# How to find input signal formula

We have a PC with digital-to-analog converter. With help of this converter we generate “pure” sine: y(t)=A*sin(2π*f*t+ ψ) with industrial frequency 50 Hz. This signal goes as input to electricity generating plant which has a goal to raise this signal and give to its own output. During this signal raise it gets distorted (there is some non-linear element in the plant scheme) and on the output of the plant we get not “pure” signal (using Furier expansion we have harmonics of higher than 50 Hz frequencies: 100 Hz, 150 Hz, 200 Hz and so on). We can see these higher frequencies when we analyze signal from the analog-to-digital converter (the same PC with digital-to-analog converter) that arrives from the output of the same(as in beginning of this post) electricity generating plant and the signal gets decreased to the same level as it was at input of electricity generating plant. THE PROBLEM IS: feed the electricity generating plant with signal that on the output it will be “pure” sine(there is a constraint: difference between main harmonic and any other from the first eleven not less than 52 decibel).

Any ideas how to implement this?

I have no idea what you are trying to do. I think it's common that the 50Hz from the plant is distorted( with higher harmonics). The distortion can be from the load down the line that generate the harmonics and I don't think you can control that.

Are you trying to use feedback to lower the distortion?

Yes, Iwant to reduce distortion so that constraint "difference between main harmonic and any other from the first eleven not less than 52 decibel" was true.

I am not a power engineer by any stretch. But it is my understanding that the load down stream ( appliances and all) generate so much harmonics and feed into the power line, that it would be impossible to control that. You are driving the power through transmission lines, there is an impedance involve. Even if you can manage to clean it up at the station, down the road, it's still can be distorted.

I have no idea how do you make use of the pure 50Hz input to generate the high power output. Distortion through feed back can only be done if the output is some sort of linear device that amplify the input signal. I don't dare to pretend I have knowledge on this.

jim hardy
Gold Member
Dearly Missed
This must be a thought experiment, i presume?

Real electric machinery with iron cores is nonlinear so produces harmonics. The electric company goes to lots of trouble to make fairly pure sinewaves, by controlling the distribution of field windings in their generator rotors and using delta windings on three phase transformers to short circuit third harmonics.

Add to your fourier series for the generator terms that reduce the harmonics at wherever you are measuring.
Bsin(3wt + phi) etc.
Odd harmonics affect both peaks symmetrically ie mirror image
even harmonics affect them opposite way, ie distortion looks similar top and bottom(not mirror image) so you shouldn't need any of those.
Play with a plot of say fundamental plus third harmonic to get the feel of it.

Or add harmonic filters in hardware.

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This must be a thought experiment, i presume?
Jim Hardy, it is real experiment.

And we need an answer to the question: is it possible to find a function that goes to input of electricity generating plant such that at the ouput we get sine with constraint difference between main harmonic and any other from the first eleven not less than 52 decibel.

NascentOxygen
Staff Emeritus
As a thought experiment, I suppose you could tightly control and continuously vary throughout each cycle the excitation of the generator so as to pre-distort the generated sinewave so that after it has subsequently passed through the various non-linear devices it emerges as a relatively pure sinewave.

jim hardy
Gold Member
Dearly Missed
nascent just gave an approach.

electricity generating plant
What is the nature of this generating plant?

Real generators have a few % harmonic content in their output

our diesels were i think 5% third, 10% total
and that was before any transformers
large steam turbogenerator i'm sure is somewhat better

To me a power generator is rotating machinery and the concept of a computer generated input to it just , well, i cant imagine it.
One builds the rotating field to produce sinusoidal flux by careful machining of the steel and distribution of the field windings. I suspect the mmf curve would be "peaky" to overcome nnlinearity of B-H curve for that machine.

I have no idea what you folks are doing to produce power from a computer.

For example our PC generates signal with 3V voltage. The task of elictricity generating plant is to raise voltage (for example up to 3000V) and give it to its output. Than we use transformer that decreases signal back to 3V and feed it to A-to-D converter to check the signal.

jim hardy
Gold Member
Dearly Missed
Feedback around your "electricity generating plant" ought to help its linearity.

EDIT
Closed loop control basically measures difference between desired and actual output, adjusts input as necessary to produce desired output..

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jim hardy,

Could you tell how to implement closed loop control in my case?

jim hardy
Gold Member
Dearly Missed

But 'feedback' is the study of self correcting systems. Feedback systems develop an "Error Signal" and drive that to zero.

And you do have a measurement of actual "plant" output in the same pc that's generating the plant's input.

Subtract actual output from desired and you have error term.
I presume your error is largely harmonics of 50 hz?

One approach would be to characterize your "generating plant", ie what is its output/input transfer function
and solve mathematically for the input that gives desired output, adjust your input to that.
That'd be "open loop" control. No automatic comparison of actual vs desired output.

and you have a measurement of the higher harmonic coefficients that your plant adds;
Csin(3wt), Esin(5wt) etc;

so a closed loop control program might gradually add terms to your input function to make it an impure sine wave
Asin(wt) +Cfsin(3wt) +Efsin(5wt)
where f is calculated as you go with sign, phase and magnitude to make the plant's output become the pure sinewave you want.
That you could do empirically by trial and error.
Then make it self adjusting by the pc program at a slow rate,
then tweak up the rate to what the system will tolerate.

Your harmonics will probably change with load on the "plant" so i think you'll need closed loop control.

this is interesting - i hope you keep us posted.

Is -52 db 1/400 ?
So, you're shooting for what , 1/4 % harmonic content?
i wonder how good is that transformer between your 3kv output and ADC. It's in the loop, you know.

Have you studied "Automatic Control Systems" or Modern Feedback Control"?
Do some reading. It's not intuitive but almost so.
Maxwell Maltz wrote an interesting book "Psycho Cybernetics" on subject of feedback control for self improvement. It's as powerful in psychology as it s in industry.