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3-phase systems

  1. Feb 6, 2013 #1
    Hello all,
    I'm having a bit of a difficult time following a specific conversation that I had with one of my professors. Occasionally, we would be given a 3-phase load (balanced or unbalanced), with merely the wires shown (the formation of the sources was not revealed. See the image below.
    I asked what formation do we assume the sources are in, and he said that it doesn't matter. However, I was analyzing a few questions assuming wye connection, followed by delta connection, and I was getting different results; meaning that it did appear to matter.

    As an example, say we are given a line voltage of 208V for a) in the image.
    If we assume wye orientation of the sources, then in phasor form we would have,
    [tex](U_{23}, U_{31}, U_{12}) = (208e^{j30}, 208e^{-j90}, 208e^{j150})[/tex]
    All of these are leading their respective phase voltages in wye.

    If we assume everything remains the same but we merely change the sources to delta configuration we get the following:
    [tex](U_{23}, U_{31}, U_{12}) = (208e^{j0}, 208e^{-j120}, 208e^{j120})[/tex]
    This is due to the fact that the phase voltages are the same as the line voltages in this orientation.

    Furthermore, there is an actual conversion from one to the other. However, I am just not seeing how you can assume the original orientation and get the same results. Any idea where I am going wrong, or what?

  2. jcsd
  3. Feb 6, 2013 #2


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    You are varying the load and getting different currents, as you would expect.

    How the supply voltages are generated doesn't matter except that if your load requires a neutral then you should have access to a neutral from the supply.

    The voltages are given relative to each other and in fixed phase relationships. This is OK. You can work with that.

    Just accept that the voltages are right and don't try to rewrite the problem. They only want you to examine the load, not the whole system.
  4. Feb 7, 2013 #3

    jim hardy

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    I think you are referring all angles to a current?

    When starting out, use of terms "line" and "phase" can cause confusuion, since "phase" can mean either an angle, a winding, or a conductor.
    I don't know what conventions your textbook author uses.

    My AC circuits prof cautioned us boys to maintain awareness of that confusion factor .
    We used:
    "Vline" for voltage between two machine terminals,
    "Vphase" for voltage across a winding,
    "Iline" for current entering or exiting a machine terminal
    "Iphase" for current in a winding.
    That kinda helps one keep oriented - is he analyzing inside a machine or in the transmission system.

    Sigh - then you graduate and get a job and and the transmission line guys call their wires "phases"., and the machinery guys use "phase" for both their windings and their terminals.

    It's a fact -
    wye connected phase windings in source -----> line current is same as phase current and in phase; line-line voltage = √3 X phase voltage and out of phase

    delta connected phase windings in source ----> line current is √3X phase current and out of phase; line-line voltage = phase voltage and in phase

    exactly as you observed.

    And it's a fact we use language imprecisely.

    It's all in the choice of reference for phase angle. I use line-line voltage for starting out.
    Pick one and be rigorous. You will gain fluency with practice.
    It's helpful to work a problem twice, starting with different references for zero phase angle,
    eg once using Vab as zero deg, then Van as zero deg

    old jim
    Last edited: Feb 7, 2013
  5. Feb 7, 2013 #4
    Okay. Makes sense. The different source orientations gives rise to differing currents and voltages; however, the same power is dissipated, which is the main concern. It's still rather annoying when you are asked to find a particular parameter, however, the answer is not the same as the one given in the book due to the fact they used source-delta formation when you used wye-delta formation.
  6. Feb 7, 2013 #5

    jim hardy

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    okay i thought i understood that.

    but that confuses me.

    You say different source configurations, but what is in the image? Source or loads?
    I thought it was loads.

    Okay, you have no idea whether that 208 volts was made by 208 volt windings connected delta, or by 120 volt windings connected wye.
    You are only given 208 line to line volts, where did your angles come from?
    All you know is the line to line voltages are 120 deg apart.
    After you choose something for zero degrees reference you can assign all angles relative to that. And that choice is yours, unless it's spelled out in the problem statement.
    What did you choose for zero degrees?
    I'd have used one of the line to line voltages.

