Dumb question – 90º is to quadrature as 120º is to ??? - Page 1
Forum section: electronics / beginners

author: Cerebus
author_rank: Super Contributor
timestamp: July 20, 2020, 02:42:21 pm
content: Title says it all really.Is there a word that expresses the 120º phase relationship (as seen in 3 phase mains, motors etc) in the same way that 'quadrature' describes the 90º phase relationship? Or to put it in the form you'd see in a 'fill in the blanks' junior school exam:Quadrature is to 90º as ________ is to 120ºSurely there must be such a word, but for the life of me I can't recall ever having heard or read it. I've hunted and pecked through dictionaries using all the variants ontri–andtern–that I can think of and come up empty.Can somebody fill in the blank?

author: schmitt trigger
author_rank: Super Contributor
timestamp: July 20, 2020, 02:45:57 pm
content: Never heard either, of aspecific single wordwhich would mean the 120 degree relationship of three phase voltages.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 20, 2020, 03:05:12 pm
content: "Triature" I guess would be the analogous term, but yeah, no one uses it.Perhaps it will be some comfort to know that, as long as there is a phase shift, that shift can be used to construct any other angle, with appropriate transformer windings. In that sense -- linear independence -- any phase shift has a quadrature of sorts. But we do reserve the special case of 90° for that exact term.Tim

author: Benta
author_rank: Super Contributor
timestamp: July 20, 2020, 03:21:32 pm
content: Common usage from my knowledge is: single-phase, split-phase (180), three-phase (120) and quadrature (90).

author: langwadt
author_rank: Super Contributor
timestamp: July 20, 2020, 03:29:13 pm
content: Quote from: T3sl4co1l on July 20, 2020, 03:05:12 pmn*180 degree being special case, you can't construct other angles from that

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 20, 2020, 03:30:41 pm
content: Exactly; "any phase shift" being a nontrivial angle, i.e. other than 0 and 180.

author: TimFox
author_rank: Super Contributor
timestamp: July 20, 2020, 03:53:54 pm
content: A set of vectors or functions {x} is linearly dependent if there exist a collection of scalars {a} such thata1x1+a2x2+ ... = 0The three phases 120 deg apart are linearly dependent, however any two phases (excluding 180 deg) are linearly independent.In linear algebra, a set of linearly independent functions or vectors can be used as a "basis set" to construct the other functions or vectors. Orthogonal functions (such as the two quadrature phases) are convenient, but not necessary to form a basis set.

author: SilverSolder
author_rank: Super Contributor
timestamp: July 20, 2020, 04:24:07 pm
content: Quote from: TimFox on July 20, 2020, 03:53:54 pmSo you only need 2 vectors, 120 deg apart, to define the third "missing" vector in a 3 phase system?

author: langwadt
author_rank: Super Contributor
timestamp: July 20, 2020, 05:12:50 pm
content: Quote from: SilverSolder on July 20, 2020, 04:24:07 pmyes

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 20, 2020, 05:32:25 pm
content: Of course, you need three wires to define those two vectors -- two signals and ground. Or, for special cases, two wires with voltage and current -- thus an impedance can be any phase. For power transmission though, we need the added degree of freedom. (Thus, the power itself has direction, and the load can have direction with respect to that as well (power factor).)It's easy to see why three phase is better -- we could start with Tesla's original four wire quadrature system, and combine two wires together since we don't need the circuits isolated. The common has to be sqrt(2) larger to handle the vector sum currents. Now we have a 3-wire system, but it's asymmetrical. If we push the corners of the triangle, moving from isosceles right, to equilateral, we find the currents, voltages and phases equalize, and the wire size has increased only very slightly (sqrt(3) instead of sqrt(2)).**Which I think is kind of a disingenuous way to put it? But it's been so long since I did the relations for 3-phase that I forget where exactly all the sqrts of 3 go.Also, just to finish out the thread of linear in/dependence -- because electricity only has two degrees of freedom in transmission lines (more fundamentally: propagating forwards or backwards), single phase is dependent, any nontrivial phase shift is independent, and any additional angles are redundant (dependent again).This is why there is no such thing as 4-phase or more. (Higher phases are used from time to time for special purposes -- take the 12-pulse rectifier for example. Here, the phase matters in relation to a nonlinear element, the diode. The power is still ultimately drawn from a single 3-phase circuit. The multiple phases are constructed using a multiwinding transformer, e.g. wye and delta, which give a natural 30 degree phase shift.)Tim

