 align:middle line:84% is basically three wires going along in all these towers. 00:26:29.520 --> 00:26:32.390 align:middle line:84% That's why is because basically they don't need 00:26:32.390 --> 00:26:35.477 align:middle line:90% to carry six conductors do it. 00:26:35.477 --> 00:26:37.560 align:middle line:84% They only need to carry three conductors, or three 00:26:37.560 --> 00:26:40.680 align:middle line:84% heftily sized conductors, in order to do that. 00:26:40.680 --> 00:26:42.610 align:middle line:84% So that's a tremendous advantage. 00:26:42.610 --> 00:26:46.260 align:middle line:84% That advantage also applies to things like motors. 00:26:46.260 --> 00:26:48.690 align:middle line:84% So if you wind your motor, you can get away with less-- 00:26:48.690 --> 00:26:51.840 align:middle line:84% effectively, less copper to do the same thing. 00:26:51.840 --> 00:26:54.600 align:middle line:84% It also applies to fluxes and transformers. 00:26:54.600 --> 00:26:56.220 align:middle line:84% We showed if you're going to have 00:26:56.220 --> 00:27:00.510 align:middle line:84% three-phase carrying of flux, essentially what 00:27:00.510 --> 00:27:04.308 align:middle line:84% we're doing here is that we're using the other phases to be 00:27:04.308 --> 00:27:05.850 align:middle line:84% our return conductors in the same way 00:27:05.850 --> 00:27:08.280 align:middle line:84% you can use your other legs in a three-phase transformer 00:27:08.280 --> 00:27:09.790 align:middle line:90% to be your flux returns. 00:27:09.790 --> 00:27:12.180 align:middle line:84% So there's tremendous advantage in reducing 00:27:12.180 --> 00:27:15.870 align:middle line:84% the size of equipment by using polyphase. 00:27:15.870 --> 00:27:16.980 align:middle line:90% Now, I should say-- 00:27:16.980 --> 00:27:19.470 align:middle line:84% I'll give you one little tiny caveat 00:27:19.470 --> 00:27:26.190 align:middle line:84% to that, which is that if I thought about the insulation 00:27:26.190 --> 00:27:27.240 align:middle line:90% rating of these-- 00:27:27.240 --> 00:27:31.260 align:middle line:84% so the voltage between this conductor and the neutral 00:27:31.260 --> 00:27:36.210 align:middle line:84% is VS. While I haven't calculated it for you 00:27:36.210 --> 00:27:44.410 align:middle line:84% yet, the voltage rating between this phase and, say, 00:27:44.410 --> 00:27:47.590 align:middle line:84% this phase is actually the square root of 3 VS. 00:27:47.590 --> 00:27:51.108 align:middle line:84% So it turns out you need a little bit more insulation 00:27:51.108 --> 00:27:52.900 align:middle line:84% if you're going to put this conductor right 00:27:52.900 --> 00:27:55.108 align:middle line:84% next to this conductor than if you put this conductor 00:27:55.108 --> 00:27:56.960 align:middle line:90% next to the ground. 00:27:56.960 --> 00:27:58.810 align:middle line:84% But if I cared about insulation, I 00:27:58.810 --> 00:28:01.240 align:middle line:84% could just turn down the voltage, 00:28:01.240 --> 00:28:03.310 align:middle line:84% and I'd still get an advantage of the 2 00:28:03.310 --> 00:28:06.370 align:middle line:84% over the square root of 3 in terms of the amount of power 00:28:06.370 --> 00:28:08.030 align:middle line:90% I could handle for a given loss. 00:28:08.030 --> 00:28:11.740 align:middle line:84% So essentially, depending upon whether you only 00:28:11.740 --> 00:28:15.280 align:middle line:84% care about your conductor loss or you care about insulation is 00:28:15.280 --> 00:28:17.410 align:middle line:84% what costs you everything, it's somewhere between 2 00:28:17.410 --> 00:28:19.202 align:middle line:84% over the square root of 3 and a factor of 2 00:28:19.202 --> 00:28:21.360 align:middle line:90% advantage to having polyphase. 