Lecture 17: Inverters, Part 1

00:51:07
https://www.youtube.com/watch?v=So_UGo4dSJs

Ringkasan

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.

Takeaways

  • 🔌 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.

Garis waktu

  • 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.

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Peta Pikiran

Video Tanya Jawab

  • 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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Gulir Otomatis:
  • 00:00:09
    okay why don't we get
  • 00:00:12
    started we're going to switch topics
  • 00:00:15
    today and we're going to talk about a
  • 00:00:17
    different class of power converter
  • 00:00:19
    circuit uh called an inverter so
  • 00:00:26
    inverters or DC to AC
  • 00:00:33
    converters uh are important for a lot of
  • 00:00:36
    applications right so if you're going to
  • 00:00:38
    build a motor drive a lot of motors need
  • 00:00:39
    to run off AC if you're going to have an
  • 00:00:41
    uninterruptible power supply to power
  • 00:00:44
    your AC powered devices when the grid
  • 00:00:46
    goes out you need it if you're getting
  • 00:00:49
    power from a a wind turbine or or for
  • 00:00:52
    example a DC solar panel you need to
  • 00:00:55
    take that and convert it into AC in
  • 00:00:57
    order to feed the power into the grid so
  • 00:00:59
    there's a lot of where you need to come
  • 00:01:01
    from
  • 00:01:01
    DC input input out AC output um this is
  • 00:01:06
    the topic of
  • 00:01:09
    kpvs chapter
  • 00:01:13
    8 and we're going to spend the next few
  • 00:01:16
    lectures talking about some of the the
  • 00:01:18
    issues associated with DC AC
  • 00:01:21
    conversion now before we jump into that
  • 00:01:25
    let's just have a really Brief Review of
  • 00:01:28
    expressing waveforms the periodic
  • 00:01:30
    waveforms in terms of 4A series just
  • 00:01:33
    because it's going to be really useful
  • 00:01:35
    in thinking about what kinds of AC
  • 00:01:37
    waveforms might we want to Sy synthesize
  • 00:01:40
    right so if I have a periodic waveform F
  • 00:01:42
    of
  • 00:01:44
    T right I might Express that as some DC
  • 00:01:48
    term
  • 00:01:49
    plus um Nal 1 to Infinity of a subn sin
  • 00:01:55
    of n Omega
  • 00:01:57
    t plus b subn
  • 00:02:00
    cosine of n Omega T where the this is
  • 00:02:05
    the angular frequency associated with
  • 00:02:07
    the fundamental period capital T So
  • 00:02:11
    Omega KN is equal to 2 pi over the
  • 00:02:14
    period and then we can go find using
  • 00:02:17
    orthogonality the expression to uh get
  • 00:02:21
    the 4 a series coefficients so a subn
  • 00:02:24
    would be equal to 2 over T the integral
  • 00:02:27
    over T of f of t
  • 00:02:30
    s of n Omega T DT and B subn would
  • 00:02:36
    simply be 2 over T integral over
  • 00:02:39
    t f of T cosine of n Omega T DT okay so
  • 00:02:47
    I can take any periodic waveform break
  • 00:02:49
    it down into uh some Harmon fundamental
  • 00:02:53
    and Har DC fundamental and harmonic
  • 00:02:55
    description and one way to do that is in
  • 00:02:57
    terms of s and cosine components and
  • 00:03:00
    we'll see why we picked this particular
  • 00:03:03
    representation
  • 00:03:06
    shortly okay so it turns out that
  • 00:03:09
    different
  • 00:03:10
    waveforms have um different special
  • 00:03:15
    characteristics all right so I'd like to
  • 00:03:17
    think about a
  • 00:03:19
    few uh different kinds of waveforms and
  • 00:03:22
    some of this you've seen some of this um
  • 00:03:25
    maybe will be a little bit less familiar
  • 00:03:27
    the first kind of waveform we might
  • 00:03:29
    think of is an even
  • 00:03:32
    waveform right what does it mean for a
  • 00:03:35
    waveform to be even um if I have t in
  • 00:03:39
    even waveform looks symmetric about t
  • 00:03:43
    equals z okay so it flips about t equal
  • 00:03:46
    Z so maybe I have a waveform that looks
  • 00:03:48
    like this say this is T over2 and this
  • 00:03:51
    is minus t
  • 00:03:53
    over2 okay and it might look like this
  • 00:03:55
    for example okay so if I just flip it
  • 00:03:59
    about T equals z nothing
  • 00:04:02
    changes
  • 00:04:03
    okay well why might I care about an even
  • 00:04:07
    waveform um because all the a subn
  • 00:04:13
    terms are zero in that case right uh one
  • 00:04:17
    way to think about that is how do I find
  • 00:04:21
    the a subn terms I
  • 00:04:24
    take F of T if this is f of
  • 00:04:28
    T and I multip multiply it by sin n
  • 00:04:30
    Omega T So if I multip it by sin Omega T
  • 00:04:33
    maybe I'd be multiplying it by something
  • 00:04:35
    like looks like this
  • 00:04:38
    um and then i' take the White and the
  • 00:04:40
    orange and multiply them and integrate
  • 00:04:42
    them and whatever's over
  • 00:04:44
    here exactly is the negative of what's
  • 00:04:48
    over here and I get
  • 00:04:49
    zero okay in the integral when I
  • 00:04:51
    integrate it out right so one way to
  • 00:04:54
    think about it is that uh an even times
  • 00:04:58
    an odd is odd and then when I take the
  • 00:05:01
    integral or of an odd waveform I get
  • 00:05:03
    zero okay another way to think about it
  • 00:05:06
    is signs are odd
  • 00:05:09
    waveforms and this is an even waveform
  • 00:05:11
    so it makes sense that I ought to build
  • 00:05:13
    an even waveform out of even components
  • 00:05:16
    right and the cosine terms are the even
  • 00:05:19
    components of my 4A Series so an even
  • 00:05:23
    waveform will only have B subn ter B
  • 00:05:26
    subn terms right only cosines and DC
  • 00:05:31
    okay uh of course we can also have an
  • 00:05:33
    odd
  • 00:05:35
    waveform right uh even is X of T is
  • 00:05:39
    equal to X of minus t right it flips
  • 00:05:43
    about the T equals z axis odd is X of T
  • 00:05:48
    is equal to Min - x of minus t okay so
  • 00:05:52
    what does that
  • 00:05:54
    mean an odd waveform would mean um if I
  • 00:05:58
    had this
  • 00:06:00
    then I should have uh
  • 00:06:03
    this okay and then I could
  • 00:06:07
    um can you I could I could replicate
  • 00:06:10
    this cycle to cycle something like this
  • 00:06:12
    for example okay where this is minus t
  • 00:06:15
    over2 and this is T
