How to determine saturation in DC smoothing choke with capacitor, and how to simulate in LTspice?

Question

This question addresses some of the issues with a choke made from a microwave oven transformer for producing smooth DC from a phase-fired SCR controller, as discussed in this question.

The choke measured 3 mH and has 10000 μF capacitance on a nominal 22 Ω load, which will see an initial voltage of about 220 VDC and then lowered to about 75 VDC for continuous operation.

I ran the following simulations using an ideal inductor model, showing waveforms for current and voltage at 50% phase modulation (90°) for 220 V, and 20% modulation (144 °) for about 75 VDC. The current through the choke was 19.2 A RMS at 50% and 7.7 A RMS at 20%. The power dissipated in the choke, based on 50 mΩ winding of 30 turns (30 ft) of #12 AWG wire, was 7.7 W at 20% and 18.8 W at 50%. However, the actual winding may have been as much as 100 ft, so actual wattage could be three times the above figures.

Simulation at 50%:

Simulation at 20%:

Then, to simulate what might happen if the choke saturated, I applied an effective short across the choke using a low R_DS(on) NMOSFET, 1 ms after the SCR firing at 90° (50% modulation). The choke current up to that point rose from 62.6 to 71.3 A, and then suddenly dropped to 40 A in 1 ms, followed by a climb to 140 A in another 1 ms, and finally dropped smoothly to 120 A, and finally suddenly dropped to about 60 A at the next SCR firing at 90°. This corresponds to 122 A RMS. So this could explain the overheating of the choke in the application in question.

I would like to know if this simulation of saturation is reasonably accurate, and if not, how it should be done. It will be necessary to observe the choke current in the application, and obviously, this would be done with an oscilloscope having a channel fully isolated from ground, across a high side shunt, or a non-contact current probe.

Finally, are there some design techniques to build a choke that does not saturate at up to 20 A RMS with 10 A DC, to obtain a reasonably smooth DC output?

(edit) I also ran the simulation replacing the inductor with a 10 mΩ resistor, and that resulted in 32.6 A RMS. So I think there is some resonance happening with 3 mH inductor and 10,000 μF capacitor. Resonant frequency is about 29 Hz.

(edit2) After some thought and analysis I realized that the MOSFET just drew current that was stored in the inductor. So I tried using a voltage controlled switch, but that also did not do what I wanted to simulate saturation. I think perhaps the way to model this would be to add a second coupled coil and throw the switch across it. However, that would probably show the same behavior. What I need to do is measure the total current into the combination of the choke and switch, which is as follows (for 3 mH and 10,000 μF, 50% modulation):

Ideal inductor: I(t) = 19.4 V(out) = 244 V

Saturation 8 ms: I(t) = 20.0 V(out) = 240 V

Saturation 7 ms: I(t) = 21.0 V(out) = 229 V

Saturation 6 ms: I(t) = 30.6 V(out) = 254 V (Resonance?)

(edit3) I found an example of a non-linear inductor model (behavioral flux) and made a simulation of this basic circuit but using a rectangular pulse instead of the phase modulated sine wave. The waveforms show the faster rise of current after saturation (which I set at 20 A). However, I had problems with the simulator (time step too small) when I tried to use ON time of less than 3 ms out of 10 ms period. I set maximum timestep to 1 μs and that worked for this simulation, but it did not for another case. Hopefully this schematic is clear enough.

I am trying to use the Chan transformer model (as suggested by @AConcernedCitizen) but have not yet figured out just how. I have just used LTspice library components and I have little experience with custom models, so I'd like to find a complete example. Here are some resources I'm looking at:

https://groups.io/g/LTspice/topic/creating_a_chan_transformer/73221313?20,0,0,0::recentpostdate%2Fsticky,,,20,2,0,73221313

https://passive-components.eu/modeling-inductors-with-ltspice/

Here is my attempt to use the Chan inductor model, for the MOT transformer choke that measured 3 mH. I used the following values:

Hc=50 (32-72 A/m for electrical steel)

Bs=3 (high value for electrical steel)

Br=1.5 (nominal value for electrical steel)

A=0.001242 (E-I core legs 70 x 18 mm)

Lm=0.000212 (E-I core 70 x 105 x 88 mm)

Lg=0.003 (the gap was 1 mm, but I assume there are three of them

N=75 (this is estimated, but should be 50-100 turns)

Simulation with 300 V pulse 5 ms ON, 10 ms OFF:

I calculated the inductance by using the voltage V across the choke, and the slope of the current A/S, where L = V / (A/S), which in this case is 2.9 mH.

Answer 1

Your schematics are hideous and, I'm sorry to say, I won't bother deciphering them. But, since your question is about modelling a saturable choke in LTspice (note the spelling) then you have at least 4 alternatives:

1. The Chan core uses an inductor with these parameters:
   Bs = saturation flux density [T]
   Br = remanent flux density [T]
   Hc = coercive force [A/m]
   A = core area [m^2]
   Lm = core length [m]
   Lg = gap length [m]
   N = number of turns
2. The Jiles-Atherton core, you can find libraries for it either in the Ltspice Group, or in this user's files collection: Bordodynov. I think there are also examples of usage.
3. A behavioural approach made with diodes, e.g. as seen in this IsSpice document.
4. The behavioural inductor with Flux=<expr>. E.g. a 1 mH can be modelled as Flux=1m*tanh(x). You will get a smooth tanh()-like curve but, it will not have a hysteresis (zero width).

I'd recommend the Chan core if only for the simplicity of the parameters and its native availability in LTspice.

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[edit]

Here are the Chan core and the behavioural Flux inductor:

This is to exemplify how the Flux approach will not give hysteresis, only a fake saturation. Since your latest reply just came, I see you're using some unusual values for Bs. Even Magnesil has 1.6 T (with Br=1.5 Hc=40).

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[edit 2]

Your latest comment is a surprise:

But I'm not familiar with your simulator.

It's LTspice, what you're using, but I'll describe the circuit, anyway.

The purpose for this example was to show how the Chan and the Flux core can be used, while showing the differences mentioned at point 4, above. Note that the expression for the Flux differes from the one in your example in that it uses pwrs() instead of a raw power, otherwise there would not be a symmetric response around the zero point (e.g. pwrs() preserves the sign, ** does not).

If you split the schematic vertically, there are two halves: to the left the Chan core and to the right the Flux core. Describing one half: L1 is the Chan core with some (quasi-)random parameters for a (quasi-)random ferrite core. It is driven by a triangular current source, asin(sin(x)), scaled to have the amplitude given by the parameter A (0.1 A here). The voltage across L1 is V(x) which is integrated by G1+C1 with the appropriate time constant to give the voltage V(B1), representing the flux density (T). This is plotted against I(L1), scaled to give the coercive force. Together they are showing the hysteresis graph of the core and you can see that there is, indeed, a hysteresis window.

The Flux core, however, not only it needs adjusting the integration gain (7 in G2 vs 1 in G1), but it also shows no hysteresis window -- it's just a tanh() limiting inductor, no memory.

The two circuits at the bottom are used to determine the values of the inductances, by supplying a unity dI/dt and reading the voltage across as Henry with a 1:1 relation to Volts.