00:28:21.360 --> 00:28:24.890 align:middle line:84% So it's a really big advantage in practice. 00:28:24.890 --> 00:28:26.290 align:middle line:84% So if you're at really low power, 00:28:26.290 --> 00:28:27.790 align:middle line:84% maybe you don't need the complexity. 00:28:27.790 --> 00:28:30.100 align:middle line:84% But if you want to transmit lots of power, 00:28:30.100 --> 00:28:32.700 align:middle line:90% polyphase is really your friend. 00:28:32.700 --> 00:28:35.845 align:middle line:90% 00:28:35.845 --> 00:28:38.440 align:middle line:90% What else can we do? 00:28:38.440 --> 00:28:43.120 align:middle line:84% Here, I showed my source is connected in y, 00:28:43.120 --> 00:28:45.280 align:middle line:90% and my load is connected in y. 00:28:45.280 --> 00:28:49.160 align:middle line:84% And that's what lets me throw out 00:28:49.160 --> 00:28:52.040 align:middle line:84% a lot of the required heavy copper conductors. 00:28:52.040 --> 00:28:55.190 align:middle line:84% But there's nothing that says I couldn't come back 00:28:55.190 --> 00:29:01.490 align:middle line:84% here and create a polyphase source that was like this again. 00:29:01.490 --> 00:29:09.180 align:middle line:84% Here's VA, here's VB, and here's VC. 00:29:09.180 --> 00:29:12.940 align:middle line:90% 00:29:12.940 --> 00:29:15.250 align:middle line:90% And here's my neutral. 00:29:15.250 --> 00:29:17.260 align:middle line:84% There's nothing that says I actually 00:29:17.260 --> 00:29:20.740 align:middle line:84% have to connect my loads the same way. 00:29:20.740 --> 00:29:22.400 align:middle line:90% I could do something different. 00:29:22.400 --> 00:29:27.460 align:middle line:84% I could, for example, go connect my loads like this. 00:29:27.460 --> 00:29:29.680 align:middle line:84% I could connect my source and delta-- 00:29:29.680 --> 00:29:32.370 align:middle line:84% my source in y and my load in delta, for example. 00:29:32.370 --> 00:29:35.920 align:middle line:90% 00:29:35.920 --> 00:29:40.960 align:middle line:84% So that means that for each of these loads, if this 00:29:40.960 --> 00:29:45.790 align:middle line:84% is V sub a and this is V sub b, I'm 00:29:45.790 --> 00:29:48.400 align:middle line:84% now going to have a different voltage across the actual load 00:29:48.400 --> 00:29:51.907 align:middle line:84% resistors than if I did this trick. 00:29:51.907 --> 00:29:53.240 align:middle line:90% Well, what would that look like? 00:29:53.240 --> 00:29:55.100 align:middle line:90% What does V ab look like? 00:29:55.100 --> 00:30:01.270 align:middle line:84% Well, this is where phasors come in really handy here. 00:30:01.270 --> 00:30:08.225 align:middle line:84% So if I said, OK, here's my complex plane, 00:30:08.225 --> 00:30:13.000 align:middle line:84% and I'm just going to draw the real and the imaginary axis. 00:30:13.000 --> 00:30:14.680 align:middle line:90% I could say that-- 00:30:14.680 --> 00:30:16.690 align:middle line:90% let me just keep consistent. 00:30:16.690 --> 00:30:25.460 align:middle line:84% VA is-- here's VA, and it has magnitude-- 00:30:25.460 --> 00:30:28.970 align:middle line:84% it has phase of minus 90 degrees and a magnitude of VS. 00:30:28.970 --> 00:30:30.500 align:middle line:90% And here's VB. 00:30:30.500 --> 00:30:36.930 align:middle line:84% It also has a magnitude of VS. So here's-- this is-- 00:30:36.930 --> 00:30:38.470 align:middle line:90% I should say, be careful. 00:30:38.470 --> 00:30:39.820 align:middle line:90% This is VA hat. 00:30:39.820 --> 00:30:41.770 align:middle line:90% That's my phasor for VA. 00:30:41.770 --> 00:30:44.070 align:middle line:90% This is VB hat. 00:30:44.070 --> 00:30:47.950 align:middle line:84% What would my phasor for VAB look like? 00:30:47.950 --> 00:30:50.560 align:middle line:84% Well, I can do subtraction in the phasor plane. 