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cadtelsim10-Marble
10-Marble
April 16, 2023
Solved

Total Harmonic Distortion of AC current using Fourier Analysis

  • April 16, 2023
  • 2 replies
  • 6660 views

So, I've been able to work through all the values so far but seems like I have a problem with the summation notation since the THD of alpha does not converge to a solution:

 

VM_10380528_0-1681678396577.png

 

VM_10380528_1-1681678415655.png

 

VM_10380528_2-1681678434105.png

 

 

Best answer by Werner_E

Not sure why, but the problem is "only" n=2 and function I.a

 

Werner_E_0-1681692024874.png

The function you integrate does not look malicious

Werner_E_1-1681692585902.png

Some additional observations:

Werner_E_6-1681693559643.png

 

 

EDIT:

Solution - Set the system variable TOL to a lower value. Either write TOL:=10^-8 at the top of the sheet in front of the function definitions or use the menu.

Doing so makes the integral converge

Werner_E_3-1681692804476.png

 

The plot below with variable values of alpha takes very long. I stopped it and used a larger step width to speed it up.

It looks like THD is independent from alpha

Werner_E_4-1681693179472.pngWerner_E_5-1681693497267.png

 

2 replies

P
ppal_25568718-Opal
18-Opal
April 16, 2023

File?

C
cadtelsim10-MarbleAuthor
10-Marble
April 16, 2023

I get a notification saying I can't post the file using the email, is there any way to attach the file here?

P
ppal_25568718-Opal
18-Opal
April 16, 2023

ppal_0-1681682107484.png

Drag and drop.

W
Werner_E25-Diamond IAnswer
25-Diamond I
April 17, 2023

Not sure why, but the problem is "only" n=2 and function I.a

 

Werner_E_0-1681692024874.png

The function you integrate does not look malicious

Werner_E_1-1681692585902.png

Some additional observations:

Werner_E_6-1681693559643.png

 

 

EDIT:

Solution - Set the system variable TOL to a lower value. Either write TOL:=10^-8 at the top of the sheet in front of the function definitions or use the menu.

Doing so makes the integral converge

Werner_E_3-1681692804476.png

 

The plot below with variable values of alpha takes very long. I stopped it and used a larger step width to speed it up.

It looks like THD is independent from alpha

Werner_E_4-1681693179472.pngWerner_E_5-1681693497267.png

 

    W
    WalterSchrabmai12-Amethyst
    12-Amethyst
    April 17, 2023

    Great Werner_E! Well done! Congratulation

    walter

      W
      Werner_E25-Diamond I
      25-Diamond I
      April 17, 2023

      Its not that difficult to track down errors like this using "try..on error".

      Werner_E_1-1681737653957.png

      It was surprising that just the single value n=9 threw the error and all others worked fine.

      The usual way would be to increase the value of CTOL and see if convergence could be achieved that way. Not sure why I had the idea to decrease TOL 😉

       

        C
        cadtelsim10-MarbleAuthor
        10-Marble
        April 17, 2023
        Thank you, Werner for the tips and solutions. It wouldn't have occurred to me. I'm a new mathcad user and despite having serious issues with it every day I'm more interested in it than MATLAB. Any suggestions for improvement?


        Vina Mofidi

        Sch Elect Comptr & Energy Engr

        Arizona State University


        email: Vmofidi@asu.edu



        C
        cadtelsim10-MarbleAuthor
        10-Marble
        April 17, 2023

        Thank you for the tip. Its interesting to find out why value of n=9 creates an error. I appreciate your help.

        W
        Werner_E25-Diamond I
        25-Diamond I
        April 17, 2023
        @cadtelsim wrote:

        Thank you for the tip. Its interesting to find out why value of n=9 creates an error. I appreciate your help.

        Yeah, if you find out, let us know.

        ttokoro
        21-Topaz I
        ttokoro21-Topaz I
        21-Topaz I
        April 18, 2023

        image.png

        ttokoro_0-1681790832948.png

         

        image.pngimage.png

        ttokoro_1-1681790882387.png

         

        image.pngimage.png

        ttokoro_2-1681790920966.png

         

        image.pngimage.png

        t.t.
          V
          VM_101391711-Visitor
          1-Visitor
          April 18, 2023

          Thank you for the detailed analysis. This complete analysis will be instrumental in learning features of Mathcad along with the limitations of THD of ac current related to the delay angle. I'll fully study this document.

          ttokoro
          21-Topaz I
          ttokoro21-Topaz I
          21-Topaz I
          April 18, 2023

          image.png

          t.t.
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