# Estimate the total harmonic distortion present

1. Aug 24, 2016

### Hndstudent

• Thread moved from the technical forums, so no Homework Help Template is shown.
The supply current was sampled 1024 times over a very short time interval. The data so obtained is given in column B of the accompanying Excel worksheet1. This worksheet has been set up to give a graph showing the spectral components of the data.

Question 3

1. i) Obtain the Fourier Transform for the data using the Fourier Analysis tool of Excel. The transformed data should commence in cell D2.

2. ii) Identify the principal frequencies in the current waveform.

3. iii) Estimate the total harmonic distortion [THD] present in the current waveform using the formula:

n max
THD(I)=1/I1 SQRT Σ (In)^2 x 100%
n=2

where I1 is the r.m.s. value of the fundamental current, In the r.m.s value of the nth harmonic and n(max) is the number of the highest measurable or significant harmonic.

[Note the vertical axis of the spectrum graph is scaled in (current)2.]

iv) Attempt to synthesise the shape of the original waveform from its principal harmonics [e.g. sketch the waveforms of the harmonics on the same time axis and add them together].

I am struggling with 3iii.

for I1 rms I have SQRT 15.8 + 8.77 + 6.25 = 5.55A

n max I have 15.8 as its the highest magnitude.

But I'm not sure what to do to find In?

any help would be appreciated.

2. Aug 25, 2016

### Staff: Mentor

In, or $I_n$ to make it clear, should be the rms magnitudes of the individual harmonic components.

Perhaps you could attach the Excel spreadsheet, or even a textfile of the datapoints you were given so that others might duplicate the problem?

3. Aug 25, 2016

### Hndstudent

Hi Gneill,

please find attached original worksheet. and a screen shot of the completed waveform.

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4. Aug 26, 2016

### Hndstudent

Hi Gneill, I am still struggling to work out $I_n$. And am I close with my I1 rms and n max answers?

Thanks

5. Aug 26, 2016

### Staff: Mentor

$I_1$ will be the magnitude of the fundamental alone. That is, the single peak that corresponds to the fundamental frequency associated with the current. In general this is the peak with the lowest frequency. The other peaks should be located at some multiples of that frequency. In your data the fundamental corresponds to the 15.878 at a frequency of about 53 Hz.

$n_{max}$ is the number of the frequency component peak with the highest frequency that you intend to deem as "significant". The peaks are numbered from 1 to $n_{max}$, with "1" being associated with the fundamental. If you plot your FFT values, how many significant peaks can you see over the whole domain? It looks like you've already picked them out and there are three of them. So $n_{max}$ = 3.

As an aside, I have noticed that different implementations of the FFT algorithm tend to apply different normalizing factors to the returned values. You might find, for example, that in order to recover the actual component contributions to your "signal" that you have to multiply the returned values by some constant, typically 2. The "DC" contribution (if any) is usually exempt from this normalization (I don't know why this is).

As an exercise you might try concocting your own "signal" with known components at particular frequencies and see how your Excel FFT handles it. Maybe something like:

$f(t) = 10 sin(ω_o t) + 3 sin(5 ω_o t) + 2 sin(8 ω_o t)$

where you choose the fundamental frequency $ω_o$ in radians/sec as you wish. Also pick a suitable sampling frequency to "sample" the signal generate the raw datapoints. See if you can "recover" the harmonic frequencies and their magnitudes from the FFT data.

6. Mar 23, 2017

### David J

Hi, is this thread still active as I have a question relating to this topic. Please advise or should i start a new thread ?? Thanks

7. Mar 23, 2017

### Staff: Mentor

Probably best to start a new thread. It's unlikely that the OP is still interested in pursuing this thread at this time.