Lecture 17: Inverters, Part 1
الملخص
TLDRLa vidéo aborde le fonctionnement des onduleurs, qui convertissent le courant continu (CC) en courant alternatif (CA). Les onduleurs sont cruciaux pour des applications telles que les entraînements de moteurs, les alimentations sans interruption et l'intégration d'énergie renouvelable. L'instructeur explique comment exprimer des formes d'onde périodiques à l'aide de séries de Fourier, en se concentrant sur les formes d'onde paires, impaires et symétriques. Il décrit également la structure de base d'un onduleur triphasé, les méthodes de synthèse d'une onde sinusoïdale à partir de signaux CC, et les considérations pratiques pour le contrôle des interrupteurs dans les circuits d'onduleurs. Les concepts de symétrie des formes d'onde sont discutés pour optimiser la filtration des harmoniques et améliorer la qualité de la sortie CA.
الوجبات الجاهزة
- 🔌 Les onduleurs convertissent le CC en CA.
- ⚙️ Ils sont essentiels pour les moteurs et les systèmes d'alimentation.
- 📊 Les formes d'onde peuvent être exprimées avec des séries de Fourier.
- 🔄 Les formes d'onde paires et impaires ont des caractéristiques distinctes.
- 🔁 La symétrie à demi-cycle élimine les harmoniques paires.
- 📏 L'angle de commutation contrôle l'amplitude fondamentale.
- 🔋 Les onduleurs à source de tension sont courants.
- 🔄 Les onduleurs à source de courant sont utilisés à haute puissance.
- ⚠️ Le contrôle des interrupteurs est crucial pour éviter les courts-circuits.
- 🎛️ La filtration des harmoniques améliore la qualité de la sortie.
الجدول الزمني
- 00:00:00 - 00:05:00
Introduction au sujet des onduleurs, qui sont des convertisseurs de courant continu (CC) en courant alternatif (CA), utilisés dans diverses applications telles que les entraînements de moteurs et les systèmes d'alimentation sans interruption.
- 00:05:00 - 00:10:00
Présentation de la décomposition des formes d'onde périodiques en séries de Fourier, en utilisant des termes de sinus et de cosinus pour exprimer les caractéristiques des formes d'onde AC.
- 00:10:00 - 00:15:00
Discussion sur les formes d'onde paires et impaires, où les formes d'onde paires n'ont que des termes cosinus et les formes d'onde impaires n'ont que des termes sinus, ce qui influence leur représentation en série de Fourier.
- 00:15:00 - 00:20:00
Introduction à la symétrie demi-onde, où une forme d'onde est symétrique par rapport à la moitié de son cycle, entraînant l'annulation des termes harmoniques pairs dans sa décomposition en série de Fourier.
- 00:20:00 - 00:25:00
Explication de la structure de base d'un onduleur triphasé, avec des interrupteurs permettant de générer des tensions AC à partir d'une source CC, et des exemples d'applications pratiques.
- 00:25:00 - 00:30:00
Démonstration de la synthèse d'une onde sinusoïdale approximative en contrôlant les interrupteurs de l'onduleur, en se concentrant sur la minimisation des pertes de commutation.
- 00:30:00 - 00:35:00
Analyse de l'importance de la symétrie demi-onde pour réduire le contenu harmonique et faciliter le filtrage des formes d'onde générées par l'onduleur.
- 00:35:00 - 00:40:00
Discussion sur le contrôle de l'amplitude fondamentale de la tension de sortie de l'onduleur en ajustant l'angle de commutation, et comment cela affecte les harmoniques générées.
- 00:40:00 - 00:45:00
Exploration des implications pratiques de la commutation des interrupteurs dans un onduleur, y compris la nécessité d'éviter les courts-circuits et de gérer les temps morts.
- 00:45:00 - 00:51:07
Conclusion sur les différentes configurations d'onduleurs, y compris les onduleurs à source de courant, et l'importance de la conception pour des applications à haute puissance.
الخريطة الذهنية
فيديو أسئلة وأجوبة
Qu'est-ce qu'un onduleur ?
Un onduleur est un dispositif qui convertit le courant continu (CC) en courant alternatif (CA).
Pourquoi les onduleurs sont-ils importants ?
Ils sont essentiels pour des applications comme les entraînements de moteurs, les alimentations sans interruption et l'intégration d'énergie renouvelable au réseau.
Comment les formes d'onde sont-elles exprimées ?
Les formes d'onde périodiques peuvent être exprimées à l'aide de séries de Fourier, en utilisant des termes sinusoïdaux et cosinus.
Quelles sont les caractéristiques des formes d'onde paires et impaires ?
Les formes d'onde paires sont symétriques par rapport à l'axe vertical, tandis que les formes d'onde impaires sont symétriques par rapport à l'origine.
Qu'est-ce qu'une forme d'onde symétrique à demi-cycle ?
Une forme d'onde symétrique à demi-cycle est une onde qui se renverse lorsqu'on la déplace d'un demi-cycle.
Comment contrôler l'amplitude fondamentale d'une onde sinusoïdale ?
On peut contrôler l'amplitude fondamentale en ajustant l'angle de commutation dans le circuit de l'onduleur.
Qu'est-ce qu'un onduleur à source de tension ?
C'est un type d'onduleur qui utilise une source de tension CC pour générer une sortie CA.
Qu'est-ce qu'un onduleur à source de courant ?
C'est un type d'onduleur qui utilise une source de courant CC pour générer une sortie CA.
Pourquoi est-il important de contrôler les pertes de commutation ?
Minimiser les pertes de commutation est crucial pour améliorer l'efficacité, surtout à des niveaux de puissance élevés.
Comment les interrupteurs sont-ils contrôlés dans un onduleur ?
Les interrupteurs doivent être contrôlés pour éviter les courts-circuits et assurer un fonctionnement sûr.
