need help to compute Irms of this topology

[iso14000]

Hi Folks

I would like to compute rms current flowing into R1 according duty ratio that drive the Mosfet.

the goal is to modulate power given to a heater in such a way my EV still charge without making my contract gives up .
I'm living in France , so mains rms is 230V , my contrat is for 30A , and these two loads are two much burden together for that figure.
So I imagined that simple buck with a large inductance to allow CCM. I don't want to be a bad guy for EMC.

I tried to wrote "something" with duty as input and current as output for an equation (I believed it was close to a PFC one)...
and I failled!

if any of you have an idea....

thanks

[jwet]

Since you've gotten no responses- I will try.  First let's nail down the problem-

If I understand correctly- you have a circuit in your garage that can deliver 230V at 30A and you want to power a heater and an EV Charger.  The total is more than 30 amps so you want to decrease the heater output when you're charging to stay under the total of 30 amps.

In your SPICE model, it looks like you're rectifying and filtering the line input to make "DC" and then applying a PWM to drive your "Heater"- the 30 ohm resistor shown in the circuit. 

What you're after finally is a closed form solution (equation) for Irms vs duty cycle of the FET drive to the low side of your load.  You've included inductors to smooth out the transitions for EMI.

Is this correct?

First- let's eliminate the inductors- they may be required but they make analysis harder at the beginning.

Second- Calculate the RMS of a pulsed waveforms- go back to RMS definition - square root of sum of squares over a period- square roof (Ipk^2 x Duty + 0 * (1-duty)).  This give you just I sqr(D)


Example is you have 10 amps peak through your load (this would be a Vin of 300VDC divided by your 30 ohms) and drove the FET at 10% Duty Irms would be 3.16 amps.  At 50% duty, you'd have 7.07 amps, at 1%, you'd have 1 amp.

I hope this helps- thank me with the thank button if so.

[T3sl4co1l]

Rectifying mains is somewhat cutting off your nose to spite your face: the power factor is typically around 0.5.  Power factor is bad because it's only drawing current on the peaks, which about doubles the RMS current draw at any given setting (actually a bit worse at light load, and a bit better at heavy load; it depends).

I presume you want to maximize capacity under the constraints (given Irms input).

If you had a PFC front-end, that would be fine, but that's a lot more complexity.

Note that phase control (TRIAC stuff) and pulse skipping (integral cycle control) also have poor power factor.  Cycle control is a funny case, because the power factor is 1 during a cycle, but considering many cycles, it has the same on-off behavior as any other switching scheme (PF = sqrt(D) or something like that).

The other way is to PWM the AC directly, which is also complicated but for slightly different reasons.

For ease of use, I might suggest getting a VARIAC and... put a servo on it or something?  Next best thing maybe: get a switching supply of adequate total capacity, and PWM the output from that.

Not sure offhand if there's a high PF, continuous heater controller out there already.

Tim

[Siwastaja]

How is your contract being monitored? Does it involve actual monitoring or is it just the main fuse size? Here it's just the fuse, so you can utilize the fact that the gG type fuse does not blow below 1.25*In or so, and even at 1.5*In it takes ages (tens of minutes, hours) to blow. Therefore, a simple on/off relay switching once every 5 minutes or so would do the job without wearing out too quickly.

[jwet]

Tim- I figured we'd get to this DC business soon enough- this is clearly not the right approach but I tend to play these balls where I find them.  It does make for easy analysis.

I was going to leave it as a exercise to the student to derive the RMS given a Triac driven by a PWM.

Regards

[iso14000]

Hi

thanks for your answers and advices.
needless to say that I'm not native in English.

okay, so
@Tim, you probably missed that the cap after the bridge is very low, near the one we can found on a regular PFC topology. so we aren't in the double alternance rectification case.
funilly I found with the actual topology (absolutly theorical) a PF very close to 1 (thx LTspice!) , and final ripple seen by AC line is reduced (thanks to the laaaarge inductance input)

I absolutly don't want to chopper the AC by a TRIAC.... it is not the good way to proceed and it is simply forbiden.

I won’t try for real this topology, but I got stuck on this calculation and wondered if, by accident, some of you have ever calculated such a thing

@Siwastaja
my contract is monitored by a connected energy meter from my elec supplier... it allows overloads for a few ms just the time to have the "load shedding" activated

[iso14000]

@John : yes correct (and thx)

so you are saying that finally....... to compute the Irms seen by the load .... I can simply ignore the inductance ?

[iso14000]

sorry John, you cannot remove inductor, by simulation there is a large difference for the same duty ....

[T3sl4co1l]

Oh dear, it is 470n, yes, that makes things a bit better.

Tim

[iso14000]

you won't believe me...
... I performed several simulation to find a clue about the law I dig for...
... and guess what... it is linear 

amazing!