00:30:50.560 --> 00:30:52.350 align:middle line:90% I can just do it geometrically. 00:30:52.350 --> 00:30:54.580 align:middle line:84% So what that would look like is VA looks like that. 00:30:54.580 --> 00:30:55.680 align:middle line:90% VAB looks like that. 00:30:55.680 --> 00:31:00.270 align:middle line:84% VA minus VB, which is VAB hat, would be just VA 00:31:00.270 --> 00:31:02.190 align:middle line:90% plus the negative of VB. 00:31:02.190 --> 00:31:04.100 align:middle line:84% And it would look something like this. 00:31:04.100 --> 00:31:08.892 align:middle line:90% 00:31:08.892 --> 00:31:12.560 align:middle line:90% So this would be VAB hat. 00:31:12.560 --> 00:31:16.250 align:middle line:84% And it turns out that the length of this vector 00:31:16.250 --> 00:31:20.850 align:middle line:84% is the square root of three VS. This is just basic trigonometry. 00:31:20.850 --> 00:31:25.970 align:middle line:84% And the phase of this vector is pi over 6. 00:31:25.970 --> 00:31:31.830 align:middle line:84% So VAB will lead VA by pi over 6. 00:31:31.830 --> 00:31:36.140 align:middle line:84% So what I would get is VAB of t would 00:31:36.140 --> 00:31:40.610 align:middle line:84% be equal to the square root of 3 VS times 00:31:40.610 --> 00:31:48.950 align:middle line:84% sine of omega t plus pi over 6 because it leads VA 00:31:48.950 --> 00:31:51.000 align:middle line:90% by pi over 6. 00:31:51.000 --> 00:31:54.420 align:middle line:90% Any questions about that? 00:31:54.420 --> 00:31:55.270 align:middle line:90% Yeah? 00:31:55.270 --> 00:31:56.645 align:middle line:84% AUDIENCE: This is just semantics, 00:31:56.645 --> 00:32:00.300 align:middle line:84% but is there a reason why we use sine instead of cos? 00:32:00.300 --> 00:32:01.900 align:middle line:90% DAVID PERREAULT: No. 00:32:01.900 --> 00:32:04.340 align:middle line:84% I just decided to start with sines today. 00:32:04.340 --> 00:32:04.840 align:middle line:90% Yeah. 00:32:04.840 --> 00:32:06.382 align:middle line:84% I mean, you could do it with cosines, 00:32:06.382 --> 00:32:09.230 align:middle line:84% and then everything would be rotated by 90 degrees. 00:32:09.230 --> 00:32:09.910 align:middle line:90% You know what? 00:32:09.910 --> 00:32:12.640 align:middle line:84% The real reason I'm using sines is because they're 0 at t 00:32:12.640 --> 00:32:15.040 align:middle line:84% equals 0, so they're easy to draw. 00:32:15.040 --> 00:32:15.640 align:middle line:90% But no. 00:32:15.640 --> 00:32:17.890 align:middle line:84% You could do-- in fact, if you don't like it, 00:32:17.890 --> 00:32:22.550 align:middle line:84% just weight pi over 6 and then you've got cosines. 00:32:22.550 --> 00:32:23.050 align:middle line:90% Yeah. 00:32:23.050 --> 00:32:25.660 align:middle line:84% The thing that's important about three-phase, 00:32:25.660 --> 00:32:31.240 align:middle line:84% however, is making sure which order is which. 00:32:31.240 --> 00:32:33.040 align:middle line:84% And, in fact, we'll talk about this. 00:32:33.040 --> 00:32:36.570 align:middle line:84% But they often color-code the leads-- 00:32:36.570 --> 00:32:39.053 align:middle line:84% you need these different leads that you're wiring. 00:32:39.053 --> 00:32:41.470 align:middle line:84% And you've got to make sure you get your phase order right 00:32:41.470 --> 00:32:46.630 align:middle line:84% because otherwise, things rotate in the opposite direction 00:32:46.630 --> 00:32:48.220 align:middle line:90% from what you think. 00:32:48.220 --> 00:32:51.250 align:middle line:84% And there's a very famous example 00:32:51.250 --> 00:32:56.110 align:middle line:84% of this, where there was there was a famous English researcher 00:32:56.110 --> 00:33:00.070 align:middle line:84% that used to make three-phase, essentially, railguns using 00:33:00.070 --> 00:33:01.530 align:middle line:90% polyphase power. 