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- 00:00:09okay why don't we get
- 00:00:12started we're going to switch topics
- 00:00:15today and we're going to talk about a
- 00:00:17different class of power converter
- 00:00:19circuit uh called an inverter so
- 00:00:26inverters or DC to AC
- 00:00:33converters uh are important for a lot of
- 00:00:36applications right so if you're going to
- 00:00:38build a motor drive a lot of motors need
- 00:00:39to run off AC if you're going to have an
- 00:00:41uninterruptible power supply to power
- 00:00:44your AC powered devices when the grid
- 00:00:46goes out you need it if you're getting
- 00:00:49power from a a wind turbine or or for
- 00:00:52example a DC solar panel you need to
- 00:00:55take that and convert it into AC in
- 00:00:57order to feed the power into the grid so
- 00:00:59there's a lot of where you need to come
- 00:01:01from
- 00:01:01DC input input out AC output um this is
- 00:01:06the topic of
- 00:01:09kpvs chapter
- 00:01:138 and we're going to spend the next few
- 00:01:16lectures talking about some of the the
- 00:01:18issues associated with DC AC
- 00:01:21conversion now before we jump into that
- 00:01:25let's just have a really Brief Review of
- 00:01:28expressing waveforms the periodic
- 00:01:30waveforms in terms of 4A series just
- 00:01:33because it's going to be really useful
- 00:01:35in thinking about what kinds of AC
- 00:01:37waveforms might we want to Sy synthesize
- 00:01:40right so if I have a periodic waveform F
- 00:01:42of
- 00:01:44T right I might Express that as some DC
- 00:01:48term
- 00:01:49plus um Nal 1 to Infinity of a subn sin
- 00:01:55of n Omega
- 00:01:57t plus b subn
- 00:02:00cosine of n Omega T where the this is
- 00:02:05the angular frequency associated with
- 00:02:07the fundamental period capital T So
- 00:02:11Omega KN is equal to 2 pi over the
- 00:02:14period and then we can go find using
- 00:02:17orthogonality the expression to uh get
- 00:02:21the 4 a series coefficients so a subn
- 00:02:24would be equal to 2 over T the integral
- 00:02:27over T of f of t
- 00:02:30s of n Omega T DT and B subn would
- 00:02:36simply be 2 over T integral over
- 00:02:39t f of T cosine of n Omega T DT okay so
- 00:02:47I can take any periodic waveform break
- 00:02:49it down into uh some Harmon fundamental
- 00:02:53and Har DC fundamental and harmonic
- 00:02:55description and one way to do that is in
- 00:02:57terms of s and cosine components and
- 00:03:00we'll see why we picked this particular
- 00:03:03representation
- 00:03:06shortly okay so it turns out that
- 00:03:09different
- 00:03:10waveforms have um different special
- 00:03:15characteristics all right so I'd like to
- 00:03:17think about a
- 00:03:19few uh different kinds of waveforms and
- 00:03:22some of this you've seen some of this um
- 00:03:25maybe will be a little bit less familiar
- 00:03:27the first kind of waveform we might
- 00:03:29think of is an even
- 00:03:32waveform right what does it mean for a
- 00:03:35waveform to be even um if I have t in
- 00:03:39even waveform looks symmetric about t
- 00:03:43equals z okay so it flips about t equal
- 00:03:46Z so maybe I have a waveform that looks
- 00:03:48like this say this is T over2 and this
- 00:03:51is minus t
- 00:03:53over2 okay and it might look like this
- 00:03:55for example okay so if I just flip it
- 00:03:59about T equals z nothing
- 00:04:02changes
- 00:04:03okay well why might I care about an even
- 00:04:07waveform um because all the a subn
- 00:04:13terms are zero in that case right uh one
- 00:04:17way to think about that is how do I find
- 00:04:21the a subn terms I
- 00:04:24take F of T if this is f of
- 00:04:28T and I multip multiply it by sin n
- 00:04:30Omega T So if I multip it by sin Omega T
- 00:04:33maybe I'd be multiplying it by something
- 00:04:35like looks like this
- 00:04:38um and then i' take the White and the
- 00:04:40orange and multiply them and integrate
- 00:04:42them and whatever's over
- 00:04:44here exactly is the negative of what's
- 00:04:48over here and I get
- 00:04:49zero okay in the integral when I
- 00:04:51integrate it out right so one way to
- 00:04:54think about it is that uh an even times
- 00:04:58an odd is odd and then when I take the
- 00:05:01integral or of an odd waveform I get
- 00:05:03zero okay another way to think about it
- 00:05:06is signs are odd
- 00:05:09waveforms and this is an even waveform
- 00:05:11so it makes sense that I ought to build
- 00:05:13an even waveform out of even components
- 00:05:16right and the cosine terms are the even
- 00:05:19components of my 4A Series so an even
- 00:05:23waveform will only have B subn ter B
- 00:05:26subn terms right only cosines and DC
- 00:05:31okay uh of course we can also have an
- 00:05:33odd
- 00:05:35waveform right uh even is X of T is
- 00:05:39equal to X of minus t right it flips
- 00:05:43about the T equals z axis odd is X of T
- 00:05:48is equal to Min - x of minus t okay so
- 00:05:52what does that
- 00:05:54mean an odd waveform would mean um if I
- 00:05:58had this
- 00:06:00then I should have uh
- 00:06:03this okay and then I could
- 00:06:07um can you I could I could replicate
- 00:06:10this cycle to cycle something like this
- 00:06:12for example okay where this is minus t
- 00:06:15over2 and this is T
- 00:06:17over2 okay so basically I go across the
- 00:06:23axis and then flip down I flip both this
- 00:06:25way and this way and I get some
- 00:06:27symmetry okay
- 00:06:30and so that's a
- 00:06:33uh that characteristic what what do I
- 00:06:36have about that well here right this is
- 00:06:41composed of only odd waveforms I could
- 00:06:42make the same kind of argument and say
- 00:06:44that b subn ought to equal
- 00:06:48zero okay so I only build an odd
- 00:06:52waveform out of sine waves why because
- 00:06:54signs are odd and hence those are the
- 00:06:56subcomponents that I get okay any
- 00:06:59questions about
- 00:07:03that so many way many people will be
- 00:07:06familiar with even and odd there's
- 00:07:07another
- 00:07:09decomposition that we can think
- 00:07:11of which is um one where we talk about
- 00:07:16something that's halfwave
- 00:07:25symmetric and what does halfway of
- 00:07:27symmetric means that means X of T is
- 00:07:30equal to minus X of tus capital T / 2
- 00:07:35okay so what is a halfwave symmetric
- 00:07:37waveform look like a half wave symmetric