author: TimFox
author_rank: Super Contributor
timestamp: July 20, 2020, 08:03:27 pm
content: When first I encountered 3-phase loads in my mis-spent youth, I came up with this mnemonic to calculate the actual power. Example: 207.8 V phase-to-phase with 10 A current per phase. Imagine three 120 V light bulbs connected from phase to neutral. The actual neutral wire can be omitted in this thought experiment, as it passes no current. Each bulb pulls 10 A at 120 V, or 1200 W. Therefore, the total power from the source is 3600 W. The root-3 comes into play through converting 208 V phase-phase to 120 V = (207.8 V) / (root 3) phase-to-neutral.In a 12-pulse rectifier circuit, the wye and delta windings actually give60degree phase shift, half-way between the 120 deg phases of either wye or delta, to define six phases 60 deg apart.

author: TimFox
author_rank: Super Contributor
timestamp: July 20, 2020, 08:05:17 pm
content: Quote from: langwadt on July 20, 2020, 05:12:50 pmWith a quadrature pair of phases (0 and 90 deg) and appropriate transformers you could also define all three phases of a three-phase system. The math (determining the scalar co-efficients) is left as an exercise for the reader.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 20, 2020, 09:09:30 pm
content: Hmm, if it were 60 degrees, it wouldn't be useful for a rectifier? 6-pulse is already a pulse every 60 degrees.https://en.wikipedia.org/wiki/Delta-wye_transformersays 30, 150, etc.Tim

author: langwadt
author_rank: Super Contributor
timestamp: July 20, 2020, 09:40:48 pm
content: Quote from: TimFox on July 20, 2020, 08:05:17 pmand that is basically how much signal processing like software defined radio works, splitting a signal into I/Q or combining I/Q to generate a signal

author: rsjsouza
author_rank: Super Contributor
timestamp: July 20, 2020, 10:32:46 pm
content: I vaguely recall the term Triad (tríade, in portuguese) of vectors to describe the 120° relationship, but any searches came up empty. It's been more than a couple of decades ago, so...

author: Cerebus
author_rank: Super Contributor
timestamp: July 21, 2020, 01:18:39 am
content: Yep, so, as I suspected and kind of hoped, it's not my massive ignorance, it's just that we don't have a term for it.Kind of odd when you think about it. We've got antiphase and other names for 180º (or2π/2), nothing for 120º (or2π/3), we've got quadrature for 90º (or2π/4) and we've got in-phase for 0º. Given the ubiquity of 120º in power and motor electrics/electronics it's odd that it hasn't collected a short name over the years the way the other phase relationships have.On a slightly different note, it's quite common for someone to start a thread and then you see nothing more of them in it. I've often wondered why, and I've read others musing about it in threads where it's happened. Aside from Tim starting off a tangent about the composability of phase, I noted when I was considering where and when to comment that it's actually quite difficult to pick what to reply to out of on-topic replies. I think you've either a choice of letting it run to a conclusion or, treez like, replying to or thanking every contribution. So, next time you wonder why an OP seems to have abandoned a thread, perhaps they are just paralysed while deciding what to reply to or how to reply.

