# Harmonic Distortion in a current waveform

1. Mar 23, 2017

### David J

1. The problem statement, all variables and given/known data

Estimate the total harmonic distortion [THD] present in the current waveform using the formula:

2. Relevant equations
$THD\left(I\right)=\frac{1}{I1}\sqrt{\sum_{n=2}^\max\left(In\right)^2}\times 100\%$

3. The attempt at a solution
I have attached a worksheet for this. The work sheet has generated a graph. In the graph there are 3 peaks. The vertical axis is $i^2$ The first peak is showing the $i^2$ value of 15.87849655. The second peak is showing the $i^2$ value of 8.770681646 and the third peak is showing the $i^2$ value of 6.253185768.
The first peak is the fundamental. Peaks 2 and 3 are harmonics.

$I1=\sqrt{15.87849655}=3.984783$

$In=\sqrt{8.770681646+6.253185768}=3.876063391$

$THD\left(I\right)=\frac{1}{3.984783}\times 3.876063391\times 100\%$

$THD\left(I\right)=0.250954686\times 3.876063391\times 100\%$

$THD\left(I\right)=0.972716\times 100\%$

$THD\left(I\right)=97.2716\%$

I think this is correct but would appreciate any comments if I am wrong. I have attached the excel spread sheet to be read in conjunction with this question and answer.

Thanks again

#### Attached Files:

• ###### Worksheet for Harmonics Question.xlsx
File size:
119.4 KB
Views:
53
2. Mar 23, 2017

### Staff: Mentor

I didn't check it in detail, but it looks like you did it correctly. BTW, there are different kinds of THD, so I assume they asked for the THD with respect to the fundamental, which is the equation that you used. The THD with respect to the RMS sum of the currents cannot exceed 100%, but the THD with respect to the fundamental can if there is enough distortion.

3. Mar 24, 2017

### David J

Thanks for your input. I have attached the question FYI. It states to use this equation.

This was question (iii) of (iv) in a series. Question (iv) asks

"attempt to synthesise the shape of the original waveform from its principal harmonics [ eg sketch the waveforms of the harmonics on the same axis and add them together]

I think this is referring to the original wave form that was generated in the excel spread sheet I attached in post 1 of this thread. I am a little confused by this and was wondering if you could possibly help me understand the question a little better. What exactly is it asking me to do? How can I add 2 waveforms together ??

#### Attached Files:

• ###### Harmonics question.JPG
File size:
41 KB
Views:
75
4. Mar 24, 2017

### Staff: Mentor

Yeah, it sounds like it. If you just do a time domain plot of your B column versus your times in the A column, that will plot the original waveform.

You can try to reproduce that waveform by adding together the 3 sine waves (fundamental and harmonics) with the associated amplitudes from the Fourier plot and by adjusting their relative phases by hand. Or you could use the phase data from the Fourier analysis so you don't have to do the adjusting and adding by hand...

5. Mar 26, 2017

### David J

Hello again, well I had a go at this as you suggested and ended up with a somewhat different waveform which I am assuming to be the original. I attached the updated spreadsheet with this post. I tend to think this is correct. Do you think this is what the question was asking all along ??

#### Attached Files:

• ###### Synthesised Wave form.xlsx
File size:
51.7 KB
Views:
57
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