- 00:07:39waveform looks like um looks like this
- 00:07:44suppose I have
- 00:07:47something that looks like this between 0
- 00:07:50and T
- 00:07:51over2 okay if I go back half a cycle I
- 00:07:55flip it all right so here I'll slide
- 00:07:58back half a cycle and I flip it and I'll
- 00:08:00get a waveform that looks like this okay
- 00:08:03so um here's what my halfwave symmetric
- 00:08:06waveform would look like and so forth
- 00:08:09okay where this is minus t over2 right
- 00:08:12so if I if I go at any point in the
- 00:08:14waveform and I go back half a
- 00:08:17cycle I
- 00:08:19flip
- 00:08:21okay well why might I be
- 00:08:24interested um in halfwave symmetry
- 00:08:29well that's because all of the a sub
- 00:08:352ks and B sub 2ks are equal to
- 00:08:40zero okay all the even harmonic terms
- 00:08:43are equal to
- 00:08:45zero okay why would that be the case
- 00:08:49well how would I find uh say the second
- 00:08:52harmonic component of this thing I would
- 00:08:55multiply it for for example suppose I
- 00:08:57wanted the
- 00:08:582A the the the a sub 2 component I would
- 00:09:01multiply it by S of 2 Omega T which be
- 00:09:04multiplying it by this and multiplying
- 00:09:06it by this and then integrating over the
- 00:09:08full cycle and you can see that the
- 00:09:10product of orange and white here this
- 00:09:12half of the waveform is exactly the
- 00:09:15complement of the product the orange and
- 00:09:17white in this half of the waveform when
- 00:09:18I integrate them I get
- 00:09:20zero okay the same thing would have been
- 00:09:23true had I had a cosine wave okay so the
- 00:09:27point of being half wve symmetric is
- 00:09:29that because of the orthogonality
- 00:09:31involved all of the even terms are
- 00:09:35zero okay so it has no even
- 00:09:38harmonic now the complement to this is
- 00:09:42something I would call a halfwave
- 00:09:44[Music]
- 00:09:50repeating okay and it looks like
- 00:09:55this if I had something that was doing
- 00:09:59this this in one half of the waveform
- 00:10:01for t/2 to zero it would just repeat
- 00:10:04half a cycle back that is X of T is
- 00:10:07equal to X of T minus capital T / 2 okay
- 00:10:13so if I have defined a period capital T
- 00:10:17that just means the waveform repeats
- 00:10:19twice in that Capital period
- 00:10:21T okay or another way to think about it
- 00:10:24is um the fundamental period of this
- 00:10:27waveform is actually
- 00:10:30t/2 okay but if we Define if we're
- 00:10:33looking at across some period T this
- 00:10:36comprises
- 00:10:38only a sub
- 00:10:432ks and B sub
- 00:10:452ks that is a sub 2N + 1 and B sub 2N +
- 00:10:521 is equal to 0 right so this has no
- 00:10:56even
- 00:10:57harmonics this kind of waveform only has
- 00:10:59even harmonics it has no odd harmonics
- 00:11:01or
- 00:11:02fundamental
- 00:11:04okay any questions about
- 00:11:08that yeah is that only the case if we
- 00:11:11Define the period to be T yes right now
- 00:11:15why might I do
- 00:11:16that because firstly we can um sometimes
- 00:11:22decompose waveforms right I could say
- 00:11:25that okay I could come up with some
- 00:11:27waveform f of t
- 00:11:29okay and I could say you know so so I
- 00:11:32could take some arbitrary F of T and
- 00:11:35come up with f of
- 00:11:37T is equal to some even
- 00:11:41component plus some odd
- 00:11:44component okay and decompose that into
- 00:11:47different parts where F
- 00:11:49even is equal to X of t plus x ofus t /
- 00:11:562 and F OD is equal to X of T minus x
- 00:12:01ofus t / 2 okay so essentially I can
- 00:12:06decompose a waveform into one term that
- 00:12:10basically is all the cosine components
- 00:12:13in DC and one element that is only the
- 00:12:17sign
- 00:12:18terms okay so I get this decomposition
- 00:12:22and because it signs and cosiness split
- 00:12:26the even and odd components of the the
- 00:12:29waveform happen to be
- 00:12:30orthogonal okay
- 00:12:33likewise I could make a
- 00:12:36decomposition of f of T any waveform F
- 00:12:40of T to have a f of halfwave
- 00:12:43symmetric element plus a half of f of
- 00:12:48halfwave
- 00:12:49repeating component and again this is
- 00:12:53going to be the fundamental and odd
- 00:12:56harmonics this is going to be DC and
- 00:12:58even harmonics
- 00:12:59okay and those are sort of time waveform
- 00:13:01decompositions but they're into
- 00:13:03different parts of the um of the 4A
- 00:13:09components okay any questions about
- 00:13:14that okay so that's just a little kind
- 00:13:16of review and perhaps an extension of
- 00:13:20different ways we might um think of
- 00:13:22getting the components we'll see in a
- 00:13:25while why we might think of decomposing
- 00:13:28things that way or think carefully about
- 00:13:31whether my waveform is even or odd or
- 00:13:33halfwave symmetric or or not
- 00:13:38okay but let's start talking about um an
- 00:13:43inverter what would be the basic
- 00:13:45structure of a three-phase inverter well
- 00:13:48one basic structure might be to have
- 00:13:50some DC waveform and of course by the
- 00:13:54way whether I talk about something this
- 00:13:57structure as an inverter going flowing
- 00:14:00power DC to AC or is a rectifier flowing
- 00:14:03power AC to DC it really just depends
- 00:14:05upon the power flow Direction and in
- 00:14:07fact um the same circuit structure can
- 00:14:10do either thing okay uh how you
- 00:14:14implement the switches however may be
- 00:14:16different okay and in fact where did the
- 00:14:18term inverter come from it came from the
- 00:14:21notion of inverting rectifier the
- 00:14:23first kind of power electronic solid
- 00:14:27state or actually wasn't even solid
- 00:14:28state it was tube power electronic
- 00:14:30component that people were able to build
- 00:14:32was a rectifier and they eventually
- 00:14:34figured out that with certain kinds of
- 00:14:36controlled rectifiers they could go DC
- 00:14:38power to AC power so they called that an
- 00:14:40inverting rectifier and then they
- 00:14:42eventually just started calling it an
- 00:14:43inverter okay so that's where the term
- 00:14:45comes from but here's a basic
- 00:14:48structure okay maybe I would have uh
- 00:14:51four
- 00:14:53switches S1
- 00:15:00uh let me get my switch numberings right
- 00:15:02S2
- 00:15:04S3 and S4 and we'll see why we number
- 00:15:07them this way and here is