  • 00:06:17
    over2 okay so basically I go across the
  • 00:06:23
    axis and then flip down I flip both this
  • 00:06:25
    way and this way and I get some
  • 00:06:27
    symmetry okay
  • 00:06:30
    and so that's a
  • 00:06:33
    uh that characteristic what what do I
  • 00:06:36
    have about that well here right this is
  • 00:06:41
    composed of only odd waveforms I could
  • 00:06:42
    make the same kind of argument and say
  • 00:06:44
    that b subn ought to equal
  • 00:06:48
    zero okay so I only build an odd
  • 00:06:52
    waveform out of sine waves why because
  • 00:06:54
    signs are odd and hence those are the
  • 00:06:56
    subcomponents that I get okay any
  • 00:06:59
    questions about
  • 00:07:03
    that so many way many people will be
  • 00:07:06
    familiar with even and odd there's
  • 00:07:07
    another
  • 00:07:09
    decomposition that we can think
  • 00:07:11
    of which is um one where we talk about
  • 00:07:16
    something that's halfwave
  • 00:07:25
    symmetric and what does halfway of
  • 00:07:27
    symmetric means that means X of T is
  • 00:07:30
    equal to minus X of tus capital T / 2
  • 00:07:35
    okay so what is a halfwave symmetric
  • 00:07:37
    waveform look like a half wave symmetric
  • 00:07:39
    waveform looks like um looks like this
  • 00:07:44
    suppose I have
  • 00:07:47
    something that looks like this between 0
  • 00:07:50
    and T
  • 00:07:51
    over2 okay if I go back half a cycle I
  • 00:07:55
    flip it all right so here I'll slide
  • 00:07:58
    back half a cycle and I flip it and I'll
  • 00:08:00
    get a waveform that looks like this okay
  • 00:08:03
    so um here's what my halfwave symmetric
  • 00:08:06
    waveform would look like and so forth
  • 00:08:09
    okay where this is minus t over2 right
  • 00:08:12
    so if I if I go at any point in the
  • 00:08:14
    waveform and I go back half a
  • 00:08:17
    cycle I
  • 00:08:19
    flip
  • 00:08:21
    okay well why might I be
  • 00:08:24
    interested um in halfwave symmetry
  • 00:08:29
    well that's because all of the a sub
  • 00:08:35
    2ks and B sub 2ks are equal to
  • 00:08:40
    zero okay all the even harmonic terms
  • 00:08:43
    are equal to
  • 00:08:45
    zero okay why would that be the case
  • 00:08:49
    well how would I find uh say the second
  • 00:08:52
    harmonic component of this thing I would
  • 00:08:55
    multiply it for for example suppose I
  • 00:08:57
    wanted the
  • 00:08:58
    2A the the the a sub 2 component I would
  • 00:09:01
    multiply it by S of 2 Omega T which be
  • 00:09:04
    multiplying it by this and multiplying
  • 00:09:06
    it by this and then integrating over the
  • 00:09:08
    full cycle and you can see that the
  • 00:09:10
    product of orange and white here this
  • 00:09:12
    half of the waveform is exactly the
  • 00:09:15
    complement of the product the orange and
  • 00:09:17
    white in this half of the waveform when
  • 00:09:18
    I integrate them I get
  • 00:09:20
    zero okay the same thing would have been
  • 00:09:23
    true had I had a cosine wave okay so the
  • 00:09:27
    point of being half wve symmetric is
  • 00:09:29
    that because of the orthogonality
  • 00:09:31
    involved all of the even terms are
  • 00:09:35
    zero okay so it has no even
  • 00:09:38
    harmonic now the complement to this is
  • 00:09:42
    something I would call a halfwave
  • 00:09:44
    [Music]
  • 00:09:50
    repeating okay and it looks like
  • 00:09:55
    this if I had something that was doing
  • 00:09:59
    this this in one half of the waveform
  • 00:10:01
    for t/2 to zero it would just repeat
  • 00:10:04
    half a cycle back that is X of T is
  • 00:10:07
    equal to X of T minus capital T / 2 okay
  • 00:10:13
    so if I have defined a period capital T
  • 00:10:17
    that just means the waveform repeats
  • 00:10:19
    twice in that Capital period
  • 00:10:21
    T okay or another way to think about it
  • 00:10:24
    is um the fundamental period of this
  • 00:10:27
    waveform is actually
  • 00:10:30
    t/2 okay but if we Define if we're
  • 00:10:33
    looking at across some period T this
  • 00:10:36
    comprises
  • 00:10:38
    only a sub
  • 00:10:43
    2ks and B sub
  • 00:10:45
    2ks that is a sub 2N + 1 and B sub 2N +
  • 00:10:52
    1 is equal to 0 right so this has no
  • 00:10:56
    even
  • 00:10:57
    harmonics this kind of waveform only has
  • 00:10:59
    even harmonics it has no odd harmonics
  • 00:11:01
    or
  • 00:11:02
    fundamental
  • 00:11:04
    okay any questions about
  • 00:11:08
    that yeah is that only the case if we
  • 00:11:11
    Define the period to be T yes right now
  • 00:11:15
    why might I do
  • 00:11:16
    that because firstly we can um sometimes
  • 00:11:22
    decompose waveforms right I could say
  • 00:11:25
    that okay I could come up with some
  • 00:11:27
    waveform f of t
  • 00:11:29
    okay and I could say you know so so I
  • 00:11:32
    could take some arbitrary F of T and
  • 00:11:35
    come up with f of
  • 00:11:37
    T is equal to some even
  • 00:11:41
    component plus some odd
  • 00:11:44
    component okay and decompose that into
  • 00:11:47
    different parts where F
  • 00:11:49
    even is equal to X of t plus x ofus t /
  • 00:11:56
    2 and F OD is equal to X of T minus x
  • 00:12:01
    ofus t / 2 okay so essentially I can
  • 00:12:06
    decompose a waveform into one term that
  • 00:12:10
    basically is all the cosine components
  • 00:12:13
    in DC and one element that is only the
  • 00:12:17
    sign
  • 00:12:18
    terms okay so I get this decomposition
  • 00:12:22
    and because it signs and cosiness split
  • 00:12:26
    the even and odd components of the the
  • 00:12:29
    waveform happen to be
  • 00:12:30
    orthogonal okay
  • 00:12:33
    likewise I could make a
  • 00:12:36
    decomposition of f of T any waveform F
  • 00:12:40
    of T to have a f of halfwave
  • 00:12:43
    symmetric element plus a half of f of
  • 00:12:48
    halfwave
  • 00:12:49
    repeating component and again this is
  • 00:12:53
    going to be the fundamental and odd
  • 00:12:56
    harmonics this is going to be DC and
  • 00:12:58
    even harmonics
  • 00:12:59
    okay and those are sort of time waveform
  • 00:13:01
    decompositions but they're into
  • 00:13:03
    different parts of the um of the 4A
  • 00:13:09
    components okay any questions about
  • 00:13:14
    that okay so that's just a little kind
  • 00:13:16