00:33:01.530 --> 00:33:05.430 align:middle line:84% And you use it to throw a projectile off the end. 00:33:05.430 --> 00:33:08.390 align:middle line:84% And he was doing a demo for the, I think, the Prince of Wales, 00:33:08.390 --> 00:33:10.350 align:middle line:90% like, the royalty in England. 00:33:10.350 --> 00:33:14.270 align:middle line:84% And in between, he actually-- somebody had shut it down. 00:33:14.270 --> 00:33:16.860 align:middle line:84% And he reconnected, and he reconnected it backwards. 00:33:16.860 --> 00:33:19.550 align:middle line:84% So instead of throwing the projectile that way, 00:33:19.550 --> 00:33:22.160 align:middle line:84% it threw the projectile that way and almost took the head off 00:33:22.160 --> 00:33:23.500 align:middle line:90% of the Prince of Wales. 00:33:23.500 --> 00:33:27.030 align:middle line:84% So you do have to be careful about what your phase order is. 00:33:27.030 --> 00:33:30.570 align:middle line:84% But whether it's sine or cosine, take your pick. 00:33:30.570 --> 00:33:37.120 align:middle line:84% So what this says is, if I did this, I get this scaling. 00:33:37.120 --> 00:33:40.860 align:middle line:84% If I looked at the other line-to-line phases-- 00:33:40.860 --> 00:33:42.600 align:middle line:90% this is VAB I just plotted-- 00:33:42.600 --> 00:33:45.450 align:middle line:84% I will get another three-phase set that 00:33:45.450 --> 00:33:46.873 align:middle line:90% essentially looks like this. 00:33:46.873 --> 00:33:50.360 align:middle line:90% 00:33:50.360 --> 00:33:52.430 align:middle line:84% So I get a scaling by the square root of 3, 00:33:52.430 --> 00:33:54.020 align:middle line:90% and I get a phase shift. 00:33:54.020 --> 00:33:56.810 align:middle line:84% And it may be that maybe I have a load that wants 00:33:56.810 --> 00:33:58.020 align:middle line:90% to have higher resistance. 00:33:58.020 --> 00:34:01.432 align:middle line:84% So that scale of square root of 3 and voltage does me some good. 00:34:01.432 --> 00:34:03.890 align:middle line:84% And what we're going to see is there are certain converters 00:34:03.890 --> 00:34:05.900 align:middle line:84% where if I can generate a natural phase 00:34:05.900 --> 00:34:09.860 align:middle line:84% shift by a square root of 3, I get an advantage. 00:34:09.860 --> 00:34:11.790 align:middle line:90% So that can be handy in itself. 00:34:11.790 --> 00:34:13.350 align:middle line:84% But here's the other piece of it. 00:34:13.350 --> 00:34:16.245 align:middle line:84% By adding up, I can take transformers-- 00:34:16.245 --> 00:34:18.620 align:middle line:84% if I had this three-phase set, I could take transformers, 00:34:18.620 --> 00:34:20.870 align:middle line:84% take a piece of this voltage, a piece of this voltage, 00:34:20.870 --> 00:34:23.719 align:middle line:84% and a piece of this voltage, and if I do that in a balanced way, 00:34:23.719 --> 00:34:26.210 align:middle line:84% I can actually create three-phase sets 00:34:26.210 --> 00:34:30.040 align:middle line:84% with any arbitrary phase shift that I want. 00:34:30.040 --> 00:34:33.350 align:middle line:84% And that turns out to be handy for some kinds of converters 00:34:33.350 --> 00:34:35.350 align:middle line:84% you might want to build because we can do things 00:34:35.350 --> 00:34:36.429 align:middle line:90% like we talked about-- 00:34:36.429 --> 00:34:39.550 align:middle line:84% harmonic cancellation or ripple cancellation with interleaving. 