author: Circlotron
author_rank: Super Contributor
timestamp: July 21, 2020, 02:43:46 am
content: Quote from: T3sl4co1l on July 20, 2020, 03:05:12 pmMy guess would be "hexature"Two phases = quadThree phases = hex

author: TimFox
author_rank: Super Contributor
timestamp: July 21, 2020, 02:54:59 am
content: A 12-pulse rectifier uses two 6-pulse rectifiers in parallel (12 diodes) to feed a common DC bus. A single wye or delta secondary with six diodes is a six-pulse rectifier, the generalization of four diodes making a full-wave bridge with a single secondary winding. Since the three points on either a wye or delta are 120 degrees apart, the points on a wye are 60 degrees shifted from those on a delta.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 21, 2020, 02:57:34 am
content: Quote from: Circlotron on July 21, 2020, 02:43:46 amThe etymology comes from a square (quadrilateral); a regular "hexalateral" has 120° interior angles. This works better.Quote from: Cerebus on July 21, 2020, 01:18:39 amAs you've likely noticed, I often take the opposite tack and simply grab something in the thread to write about, and do that. Sometimes it's even helpful!Tim

author: Circlotron
author_rank: Super Contributor
timestamp: July 21, 2020, 04:45:47 am
content: Quote from: TimFox on July 21, 2020, 02:54:59 amIf it's a six-pulse delta fed rectifier then the pulses must be 60 deg apart to add up to 6x60=360 deg. For a wye fed rectifier in parallel to add pulses halfway between the delta pulses it would have to be 30 deg shifted from the delta because it's own pulses are spaced every 60 deg also.

author: gcewing
author_rank: Regular Contributor
timestamp: July 21, 2020, 07:06:53 am
content: I think the positive and negative half cycles are counted as separate pulses. So one set of 3-phase windings gives 6 pulses, and another set 60 degrees away gives another 6 pulses, for a total of 12 pulses.

author: sibeen
author_rank: Frequent Contributor
timestamp: July 21, 2020, 07:42:30 am
content: Quote from: TimFox on July 21, 2020, 02:54:59 amNup, the phase difference between a wye and a delta is 30 degrees.In a six pulse rectifier there are 6 pulses (peaks) in one cycle and therefore there is 60 degrees between the peaks (6 x 60 = 360 degrees). To make a 12 pulse rectifier we add another 6 pulse rectifier to the original and phase shift the incoming voltage by 30 degrees. We now have 12 pulses (peaks) spaced at 30 degrees giving a total of 360 degrees.As an aside the rectifiers do not have to be placed in series but can also be operated in parallel. In a parallel topology each thyristor sees the total voltage across it but only requires to be sized for half the current. For a series connected bridge the thyristor can be a lower voltage device but must be capable of carrying the full load current.

author: Siwastaja
author_rank: Super Contributor
timestamp: July 21, 2020, 09:37:17 am
content: Don't try to invent any more fancy words.Motor control literature is a total mess for a beginner, or even more experienced designer, to try to understand because everyone though it would be more fancy if they come up with scienc-y names for each trivial thing.My real-world observations show that the more people use these terms, the less they understand what they are talking about, finally to the point it's only cargo-cult engineering and getting things done only by directly utilizing the work done by others (i.e., buying modules and/or IPR).If you are writing a fictional novel and want to keep the readers attention, by all means come up with as many fancy words as possible. Science and engineering should work the opposite way, keep everything well-defined and unambiguous.If you have a vector, call that a vector, don't call it "space vector" just because space is a fancy place with the Moon, satellites and all. Similarly, if you have a 120 degree phase shift, do everybody a favor and call it a 120 degree phase shift.

author: sibeen
author_rank: Frequent Contributor
timestamp: July 21, 2020, 09:49:35 am
content: 'Space Vector" is a very well known term in power electronics for a form of modulation for the control of converters. SVPWM = Space Vector Pulse Width Modulation.

