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How to calculate the unbalanced neutral current in a 3 phase circuit

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    How to calculate the unbalanced neutral current in a 3 phase circuit

    I was teaching a class in sharing the grounded conductor in a single phase circuit.
    We only have 3 phase power in our class. I built a simple circuit with 2 equal loads on 2 seperate phases with a shared grounded conductor. I figured that the current in the grounded conductor in a three phase circuit would not be as low as in a single phase situation, but it would be significantly less than in the 2 hots.
    When we measured the currents, the neutral was almost the same as the hots. what gives?
    So does anyone know the formula for calculating the current in the grounded conductor in an unbalanced 3 phase circuit? I went over lots forums and archived forums and couldn't find any thing. I appreciate any help you can give.

    #2
    I kinda like this site...
    http://www.3phasepower.org/3phasepowercalculation.htm

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      #3

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        #4
        Exactly the reason 310.15(B)(5)(b) exists.

        (b) In a 3-wire circuit consisting of two phase conductors and the neutral conductor of a 4-wire, 3-phase, wye-connected system, a common conductor carries approximately the same current as the line-to-neutral load currents of the other conductors and shall be counted when applying the provisions of 310.15(B)(3)(a)
        I live for today, I'm just a day behind.

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          #5
          Here is where vector mathematics comes in handy, and something you should be teaching to your students. Assuming resistive loads and all currents being equal in magnitude, you will have Iaba + Ib

          In your example, you are missing the Ic. If Ic was present, then the total neutral current would be + = 0

          Click image for larger version

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            #6
            Originally posted by rmann View Post
            When we measured the currents, the neutral was almost the same as the hots. what gives?
            That question has been answered. But let me suggest that you take the same two phase wires that you used for your experiment and connect them instead to the primary of a single phase transformer. The voltage ratio is not important, but for discussion sake let us say the secondary voltage is 120/240. Try your experiment again, this time using the transformer secondary as your voltage source.
            Charles E. Beck, P.E., Seattle
            Comments based on 2017 NEC unless otherwise noted.

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              #7
              Originally posted by 480sparky View Post
              That is fine where load power factor is identical on all three phases. But not if the power factors differ.

              Si hoc legere scis nimium eruditionis habes.

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                #8
                Originally posted by Besoeker View Post
                That is fine where load power factor is identical on all three phases. But not if the power factors differ.

                That is certainly a fact, but in any electricians training and testing I have seen they are looking for what 480 posted.

                They don't usally consider PF in the questions involving neutral current.

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                  #9
                  Originally posted by iwire View Post
                  That is certainly a fact, but in any electricians training and testing I have seen they are looking for what 480 posted.
                  They don't usally consider PF in the questions involving neutral current.
                  I'm sure what you say is correct. But it's a bit of a shame, I think. By all means give the expression that 480 posted but with the caveat that it applies to very specific circumstances, not all. Even not most.
                  Nah, on reflection, I don't think it should be taught to electricians. Is it of any practical use?
                  For the simple example I gave, the neutral current is nearly three times the magnitude that you would get by evaluating that expression.
                  Si hoc legere scis nimium eruditionis habes.

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                    #10
                    Originally posted by Besoeker View Post
                    I'm sure what you say is correct. But it's a bit of a shame, I think. By all means give the expression that 480 posted but with the caveat that it applies to very specific circumstances, not all. Even not most.
                    Nah, on reflection, I don't think it should be taught to electricians. Is it of any practical use?
                    For the simple example I gave, the neutral current is nearly three times the magnitude that you would get by evaluating that expression.
                    Do not confuse the situation with real life facts, we get flustered
                    "Electricity is really just organized lightning." George Carlin


                    Derek

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                      #11
                      Big Thanks!

                      Thank you all for your great responses. I teach what's called a "pre apprentice" program at the san Diego Job Corps so a lot of your responses are way beyond my students( and me too). I think the Vector math that Rick submitted will be really helpful. somehow the visual really makes it clear. Thanks again. I'll be BACK!

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                        #12
                        I have no problem with teaching someone the basic formulas, then also informing them that things like power factor and harmonic currents can complicate what is really there. For the average installer or basic troubleshooting person, that is what they need to know. If they get into a situation where that additional information they can turn to the books or places like this forum for help. Kind of what I do myself as I do not run into power factor or harmonic problems frequently enough to remember formulas, or even some of the technicalities that apply. Just knowing Ohms law, Kirchoff's laws gets most average installers and troubleshooters through what they run into the most. Knowing what else may be lurking and where to go for more help with it is important though.
                        I live for today, I'm just a day behind.

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                          #13
                          Originally posted by rmann View Post
                          ... somehow the visual really makes it clear...!
                          http://forums.mikeholt.com/attachmen...9&d=1244942631

                          My Excel calculator (embedded in the Word file linked above) may help with the visual. Has numeric entry for line currents and power factor, calculates neutral current, and plots the vectors.
                          I will have achieved my life's goal if I die with a smile on my face.

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                            #14
                            Er fellas...... isn't this thread on neutral current?
                            "Electricity is really just organized lightning." George Carlin


                            Derek

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                              #15
                              To the mystery mod who deleted my posts, I was not bickering. I was correcting some misinformation in other posts.
                              Don't mess with B+!
                              (Signal Corps. Motto)

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