- 00:15:10my load in this case if I'm going to go
- 00:15:12from DC to power to AC power and let me
- 00:15:15call the output here
- 00:15:17VX okay so I'm going to come from some
- 00:15:20DC voltage and I'm going to deliver
- 00:15:22power at AC into some voltage VX
- 00:15:26okay um what
- 00:15:29voltages VX can I synthesize with this
- 00:15:32structure um well let's think about this
- 00:15:35if I have um switches
- 00:15:41on what voltage VX do I get well if S1
- 00:15:45and S2 are
- 00:15:48on I get plus
- 00:15:51VDC if S2 and S3 are
- 00:15:55on I get zero right because I've just
- 00:15:58shorted out the load on the bottom if S3
- 00:16:01and S4 are on well then VX becomes minus
- 00:16:09VDC and if S4 and S1 are on top two
- 00:16:14switches I again get zero right so I
- 00:16:16sort of have two ways I can apply a zero
- 00:16:19voltage across the load I can apply a
- 00:16:21positive voltage and I can apply a
- 00:16:23negative voltage all right so I can sort
- 00:16:26of go one way the other way and two ways
- 00:16:29I can get zero okay and what we're going
- 00:16:32to see is that means given a DC voltage
- 00:16:34I can put AC on the load okay and this
- 00:16:37is a very
- 00:16:39common singlephase inverter
- 00:16:42structure if I have say a typical thing
- 00:16:46is if I have an inductive and resistive
- 00:16:50load right maybe I would implement it
- 00:16:53this
- 00:16:56way okay I would have say a mosfet here
- 00:17:01and a mosfet here for my
- 00:17:03switches and keep in mind these guys
- 00:17:06well I don't usually draw it they have
- 00:17:07internal body diodes like this
- 00:17:14okay so this would be a typical
- 00:17:19structure where internally I have these
- 00:17:21diodes okay and here's VX
- 00:17:26again okay just to illustrate you know
- 00:17:30this kind of structure being very common
- 00:17:31what I have here is um sort of one of
- 00:17:36these things you plug into the cigarette
- 00:17:39lighter in your car to generate AC from
- 00:17:42uh you know to power your laptop or
- 00:17:45something when you're on a trip or
- 00:17:46something and you know as is all D
- 00:17:48always dangerous give me a power
- 00:17:50converter because usually I'll just take
- 00:17:51it apart um but what you'll see
- 00:17:54is on one side of this thing there's
- 00:17:58kind of four switches and you'll see the
- 00:18:00in fact you we were talking about
- 00:18:01insulation pads last time I'll pass this
- 00:18:03around you can see the insulation pad
- 00:18:04here and then you'll see this
- 00:18:06Transformer and you'll see a set of
- 00:18:08diodes here which are right here that's
- 00:18:12an isolated dcdc converter so that takes
- 00:18:14the 12 volts or 14 volts from your car
- 00:18:16battery and generates a higher voltage
- 00:18:19and then there's four more switches
- 00:18:22which are the ones
- 00:18:23here those are your four
- 00:18:26mosfets and those are going to generate
- 00:18:28a
- 00:18:29and it goes to two plugs so you can plug
- 00:18:31in your toys and you know play your
- 00:18:33gaming system or whatever you want so um
- 00:18:36this is just to illustrate you know one
- 00:18:38very simple example of an
- 00:18:40inverter okay and it'll have exactly
- 00:18:43this structure right so we have an
- 00:18:44isolated DCd converter to get get us
- 00:18:47voltage gain and then this
- 00:18:49inverter
- 00:18:51okay um what would this when I'm drawing
- 00:18:54this load VX what am I meaning well it
- 00:18:57depends what my load is but I could
- 00:18:59imagine maybe I would have an
- 00:19:02inductor and a capacitor and
- 00:19:07some you know resistor that's getting my
- 00:19:11AC load um right so this filters out
- 00:19:15higher harmonics or this could be a
- 00:19:19machine winding where there's a you know
- 00:19:21sort of phase inductance from the
- 00:19:23machine winding and a resistor it just
- 00:19:24sort of depends on what you're driving
- 00:19:26for a load okay or it could be an induct
- 00:19:28filter and that could run into the grid
- 00:19:31right so that's the basic notion of what
- 00:19:34the structure of an inverter
- 00:19:36is why don't we think about how could we
- 00:19:39well approximate a sinusoid by
- 00:19:43switching these transistors S1 to S4 and
- 00:19:47the case I'd like to start with is
- 00:19:49perhaps the simplest one I'd like to
- 00:19:50switch each switch on and off only once
- 00:19:54per AC output cycle and let's imagine
- 00:19:57for the moment that what I want is
- 00:19:58something that approximates a sine wave
- 00:20:00at the output or crudely approximates a
- 00:20:02sine wave at the output okay why am I
- 00:20:05focusing on Switching only once per
- 00:20:07cycle well the number of times I switch
- 00:20:11per cycle is going to have to do with my
- 00:20:12switching losses right we talked about
- 00:20:14switching
- 00:20:15losses and so especially at very high
- 00:20:19power levels I really want to minimize
- 00:20:21the number of times I switch per cycle
- 00:20:24um in order to reduce those switching
- 00:20:27losses okay
- 00:20:29so the obsession with not switching very
- 00:20:31often comes from mitigating those losses
- 00:20:35and so I want to just treat the simplest
- 00:20:37case and this is actually what one might
- 00:20:39do at very high power levels where you
- 00:20:41really don't want to switch very often
- 00:20:43okay um or very high frequency levels I
- 00:20:47should say Okay so let's think about
- 00:20:51what we might do let me plot things in
- 00:20:53terms of electrical angle
- 00:20:59okay so here is
- 00:21:09um here is you know so it's two pi and 2
- 00:21:12pi this is Omega T this is electrical
- 00:21:15angle and what I was hoping to
- 00:21:17synthesize is you know some sine wave
- 00:21:20right so maybe it would look like
- 00:21:25this an ideal S Wave if I could synth it
- 00:21:28would look like this okay now I clearly
- 00:21:32can't synthesize that with my inverter
- 00:21:35but what could I do well I can generate
- 00:21:39a positive voltage right so maybe what I
- 00:21:42would do is let's just
- 00:21:44suppose um so starting sometime here I
- 00:21:49will have I will apply plus VDC maybe
- 00:21:52I'll do that at some electrical angle
- 00:21:55Delta okay so in this time period I will
- 00:21:58Sy the size plus
- 00:22:00VDC and what I'm going to do is I'm
- 00:22:02going to do this I'm going to do this
- 00:22:04between Delta and Pi minus