[jwet]

ISO- I never thought the inductors wouldn't affect the result.  I just thought we could start without and iterate.  This does create an outer bound.  I guess I'm not too surprised that its linear either with the inductors in place- buck converters generally follow this rule.  We would have gotten to the same result as we went back and forth.

One thing that might simplify things is a control system like the following.  Put a current transformer over the main input and measure it.  Control the heater based on how close this gets to 30 amps, cut back the heater output based on the total current.  All analog and pretty simple.  I would use the Triac type of control probably with a zero crossing opto (MOC2011), etc.  Could do it without any micros or computation.

Have fun- nice problem.

[DavidAlfa]

Can't EVs adjust their load from the system software?

[Faringdon]

...so you want to reduce  current to your heater, so the combined power draw of your electric car, and the heater, is less then 30A.

...So really, do symetrical mains phase cutting with triac.....it will give good harmonics because it is  symetrical....cuts on the leading and lagging edge.

If you are going to do a switcher though.......just remember you are getting an overall sinusoidal input current (when filtered)......so you know what the peak current will be......so do your buck or bridge, or whatever....do the design for it at the case of mains peak......the rest will follow in  good order, as long as your topology makes imains follow vmains.

Easiest way for you is to  do a full bridge, with the resistor in the bridge, and just duty cycle it at HF, with only small capacitance after the bridge (like you are doing)...then your power througput will be according to the duty cycle....OR TRY THE SyMETRICAL TRIAC METHOD I PREVIOUSLY DESCRIBED. (woops sorry about capitals).

Do you want me to send you a ltspice sim of the bridge and the sym triac?

[iso14000]

the EV charger cannot be modulated.
I don't want to use a triac : not EMC friendly

I always have fun and learn from another people's spice , yes publish it here.

So to get back on the math, based on the average voltage value of an inductor overall a _full_ cycle in CCM (I mean, the sinus envelope) =0
 I derive the average voltage across the resistor.
If , as I guess, there is a coefficient K between average current in resistance and rms current, then indeed, the power is linear with D.C.

I don't give up trying to find an algebra for Irms ... but until know I don't catch it.

[Siwastaja]

I don't want to use a triac : not EMC friendly

There is nothing EMC unfriendly about triac, they are used everywhere no problem.

Your problem is apparently that you have to cut power off quickly per the ridiculously strict requirements ("few ms") from the power company.

I don't see what you think you are gaining by rectifying and working on the DC domain; it's only going to make things worse, much worse, by worsening power factor because of inherently small conduction angle. You could do active PFC (or, if the power company really applies a fixed current threshold and not some kind of RMS measurement over a full cycle, even constant-current type anti-PFC circuit just for this case) of course...

I think what you should really do is re-evaluate the exact conditions given by the power company, I don't buy the "few ms" story as is. You need to define the problem very exactly in engineering terms before you can find the right solution to it.

[f4eru]

I don't think this few ms is true. Probably moer in the 500ms-1s range.

Any load with a motor draws large amounts of power when starting.

Those cutoff curves are normalized and mandatory.
see an example : https://www.domomat.com/401003-disjoncteur-de-branchement-erdf-fiche-technique-legrand-domomat.pdf


One simple way to do load shedding on the resistive heater is to divide it down:
take a 3 phase heater resistor, and use binary division by combining:
1xR
2xR //
-> 2 bits, 4 combinations

If you use 2 of those 3-phase resistor sets in your tank :
2xR series
1xR
2xR //
-> 3 bits, 8 combinations. PF always good, no need for PWM, EMC is good also.
you can go farther down low power by serializing even more with switches.

[iso14000]

HI all

I should have wrote "hundreds of ms"... of course , sorry.

dimming such a load with a triac will make abrupt conduction , leading with EMC issue, and power factor degradation. it is simply forbidden .
I can't either change the water heater resistance.

but finally , I simply described the context for the topology I purposed, let's imagine it is a exam °-D

my real challenge is math. because I found this topology almost "by accident" and after simulation it reveals a good power factor.
who can give me a clue of how to derive Irms seen by the resistance? I'm stuck

[f4eru]

Nope, triac regulations are not forbidden.
There are extensive exemptions in EMC rules for allowing them.

[iso14000]

mmm.... in full wave yes ... and for low power lighting yes...
and did you solve the little math?

[Faringdon]

In your schem, you have the inductor in line with the resistor...so the zigzag switching  current goes through the resistive heater , which is probably a big coil structure...with lots of wiring to it........and will cause a radiated EMC problem....this is why you should have a capacitor in parallel with the resistor, and then go from there....but you need the bridge topology that i spoke of before......basically, you end up with a class D amplifier type topology......but instead of a speaker coil..you have your heater....give me a shout if you want me to send you the ltspice sims?

With a bridge topology you have power strokes all the time...whereas with your topolgy, you have an on stroke for power...and then you freewheel the current, and no current comes in from the mains during the freewheel...so you are limited in power...whereas with the bridge you get a power stroke all the time.

[iso14000]

and for the math... do you gotta clue?