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    Transformer and rectifier math

    All,
    I posted this question over at plcs.net, and didn't really get a good answer so I'm asking here:

    My transformer and rectifier math for 3-phase supply is a bit rusty.

    I'm looking to design a nominal 70VDC power supply for a large number of servos. They require 75VDC, but with the number of servos I'm looking to run, the factory-supplied power supplies will consume too much room in the control cabinet, and be too heavy.

    I'm looking at building a DC supply using:

    (3) 1kva 48VAC secondary transformers wired together with a delta secondary (fed from a 208VAC 3-phase source)
    (1) 3-phase, 60A bridge rectifier module
    (2) 18,000uF filter caps

    The transformers are rated at 234VAC primary, 48VAC secondary; if I feed this power supply from 208VAC, that should give me a ~42VAC secondary voltage.

    I will rectify the outputs of the transformers, and if my math is right, I should get 42V x 1.65 = ~70VDC. With filtering caps, I should have a fairly solid DC supply. The servos have a 90VDC max rating, so I have plenty of headroom.

    Is my math correct to derive my peak DC voltage, using the 1.65 multiplication factor for bridge rectified 3-phase voltage? Nominal DC voltage should be close to peak, with adequate filtering, yes?

    My math came from this equation:



    I'm also slightly unclear on what my ultimate capacity of the power supply will be; if the transformers' secondaries can each supply 20A, I should have 60A DC available, yes?

    I haven't done much power supply design with a three-phase source (any, in fact). A single phase supplied DC supply would be easier, but it won't give me the capacity I need without a monster transformer.


    Thanks for the help.

    SceneryDriver

    #2
    I don't remember the formula, but I'm pretty sure the DC from a three phase bridge is close to 1.35 x RMS AC
    Last edited by electrofelon; 07-10-19, 09:12 AM. Reason: Added RMS
    Ethan Brush - East West Electric. NY, WA. MA

    "You can't generalize"

    Comment


      #3
      https://forums.mikeholt.com/showthread.php?t=120366
      Ethan Brush - East West Electric. NY, WA. MA

      "You can't generalize"

      Comment


        #4
        How are you getting from a 3 phase input to a single phase output?

        Also, have you thought about the harmonic currents this will induce into the AC supply?

        the factory-supplied power supplies will consume too much room in the control cabinet, and be too heavy.
        Before I went too far down the road of building custom supplies, I'd probably ask myself if there is a reason the factory supplied units are larger and heavier than what you have in mind.

        Comment


          #5
          Scenery - how much is the load?

          You can buy off the shelf 5 kW Vienna bridge 3 phase PFC rectifiers a lot cheaper than designing a straight rectifier with big caps.
          About the size of 2 packs of playing cards, that should fit, eh.


          Post your amperage needs and can probably give you a part number even. Lots of sources, Vicor, Murata, Kepco, Aveox, etc....

          Comment


            #6
            The following PDF contains everything you are looking fir:

            https://cds.cern.ch/record/987551/files/p133.pdf

            Lots of calculus but they give the solved equations so you can safely ignore the calculus equations.

            Second you are missing voltage ripple in your calculations. Vdc=Vp-Idc/4FC where:
            Vdc is average voltage out
            Idc is in Amps
            Vp is the peak AC voltage, RMS x 1.009 for a six pulse rectifier
            F is frequency in Hz
            C is capacitance in Farads (18,000 / 1,000,000)

            This is the formula usually used for capacitor sizing.

            Also be aware that these are frequently used as precharge circuits for large drive systems. But one thing missing above is startup. At startup the capacitor appears as a huge short circuit and can easily burn up your rectifier. In a drive they just put a resistor in series. Since the precharge is essentially startup use only a contactor opens at the end of precharge. In your case though since your whole circuit is precharge you'd have to do the opposite...insert a contactor to bypass the resistor on startup.

            Sent from my SM-T350 using Tapatalk

            Comment


              #7
              What is the most suitable term for the resultant DC voltage from a 6 pulse rectifier, considering the ripple? I hear "average" used most of the time. Why not RMS?
              Ethan Brush - East West Electric. NY, WA. MA

              "You can't generalize"

              Comment


                #8
                Originally posted by electrofelon View Post
                I don't remember the formula, but I'm pretty sure the DC from a three phase bridge is close to 1.35 x RMS AC
                It is. With a lot of smoothing you might get get closer to 1.42Vac

                Comment


                  #9
                  Originally posted by electrofelon View Post
                  I don't remember the formula, but I'm pretty sure the DC from a three phase bridge is close to 1.35 x RMS AC
                  Yes, VDC = 3sqrt(2)/pi x VLine-Line RMS = ~1.35 VLine-Line RMS

                  About 1.4VDC should also be subtracted from the output to account for voltage drops in a pair of diodes inside the bridge.