- 00:22:07Delta okay and how would I do that in
- 00:22:11this time period what what switch
- 00:22:13pattern would let me synthesize plus
- 00:22:16VDC S12 S1 S2 will give
- 00:22:20me plus VDC now I want to synthesize
- 00:22:24zero okay in this time period and I'm
- 00:22:27going to do that between Pius Delta and
- 00:22:29Pi +
- 00:22:32Delta okay I can get zero just by
- 00:22:36leaving switch S2 on and going to switch
- 00:22:38S3 so I can have S2
- 00:22:41S3 okay now I'm in the negative half of
- 00:22:44the cycle so maybe I want to syn maybe I
- 00:22:47want to make this minus
- 00:22:51VDC right so I will
- 00:22:55then switch here and for from Pi + Delta
- 00:22:59to 2 pi minus
- 00:23:01Delta I will
- 00:23:04have minus VDC and I get that with what
- 00:23:07switch
- 00:23:09pattern S3 S4 so I've turned off S2 and
- 00:23:13now I've turned on
- 00:23:15S4 and then I can get back to
- 00:23:17synthesizing zero with S4
- 00:23:21S1 so right so here's my
- 00:23:25pattern okay
- 00:23:29and it looks like
- 00:23:31this okay does that make sense
- 00:23:34everybody so what have I done each
- 00:23:37switch turns on if I look over two Pi
- 00:23:40one AC cycle each switch turns on once
- 00:23:43per cycle each switch turns off once per
- 00:23:46cycle okay so that's the minimum I can
- 00:23:48sort of
- 00:23:49do um and synthesize this kind of
- 00:23:51waveform now what can you tell me I I
- 00:23:54drew a sine
- 00:23:55wave here right
- 00:24:00um and I want in some measure for my
- 00:24:04synthesized AC output voltage of my
- 00:24:06inverter this
- 00:24:08VX right this is
- 00:24:11vx to try to approximate that sine wave
- 00:24:15in some
- 00:24:19fashion this is you know V sin Omega T
- 00:24:23well s Omega T is odd right so if I want
- 00:24:27to do a good job with as least kind of
- 00:24:29unwanted harmonic content as I can it
- 00:24:32makes sense that because sign is odd I
- 00:24:36also ought to use only odd components
- 00:24:39right so I ought to synthesize it with
- 00:24:40an odd waveform and what do I know about
- 00:24:43this waveform this waveforms odd and I
- 00:24:45should maybe I'll just draw it out here
- 00:24:47right it is indeed this is minus Delta
- 00:24:53this white waveform here VX is indeed
- 00:24:57odd right it reflects if I flip it
- 00:25:00across tal 0 and I flip it I get the
- 00:25:02same thing right so what I know is this
- 00:25:05white waveform it's odd it's comprising
- 00:25:07only s components so it comprises only
- 00:25:10you know s Omega T some amount of s of 3
- 00:25:12omega T some amount of s I'm sorry it
- 00:25:16has only sign terms as far as I have
- 00:25:18told you so far okay there's no cosine
- 00:25:21terms in this thing so that means it's
- 00:25:23good because I'm kind of building it out
- 00:25:24of its the things I would want to build
- 00:25:26it up any questions about that
- 00:25:32what else did I do in this waveform
- 00:25:36well you notice that this half of the
- 00:25:40waveform for the negative
- 00:25:42sign is exactly the
- 00:25:46flip I come back half cycle and I flip
- 00:25:48it for the first half of the cycle right
- 00:25:52what characteristic has
- 00:25:57that it's halfwave
- 00:25:59symmetric so what that means is that
- 00:26:01this white waveform that I've
- 00:26:03synthesized has no even
- 00:26:06harmonics right so if I did a forier
- 00:26:09decomposition on this white waveform
- 00:26:11what I know is it has well it has no DC
- 00:26:15it has no cosine terms and it has no
- 00:26:17even harmonics right so the lowest
- 00:26:19harmonic component can only be the third
- 00:26:22right and then the fifth and the seventh
- 00:26:24and so forth Okay so
- 00:26:29um the reason I chose this pattern just
- 00:26:32this way for both being odd because I
- 00:26:34was trying to happen to be trying to
- 00:26:35match a sine wave but more importantly
- 00:26:38that I made it halfwave symmetric I've
- 00:26:39gotten rid of even harmonic components
- 00:26:42and if I imagined that I was going to
- 00:26:43come up here and say oh
- 00:26:47um you know I'm going to take this VX
- 00:26:51here and try to synthesize some output
- 00:26:54voltage vac by filtering it if I can get
- 00:26:57rid of my even harmonics I can more
- 00:27:00easily filter that waveform right when
- 00:27:03we thought about sort of DC to DC
- 00:27:05converters I'm trying to separate out DC
- 00:27:08from any AC stuff that's kind of easy
- 00:27:11right because they're kind of infinitely
- 00:27:13separated in frequency or at least on a
- 00:27:15log scale um if I'm trying to separate
- 00:27:19out some fundamental that I want to
- 00:27:20create and I want to get my fundamental
- 00:27:22here but I've got second harmonic here I
- 00:27:25need a very good filter to you know keep
- 00:27:27one Omega T and kill 2 Omega T right
- 00:27:31well by making it halfway symmetric I
- 00:27:33don't need to kill 2 omega-3 I just need
- 00:27:35to kill three Omega T all right so
- 00:27:37there's a large motivation to control
- 00:27:40the harmonic content of your waveforms
- 00:27:42by picking waveform symmetries and hence
- 00:27:45the interest in halfwave symmetric
- 00:27:48waveforms
- 00:27:53questions
- 00:27:55okay why did I bother and by the way I
- 00:27:59should have said you know if I had made
- 00:28:01my angle Delta equals
- 00:28:04z okay at Delta equals 0 this would just
- 00:28:07be a sine wave right so at Delta equals
- 00:28:110 what I would get is um I would get U
- 00:28:17my voltage VX would simply equal
- 00:28:20VDC
- 00:28:23times
- 00:28:24uh summation n = 1 to Infinity
- 00:28:28of 4 Pi
- 00:28:30n sin of n Omega
- 00:28:35T right where did I get that from that
- 00:28:37is just the 4A series for a square wave
- 00:28:41okay you can look it up in any book and
- 00:28:43so what that says is that first of all
- 00:28:46it's a sine wave series because it's odd
- 00:28:49right so I knew all the even terms went
- 00:28:52away it because it's halfwave symmetric
- 00:28:55a square wave is halfwave symmetric
- 00:28:58then or 50% Dy cycle square waves
- 00:29:00halfway symmetric then it doesn't have
- 00:29:03any this is n odd
- 00:29:07only uh summation and that means it's 4
- 00:29:11over Pi sin of Omega t plus 4 over 3 Pi
- 00:29:15sin 3 omega T and so forth it has
- 00:29:17harmonics that sort of fall off as one
- 00:29:19over n but only odd
- 00:29:21components does that make sense