    of review and perhaps an extension of
  • 00:13:20
    different ways we might um think of
  • 00:13:22
    getting the components we'll see in a
  • 00:13:25
    while why we might think of decomposing
  • 00:13:28
    things that way or think carefully about
  • 00:13:31
    whether my waveform is even or odd or
  • 00:13:33
    halfwave symmetric or or not
  • 00:13:38
    okay but let's start talking about um an
  • 00:13:43
    inverter what would be the basic
  • 00:13:45
    structure of a three-phase inverter well
  • 00:13:48
    one basic structure might be to have
  • 00:13:50
    some DC waveform and of course by the
  • 00:13:54
    way whether I talk about something this
  • 00:13:57
    structure as an inverter going flowing
  • 00:14:00
    power DC to AC or is a rectifier flowing
  • 00:14:03
    power AC to DC it really just depends
  • 00:14:05
    upon the power flow Direction and in
  • 00:14:07
    fact um the same circuit structure can
  • 00:14:10
    do either thing okay uh how you
  • 00:14:14
    implement the switches however may be
  • 00:14:16
    different okay and in fact where did the
  • 00:14:18
    term inverter come from it came from the
  • 00:14:21
    notion of inverting rectifier the
  • 00:14:23
    first kind of power electronic solid
  • 00:14:27
    state or actually wasn't even solid
  • 00:14:28
    state it was tube power electronic
  • 00:14:30
    component that people were able to build
  • 00:14:32
    was a rectifier and they eventually
  • 00:14:34
    figured out that with certain kinds of
  • 00:14:36
    controlled rectifiers they could go DC
  • 00:14:38
    power to AC power so they called that an
  • 00:14:40
    inverting rectifier and then they
  • 00:14:42
    eventually just started calling it an
  • 00:14:43
    inverter okay so that's where the term
  • 00:14:45
    comes from but here's a basic
  • 00:14:48
    structure okay maybe I would have uh
  • 00:14:51
    four
  • 00:14:53
    switches S1
  • 00:15:00
    uh let me get my switch numberings right
  • 00:15:02
    S2
  • 00:15:04
    S3 and S4 and we'll see why we number
  • 00:15:07
    them this way and here is
  • 00:15:10
    my load in this case if I'm going to go
  • 00:15:12
    from DC to power to AC power and let me
  • 00:15:15
    call the output here
  • 00:15:17
    VX okay so I'm going to come from some
  • 00:15:20
    DC voltage and I'm going to deliver
  • 00:15:22
    power at AC into some voltage VX
  • 00:15:26
    okay um what
  • 00:15:29
    voltages VX can I synthesize with this
  • 00:15:32
    structure um well let's think about this
  • 00:15:35
    if I have um switches
  • 00:15:41
    on what voltage VX do I get well if S1
  • 00:15:45
    and S2 are
  • 00:15:48
    on I get plus
  • 00:15:51
    VDC if S2 and S3 are
  • 00:15:55
    on I get zero right because I've just
  • 00:15:58
    shorted out the load on the bottom if S3
  • 00:16:01
    and S4 are on well then VX becomes minus
  • 00:16:09
    VDC and if S4 and S1 are on top two
  • 00:16:14
    switches I again get zero right so I
  • 00:16:16
    sort of have two ways I can apply a zero
  • 00:16:19
    voltage across the load I can apply a
  • 00:16:21
    positive voltage and I can apply a
  • 00:16:23
    negative voltage all right so I can sort
  • 00:16:26
    of go one way the other way and two ways
  • 00:16:29
    I can get zero okay and what we're going
  • 00:16:32
    to see is that means given a DC voltage
  • 00:16:34
    I can put AC on the load okay and this
  • 00:16:37
    is a very
  • 00:16:39
    common singlephase inverter
  • 00:16:42
    structure if I have say a typical thing
  • 00:16:46
    is if I have an inductive and resistive
  • 00:16:50
    load right maybe I would implement it
  • 00:16:53
    this
  • 00:16:56
    way okay I would have say a mosfet here
  • 00:17:01
    and a mosfet here for my
  • 00:17:03
    switches and keep in mind these guys
  • 00:17:06
    well I don't usually draw it they have
  • 00:17:07
    internal body diodes like this
  • 00:17:14
    okay so this would be a typical
  • 00:17:19
    structure where internally I have these
  • 00:17:21
    diodes okay and here's VX
  • 00:17:26
    again okay just to illustrate you know
  • 00:17:30
    this kind of structure being very common
  • 00:17:31
    what I have here is um sort of one of
  • 00:17:36
    these things you plug into the cigarette
  • 00:17:39
    lighter in your car to generate AC from
  • 00:17:42
    uh you know to power your laptop or
  • 00:17:45
    something when you're on a trip or
  • 00:17:46
    something and you know as is all D
  • 00:17:48
    always dangerous give me a power
  • 00:17:50
    converter because usually I'll just take
  • 00:17:51
    it apart um but what you'll see
  • 00:17:54
    is on one side of this thing there's
  • 00:17:58
    kind of four switches and you'll see the
  • 00:18:00
    in fact you we were talking about
  • 00:18:01
    insulation pads last time I'll pass this
  • 00:18:03
    around you can see the insulation pad
  • 00:18:04
    here and then you'll see this
  • 00:18:06
    Transformer and you'll see a set of
  • 00:18:08
    diodes here which are right here that's
  • 00:18:12
    an isolated dcdc converter so that takes
  • 00:18:14
    the 12 volts or 14 volts from your car
  • 00:18:16
    battery and generates a higher voltage
  • 00:18:19
    and then there's four more switches
  • 00:18:22
    which are the ones
  • 00:18:23
    here those are your four
  • 00:18:26
    mosfets and those are going to generate
  • 00:18:28
    a
  • 00:18:29
    and it goes to two plugs so you can plug
  • 00:18:31
    in your toys and you know play your
  • 00:18:33
    gaming system or whatever you want so um
  • 00:18:36
    this is just to illustrate you know one
  • 00:18:38
    very simple example of an
  • 00:18:40
    inverter okay and it'll have exactly
  • 00:18:43
    this structure right so we have an
  • 00:18:44
    isolated DCd converter to get get us
  • 00:18:47
    voltage gain and then this
  • 00:18:49
    inverter
  • 00:18:51
    okay um what would this when I'm drawing
  • 00:18:54
    this load VX what am I meaning well it
  • 00:18:57
    depends what my load is but I could
  • 00:18:59
    imagine maybe I would have an
  • 00:19:02
    inductor and a capacitor and
  • 00:19:07
    some you know resistor that's getting my
  • 00:19:11
    AC load um right so this filters out
  • 00:19:15
    higher harmonics or this could be a
  • 00:19:19
    machine winding where there's a you know
  • 00:19:21
    sort of phase inductance from the
  • 00:19:23
