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Total Harmonic Distortion of AC current using Fourier Analysis

cadtelsim
10-Marble

Total Harmonic Distortion of AC current using Fourier Analysis

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

 

 

ACCEPTED SOLUTION

Accepted Solutions
Werner_E
25-Diamond I
(To:cadtelsim)

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

 

View solution in original post

15 REPLIES 15
ppal
17-Peridot
(To:cadtelsim)

File?

cadtelsim
10-Marble
(To:ppal)

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

ppal
17-Peridot
(To:cadtelsim)

ppal_0-1681682107484.png

Drag and drop.

cadtelsim
10-Marble
(To:ppal)

 
Werner_E
25-Diamond I
(To:cadtelsim)

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

 

Great Werner_E! Well done! Congratulation

walter

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 😉

 

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



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

Werner_E
25-Diamond I
(To:cadtelsim)


@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
20-Turquoise
(To:cadtelsim)

image.png

ttokoro_0-1681790832948.png

 

image.pngimage.png

ttokoro_1-1681790882387.png

 

image.pngimage.png

ttokoro_2-1681790920966.png

 

image.pngimage.png

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
20-Turquoise
(To:VM_10139171)

image.png

ttokoro
20-Turquoise
(To:ttokoro)

To calculate correctry, TOL is sensitive and integral from -L to L gives bug error at 80 to 100 degree.

Divide it from -L to 0 and from 0 to L makes good answer. Prime 9.

 

image.pngimage.pngimage.pngimage.pngimage.pngimage.png

Thank you for the detailed response. I will do my best to replicate this to understand Mathcad features better. 

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