Look at the figure popping up all over the page: tesla (T), flux density. This has units of Vs/m^2. That area is Ae. Vs is flux, as in the area under the curve, the curve being the applied voltage. This will be the per-turn figure, so you can apply more voltage or lower frequency (longer pulse width = more flux) with more turns, for the same flux density.
It seems they don't give a material designation / mix, on this part of the sheet anyway, or other material properties like density (aside from weight being given), or saturation flux, mechanical strength, etc. (Permeability is given in a roundabout way: AL = mu_r mu_0 Ae / le, so evidently mu_r ~ 2070. Which varies with temperature, generally, so that's another material property that's missing.)
(Or it's in the Chinese characters, which I just can't read.)
So, 360V at 50kHz is:
N = V / (4 Bmax Ae F)
(The 4 comes from the bipolar square wave; you would use 2 for a unipolar (half wave) forward/flyback converter, or 4.44 for a symmetrical sine wave.)
= (360V) / ( 4 (100mT) (1225 mm^2) (50kHz) )
Note that using T == uVs/mm^2 and frequency in MHz (0.05MHz) gives the same scaling, so, 360 / 4 / 0.1 / 1225 / 0.05 = 14.69. The nearest multiple of 6, is 12 or 18; 12 would give Bmax = 122mT, which is probably not unreasonable for this core. (Judging by the core loss plots, much over 150mT is probably not a great idea, at least short of gluing water-cooling plates to it.)
With 360V/33A = 10.9 ohms on the primary side, performance will be limited by leakage inductance. Suggest using copper tape/strap for secondary, and using several layers worth in parallel, interleaved with layers of primary. Primary must be Litz cable, for low AC resistance. This arrangement reduces leakage to acceptable levels, say with a PSPSPSP build. (Turns per layer don't matter so much; probably, three turns per secondary would work out well enough, then connect them in parallel. Or for FWCT output, stack two strips and wind them together, then connect opposite ends in series to make the CT winding. And connect all three sets in parallel. Doing a single turn per layer is probably harder, because of how much strip width you need to carry that current; not easy to get out of the way of the next primary layer.)
Note two things about your system:
1. You don't have transistors hard-switching into capacitors. You use inductors.
2. You need some PWM anyway, to regulate the output voltage (presumably). Or current, as the case may be.
Which, these numbers sound suspiciously welder-ly..?
Oh right, you posted this before:
https://www.eevblog.com/forum/projects/igbt-brick-based-inverter-design-question/Context always pays off!
Right. I was going to say, you need extra output voltage (slightly lower turns ratio), so that PWM isn't saturating at nominal output and it can achieve regulation. But since this isn't just any DC power supply, that probably won't be important.
3. You'll most likely be using a full-wave forward converter, into a FWCT or FWB rectifier, into a choke-input filter. Whether there's a filter capacitor or not, and what value, depends; it certainly can't be so large that the electrode just sparks as soon as it touches anything and never starts a smooth arc. Below that value, there is room for adjustment, and it should be feasible to have good filtering (smooth arc, even at high frequency, and stable down to fairly low currents) without taking up a ton of space/cost (e.g., film capacitors, or extra filter inductors?).
4. You'll be using a current mode controller, which adjusts PWM to set the desired output (rectifier into filter inductor) current; if voltage regulation is required (e.g. for MIG I suppose), then that can be added with an outer loop (voltage error amplifier). Current mode control protects the IGBTs first and foremost, and is easy to control (output current is simply proportional to control input voltage).
5. In addition, you can have desat protection, as a more crude current-limiting mechanism; something of a last resort. This is highly recommended to avoid burning through too many transistors during development.
Desat protection is normally integrated with the gate drivers, which will be isolated, and you simply use as many isolated channels as you have transistors (so, H-bridge, 4 needed). The control circuit can then sit at SELV or earth potential, no need to contact the live AC side of things. (You will still need an isolation transformer or differential probe to check operation of the bridge itself.)
6. I STRONGLY recommend you build multiple scale models of this, first. The same controller can be used on everything, even the same gate drivers (if you design them for final scale, or purchase ready-made ones of the same rating -- a very convenient option, I might add). You can fully debug your controls against a small scale inverter, then scale up the voltage, then current, then both voltage and current. You will see effects, at scale, that were negligible at smaller scales: especially the effects of stray inductance, its effects on the bridge itself (peak voltage, limited dI/dt), and on surrounding circuitry (induced voltages, transients, interference). Naive wiring of these things absolutely will inject enough voltage/current into nearby circuits to destroy them -- and then, on top of replacing your grenaded IGBTs*, you have to replace whatever components burned in the gate drivers and control circuitry too! (All the more reason to isolate the controls!)
*Depending on how much supply capacitance you have, IGBTs will literally explode, emitting shrapnel. Use protective covers, wear eye protection -- the usual. The mechanical effects can be lessened by using a semiconductor fuse**, but IGBTs can only be saved through quick control action.
**So called because they operate fast enough to save
some semiconductors, namely the most robust kinds: diodes and SCRs. These fail in some ~ms of mains fault current. IGBTs fail in some 10s of µs, in which time the fuse hasn't even begun to warm up, let alone melt. Depends on supply capacitance, because electrolytics are more than capable of delivering mains-fault-magnitude currents, albeit only briefly. Since you'll be using an SCR input stage I believe?, it will need generous filter capacitance, so this should hazard will be present.
Tim
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