    machine winding and a resistor it just
  • 00:19:24
    sort of depends on what you're driving
  • 00:19:26
    for a load okay or it could be an induct
  • 00:19:28
    filter and that could run into the grid
  • 00:19:31
    right so that's the basic notion of what
  • 00:19:34
    the structure of an inverter
  • 00:19:36
    is why don't we think about how could we
  • 00:19:39
    well approximate a sinusoid by
  • 00:19:43
    switching these transistors S1 to S4 and
  • 00:19:47
    the case I'd like to start with is
  • 00:19:49
    perhaps the simplest one I'd like to
  • 00:19:50
    switch each switch on and off only once
  • 00:19:54
    per AC output cycle and let's imagine
  • 00:19:57
    for the moment that what I want is
  • 00:19:58
    something that approximates a sine wave
  • 00:20:00
    at the output or crudely approximates a
  • 00:20:02
    sine wave at the output okay why am I
  • 00:20:05
    focusing on Switching only once per
  • 00:20:07
    cycle well the number of times I switch
  • 00:20:11
    per cycle is going to have to do with my
  • 00:20:12
    switching losses right we talked about
  • 00:20:14
    switching
  • 00:20:15
    losses and so especially at very high
  • 00:20:19
    power levels I really want to minimize
  • 00:20:21
    the number of times I switch per cycle
  • 00:20:24
    um in order to reduce those switching
  • 00:20:27
    losses okay
  • 00:20:29
    so the obsession with not switching very
  • 00:20:31
    often comes from mitigating those losses
  • 00:20:35
    and so I want to just treat the simplest
  • 00:20:37
    case and this is actually what one might
  • 00:20:39
    do at very high power levels where you
  • 00:20:41
    really don't want to switch very often
  • 00:20:43
    okay um or very high frequency levels I
  • 00:20:47
    should say Okay so let's think about
  • 00:20:51
    what we might do let me plot things in
  • 00:20:53
    terms of electrical angle
  • 00:20:59
    okay so here is
  • 00:21:09
    um here is you know so it's two pi and 2
  • 00:21:12
    pi this is Omega T this is electrical
  • 00:21:15
    angle and what I was hoping to
  • 00:21:17
    synthesize is you know some sine wave
  • 00:21:20
    right so maybe it would look like
  • 00:21:25
    this an ideal S Wave if I could synth it
  • 00:21:28
    would look like this okay now I clearly
  • 00:21:32
    can't synthesize that with my inverter
  • 00:21:35
    but what could I do well I can generate
  • 00:21:39
    a positive voltage right so maybe what I
  • 00:21:42
    would do is let's just
  • 00:21:44
    suppose um so starting sometime here I
  • 00:21:49
    will have I will apply plus VDC maybe
  • 00:21:52
    I'll do that at some electrical angle
  • 00:21:55
    Delta okay so in this time period I will
  • 00:21:58
    Sy the size plus
  • 00:22:00
    VDC and what I'm going to do is I'm
  • 00:22:02
    going to do this I'm going to do this
  • 00:22:04
    between Delta and Pi minus
  • 00:22:07
    Delta okay and how would I do that in
  • 00:22:11
    this time period what what switch
  • 00:22:13
    pattern would let me synthesize plus
  • 00:22:16
    VDC S12 S1 S2 will give
  • 00:22:20
    me plus VDC now I want to synthesize
  • 00:22:24
    zero okay in this time period and I'm
  • 00:22:27
    going to do that between Pius Delta and
  • 00:22:29
    Pi +
  • 00:22:32
    Delta okay I can get zero just by
  • 00:22:36
    leaving switch S2 on and going to switch
  • 00:22:38
    S3 so I can have S2
  • 00:22:41
    S3 okay now I'm in the negative half of
  • 00:22:44
    the cycle so maybe I want to syn maybe I
  • 00:22:47
    want to make this minus
  • 00:22:51
    VDC right so I will
  • 00:22:55
    then switch here and for from Pi + Delta
  • 00:22:59
    to 2 pi minus
  • 00:23:01
    Delta I will
  • 00:23:04
    have minus VDC and I get that with what
  • 00:23:07
    switch
  • 00:23:09
    pattern S3 S4 so I've turned off S2 and
  • 00:23:13
    now I've turned on
  • 00:23:15
    S4 and then I can get back to
  • 00:23:17
    synthesizing zero with S4
  • 00:23:21
    S1 so right so here's my
  • 00:23:25
    pattern okay
  • 00:23:29
    and it looks like
  • 00:23:31
    this okay does that make sense
  • 00:23:34
    everybody so what have I done each
  • 00:23:37
    switch turns on if I look over two Pi
  • 00:23:40
    one AC cycle each switch turns on once
  • 00:23:43
    per cycle each switch turns off once per
  • 00:23:46
    cycle okay so that's the minimum I can
  • 00:23:48
    sort of
  • 00:23:49
    do um and synthesize this kind of
  • 00:23:51
    waveform now what can you tell me I I
  • 00:23:54
    drew a sine
  • 00:23:55
    wave here right
  • 00:24:00
    um and I want in some measure for my
  • 00:24:04
    synthesized AC output voltage of my
  • 00:24:06
    inverter this
  • 00:24:08
    VX right this is
  • 00:24:11
    vx to try to approximate that sine wave
  • 00:24:15
    in some
  • 00:24:19
    fashion this is you know V sin Omega T
  • 00:24:23
    well s Omega T is odd right so if I want
  • 00:24:27
    to do a good job with as least kind of
  • 00:24:29
    unwanted harmonic content as I can it
  • 00:24:32
    makes sense that because sign is odd I
  • 00:24:36
    also ought to use only odd components
  • 00:24:39
    right so I ought to synthesize it with
  • 00:24:40
    an odd waveform and what do I know about
  • 00:24:43
    this waveform this waveforms odd and I
  • 00:24:45
    should maybe I'll just draw it out here
  • 00:24:47
    right it is indeed this is minus Delta
  • 00:24:53
    this white waveform here VX is indeed
  • 00:24:57
    odd right it reflects if I flip it
  • 00:25:00
    across tal 0 and I flip it I get the
  • 00:25:02
    same thing right so what I know is this
  • 00:25:05
    white waveform it's odd it's comprising
  • 00:25:07
    only s components so it comprises only
  • 00:25:10
    you know s Omega T some amount of s of 3
  • 00:25:12
    omega T some amount of s I'm sorry it
  • 00:25:16
    has only sign terms as far as I have
  • 00:25:18
    told you so far okay there's no cosine
  • 00:25:21
    terms in this thing so that means it's
  • 00:25:23
    good because I'm kind of building it out
  • 00:25:24
    of its the things I would want to build
  • 00:25:26
    it up any questions about that
  • 00:25:32
    what else did I do in this waveform
  • 00:25:36
    well you notice that this half of the
  • 00:25:40
    waveform for the negative
  • 00:25:42
    sign is exactly the
  • 00:25:46
    flip I come back half cycle and I flip
  • 00:25:48