- 00:29:24everybody
- 00:29:26okay um
- 00:29:28I came in and I introduced this angle
- 00:29:31Delta right and I I said what you could
- 00:29:34do for Delta equals z and so forth um
- 00:29:37why do I have it there what can I do
- 00:29:39with my angle Delta right I have my one
- 00:29:42control variable that I can use and I'm
- 00:29:44still switching each switch only once
- 00:29:47per
- 00:29:48cycle okay what can I do I can basically
- 00:29:52vary Delta between zero that's my
- 00:29:54perfect square wave and you know
- 00:29:56something less than Pi / 2
- 00:29:58okay and I can really use
- 00:30:03Delta to do kind of two things one I can
- 00:30:08vary the
- 00:30:13fundamental and two I can control
- 00:30:19harmonics I can't do both at the same
- 00:30:22time but I can use that as a control
- 00:30:24variable without switching more times
- 00:30:26per cycle
- 00:30:29okay what would I do in terms of varying
- 00:30:32the fundamental very often you know if
- 00:30:34I'm driving a motor or something right
- 00:30:38um how hard I'm driving the motor kind
- 00:30:40of has to do with the amplitude of the
- 00:30:42waveform I'm driving it with right so if
- 00:30:44I can have some means of amplitude
- 00:30:46control that's a good thing okay let's
- 00:30:49just think about what is the fundamental
- 00:30:51of VX here look like right so
- 00:30:56VX I said we can you know we can express
- 00:31:00uh
- 00:31:02VX uh as the sum of odd harmonics only
- 00:31:07right as odd harmonic sign terms only
- 00:31:10what is
- 00:31:11V1 right so so you know VX of t i could
- 00:31:16express as being V1 s of Omega
- 00:31:22t plus V3 sin of 3 omega t
- 00:31:28plus V5 sin 5 Omega
- 00:31:34T and so forth
- 00:31:37right but if what I'm mainly interested
- 00:31:39in is controlling the fundamental is the
- 00:31:41the thing I'm driving what is that
- 00:31:43fundamental well we come back you know
- 00:31:46basically we come back to this
- 00:31:48expression
- 00:31:50here okay to figure out
- 00:31:53what V1 is so why don't we write V1 V1
- 00:31:58in this expression would simply be equal
- 00:32:00to 2 over T in this case I'm doing it in
- 00:32:05electrical angle 2 pi integral from
- 00:32:08integral over 0 to 2
- 00:32:11pi uh
- 00:32:13VX s of Omega not t d Omega
- 00:32:20T right because I have this so I'm going
- 00:32:24to multiply that by the sine wave
- 00:32:26actually conveniently I've drawn the
- 00:32:27sine wave up there right I can I could
- 00:32:29just say that's going to be equal to uh
- 00:32:34this is one over Pi but I can do it over
- 00:32:36only half the cycle and I can get 2 over
- 00:32:39Pi um the integral from Delta to Pi
- 00:32:42minus
- 00:32:43Delta of
- 00:32:45VDC
- 00:32:47s of Omega t d Omega
- 00:32:52T
- 00:32:53right all I'm doing is I'm multiplying
- 00:33:00essentially I'm multiplying this green
- 00:33:03waveform or a unit height version of
- 00:33:05this green
- 00:33:10waveform by the white waveform and
- 00:33:13integrating it to find V1 and because
- 00:33:15the two halves of the integral are the
- 00:33:17same I can just do it over half a cycle
- 00:33:19and double it
- 00:33:21okay and if I do that that becomes very
- 00:33:23convenient because this just becomes
- 00:33:25minus cosine so what I get is I get uh 2
- 00:33:29over
- 00:33:31Pi
- 00:33:33VDC
- 00:33:35uh
- 00:33:39cosine of Delta minus cosine of Pius
- 00:33:44Delta right which just gives
- 00:33:47me I could rewrite this as being equal
- 00:33:50to 4 VDC over Pi cosine of Delta
- 00:33:58that make sense
- 00:34:02everybody so what am I
- 00:34:04saying if I made Delta equals zero
- 00:34:07that's my Square wave case right I just
- 00:34:10get a fundamental that's four over Pi
- 00:34:12VDC right that's exactly what I said
- 00:34:14before for the square wave case as I
- 00:34:18keep increasing Delta I you know make it
- 00:34:21nonzero further into the cycle this way
- 00:34:23and further into the cycle that
- 00:34:25way I reduce my fundamental why because
- 00:34:30basically as Delta becomes bigger I'm
- 00:34:33reducing the amount of overlap between
- 00:34:35the White waveform and the green
- 00:34:37waveform and when I multiply and
- 00:34:38integrate I get a smaller number and
- 00:34:40that goes as a cosine of
- 00:34:41Delta okay so what I can do is if what I
- 00:34:45cared about
- 00:34:47mainly was the fundamental amplitude of
- 00:34:51my output I can modulate that for a
- 00:34:55fixed DC voltage by modulating
- 00:34:59Delta okay I have a means of controlling
- 00:35:02the fundamental
- 00:35:05amplitude does that make sense
- 00:35:08everybody I want to drive my motor
- 00:35:10easier I use a bigger Delta I you know I
- 00:35:12drive it with less fundamental amplitude
- 00:35:15if I want more fundamental amplitude I
- 00:35:17use a smaller Delta and the most I can
- 00:35:19do is a square wave where I get a
- 00:35:20fundamental as four over Pi *
- 00:35:24VDC questions
- 00:35:30what else could I do with this thing
- 00:35:33well I can pick Delta to control the
- 00:35:35fundamental another way to control the
- 00:35:38fundamental would be to directly control
- 00:35:42VDC right so in that inverter I'm
- 00:35:45passing around right they have a they
- 00:35:47have an isolated DCd converter well
- 00:35:49guess what they can use that if they
- 00:35:50want to control the VDC that they get
- 00:35:53right so if you have a dcdc converter
- 00:35:56before your inverter you get to control
- 00:35:58this because you have a converter that
- 00:35:59can control it all right so maybe I
- 00:36:02don't need to use Delta to control the
- 00:36:04fundamental maybe I can do something
- 00:36:06else with
- 00:36:07it well the other thing I can do is
- 00:36:09harmonic
- 00:36:10control let's ask the
- 00:36:13question um what
- 00:36:15does what does V3 look
- 00:36:20like well
- 00:36:23V3 is equal to 2 over 2 pi
- 00:36:29integral from 0 to 2 pi of uh of VX of
- 00:36:36T Time s of 3 omega T 3 omega t d Omega
- 00:36:43not
- 00:36:45t right and likewise so what I'm doing
- 00:36:49in this
- 00:36:50case is I'm going to
- 00:36:53multiply this waveform by sin 3 omega T
- 00:36:56right so I'm going to mly it by
- 00:36:58something that looks like
- 00:37:07this right and then I'm going to that's
- 00:37:10a that's horribly asymmetric but I'm
- 00:37:12going to multiply it by sin3 Omega T not
- 00:37:14t and then integrate it right well okay