00:34:39.550 --> 00:34:44.968 align:middle line:84% I have a natural way to generate phase-shifted sets of signals 00:34:44.968 --> 00:34:46.510 align:middle line:84% if I have a balanced three-phase set, 00:34:46.510 --> 00:34:49.190 align:middle line:84% and I can generate other balanced three-phase sets. 00:34:49.190 --> 00:34:52.090 align:middle line:84% And when I say balanced, I mean the three of them 00:34:52.090 --> 00:34:55.540 align:middle line:84% add to 0 instantaneously at any given time. 00:34:55.540 --> 00:34:59.740 align:middle line:84% I guess I left off my third phase here, 00:34:59.740 --> 00:35:02.640 align:middle line:84% which should have been like this-- 00:35:02.640 --> 00:35:04.710 align:middle line:90% VC. 00:35:04.710 --> 00:35:06.155 align:middle line:90% Any questions about that? 00:35:06.155 --> 00:35:09.950 align:middle line:90% 00:35:09.950 --> 00:35:17.050 align:middle line:84% So in terms of the benefit of doing polyphase, 00:35:17.050 --> 00:35:21.370 align:middle line:84% we've said we can transfer constant power, 00:35:21.370 --> 00:35:23.650 align:middle line:84% and hence, get constant torque, generate 00:35:23.650 --> 00:35:25.610 align:middle line:90% rotating magnetic fields. 00:35:25.610 --> 00:35:30.220 align:middle line:84% We can send energy at much lower transmission loss, which 00:35:30.220 --> 00:35:32.020 align:middle line:84% is why all long distance things are either 00:35:32.020 --> 00:35:35.830 align:middle line:84% done as polyphase AC or sometimes high voltage DC, 00:35:35.830 --> 00:35:38.230 align:middle line:84% depending upon what you're doing. 00:35:38.230 --> 00:35:42.550 align:middle line:84% There is another huge advantage to polyphase, 00:35:42.550 --> 00:35:46.580 align:middle line:84% and we're going to see this as we start to look at converters, 00:35:46.580 --> 00:35:48.200 align:middle line:90% and that's the following. 00:35:48.200 --> 00:35:54.910 align:middle line:84% Suppose I went and built a system like this. 00:35:54.910 --> 00:35:59.540 align:middle line:90% But let me imagine-- 00:35:59.540 --> 00:36:02.230 align:middle line:84% in fact, what I'll do is let me connect up a y-connected load 00:36:02.230 --> 00:36:03.490 align:middle line:90% here. 00:36:03.490 --> 00:36:06.220 align:middle line:84% So I'll go-- and it doesn't actually 00:36:06.220 --> 00:36:08.320 align:middle line:84% matter if the load is y or delta, 00:36:08.320 --> 00:36:10.840 align:middle line:90% but it's clearer to see here. 00:36:10.840 --> 00:36:17.115 align:middle line:84% So suppose I have some set of loads that looks like this. 00:36:17.115 --> 00:36:28.310 align:middle line:90% 00:36:28.310 --> 00:36:29.972 align:middle line:90% Actually, no. 00:36:29.972 --> 00:36:30.930 align:middle line:90% Let me back up on that. 00:36:30.930 --> 00:36:32.520 align:middle line:84% Let me do the delta-connected load. 00:36:32.520 --> 00:36:33.900 align:middle line:84% It's actually easier to see in delta. 00:36:33.900 --> 00:36:34.400 align:middle line:90% Sorry. 00:36:34.400 --> 00:36:36.890 align:middle line:90% 00:36:36.890 --> 00:36:40.410 align:middle line:84% It applies either way, but suppose I do this. 00:36:40.410 --> 00:36:42.000 align:middle line:90% Suppose I connect up. 00:36:42.000 --> 00:36:47.240 align:middle line:84% I have some load here, and then I 00:36:47.240 --> 00:36:52.765 align:middle line:84% connect another load here and then the last load here. 00:36:52.765 --> 00:36:58.700 align:middle line:90% 00:36:58.700 --> 00:37:02.945 align:middle line:84% So there's no neutral point connection in this thing. 00:37:02.945 --> 00:37:08.390 align:middle line:84% And If I looked at these things-- now, 00:37:08.390 --> 00:37:11.160 align:middle line:84% these could be resistors, in which case everything is simple. 00:37:11.160 --> 00:37:14.390 align:middle line:84% But if I'm going to start to create rectifiers 00:37:14.390 --> 00:37:18.215 align:middle line:84% or other elements, just because my voltages are 00:37:18.215 --> 00:37:20.340 align:middle line:84% sine waves doesn't mean my currents are sine waves. 