                  Originally posted by electrofelon View Post
                  What is the most suitable term for the resultant DC voltage from a 6 pulse rectifier, considering the ripple? I hear "average" used most of the time. Why not RMS?
                  I guess it depends on the requirements of the load that is served by the DC supply.
                  RMS or Root Mean Square is the square root of the average (aka "mean") of one (or the sum of more than one) quantities that are squared, usually voltages or currents in electrical applications. RMS is more meaningful in AC power applications than the peak voltage of a waveform because power can than be directly calculated as P = V x I =V2/R =I2R for resistive loads when V and I are RMS quantities. Also, heating of conductors is proportional to I2R and therefore to the "mean square" of the AC current waveform even if harmonics or other frequencies are present.

                  It's more likely that the average value of the DC supply voltage is a more useful quantity than RMS for loads that use DC, unless you wanted to accurately quantify the total power into a resistive load when there's a significant amount of ripple (which would not be a common siituation).
                  Otherwise, the average DC voltage and peak-peak ripple are more useful quantities. For example, if you had a linear voltage regulator IC fed by a rectifier then the minimum voltage on the waveform due to DC ripple is very important. The voltage drop across the regulator cannot fall below a minimum value or it falls out of regulation. An RMS spec doesn't give you enough information in this case, because very short dips in the DC voltage would have minimal effect on the RMS ripple value.

                  Comment


                    #10
                    For those without analysis tools or a math capable scope, here are visual waveforms, 100 Vrms line to neutral. (If you can read it, would not enlarge further)
                    Note that difference between avg and rms is less than the diode drop variation with temperature.
                    2.32/1.73 = 1.34 for Vdc to Vrmslinetoline for LOW LOAD, includes about 0.8V drop per diode. diode drop will be higher at higher currents.
                    Source for this was a 100 Vrms line-neutral 3 phase, full wave 6 diode bridge.
                    Ripple with no capacitance is about 14% peak to peak
                    Click image for larger version

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                    Comment


                      #11
                      Originally posted by junkhound View Post
                      For those without analysis tools or a math capable scope, here are visual waveforms, 100 Vrms line to neutral. (If you can read it, would not enlarge further)
                      Note that difference between avg and rms is less than the diode drop variation with temperature.
                      2.32/1.73 = 1.34 for Vdc to Vrmslinetoline for LOW LOAD, includes about 0.8V drop per diode. diode drop will be higher at higher currents.
                      Source for this was a 100 Vrms line-neutral 3 phase, full wave 6 diode bridge.
                      Ripple with no capacitance is about 14% peak to peak
                      Can you determine the peak diode current? That's one very important parameter for diode rectifier design. Both at stead state, and also when the power is first applied and the caps. are completely discharged.

                      Although, I still don't know how we are getting from a 3 phase supply to a single phase output, so maybe you don't know what the complete circuit is either.

                      Comment


                        #12
                        Originally posted by steve66 View Post
                        Can you determine the peak diode current? That's one very important parameter for diode rectifier design. Both at stead state, and also when the power is first applied and the caps. are completely discharged.

                        Although, I still don't know how we are getting from a 3 phase supply to a single phase output, so maybe you don't know what the complete circuit is either.
                        here is the common circuit for simple 6 diode 3 phase bridge
                        You can get EVERY voltage, current, and power dissipation from this type FEA model This is ORCAD PSpice, you can download a free student version off the orcad web site, think this schematic has few enough parts for the free version. there are other free FEA circuit anlaysis programs such a LTSpice - this has generator source impedances from another project being worked, much lower values for connection to the grid. The plot on previous reply has the output cap (C2) set to zero .

                        Click image for larger version

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                          #13
                          Originally posted by electrofelon View Post
                          What is the most suitable term for the resultant DC voltage from a 6 pulse rectifier, considering the ripple? I hear "average" used most of the time. Why not RMS?
                          RMS has to do with the AC that we don't care about...we want only the DC component.

                          Sent from my SM-T350 using Tapatalk

                          Comment


                            #14
                            190710-1948 EDT

                            paulengr:

                            A true RMS measurement includes both the DC component and any AC component added to it.

                            Most electronic voltmeters labeled "true RMS" only measure the RMS value of the AC component. An input capacitor strips out the DC component.

                            An electrodynamometer meter does read true RMS within its frequency range capabilities. And a hot-wire or thermal type also reads true RMS up to moderately high frequencies.

                            Study the definition of RMS. Look at the calculus equations for calculating RMS.

                            .

                            Comment


                              #15
                              Agreed RMS includes DC but I didn't say it did not include it, only that it's not the relevant value. Agreed the meters that aren't true RMS don't give correct values just as they don't usually handle nonsinusoidal voltages correctly either.

                              Sent from my SM-T350 using Tapatalk

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