    it for the first half of the cycle right
  • 00:25:52
    what characteristic has
  • 00:25:57
    that it's halfwave
  • 00:25:59
    symmetric so what that means is that
  • 00:26:01
    this white waveform that I've
  • 00:26:03
    synthesized has no even
  • 00:26:06
    harmonics right so if I did a forier
  • 00:26:09
    decomposition on this white waveform
  • 00:26:11
    what I know is it has well it has no DC
  • 00:26:15
    it has no cosine terms and it has no
  • 00:26:17
    even harmonics right so the lowest
  • 00:26:19
    harmonic component can only be the third
  • 00:26:22
    right and then the fifth and the seventh
  • 00:26:24
    and so forth Okay so
  • 00:26:29
    um the reason I chose this pattern just
  • 00:26:32
    this way for both being odd because I
  • 00:26:34
    was trying to happen to be trying to
  • 00:26:35
    match a sine wave but more importantly
  • 00:26:38
    that I made it halfwave symmetric I've
  • 00:26:39
    gotten rid of even harmonic components
  • 00:26:42
    and if I imagined that I was going to
  • 00:26:43
    come up here and say oh
  • 00:26:47
    um you know I'm going to take this VX
  • 00:26:51
    here and try to synthesize some output
  • 00:26:54
    voltage vac by filtering it if I can get
  • 00:26:57
    rid of my even harmonics I can more
  • 00:27:00
    easily filter that waveform right when
  • 00:27:03
    we thought about sort of DC to DC
  • 00:27:05
    converters I'm trying to separate out DC
  • 00:27:08
    from any AC stuff that's kind of easy
  • 00:27:11
    right because they're kind of infinitely
  • 00:27:13
    separated in frequency or at least on a
  • 00:27:15
    log scale um if I'm trying to separate
  • 00:27:19
    out some fundamental that I want to
  • 00:27:20
    create and I want to get my fundamental
  • 00:27:22
    here but I've got second harmonic here I
  • 00:27:25
    need a very good filter to you know keep
  • 00:27:27
    one Omega T and kill 2 Omega T right
  • 00:27:31
    well by making it halfway symmetric I
  • 00:27:33
    don't need to kill 2 omega-3 I just need
  • 00:27:35
    to kill three Omega T all right so
  • 00:27:37
    there's a large motivation to control
  • 00:27:40
    the harmonic content of your waveforms
  • 00:27:42
    by picking waveform symmetries and hence
  • 00:27:45
    the interest in halfwave symmetric
  • 00:27:48
    waveforms
  • 00:27:53
    questions
  • 00:27:55
    okay why did I bother and by the way I
  • 00:27:59
    should have said you know if I had made
  • 00:28:01
    my angle Delta equals
  • 00:28:04
    z okay at Delta equals 0 this would just
  • 00:28:07
    be a sine wave right so at Delta equals
  • 00:28:11
    0 what I would get is um I would get U
  • 00:28:17
    my voltage VX would simply equal
  • 00:28:20
    VDC
  • 00:28:23
    times
  • 00:28:24
    uh summation n = 1 to Infinity
  • 00:28:28
    of 4 Pi
  • 00:28:30
    n sin of n Omega
  • 00:28:35
    T right where did I get that from that
  • 00:28:37
    is just the 4A series for a square wave
  • 00:28:41
    okay you can look it up in any book and
  • 00:28:43
    so what that says is that first of all
  • 00:28:46
    it's a sine wave series because it's odd
  • 00:28:49
    right so I knew all the even terms went
  • 00:28:52
    away it because it's halfwave symmetric
  • 00:28:55
    a square wave is halfwave symmetric
  • 00:28:58
    then or 50% Dy cycle square waves
  • 00:29:00
    halfway symmetric then it doesn't have
  • 00:29:03
    any this is n odd
  • 00:29:07
    only uh summation and that means it's 4
  • 00:29:11
    over Pi sin of Omega t plus 4 over 3 Pi
  • 00:29:15
    sin 3 omega T and so forth it has
  • 00:29:17
    harmonics that sort of fall off as one
  • 00:29:19
    over n but only odd
  • 00:29:21
    components does that make sense
  • 00:29:24
    everybody
  • 00:29:26
    okay um
  • 00:29:28
    I came in and I introduced this angle
  • 00:29:31
    Delta right and I I said what you could
  • 00:29:34
    do for Delta equals z and so forth um
  • 00:29:37
    why do I have it there what can I do
  • 00:29:39
    with my angle Delta right I have my one
  • 00:29:42
    control variable that I can use and I'm
  • 00:29:44
    still switching each switch only once
  • 00:29:47
    per
  • 00:29:48
    cycle okay what can I do I can basically
  • 00:29:52
    vary Delta between zero that's my
  • 00:29:54
    perfect square wave and you know
  • 00:29:56
    something less than Pi / 2
  • 00:29:58
    okay and I can really use
  • 00:30:03
    Delta to do kind of two things one I can
  • 00:30:08
    vary the
  • 00:30:13
    fundamental and two I can control
  • 00:30:19
    harmonics I can't do both at the same
  • 00:30:22
    time but I can use that as a control
  • 00:30:24
    variable without switching more times
  • 00:30:26
    per cycle
  • 00:30:29
    okay what would I do in terms of varying
  • 00:30:32
    the fundamental very often you know if
  • 00:30:34
    I'm driving a motor or something right
  • 00:30:38
    um how hard I'm driving the motor kind
  • 00:30:40
    of has to do with the amplitude of the
  • 00:30:42
    waveform I'm driving it with right so if
  • 00:30:44
    I can have some means of amplitude
  • 00:30:46
    control that's a good thing okay let's
  • 00:30:49
    just think about what is the fundamental
  • 00:30:51
    of VX here look like right so
  • 00:30:56
    VX I said we can you know we can express
  • 00:31:00
    uh
  • 00:31:02
    VX uh as the sum of odd harmonics only
  • 00:31:07
    right as odd harmonic sign terms only
  • 00:31:10
    what is
  • 00:31:11
    V1 right so so you know VX of t i could
  • 00:31:16
    express as being V1 s of Omega
  • 00:31:22
    t plus V3 sin of 3 omega t
  • 00:31:28
    plus V5 sin 5 Omega
  • 00:31:34
    T and so forth
  • 00:31:37
    right but if what I'm mainly interested
  • 00:31:39
    in is controlling the fundamental is the
  • 00:31:41
    the thing I'm driving what is that
  • 00:31:43
    fundamental well we come back you know
  • 00:31:46
    basically we come back to this
  • 00:31:48
    expression
  • 00:31:50
    here okay to figure out
  • 00:31:53
    what V1 is so why don't we write V1 V1
  • 00:31:58
    in this expression would simply be equal
  • 00:32:00
    to 2 over T in this case I'm doing it in
  • 00:32:05
    electrical angle 2 pi integral from
  • 00:32:08
    integral over 0 to 2
  • 00:32:11
    pi uh
  • 00:32:13
    VX s of Omega not t d Omega
  • 00:32:20
    T right because I have this so I'm going
  • 00:32:24
    to multiply that by the sine wave