- 00:37:18because that's again halfwave symmetric
- 00:37:21I can write that as simply being equal
- 00:37:23to this is 1 over Pi but then I can
- 00:37:26double it and only do it over half the
- 00:37:28cycle and I get uh 2 over Pi the
- 00:37:33integral from Delta to Pi minus Delta
- 00:37:40VDC s of 3 3 omega t d Omega
- 00:37:47T
- 00:37:49okay it's the same game all over again
- 00:37:51but what I get is
- 00:37:54uh
- 00:37:55uh four
- 00:37:58BDC over
- 00:38:013
- 00:38:04Pi um times the cosine of 3
- 00:38:11Delta okay that's just the result of
- 00:38:13that
- 00:38:14integral okay so I can
- 00:38:17again you know if I can only you know
- 00:38:20once I've determined Delta I determine
- 00:38:22the fundamental and I determine the
- 00:38:23third
- 00:38:24harmonic right but what can I do with
- 00:38:27this
- 00:38:29well if Delta was 30° or pi/ 6 what
- 00:38:33would be the cosine of 3
- 00:38:37Delta what's the cosine of 90
- 00:38:40degrees zip right so if I pick Delta is
- 00:38:45equal to
- 00:38:4730° V3 goes to
- 00:38:51zero that's kind of
- 00:38:54nice right why is that nice I'm trying
- 00:38:57to make something that looks like a sine
- 00:38:58wave and has kind of limit the harmonic
- 00:39:01content so that I can filter it right I
- 00:39:04can by picking Delta is 30 Dees I can
- 00:39:06make V3 to go to zero what am I doing
- 00:39:08there if I come back here to this
- 00:39:11picture I said I'm multiplying the white
- 00:39:13waveform by the blue waveform but notice
- 00:39:16I drew actually Delta is exactly 30°
- 00:39:19what happens when it's 30 deges is this
- 00:39:21positive area in the
- 00:39:25multiplication is sort of a half sign
- 00:39:27bump and half sign bump exactly cancels
- 00:39:31this in each half in each half
- 00:39:33cycle and when I do that boom the third
- 00:39:37harmonic goes
- 00:39:39away all
- 00:39:40right so what am I left with if I do
- 00:39:44that
- 00:39:46um right if I thought about my
- 00:39:50system right suppose I put up um some
- 00:39:54filter like here's some filter
- 00:40:00and here's some you know vac that I want
- 00:40:03for example so here's
- 00:40:05VX and here is you know some vac that's
- 00:40:10filtered that I might care about or in
- 00:40:12some cases I might care about iix which
- 00:40:16is also related to VX by some filtering
- 00:40:19okay depends what I'm interested in but
- 00:40:22what I can think about that is taking
- 00:40:24some values of VX and then running
- 00:40:27running it through a filter transfer
- 00:40:28function that might be vac over VX and
- 00:40:31maybe I can make it look like some cut
- 00:40:33off right well what do I generally get I
- 00:40:36get um a
- 00:40:39fundamental then I get a second harmonic
- 00:40:42and a third harmonic and a fourth
- 00:40:44harmonic and a fifth harmonic and a
- 00:40:46sixth harmonic right so one two three
- 00:40:49four five six right I want to put the
- 00:40:54fundamental you know within the cut off
- 00:40:56of my filter because I'm trying to get
- 00:40:58fundamental of the output but I don't
- 00:41:00want I want to filter off all the
- 00:41:01harmonics right well I naturally by
- 00:41:04halfway
- 00:41:06symmetry I've gotten rid of two four and
- 00:41:09six so I've killed these just by how
- 00:41:12I've picked the pattern of the waveform
- 00:41:14to be halfway
- 00:41:15symmetric okay now if I magically go
- 00:41:21pick a Delta of
- 00:41:2330 then I kill off this guy
- 00:41:29okay by picking Delta exactly 30 I kill
- 00:41:32off the third and so the lowest Contents
- 00:41:34I have to deal with are the fifth and
- 00:41:37the
- 00:41:38seventh it's a heck of a lot easier to
- 00:41:40filter the fifth than it is the second
- 00:41:43or
- 00:41:43third okay so I can get much cleaner
- 00:41:47output voltage waveforms even though I'm
- 00:41:49not switching very often by being very
- 00:41:51clever in how I picked my switching
- 00:41:53angles
- 00:41:57any questions about
- 00:42:03that and we are going to see and and
- 00:42:06this can all be related back to um some
- 00:42:11games about
- 00:42:13um how I'm picking the W precise wave or
- 00:42:17I
- 00:42:18synthesize with the states I have which
- 00:42:21are basically plus VDC minus VDC and
- 00:42:24zero okay
- 00:42:28let me just give you a little bit of
- 00:42:30extra um kind of color about inverters
- 00:42:34and we're going to talk about expanding
- 00:42:36out on this in a lot of different
- 00:42:38dimensions as we move forward but I
- 00:42:40wanted to give you sort of an idea of
- 00:42:41like what's the the
- 00:42:44fundamental no pun intended smallest
- 00:42:47thing I can do to to get nice waveforms
- 00:42:51okay one thing relates to um how I
- 00:42:56control these switches in the real world
- 00:42:58and I mentioned this because there's the
- 00:42:59theoretically controlling the switches
- 00:43:01and then there's the Practical
- 00:43:02considerations okay if I come to this
- 00:43:05thing suppose I put this kind of filter
- 00:43:07in here right so suppose you know this
- 00:43:09is equal to this box that I'm drawing
- 00:43:13right so basically I've got an inductive
- 00:43:16load right so if this load is somewhat
- 00:43:18inductive or maybe it's resistive this
- 00:43:21is what a motor winding might look like
- 00:43:23right
- 00:43:24um I've got to be careful never to open
- 00:43:27circuit that winding right so suppose I
- 00:43:31have um S1 and S2
- 00:43:35on right and I wanted to do that
- 00:43:38switching pattern what's the next thing
- 00:43:39I'm going to
- 00:43:43do what would be my next state after S1
- 00:43:46and S2 is
- 00:43:48on S2 S3 right so I'm going to turn off
- 00:43:51S1 and turn on
- 00:43:54S3 okay now when you think about doing
- 00:43:57that in the real world you got to be a
- 00:43:58little bit careful right if I ever
- 00:44:01turned on S1 and S3 together unfortunate
- 00:44:04things would happen right that's called
- 00:44:06a shoot through and you know if you do
- 00:44:08it too long you will kill the switches
- 00:44:11right because you'll Short Circuit the
- 00:44:12DC bus and he can Source a lot of
- 00:44:14current into that so you got to make
- 00:44:15sure S1 and S3 are never on together and
- 00:44:18S2 and S4 are never on together at the
- 00:44:21same time you really really don't want
- 00:44:22to open circuit that load but the nice
- 00:44:24thing about this structure and by the