00:37:20.340 --> 00:37:21.440 align:middle line:90% If you think about-- 00:37:21.440 --> 00:37:22.940 align:middle line:84% right at the beginning of class we 00:37:22.940 --> 00:37:29.120 align:middle line:84% said we could have a rectifier waveform whose current looked 00:37:29.120 --> 00:37:31.650 align:middle line:84% like a square wave or something like that. 00:37:31.650 --> 00:37:35.570 align:middle line:84% The currents don't have to follow and be linear 00:37:35.570 --> 00:37:36.750 align:middle line:90% compared to the voltages. 00:37:36.750 --> 00:37:38.340 align:middle line:84% They don't have to be proportional. 00:37:38.340 --> 00:37:42.620 align:middle line:84% So let me just imagine that these are some kind of nonlinear 00:37:42.620 --> 00:37:43.410 align:middle line:90% elements. 00:37:43.410 --> 00:37:45.413 align:middle line:90% And the only thing I'm-- 00:37:45.413 --> 00:37:47.330 align:middle line:84% the only constraint I'm going to place on them 00:37:47.330 --> 00:37:52.400 align:middle line:84% is they act in a way that whatever this guy is doing, 00:37:52.400 --> 00:37:56.550 align:middle line:84% this guy is doing a third of a cycle later. 00:37:56.550 --> 00:38:02.040 align:middle line:84% So what I'm saying is if this were some current-- 00:38:02.040 --> 00:38:11.970 align:middle line:84% I'll call it Ix of t, then this current-- 00:38:11.970 --> 00:38:16.140 align:middle line:84% and I'm not I'm not keeping to my earlier color conventions, 00:38:16.140 --> 00:38:21.320 align:middle line:84% but this current then would be Ix-- 00:38:21.320 --> 00:38:23.540 align:middle line:90% this would be I of x-- 00:38:23.540 --> 00:38:29.000 align:middle line:84% I sub x of t minus capital T over 3. 00:38:29.000 --> 00:38:32.270 align:middle line:84% I'm getting a phase shift in my currents. 00:38:32.270 --> 00:38:36.030 align:middle line:84% So then what is this current going to be? 00:38:36.030 --> 00:38:39.170 align:middle line:84% If I looked at the net line current-- 00:38:39.170 --> 00:38:40.775 align:middle line:90% so I'll look at this current-- 00:38:40.775 --> 00:38:43.460 align:middle line:90% 00:38:43.460 --> 00:38:46.940 align:middle line:84% I'm going to call this I sub b of t 00:38:46.940 --> 00:38:53.480 align:middle line:84% is simply going to be I sub x of t minus I sub x of t 00:38:53.480 --> 00:38:57.770 align:middle line:90% minus capital T over 3. 00:38:57.770 --> 00:38:59.480 align:middle line:84% I have a third of a cycle phase shift, 00:38:59.480 --> 00:39:03.380 align:middle line:84% a third of a fundamental cycle phase shift. 00:39:03.380 --> 00:39:06.560 align:middle line:84% And he's the difference between something and something shifted 00:39:06.560 --> 00:39:09.350 align:middle line:90% by a third of a cycle. 00:39:09.350 --> 00:39:11.770 align:middle line:90% Well, why is that important? 00:39:11.770 --> 00:39:19.510 align:middle line:84% Suppose I could write Ix of t as a summation. 00:39:19.510 --> 00:39:21.340 align:middle line:84% Let's assume he has no DC component. 00:39:21.340 --> 00:39:24.250 align:middle line:84% So this could be n equal to 1 to infinity of I 00:39:24.250 --> 00:39:31.030 align:middle line:84% sub n sine of n omega t plus phi sub n. 00:39:31.030 --> 00:39:36.460 align:middle line:84% That means that I sub b of t would 00:39:36.460 --> 00:39:41.020 align:middle line:84% be equal to this minus a shift of a third of a cycle, which 00:39:41.020 --> 00:39:45.310 align:middle line:84% I could rewrite as n equals 1 to infinity of I 00:39:45.310 --> 00:39:52.990 align:middle line:84% sub n times sine of n omega t plus phi sub n, 00:39:52.990 --> 00:40:02.985 align:middle line:84% minus sine of n omega t plus phi sub n, plus nT over 3. 