  • 00:32:26
    actually conveniently I've drawn the
  • 00:32:27
    sine wave up there right I can I could
  • 00:32:29
    just say that's going to be equal to uh
  • 00:32:34
    this is one over Pi but I can do it over
  • 00:32:36
    only half the cycle and I can get 2 over
  • 00:32:39
    Pi um the integral from Delta to Pi
  • 00:32:42
    minus
  • 00:32:43
    Delta of
  • 00:32:45
    VDC
  • 00:32:47
    s of Omega t d Omega
  • 00:32:52
    T
  • 00:32:53
    right all I'm doing is I'm multiplying
  • 00:33:00
    essentially I'm multiplying this green
  • 00:33:03
    waveform or a unit height version of
  • 00:33:05
    this green
  • 00:33:10
    waveform by the white waveform and
  • 00:33:13
    integrating it to find V1 and because
  • 00:33:15
    the two halves of the integral are the
  • 00:33:17
    same I can just do it over half a cycle
  • 00:33:19
    and double it
  • 00:33:21
    okay and if I do that that becomes very
  • 00:33:23
    convenient because this just becomes
  • 00:33:25
    minus cosine so what I get is I get uh 2
  • 00:33:29
    over
  • 00:33:31
    Pi
  • 00:33:33
    VDC
  • 00:33:35
    uh
  • 00:33:39
    cosine of Delta minus cosine of Pius
  • 00:33:44
    Delta right which just gives
  • 00:33:47
    me I could rewrite this as being equal
  • 00:33:50
    to 4 VDC over Pi cosine of Delta
  • 00:33:58
    that make sense
  • 00:34:02
    everybody so what am I
  • 00:34:04
    saying if I made Delta equals zero
  • 00:34:07
    that's my Square wave case right I just
  • 00:34:10
    get a fundamental that's four over Pi
  • 00:34:12
    VDC right that's exactly what I said
  • 00:34:14
    before for the square wave case as I
  • 00:34:18
    keep increasing Delta I you know make it
  • 00:34:21
    nonzero further into the cycle this way
  • 00:34:23
    and further into the cycle that
  • 00:34:25
    way I reduce my fundamental why because
  • 00:34:30
    basically as Delta becomes bigger I'm
  • 00:34:33
    reducing the amount of overlap between
  • 00:34:35
    the White waveform and the green
  • 00:34:37
    waveform and when I multiply and
  • 00:34:38
    integrate I get a smaller number and
  • 00:34:40
    that goes as a cosine of
  • 00:34:41
    Delta okay so what I can do is if what I
  • 00:34:45
    cared about
  • 00:34:47
    mainly was the fundamental amplitude of
  • 00:34:51
    my output I can modulate that for a
  • 00:34:55
    fixed DC voltage by modulating
  • 00:34:59
    Delta okay I have a means of controlling
  • 00:35:02
    the fundamental
  • 00:35:05
    amplitude does that make sense
  • 00:35:08
    everybody I want to drive my motor
  • 00:35:10
    easier I use a bigger Delta I you know I
  • 00:35:12
    drive it with less fundamental amplitude
  • 00:35:15
    if I want more fundamental amplitude I
  • 00:35:17
    use a smaller Delta and the most I can
  • 00:35:19
    do is a square wave where I get a
  • 00:35:20
    fundamental as four over Pi *
  • 00:35:24
    VDC questions
  • 00:35:30
    what else could I do with this thing
  • 00:35:33
    well I can pick Delta to control the
  • 00:35:35
    fundamental another way to control the
  • 00:35:38
    fundamental would be to directly control
  • 00:35:42
    VDC right so in that inverter I'm
  • 00:35:45
    passing around right they have a they
  • 00:35:47
    have an isolated DCd converter well
  • 00:35:49
    guess what they can use that if they
  • 00:35:50
    want to control the VDC that they get
  • 00:35:53
    right so if you have a dcdc converter
  • 00:35:56
    before your inverter you get to control
  • 00:35:58
    this because you have a converter that
  • 00:35:59
    can control it all right so maybe I
  • 00:36:02
    don't need to use Delta to control the
  • 00:36:04
    fundamental maybe I can do something
  • 00:36:06
    else with
  • 00:36:07
    it well the other thing I can do is
  • 00:36:09
    harmonic
  • 00:36:10
    control let's ask the
  • 00:36:13
    question um what
  • 00:36:15
    does what does V3 look
  • 00:36:20
    like well
  • 00:36:23
    V3 is equal to 2 over 2 pi
  • 00:36:29
    integral from 0 to 2 pi of uh of VX of
  • 00:36:36
    T Time s of 3 omega T 3 omega t d Omega
  • 00:36:43
    not
  • 00:36:45
    t right and likewise so what I'm doing
  • 00:36:49
    in this
  • 00:36:50
    case is I'm going to
  • 00:36:53
    multiply this waveform by sin 3 omega T
  • 00:36:56
    right so I'm going to mly it by
  • 00:36:58
    something that looks like
  • 00:37:07
    this right and then I'm going to that's
  • 00:37:10
    a that's horribly asymmetric but I'm
  • 00:37:12
    going to multiply it by sin3 Omega T not
  • 00:37:14
    t and then integrate it right well okay
  • 00:37:18
    because that's again halfwave symmetric
  • 00:37:21
    I can write that as simply being equal
  • 00:37:23
    to this is 1 over Pi but then I can
  • 00:37:26
    double it and only do it over half the
  • 00:37:28
    cycle and I get uh 2 over Pi the
  • 00:37:33
    integral from Delta to Pi minus Delta
  • 00:37:40
    VDC s of 3 3 omega t d Omega
  • 00:37:47
    T
  • 00:37:49
    okay it's the same game all over again
  • 00:37:51
    but what I get is
  • 00:37:54
    uh
  • 00:37:55
    uh four
  • 00:37:58
    BDC over
  • 00:38:01
    3
  • 00:38:04
    Pi um times the cosine of 3
  • 00:38:11
    Delta okay that's just the result of
  • 00:38:13
    that
  • 00:38:14
    integral okay so I can
  • 00:38:17
    again you know if I can only you know
  • 00:38:20
    once I've determined Delta I determine
  • 00:38:22
    the fundamental and I determine the
  • 00:38:23
    third
  • 00:38:24
    harmonic right but what can I do with
  • 00:38:27
    this
  • 00:38:29
    well if Delta was 30° or pi/ 6 what
  • 00:38:33
    would be the cosine of 3
  • 00:38:37
    Delta what's the cosine of 90
  • 00:38:40
    degrees zip right so if I pick Delta is
  • 00:38:45
    equal to
  • 00:38:47
    30° V3 goes to
  • 00:38:51
    zero that's kind of
  • 00:38:54
    nice right why is that nice I'm trying
  • 00:38:57
    to make something that looks like a sine
  • 00:38:58
    wave and has kind of limit the harmonic
  • 00:39:01
    content so that I can filter it right I
  • 00:39:04
    can by picking Delta is 30 Dees I can
  • 00:39:06
    make V3 to go to zero what am I doing
  • 00:39:08
    there if I come back here to this
  • 00:39:11
    picture I said I'm multiplying the white
  • 00:39:13
    waveform by the blue waveform but notice
  • 00:39:16
    I drew actually Delta is exactly 30°
  • 00:39:19