author: Cerebus
author_rank: Super Contributor
timestamp: July 21, 2020, 11:55:40 am
content: Quote from: Siwastaja on July 21, 2020, 09:37:17 amNobody's trying to, what I was trying to do was see if there was an existing word.Although my real-world experience is that people who use a phrase like "fancy words" are covering a lack of familiarity or knowledge by a fine display of oppositional defiance disorder. Where I last encountered it on here was in a Covid-19 discussion where someone who'd been smoking behind the bike sheds during biology lessons at school levelled it against those who'd actually acquired some biological knowledge. As you're surely not that type I'm going to put this down to you natively speaking a language with totally different roots to the kind of native languages spoken by the rest of us - I imagine that can make grasping the piecemeal Latin/Greek origins of scientific terms and how they are constructed perhaps a bit harder.QuoteWe're not specifically discussing motor control, or indeed any specific field of application. Terminology isn't devised to make things easier, or harder, for beginners, neither is it devised to keep the 'mysteries' of a subject hidden (except by religions and sociologists). It is devised for either brevity, unambitiousness, or both, by and for practitioners of the art under discussion. It's much easier to say "These are in quadrature." than to say "These are in a phase relationship of 90 degrees." - four words versus nine. If you had your way the words rafter, purlin, joist, toeboard, floorboard, pit-prop, sleeper and many others would not exist - there would just be the phrase "stick of wood" and discussions of building with wooden materials would be much longer and much more error prone as a result.What is unhelpful to learners here is the absence of regularity and it's the 'hole' in what ought to be a regular sequence that led me to the question "Does this word exist?".QuoteWhich is what specialised,specificterminology does. You actually seem to be arguing for something that would achieve the opposite.QuoteSurely "space vector"dis-ambiguates what kind of vector you're discussing, when there could be all sorts of vectors under discussion. And again (from an earlier discussion on here with another Finn), this is one of those places where English uses an overloaded noun, this being the use of "space" to describe "the area or boundaries of the system we're interested in" rather than "the universe outside of the Earth's atmosphere" or the space in "Kids, be quiet; I need some space to think!" or any of the other many usages of "space".And as for the other kind of space being "fancy" (dictionary:"sophisticated or expensive in a way that is intended to impress:fancy hotels and restaurants"), nope, space is quite literally the commonest thing in the universe. It's so common (dictionary:"ordinary; of ordinary qualities; without special rank or position; coarse or lower class:the dwellings of common people") that it's even commoner than me and BD139, innit. [Fx: sniffs, wipes nose on sleeve, belches.]

author: Siwastaja
author_rank: Super Contributor
timestamp: July 21, 2020, 12:41:17 pm
content: Quote from: sibeen on July 21, 2020, 09:49:35 amYes, and a very typical example where a completely arbitrary term (not based on math, for example) was invented as just aname, then later applied to places where it does not belong by people who do not understand that it's an arbitrary name describing a specific set of PWM generation schemes and nothing else, or thought that it describes some kind of physical or mathematical phenomena.Like a special case of a vector, used in motor control science.This way of misunderstanding is clearly demonstrated above:Quote from: Cerebus on July 21, 2020, 11:55:40 amSurely, indeed! People understandablyexpectit to work like this, except that there is no such a thing as a "space vector". This term has no definition, and no meaning - try to Google it! It's not a "kind" of vector. The substring "space vector" is just a part of the name of a PWM modulation scheme. Within SVPWM, there are obviously vectors - basically you modulate between two switching states that can be described as 2D vectors -, but they have no special "properties" to make them "space".So youexpect, rightly so, that itdis-ambiguates things, but in reality, it's a trap that causes confusion, because oh, that author just meant normal vectors! (Or maybe they didn't mean anything at all. I have seen completely cargo-cult discussion on motor control, as well!)This is a pattern which is valued in fictional novel writing: add non-factual, non-measurable "nuances". In science and engineering, it wastes the reader's time, because theyhaveto figure out the exact meaning. Excess attributes are as bad as are false attributes.Yes, I have seen "space vector" as a "loose" term where it makes absolutely zero sense, many times. It's just one of the many examples that actually hindered my understanding on motor control.I don't think that my native language makes it much more difficult to grasp terminology with Greek/Latin origin. I think I'm in the same position as native English speakers (who do not use such terminology in their daily life): it must be learned as a part of the learning process. For motor control, there is motor control vocabulary, and so on.In science, the target would be to optimize the size of vocabulary to provide best communication and learning results, not to maximize the length of the words vector. Not to minimize it, either.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 21, 2020, 01:00:26 pm
content: Disclaimer, haven't looked at SVPWM in detail. I've always understood the "space" to refer to state space representation. This is where you note all stateful values in the system, and pack them into a vector. Take the (per-element) derivative, multiply by the state transition matrix, add to the state vector, and equate to the input vector: you have a differential equation in one R^N vector variable. Thus you can have a general relationship between all values, and finding solutions for control purposes (input values) consists of inverting the matrix: a tough problem, but an imminently computable one.This may not be a very useful form, as the vectors aren't very large for motor control, I think, and simplifications can be made. So maybe the term isn't so applicable anymore. Or again, maybe I'm laughably wrong on my assumption hereTim