- 00:44:27way this is sometimes called a quote
- 00:44:28unquote vsi or voltage source inverter
- 00:44:32because you're coming from a DC voltage
- 00:44:35okay and generating
- 00:44:37AC is that I can have S1 and S2 on first
- 00:44:42I turn off
- 00:44:44S1 if I turn on off S1 say this
- 00:44:48current's
- 00:44:49positive um he still has to flow
- 00:44:52somewhere but he can just commutate from
- 00:44:55S1 into this diode
- 00:44:58right and so I don't have to
- 00:45:01worry and then once the diode's on I can
- 00:45:03turn on
- 00:45:04S3 right so basically I will have my Q
- 00:45:08of T of q1 of T I'll turn the switch one
- 00:45:12off and then I'll have Q3 of T and I'll
- 00:45:15turn him on after some so-called
- 00:45:19Deadtime delay between the two
- 00:45:22switches okay or even if the current was
- 00:45:24coming this way if I turn on
- 00:45:27off S1 the diode's on and then I can
- 00:45:29turn on S3 and it'll just turn off this
- 00:45:31diode naturally right so one thing I
- 00:45:33want to emphasize is in the real world
- 00:45:35you're always having some you know
- 00:45:38controls to make sure you're not
- 00:45:40shooting through your switches
- 00:45:44okay that's just a practical detail that
- 00:45:46you take care of when you lay out the
- 00:45:48controls for your inverter any questions
- 00:45:50about
- 00:45:54that what about other switches that
- 00:45:58uh well then you could get unhappy
- 00:45:59really quick right so if I had igbts and
- 00:46:03by the way igbts are very common for
- 00:46:05driving inverters what they will do is
- 00:46:07they will go put external diodes across
- 00:46:10them because otherwise you will blow
- 00:46:12them up right so in fact I later I'll
- 00:46:15bring in a an inverter module for Prius
- 00:46:17and you can actually see the the igbts
- 00:46:20and right next to them are the diodes
- 00:46:22that they put in to do it that's an old
- 00:46:24Prius inverter new Prius inverter uses
- 00:46:27silicon carbide fets I think
- 00:46:30um so that's one way to do this and as I
- 00:46:33said this is called a voltage source
- 00:46:35inverter it's not the only way you can
- 00:46:36build an inverter okay what would be
- 00:46:39another way
- 00:46:42well here's another trick suppose I took
- 00:46:46a DC voltage
- 00:46:49source and I put it in series with L
- 00:46:53big and I'll make this inductor so big
- 00:46:56that that this I becomes approximately
- 00:47:00equal to IDC right if I have a huge
- 00:47:03inductor here I can sort of make a
- 00:47:05voltage source and series with an
- 00:47:06inductor look at least on a short time
- 00:47:08scale like a current Source right so I
- 00:47:10might think of this thing as being a
- 00:47:13current Source now right so here I have
- 00:47:16some current
- 00:47:20IDC and now I might want to create an
- 00:47:25AC current from that
- 00:47:27I could do that again with a set of
- 00:47:29switches okay maybe however what I would
- 00:47:33want is switches that do
- 00:47:35this
- 00:47:48um I'm picking a different switch type
- 00:47:51just for
- 00:47:55fun okay these
- 00:47:58switches can carry unidirectional
- 00:48:01current but they can block voltage in
- 00:48:03both directions right because they will
- 00:48:06not car ever carry current that way and
- 00:48:09if I try to put a reverse voltage on
- 00:48:11them this diode will block and
- 00:48:12everything will be happy okay so then I
- 00:48:15could have a current Source essentially
- 00:48:18going in and then instead of having a
- 00:48:20filter that looks inductive maybe I will
- 00:48:22have a filter that looks capacitive
- 00:48:29something like this
- 00:48:33um and here I can have IAC or I or vac
- 00:48:38or an
- 00:48:40IAC okay so what I'm going to do is I
- 00:48:43can switch this DC current into the load
- 00:48:45this way by having these two switches
- 00:48:48on I can switch this current into the
- 00:48:51load the other way by having these two
- 00:48:54switches on
- 00:48:57or if I turn these two switches on the
- 00:48:59load gets no
- 00:49:01current or if I switch these two
- 00:49:03switches on the load gets no
- 00:49:05current that make sense so instead of
- 00:49:08synthesizing some pulsed DC voltage
- 00:49:11that's positive and negative I can
- 00:49:13synthesize a pulse AC current that's
- 00:49:15positive and negative this would be
- 00:49:17called a current Source
- 00:49:19inverter um now in Practical
- 00:49:23applications voltage source inverters
- 00:49:25especially at low Powers tend to be much
- 00:49:27more common because they're simpler to
- 00:49:29realize you don't need a big inductor
- 00:49:31and everything else people do however at
- 00:49:34high power sometimes like current Source
- 00:49:36inverters because if these switches fail
- 00:49:40you don't IM immediately short
- 00:49:42everything out like from a DC voltage
- 00:49:43source and get a huge pulse of current
- 00:49:45things take time to ramp up through this
- 00:49:47current which lets you blow fuses or
- 00:49:49shut things down or whatever so at high
- 00:49:51power sometimes people like versions of
- 00:49:53current Source inverters but more
- 00:49:55frequently people use voltage source
- 00:49:57inverters and interestingly by the way I
- 00:50:00talked about Deadtime where these two
- 00:50:03switches have to be off at the same time
- 00:50:07for a little while and we let current go
- 00:50:10through the diodes
- 00:50:12here I better never have a time when all
- 00:50:16four switches are off because then I'd
- 00:50:18be open circuiting this guy right so
- 00:50:20what I might do is you know if this
- 00:50:22switch and this switch were on I will
- 00:50:25then briefly turn this one on
- 00:50:28also and then I can turn this one off
- 00:50:31right so I have overlap in my switch on
- 00:50:33times instead of dead time in my switch
- 00:50:36on times okay but you can use apply all
- 00:50:40the same Concepts I talked about about
- 00:50:42synthesizing pulse voltage waveforms to
- 00:50:45synthesize pulse current waveforms we'll
- 00:50:47spend most of our talk time talking
- 00:50:49about voltage source inverters but I
- 00:50:51just wanted you to know there are other
- 00:50:52ways to play these
- 00:50:54games any final questions before wrap up
- 00:50:57for the
- 00:50:59day okay we'll pick this up tomorrow
- 00:51:02have a great day
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