    what happens when it's 30 deges is this
  • 00:39:21
    positive area in the
  • 00:39:25
    multiplication is sort of a half sign
  • 00:39:27
    bump and half sign bump exactly cancels
  • 00:39:31
    this in each half in each half
  • 00:39:33
    cycle and when I do that boom the third
  • 00:39:37
    harmonic goes
  • 00:39:39
    away all
  • 00:39:40
    right so what am I left with if I do
  • 00:39:44
    that
  • 00:39:46
    um right if I thought about my
  • 00:39:50
    system right suppose I put up um some
  • 00:39:54
    filter like here's some filter
  • 00:40:00
    and here's some you know vac that I want
  • 00:40:03
    for example so here's
  • 00:40:05
    VX and here is you know some vac that's
  • 00:40:10
    filtered that I might care about or in
  • 00:40:12
    some cases I might care about iix which
  • 00:40:16
    is also related to VX by some filtering
  • 00:40:19
    okay depends what I'm interested in but
  • 00:40:22
    what I can think about that is taking
  • 00:40:24
    some values of VX and then running
  • 00:40:27
    running it through a filter transfer
  • 00:40:28
    function that might be vac over VX and
  • 00:40:31
    maybe I can make it look like some cut
  • 00:40:33
    off right well what do I generally get I
  • 00:40:36
    get um a
  • 00:40:39
    fundamental then I get a second harmonic
  • 00:40:42
    and a third harmonic and a fourth
  • 00:40:44
    harmonic and a fifth harmonic and a
  • 00:40:46
    sixth harmonic right so one two three
  • 00:40:49
    four five six right I want to put the
  • 00:40:54
    fundamental you know within the cut off
  • 00:40:56
    of my filter because I'm trying to get
  • 00:40:58
    fundamental of the output but I don't
  • 00:41:00
    want I want to filter off all the
  • 00:41:01
    harmonics right well I naturally by
  • 00:41:04
    halfway
  • 00:41:06
    symmetry I've gotten rid of two four and
  • 00:41:09
    six so I've killed these just by how
  • 00:41:12
    I've picked the pattern of the waveform
  • 00:41:14
    to be halfway
  • 00:41:15
    symmetric okay now if I magically go
  • 00:41:21
    pick a Delta of
  • 00:41:23
    30 then I kill off this guy
  • 00:41:29
    okay by picking Delta exactly 30 I kill
  • 00:41:32
    off the third and so the lowest Contents
  • 00:41:34
    I have to deal with are the fifth and
  • 00:41:37
    the
  • 00:41:38
    seventh it's a heck of a lot easier to
  • 00:41:40
    filter the fifth than it is the second
  • 00:41:43
    or
  • 00:41:43
    third okay so I can get much cleaner
  • 00:41:47
    output voltage waveforms even though I'm
  • 00:41:49
    not switching very often by being very
  • 00:41:51
    clever in how I picked my switching
  • 00:41:53
    angles
  • 00:41:57
    any questions about
  • 00:42:03
    that and we are going to see and and
  • 00:42:06
    this can all be related back to um some
  • 00:42:11
    games about
  • 00:42:13
    um how I'm picking the W precise wave or
  • 00:42:17
    I
  • 00:42:18
    synthesize with the states I have which
  • 00:42:21
    are basically plus VDC minus VDC and
  • 00:42:24
    zero okay
  • 00:42:28
    let me just give you a little bit of
  • 00:42:30
    extra um kind of color about inverters
  • 00:42:34
    and we're going to talk about expanding
  • 00:42:36
    out on this in a lot of different
  • 00:42:38
    dimensions as we move forward but I
  • 00:42:40
    wanted to give you sort of an idea of
  • 00:42:41
    like what's the the
  • 00:42:44
    fundamental no pun intended smallest
  • 00:42:47
    thing I can do to to get nice waveforms
  • 00:42:51
    okay one thing relates to um how I
  • 00:42:56
    control these switches in the real world
  • 00:42:58
    and I mentioned this because there's the
  • 00:42:59
    theoretically controlling the switches
  • 00:43:01
    and then there's the Practical
  • 00:43:02
    considerations okay if I come to this
  • 00:43:05
    thing suppose I put this kind of filter
  • 00:43:07
    in here right so suppose you know this
  • 00:43:09
    is equal to this box that I'm drawing
  • 00:43:13
    right so basically I've got an inductive
  • 00:43:16
    load right so if this load is somewhat
  • 00:43:18
    inductive or maybe it's resistive this
  • 00:43:21
    is what a motor winding might look like
  • 00:43:23
    right
  • 00:43:24
    um I've got to be careful never to open
  • 00:43:27
    circuit that winding right so suppose I
  • 00:43:31
    have um S1 and S2
  • 00:43:35
    on right and I wanted to do that
  • 00:43:38
    switching pattern what's the next thing
  • 00:43:39
    I'm going to
  • 00:43:43
    do what would be my next state after S1
  • 00:43:46
    and S2 is
  • 00:43:48
    on S2 S3 right so I'm going to turn off
  • 00:43:51
    S1 and turn on
  • 00:43:54
    S3 okay now when you think about doing
  • 00:43:57
    that in the real world you got to be a
  • 00:43:58
    little bit careful right if I ever
  • 00:44:01
    turned on S1 and S3 together unfortunate
  • 00:44:04
    things would happen right that's called
  • 00:44:06
    a shoot through and you know if you do
  • 00:44:08
    it too long you will kill the switches
  • 00:44:11
    right because you'll Short Circuit the
  • 00:44:12
    DC bus and he can Source a lot of
  • 00:44:14
    current into that so you got to make
  • 00:44:15
    sure S1 and S3 are never on together and
  • 00:44:18
    S2 and S4 are never on together at the
  • 00:44:21
    same time you really really don't want
  • 00:44:22
    to open circuit that load but the nice
  • 00:44:24
    thing about this structure and by the
  • 00:44:27
    way this is sometimes called a quote
  • 00:44:28
    unquote vsi or voltage source inverter
  • 00:44:32
    because you're coming from a DC voltage
  • 00:44:35
    okay and generating
  • 00:44:37
    AC is that I can have S1 and S2 on first
  • 00:44:42
    I turn off
  • 00:44:44
    S1 if I turn on off S1 say this
  • 00:44:48
    current's
  • 00:44:49
    positive um he still has to flow
  • 00:44:52
    somewhere but he can just commutate from
  • 00:44:55
    S1 into this diode
  • 00:44:58
    right and so I don't have to
  • 00:45:01
    worry and then once the diode's on I can
  • 00:45:03
    turn on
  • 00:45:04
    S3 right so basically I will have my Q
  • 00:45:08
    of T of q1 of T I'll turn the switch one
  • 00:45:12
    off and then I'll have Q3 of T and I'll
  • 00:45:15
    turn him on after some so-called
  • 00:45:19
    Deadtime delay between the two
  • 00:45:22
    switches okay or even if the current was
  • 00:45:24