    I think you are not consistently choosing your zero degree reference.

    What if you use U23 for zero degrees in both cases?
    U23 = 208 angle 0.
    Then it's U1n, U2n, and U3n that'll be off by 30 degrees and have different amplitudes,, 120 vs 208.
    But they don't appear outside the machine.

    You will get the same line currents and voltages both ways if you are meticulous and consistent about choosing your zero degree reference.

    try it out.

    old jim
    Last edited: Feb 7, 2013
  7. Feb 14, 2013 #6
    Thanks Jim. Sorry to bump this, but I have one more thing to go over before my midterm tomorrow. When asked for the phase voltage, how exactly do you know whether or not it is the phase voltage of the source or the phase voltage of the load that is being asked of you? For example, in an unbalanced system, Y-Y connected, you will have a source phase voltage and a load phase voltage, correct?
  8. Feb 14, 2013 #7

    jim hardy

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    If the neutrals in a Y-Y are not connected together and there is unbalance, well sure , the source and load phase to neutral voltages can differ . It's called "Unstable Neutral".

    I still hold that the phrase "phase voltage" is ambiguous because it does not define what voltage was intended by whoever said it.
    Definition of voltage is potential difference, word 'difference' inferring that the two points involved in the difference ought to be defined.
    Does speaker mean opposite ends of a phase winding, or two of the lines interconnecting source and load?
    He needs to make that clear.

    If one is shown no internals of either source or load, it is probably safe to assume "phase voltage" means line to line voltage. (Note two points.)

    What i used to do when an exam question was poorly worded was:
    A. Write teacher a note like this:
    ""Your term 'phase voltage ' might mean one of three things:
    1. Line to neutral voltage at point A, in which case answer is whatever it is
    2. Line to neutral voltage at point B, in which case answer is whatever it is
    2. Line to line voltage at point C, in which case answer is whatever it is ""

    B. Or, if allowed, go up and ask him which he meant.
    Usually he would say to entire class " Mr X has pointed out an ambiguity in question Y. Here is clarification. ""

    (EDIT line to line is terminology we used in my and Fred Flintstone's days. I've seen phase to phase used for same intent.
    Don't hesitate to subscript yout notation to make it unambiguous; VA-N, VA-B, VL-L, VL-N note this defines the two points)


    I'm sensing from your questions a lack of preciseness of language in this course.
    I used to be lazy and imprecise in my use of language, and am still relatively awkward despite lots of effort to contrary. It's an ongoing struggle.

    .......................................Anecdote, hope it's not boring...

    Do you believe in "serendipity" ?
    I stumbled across a book at a library sale and bought it just for the title "Lavoisier and Faraday".
    The first essay in it was Lavoisier's "Introduction to treatise on chemistry".
    Best fifty cents i ever spent.

    Here's a link to the whole thing. I recommend you print it and read it at your liesure, after the exam.
    I took it to heart, worked at improving my preciseness in description and it benefitted me greatly over the years...
    His near-last paragraph is outrageous and you see it at work every day.
    That you ask these questions probably means that you are capable of fine discernments of meaning in words. Enjoy Lavoisier, and keep a dictionary handy. I like Webster's.
    ..What a "Foortuuuitious Circumstance*" it was for me to stumble across that book by pure random chance(?).

    (* Bert the Chimneysweep, Mary Poppins)

    ........................................... end anecdote

    Good luck on your test.
    If teacher won't define what voltage he means, give him all of them clearly and unambiguously defined.

    old jim
  9. Feb 14, 2013 #8
    Yeah, most of the questions we have worked on were balanced systems, and therefore the voltage across the load was the same as the source phase voltages. He then asked what the phase voltages for an unbalanced system were (Y-Y) and he answered the voltage across on of the phase impedances, rather than the source phase voltage. This language is really starting to unbalance me! I'm going to say something next time.