00:40:02.985 --> 00:40:07.570 align:middle line:90% 00:40:07.570 --> 00:40:10.370 align:middle line:84% So it's the difference between a signal and a signal 00:40:10.370 --> 00:40:14.240 align:middle line:84% where I'm shifting by T over 3 in time. 00:40:14.240 --> 00:40:19.860 align:middle line:84% But for the n-th harmonic, that is a phase of nT over 3. 00:40:19.860 --> 00:40:23.667 align:middle line:90% And what that means is-- 00:40:23.667 --> 00:40:24.750 align:middle line:90% actually, that should be-- 00:40:24.750 --> 00:40:25.250 align:middle line:90% I'm sorry. 00:40:25.250 --> 00:40:28.545 align:middle line:84% This should be n omega T over 3-- 00:40:28.545 --> 00:40:31.650 align:middle line:90% 00:40:31.650 --> 00:40:34.080 align:middle line:90% n omega T over 3. 00:40:34.080 --> 00:40:36.670 align:middle line:90% And omega T is just 2 pi. 00:40:36.670 --> 00:40:39.000 align:middle line:90% So it's n times 2 pi over 3. 00:40:39.000 --> 00:40:43.270 align:middle line:84% So that means every time n is a multiple of 3, 00:40:43.270 --> 00:40:45.930 align:middle line:84% I'm taking a difference between something and something 00:40:45.930 --> 00:40:48.050 align:middle line:90% with the same phase. 00:40:48.050 --> 00:40:51.800 align:middle line:84% So this is exactly the harmonic cancelation game 00:40:51.800 --> 00:40:55.860 align:middle line:84% we were talking about in previous classes. 00:40:55.860 --> 00:40:59.730 align:middle line:84% We said with inverters, if I could get two waveforms 00:40:59.730 --> 00:41:01.410 align:middle line:84% and shift them by the right angle, 00:41:01.410 --> 00:41:03.520 align:middle line:84% I would start to cancel harmonics. 00:41:03.520 --> 00:41:10.330 align:middle line:84% Well, this cancels all triple n harmonics. 00:41:10.330 --> 00:41:15.000 align:middle line:90% 00:41:15.000 --> 00:41:20.370 align:middle line:84% So that means if I have half wave symmetric waveforms, 00:41:20.370 --> 00:41:25.020 align:middle line:84% and that depends upon this non-linearity or the rectifier 00:41:25.020 --> 00:41:29.100 align:middle line:90% I use, I get no evens. 00:41:29.100 --> 00:41:33.630 align:middle line:84% And then I cancel 3 and 6 and 9, and then the lowest harmonic 00:41:33.630 --> 00:41:38.520 align:middle line:84% content I would have in the actual line waveform would be 00:41:38.520 --> 00:41:40.200 align:middle line:90% the 5th and the 7th. 00:41:40.200 --> 00:41:45.570 align:middle line:84% So suddenly, even though I may have some rectifier that 00:41:45.570 --> 00:41:47.880 align:middle line:84% draws very funky current waveforms, 00:41:47.880 --> 00:41:50.850 align:middle line:84% I start to eliminate, or actually 00:41:50.850 --> 00:41:55.440 align:middle line:84% to be accurate, cancel out harmonic content I don't like. 00:41:55.440 --> 00:41:59.130 align:middle line:84% And the three-phase waveform set will 00:41:59.130 --> 00:42:02.370 align:middle line:90% give you that very beautifully. 00:42:02.370 --> 00:42:09.570 align:middle line:84% So of all the games I'm talking about, the first couple ones 00:42:09.570 --> 00:42:10.680 align:middle line:90% you can do with two-phase. 00:42:10.680 --> 00:42:14.310 align:middle line:84% You can get a rotating magnetic field with two-phase. 00:42:14.310 --> 00:42:17.140 align:middle line:84% You can get constant power transfer with two-phase. 00:42:17.140 --> 00:42:19.800 align:middle line:84% If I add a phase, I suddenly start 00:42:19.800 --> 00:42:23.220 align:middle line:84% to get these balanced waveforms that 00:42:23.220 --> 00:42:27.040 align:middle line:90% will cancel triple n harmonics. 00:42:27.040 --> 00:42:31.170 align:middle line:84% It will also give me much lower conduction loss 00:42:31.170 --> 00:42:32.460 align:middle line:90% in my conductors. 