author: Siwastaja
author_rank: Super Contributor
timestamp: July 21, 2020, 01:02:28 pm
content: I think you have caught the etymology correctly.

author: sibeen
author_rank: Frequent Contributor
timestamp: July 21, 2020, 01:30:54 pm
content: Siwastaja, I think you'll find the concept of SVM is very well grounded in mathematics.

author: Cerebus
author_rank: Super Contributor
timestamp: July 21, 2020, 01:33:29 pm
content: Quote from: Siwastaja on July 21, 2020, 12:41:17 pmClearly your Google-fu is weak and mine is strong."What is a space-vector?"First page, eighth entry of a search for "space vector" including the quotes. (Actually it's duckduckgo-fu, but that wouldn't be so clearly understood.)Quote from:https://www.jmag-international.com/engineers_diary/021/

author: Siwastaja
author_rank: Super Contributor
timestamp: July 21, 2020, 02:12:10 pm
content: Quote from: Cerebus on July 21, 2020, 01:33:29 pmIs, or isn't. Seen wide usage where it isn't a complex number, but just a vector of real numbers, or where the intermediate Clarke transformed Iq, Id vectors magically become "space vectors". I don't know which definition or usage is correct. I would use the term only within papers which discuss Space Vector Modulation and define the term each time because I cannot find anygeneral mathematicssource for this (maybe you can?) so clearly it's an application-specific tool, not a generic mathematical term you could find a robust definition from Wikipedia or math sources, for example.Quote from: sibeen on July 21, 2020, 01:30:54 pmWhy comment if you don't bother reading what I said?This is my last post about the freaking SVM. SVM might not have been the best example. If my message didn't get through, it's OK for me. It isn't so important.Just remember that sometimes "dumbing down" a bit may help someone understand a very convoluted matter, such as motor control. I'm definitely capable of doing motor control (after years of trying to understand it, and finally getting there), and I can say for myself that dumbing down the terminology for myself, helped to grasp concepts thatsounddifficult but aren't too difficult after all. For example, I have seen that many concepts are 1:1 equivalent to switch mode converter design, but explained more clearly in literature discussing switch mode converters.

author: Cerebus
author_rank: Super Contributor
timestamp: July 21, 2020, 02:59:00 pm
content: Quote from: Siwastaja on July 21, 2020, 02:12:10 pmIn a space of spaces, a space vector would define a space. Any pure mathematician would understand that phrase off the bat, most applied mathematicians would not. (On a side note, Google seems to have reverted to ignoring word order, even when specified in advanced search, so I can't find any pages discussing the mathematics of "space vectors" because Google has a lot more content about "vector spaces" indexed, but they will be there somewhere.) I'mnotgoing to offer a definition of that usage because frankly it's at the edges of my knowledge where I am merely paddling at best - juggling spaces of spaces of spaces is the stuff of proper pure mathematicians, just like counting the number of countable infinities. Given {A: ∀a ∈ A, a ∈ {Angels}} and {P: ∀p ∈ P, p ∈ {Pins}} and a transform Dancing(A,P) => {A × P: ...}...

