I struggled with my electronics classes in school, and while I could understand the basic concepts, I found it very difficult to actually design transistor circuits that functioned well, and especially circuits that would handle any appreciable power.
I ended up joining a firm working for an old guy who had spent 50 years designing and repairing medium voltage power distribution systems, and so that is what I learned, along with PLC control systems.
One of the types of projects I use to work on was airport lighting, and those were 5KV series circuits, with stepdown transformers at each light fixture. The larger airports used imbedded electronics that operated via a superimposed high frequency control signal, and that signal was used to control stop bars, wig-wags, etc.
There were approach lights that will tell you if you are on the correct glide path, and also end of runway lights, and lights on the corners of the runway.
I talked to a guy who manufactured the end of runway corner lights, and asked him how he managed to keep his corner lights at the same output intensity even as the runway lighting overall was stepped up or down by the pilots, via clicking on the microphone button.
He said he designed an electronic circuit to sense I think line amperage, and adjust his light output to a constant value.
He mentioned that he learned medium voltage electronics at one of the big companies, I forget which one.
Had I gone to work for the medium voltage power guy, I am sure I would be well versed with power electronics, but I went with power distribution instead. So of the folks with more brain power than me (many for sure) can do it all, but my knowledge is somewhat compartmentalized, to include power distribution up to 35kV, and automated control/SCADA systems.
Part of being capable at electronic design is having a good knowledge of commercially available power electronic devices; who makes them, what their operating characteristics are, and how they can be applied to a variety of applications. I don't have that database of knowledge.
One also has to have a knowlege of microcontrollers, since those generally have to control current flow, etc.
If I were going to design an induction furnace (which I am not), I would find some proven design, with some reliable and readily available components, and go from there.
A buddy of mine purchases a used Inductotherm (tm) furnace, and that would be one way to go if setting up a furnace, assuming you could purchase repair parts.
A second option would be to purchase a new tilting induction furnace, and I have looked at those.
Cost is one factor with an induction furnace, but then there is the 3-phase electric service that is required (I have 200 A at 208V), and then utility company demand charges, harmonics potentially fed back to the power company, and finally being able to source spare parts for the electronics that will eventually begin to fail over time.
An electronic component failure in mid-melt could do a lot of damage if you are not able to clear out the partial melt from the furnace and/or crucible.
My oil-fired furnace takes about 1 hour to melt a #10 full of iron (perhaps 25 lbs of iron), and with an induction furnace, I could probably reach pouring temperature in 15 minutes.
My oil burner is simple, and while it is a typical siphon-nozzle design, I designed it to operate without an o-ring, so there is no posibility of the o-ring failing if the burner tube ever overheats (generally when one forgets to withdraw the burner tube from the furnace after the burner is turned off).
I have never had a problem with my siphon nozzle burner, and it performs extremely consistently, which is what is needed when melting iron.
If there ever was a problem with my burner, the tip could easily be replaces for a few dollars.
I have two (actually more) siphon nozzle burners, and so even if one fails in mid-melt, I can change it out and have another burner operating in a few minutes.
There is really not much to fail in my burner.
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