    coming this way if I turn on
  • 00:45:27
    off S1 the diode's on and then I can
  • 00:45:29
    turn on S3 and it'll just turn off this
  • 00:45:31
    diode naturally right so one thing I
  • 00:45:33
    want to emphasize is in the real world
  • 00:45:35
    you're always having some you know
  • 00:45:38
    controls to make sure you're not
  • 00:45:40
    shooting through your switches
  • 00:45:44
    okay that's just a practical detail that
  • 00:45:46
    you take care of when you lay out the
  • 00:45:48
    controls for your inverter any questions
  • 00:45:50
    about
  • 00:45:54
    that what about other switches that
  • 00:45:58
    uh well then you could get unhappy
  • 00:45:59
    really quick right so if I had igbts and
  • 00:46:03
    by the way igbts are very common for
  • 00:46:05
    driving inverters what they will do is
  • 00:46:07
    they will go put external diodes across
  • 00:46:10
    them because otherwise you will blow
  • 00:46:12
    them up right so in fact I later I'll
  • 00:46:15
    bring in a an inverter module for Prius
  • 00:46:17
    and you can actually see the the igbts
  • 00:46:20
    and right next to them are the diodes
  • 00:46:22
    that they put in to do it that's an old
  • 00:46:24
    Prius inverter new Prius inverter uses
  • 00:46:27
    silicon carbide fets I think
  • 00:46:30
    um so that's one way to do this and as I
  • 00:46:33
    said this is called a voltage source
  • 00:46:35
    inverter it's not the only way you can
  • 00:46:36
    build an inverter okay what would be
  • 00:46:39
    another way
  • 00:46:42
    well here's another trick suppose I took
  • 00:46:46
    a DC voltage
  • 00:46:49
    source and I put it in series with L
  • 00:46:53
    big and I'll make this inductor so big
  • 00:46:56
    that that this I becomes approximately
  • 00:47:00
    equal to IDC right if I have a huge
  • 00:47:03
    inductor here I can sort of make a
  • 00:47:05
    voltage source and series with an
  • 00:47:06
    inductor look at least on a short time
  • 00:47:08
    scale like a current Source right so I
  • 00:47:10
    might think of this thing as being a
  • 00:47:13
    current Source now right so here I have
  • 00:47:16
    some current
  • 00:47:20
    IDC and now I might want to create an
  • 00:47:25
    AC current from that
  • 00:47:27
    I could do that again with a set of
  • 00:47:29
    switches okay maybe however what I would
  • 00:47:33
    want is switches that do
  • 00:47:35
    this
  • 00:47:48
    um I'm picking a different switch type
  • 00:47:51
    just for
  • 00:47:55
    fun okay these
  • 00:47:58
    switches can carry unidirectional
  • 00:48:01
    current but they can block voltage in
  • 00:48:03
    both directions right because they will
  • 00:48:06
    not car ever carry current that way and
  • 00:48:09
    if I try to put a reverse voltage on
  • 00:48:11
    them this diode will block and
  • 00:48:12
    everything will be happy okay so then I
  • 00:48:15
    could have a current Source essentially
  • 00:48:18
    going in and then instead of having a
  • 00:48:20
    filter that looks inductive maybe I will
  • 00:48:22
    have a filter that looks capacitive
  • 00:48:29
    something like this
  • 00:48:33
    um and here I can have IAC or I or vac
  • 00:48:38
    or an
  • 00:48:40
    IAC okay so what I'm going to do is I
  • 00:48:43
    can switch this DC current into the load
  • 00:48:45
    this way by having these two switches
  • 00:48:48
    on I can switch this current into the
  • 00:48:51
    load the other way by having these two
  • 00:48:54
    switches on
  • 00:48:57
    or if I turn these two switches on the
  • 00:48:59
    load gets no
  • 00:49:01
    current or if I switch these two
  • 00:49:03
    switches on the load gets no
  • 00:49:05
    current that make sense so instead of
  • 00:49:08
    synthesizing some pulsed DC voltage
  • 00:49:11
    that's positive and negative I can
  • 00:49:13
    synthesize a pulse AC current that's
  • 00:49:15
    positive and negative this would be
  • 00:49:17
    called a current Source
  • 00:49:19
    inverter um now in Practical
  • 00:49:23
    applications voltage source inverters
  • 00:49:25
    especially at low Powers tend to be much
  • 00:49:27
    more common because they're simpler to
  • 00:49:29
    realize you don't need a big inductor
  • 00:49:31
    and everything else people do however at
  • 00:49:34
    high power sometimes like current Source
  • 00:49:36
    inverters because if these switches fail
  • 00:49:40
    you don't IM immediately short
  • 00:49:42
    everything out like from a DC voltage
  • 00:49:43
    source and get a huge pulse of current
  • 00:49:45
    things take time to ramp up through this
  • 00:49:47
    current which lets you blow fuses or
  • 00:49:49
    shut things down or whatever so at high
  • 00:49:51
    power sometimes people like versions of
  • 00:49:53
    current Source inverters but more
  • 00:49:55
    frequently people use voltage source
  • 00:49:57
    inverters and interestingly by the way I
  • 00:50:00
    talked about Deadtime where these two
  • 00:50:03
    switches have to be off at the same time
  • 00:50:07
    for a little while and we let current go
  • 00:50:10
    through the diodes
  • 00:50:12
    here I better never have a time when all
  • 00:50:16
    four switches are off because then I'd
  • 00:50:18
    be open circuiting this guy right so
  • 00:50:20
    what I might do is you know if this
  • 00:50:22
    switch and this switch were on I will
  • 00:50:25
    then briefly turn this one on
  • 00:50:28
    also and then I can turn this one off
  • 00:50:31
    right so I have overlap in my switch on
  • 00:50:33
    times instead of dead time in my switch
  • 00:50:36
    on times okay but you can use apply all
  • 00:50:40
    the same Concepts I talked about about
  • 00:50:42
    synthesizing pulse voltage waveforms to
  • 00:50:45
    synthesize pulse current waveforms we'll
  • 00:50:47
    spend most of our talk time talking
  • 00:50:49
    about voltage source inverters but I
  • 00:50:51
    just wanted you to know there are other
  • 00:50:52
    ways to play these
  • 00:50:54
    games any final questions before wrap up
  • 00:50:57
    for the
  • 00:50:59
    day okay we'll pick this up tomorrow
  • 00:51:02
    have a great day
Tags
  • Onduleur
  • Conversion CC-CA
  • Séries de Fourier
  • Formes d'onde
  • Symétrie
  • Harmoniques
  • Contrôle des interrupteurs
  • Source de tension
  • Source de courant
  • Applications d'onduleurs