Compensation of the fundamental frequency with a Capacitor in a Bridge rectifier

No. You can review the waveform sketch in post #5, it shows 45 degree current phase shift. With 90 degree shift, current center would be aligned to voltage zero crossing.

mopeters said:

I still don't know if my calculation is correct and I don't have the same circuit as I do in the simulation. My problem is that I have to dimension the capacitor so that cos (phi1) =0.8.

But I can't set the C anywhere in the simulation.

In your first post, you confirmed that my calculation is correct. Are you still of the same opinion? I am now a little unsure because many posters write otherwise, but without providing a solution or an explanation, unfortunately this is of no use to me.
So my calculation is correct?

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Sorry, I didn't examine details of your math. It appears correct for a sine-cosine setup however I used the simulator and it showed me the unexpected. The inductor current-lags-voltage truism does not apply when we alter the sine wave via On-Off switching.

So as an exploratory trip, this simulation has:
* a bit of inductive drop on the AC side,
and
* a bit of choke effect on the DC side.

It uses your specs (as best as adjustments permit).
Sine waves are retained yet current-limited. It does not include On-Off switching.
It has your 186 uF capacitor. From the look of it power factor is almost aligned.
Perhaps this fulfills your spec 0.8 figure.

At the same time, current draw is reduced from the supply. Benefit of power factor correction with the right value capacitor.

If we speak of an old-school approach I suppose that resembles it. Falstad's simulator taught me almost everything I know about power factor error and correction.
Some people rely overmuch on simulated circuitry. Some people rely overmuch on expected behavior in circuitry. This is a case where the simulator has a surprise in store. Rectifying AC changes everything in your power supply. Inductors yield different behavior with DC versus AC. So the diode-bridge creates a 'wild card' in your power supply.

The attached LTspice sim shows that vac and iac are in phase for the case of the top post.
No capacitor is needed to correct any phase shift because there is none.

But in the sim cos_phi_1 the 1Farad cap is needed.
This is academic, since in reality you would use a switched Boost PFC to give the unity power factor...the capacitor of this size and voltage is way too expensive for use ever.

I don't understand the latest simulations, they have little to do with the original question that's based on SCR phase angle control.

Adding a capacitor to correct cos phi, it seems, is only an option when there is a linear load....for a switching converter like a thyristor bridge, it is non linear, and as shown, you can correct the power factor with a capacitor, but only with an enormous value capacitor, as the attached LTspice shows.
As such, Boost PFC stage is needed, or use of say triac so that on and off can switch to give a pulse "in the middle" of the mains half sine.

You have posed an impractical problem.
With sufficient L, the DC current has no voltage ripple thus constant current.
The primary will be constant current too, meaning a squarewave.
You cannot convert a square current into a sine wave to obtain 0.8 pf. due to the harmonic distortion being > 30%.

Even more impractical is the sufficiently large inductor must also have sufficiently small DCR relative to the load and DCR/L ratios will be impractical with a 40A load.

Next question?

D.A.(Tony)Stewart said:

You cannot convert a square current into a sine wave to obtain 0.8 pf. due to the harmonic distortion being > 30%.

Click to expand...

You can. The exercise is asking for cos(phi) of 0.8, in other words displacement power factor, not overall power factor. It's only measuring fundamental wave. Harmonics are described by distortion power factor. See https://en.m.wikipedia.org/wiki/Power_factor

I agree that the problem is a bit weird because it abstracts from harmonic distortions. It makes nevertheless sense because cos(phi) is separately measured and billed for industrial consumers. I had many similar exercises in my studies, at times when phase angle control was the dominant method to control e.g. electrical drives.

The assumption of large (infinite) L is just a simplification of calculation, you can solve the exercise also for specified small L values or pure resistive loads.

The square wave current from source shifts to a phase leading current with sag.



without cap and near 40 A rms still.

THD of a square wave is 48.3% thus p.f. becomes 1/(1+0.23)= 0.81 already with no cap



Now there is possible some combination of series L and secondary shunt C that gives p.f. = 80% but the DC ripple may be too high and not independently controlled with the LC filter. This is why active PFC must be used to get p.f. =1 and you can't get any better than 81% while adding huge VAR caps than with none. Now look at the source VI plot.

D.A.(Tony)Stewart said:

Now there is possible some combination of series L and secondary shunt C that gives p.f. = 80%

Click to expand...

You are discussing a different problem, the original question is quoted below. Keywords are fundamental frequency and cos(phi).

mopeters said:

Hi I want to compensate the fundamental frequency so that cos( φ1) = 0.8 in a Bridge rectifier.

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