    Also, when given ratings for loads, does that always refer to one of the phases? For example, if it is rated at 450W, that applies to each of the phases, rather than dividing that by 3?
  10. Feb 14, 2013 #9

    jim hardy

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    Unbalanced Y-Y depends on whether the neutrals are tied together.
    If tied, load and source are of course in parallel
    if not tied , it's a network and has to be analyzed using plain old KVL and KCL....

    Parse it carefully.
    Phrase "a 450 W load.." is ambiguous. i would assume it to mean 450 W total and if not stated otherwise, balanced, ie three 150 W loads..

    Phrase "450 watt loads" certainly infers per phase but if it's not clarified by a drawing i'd ask.

    "a 450 W three phase load" is less ambiguous, a load totalling 450 watts on a three phase system. Speaker should say whether it's balanced.

    "450 W per phase" is unambiguous, but doesn't tell you wye or delta..

    If on an exam it's ambiguous, i'd ask for clarification .

    Not trying to dodge your question - My instructor went to great lengths to make such things very clear in his lectures and on his tests.

    If things in your class are really stated with that much ambiguity, give teacher a copy of Lavoisier too.
  11. Feb 15, 2013 #10
    Thanks! The exam went well. No ambiguity. I really like power.
  12. Feb 15, 2013 #11

    jim hardy

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    Great ! See - you only needed to realize how much you already know.

    Thanks for the feedback -
    If you enjoy your motors courses, try one in 'power system analysis'. It's the dynamics of rotating machinery and transmission systems, utterly fascinating and highly cerebral.
    That Auburn professor i linked wrote an excellent textbook on the subject. See if your EE professor is aware of it - it's somewhat of a classic already.

    My school had a small coal fired steam power plant, only a couple megawatts. Students taking the "Power Plant Measurements" course got some great practical experience on equipment that's not so intimidatingly gigantic. I hope your school has one.

    Best of luck to you.

    And thanks for telling us about your success.

    old jim
  13. Feb 17, 2013 #12
    Jim, did you go to Auburn?

    This is off topic, but I graduated from there in 2007. I actually had Dr. Gross for my undergraduate power class right before he retired.


  14. Feb 18, 2013 #13

    jim hardy

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    No, Auburn was one of those more highfalutin' schools.
    I went to Missouri School of Mines and Metallurgy, in Rolla, which was at the time U of Mo's engineering campus.
    It was an early "Land Grant" college so tuition was remarkably inexpensive.
    It's now got a different name and has a substantial number of female students. Back in my day it was unusual to have even one girl in a class, for in early 1960's girls just didn't go into engineering. I think enrollment was like 2,500 men and 7 women.

    Professor Gross was at that time a graduate student teaching basic EE courses. I took DC machinery and AC circuits.
    You'll see Rolla mentioned in his cv. I vividly remember his classes for their unusually clear explanations and development of concepts. He is one of those rare individuals who naturally teaches students not just the facts but how to think and deduce more of them for yourself. His preciseness in definitions is the thesis in that Lavoisier paper i linked to earlier.
    I guess great minds run on parallel tracks...even in different centuries.

    It was Prof Gross(then not yet a professor) who sparked my interest in power.
    He taught not just engineering, but excellence.
    I owe him big time.

    old jim
    Last edited: Feb 18, 2013
  15. Feb 18, 2013 #14
    Small world!

    I enjoyed his class thoroughly myself, and I agree with what you said about him teaching students how to reason things out for themselves. I remember going to his office for help several times, and he would never give me the answer...but he would guide me into realizing the answer for myself.

    I still have his power systems textbook at my office (it's informally known as the power bible here). It is an excellent reference, and to the OP I'd highly recommend it as well. I think that Amazon sells it, just look for Charles A. Gross.

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