author: TimFox
author_rank: Super Contributor
timestamp: July 21, 2020, 03:19:27 pm
content: Back to polyphase rectifiers: I stand corrected about the phase angles in 12-pulse rectifier circuits. The two diodes per phase in a six-pulse (full-wave) rectifier from a three-phase transformer give the equivalent of six phase angles, where the diode pulses in the reverse direction fill in the other three angles: 0 (and 180), 60 (and 240), and 120 (and 300). To go to twelve pulses therefore requires the 30 degree angle, giving the rest of the 12 pulses: 30 (and 210), 90 (and 270), and 150 (and 330). With the three-phase source, the 30 degree angle can be realized without using phase-shift networks (which would be frequency dependent), by suitable combinations of the original three phases. (In my defense, I only had experience with six-pulse rectifiers, and my online search gave me a misleading result.) Polyphase rectifiers are very useful with modern power electronics, since the bus voltage resulting from the rectification starts out with a modest ripple voltage, even without capacitor, while the single-phase rectifier needs a capacitor to avoid 100% pk-pk ripple.

author: max_torque
author_rank: Super Contributor
timestamp: July 21, 2020, 03:58:34 pm
content: Quote from: sibeen on July 21, 2020, 09:49:35 amWhen asked "what is a space vector" one should always reply............ "UP !!!"

author: Cerebus
author_rank: Super Contributor
timestamp: July 21, 2020, 04:24:08 pm
content: Quote from: max_torque on July 21, 2020, 03:58:34 pmSurely that would be "Up! Quickly!" to be a vector...

author: sibeen
author_rank: Frequent Contributor
timestamp: July 22, 2020, 12:05:20 am
content: Quote from: TimFox on July 21, 2020, 03:19:27 pmHmmm, I've been working in the converter related industries for over 30 years now and have never seen a 12 pulse Graetz bridge (12 pulse rectifier) implemented without a phase shifting transformer of some sort.

author: langwadt
author_rank: Super Contributor
timestamp: July 22, 2020, 12:21:00 am
content: Quote from: sibeen on July 22, 2020, 12:05:20 amthe transformer doesn't really do phase shifting, it does "suitable combinations of the original three phases" to generate the additional phases

author: Circlotron
author_rank: Super Contributor
timestamp: July 22, 2020, 03:22:36 am
content: Quote from: langwadt on July 22, 2020, 12:21:00 amCould we say then that if you had two separate transformer secondary windings and winding 1 was at zero degrees and winding 2 was 90 degrees lagging and both were 100VAC and you put them in series, the resultant voltage would be 141.4VAC and 45 deg different to winding 1?What's more, if winding 2 voltage was varied, would the phase difference of the series pair of windings be varied (asymptotically) to any value between zero and 90 deg compared to the voltage on winding 1?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 22, 2020, 03:36:36 am
content: It's not "phase shifting", when "phase shifting" is defined to be a stateful signal filtering process.When you remove power to the transformer, there's no propagation or ringdown [of any significance at mains frequencies], it's just dead. No energy stored, no state.However, say we construct a variac of a toroid with a complete layer winding, tapped to apply 3-phase (or any other combination) power. As we slide any number of brushes over this variac, their outputs will shift in phase relative to each other, and if we have done this specifically for the purpose of generating arbitrary phases, it is very much so a "phase shifting" transformer.I would say both phrases are correct, under a suitable meaning of the words, but that those words have simply been left undefined, and so can be misinterpreted.Tim

author: langwadt
author_rank: Super Contributor
timestamp: July 22, 2020, 02:54:04 pm
content: Quote from: Circlotron on July 22, 2020, 03:22:36 amif you can only add V2 to V1 you can only move 45 degree

author: TimFox
author_rank: Super Contributor
timestamp: July 22, 2020, 03:12:48 pm
content: With respect to summing two sinusoids with a 90 deg phase difference:IfV1(t) = A sinwtandV2(t) = A coswt, wherew= (2pi)f, then with appropriate (positive or negative, as required) constant real co-efficientsb1andb2in the superpositionVsup=b1V1+b2V2, a sinusoid of any magnitude and phase angle at the same frequency can be generated by proper choice of the constants.