00:42:32.460 --> 00:42:36.330 align:middle line:84% So I get much better performance out of three-phase 00:42:36.330 --> 00:42:38.130 align:middle line:90% than I get out of two-phase. 00:42:38.130 --> 00:42:40.650 align:middle line:84% Now, you said, well, what if I had four-phase? 00:42:40.650 --> 00:42:43.290 align:middle line:90% Four-phase also adds up to 0. 00:42:43.290 --> 00:42:45.480 align:middle line:84% And I can get all the benefits I talked about 00:42:45.480 --> 00:42:47.130 align:middle line:84% in four-phase, except that I'd cancel 00:42:47.130 --> 00:42:49.672 align:middle line:90% different sets of harmonics. 00:42:49.672 --> 00:42:51.630 align:middle line:84% So it wouldn't be quite as good in that regard, 00:42:51.630 --> 00:42:53.040 align:middle line:84% especially if I'm going to have things that don't 00:42:53.040 --> 00:42:54.760 align:middle line:90% have even harmonics anyways. 00:42:54.760 --> 00:43:00.210 align:middle line:84% But the beauty of it is, is that 3 is the simplest number that 00:43:00.210 --> 00:43:01.950 align:middle line:90% gives you the most benefit. 00:43:01.950 --> 00:43:06.390 align:middle line:84% So people talk about higher numbers of polyphases and people 00:43:06.390 --> 00:43:07.360 align:middle line:90% have worked on it. 00:43:07.360 --> 00:43:09.220 align:middle line:84% But in practice, you want the simplest thing 00:43:09.220 --> 00:43:11.450 align:middle line:84% that's really good, and three-phase is it. 00:43:11.450 --> 00:43:13.545 align:middle line:84% So two-phase gives you some of the benefits. 00:43:13.545 --> 00:43:14.920 align:middle line:84% You go up to three-phase, and you 00:43:14.920 --> 00:43:16.720 align:middle line:90% get all the benefits you want. 00:43:16.720 --> 00:43:18.970 align:middle line:84% And you go to more phases, well, yeah, you can get it, 00:43:18.970 --> 00:43:20.240 align:middle line:90% but it's more complicated. 00:43:20.240 --> 00:43:22.600 align:middle line:90% So why do it? 00:43:22.600 --> 00:43:28.030 align:middle line:84% So that's a lightning introduction to all the-- 00:43:28.030 --> 00:43:31.610 align:middle line:84% or many of the benefits of having a polyphase signal. 00:43:31.610 --> 00:43:34.780 align:middle line:84% So if you're in your home, and you're up 00:43:34.780 --> 00:43:38.080 align:middle line:84% to a couple of kilowatts, you're going 00:43:38.080 --> 00:43:40.010 align:middle line:90% to see single-phase systems. 00:43:40.010 --> 00:43:42.640 align:middle line:84% When you get to higher power levels for motor 00:43:42.640 --> 00:43:47.570 align:middle line:84% drives or electric vehicle drives or whatever you have, 00:43:47.570 --> 00:43:49.780 align:middle line:84% a lot of that is all done in three-phase. 00:43:49.780 --> 00:43:52.820 align:middle line:84% And all of AC power transmission is all three-phase. 00:43:52.820 --> 00:43:54.677 align:middle line:90% So if you look up on the-- 00:43:54.677 --> 00:43:57.010 align:middle line:84% look up at the towers, you're going to see three lines-- 00:43:57.010 --> 00:44:00.480 align:middle line:84% three big lines going across, and those are your three phases. 00:44:00.480 --> 00:44:01.830 align:middle line:90% So I'm going to pause there. 00:44:01.830 --> 00:44:04.830 align:middle line:84% Are there any questions about just this introduction 00:44:04.830 --> 00:44:08.010 align:middle line:84% to three-phase before we start to talk about the actual power 00:44:08.010 --> 00:44:08.990 align:middle line:90% electronics content? 00:44:08.990 --> 00:44:13.800 align:middle line:90% 00:44:13.800 --> 00:44:14.300 align:middle line:90% All right. 00:44:14.300 --> 00:44:16.675 align:middle line:84% We'll wrap it there, and we will pick this up next class. 00:44:16.675 --> 00:44:18.510 align:middle line:90% Have a great day. 00:44:18.510 --> 00:44:21.000 align:middle line:90%