Electronic – Why is the Transformer pulling so much current

AFAIK transformers are disigned to withstand a 180% current overload for short periods. (They can be overloaded this way for something like 15 minutes every 24 hours or so.) But in the long run overloading it with 200% rated current will most likely cause serious overheating and eventually damage. Maybe a good (meaning in your case probably water - or oil - cooling, which can be way more expensive than a new transformer) can provide the necessary cooling to enable the trafo to carry that kind of current.

Additional info: If your supply provides 0.1 A DC as you say, the AC current (RMS value) that comes out of the trafo is not the same as the magnitude of the DC current! In general, assuming the output current of the trafo is not distorted (meaning it keeps its beautiful sine shape - not necessarily true) you have for full-wave diode rectifiers (from: Mohan - Power Electronics):

\$I_{out(DC)}=\frac{2}{\pi}\sqrt{2}I_{sin(AC)}=0.9I_{sin(AC)}\$

meaning that the AC current will be actually 0.22 A if you want 0.2 A DC. But, since the trafo is seriously overloaded, I'm sure the current will be strongly distorted due to the saturation of the trafo iron core. At the end of the day, this will lead to extra heat generation and some other odd behavior.

All in all I don't really think it's a very good idea.

The above calculation applies only if you have a line frequency transformer (50 or 60 Hz) followed by a rectifier. If the circuit includes a high frequency transformer, the situation can be entirely different. So, if this is the case, please edit your question, so we can adjust the answer to that.

First, a bit of nomenclature. What you have are not transformers. They are DC power supplies. Sorry, but I'm picky about terms.

Second, power supplies like you are buying are usually about 90% efficient, so you'll need about 850/.9, or 950 watts.

Third, your power supplies take 120 volts in, so you will need 120 volt AC power for them. It's true that you can get this from 208 3-phase, but at your level of knowledge that's not a good idea.

So. Will 20 amps at 120 volts do what you want? The power available is 120 x 20, or 2400 watts, more than twice what you need.

Sounds good to me.

Connecting your supplies to AC is best done by connecting a standard power cord to the input of each supply. Start by looking at the data sheet which comes with the supplies. Then take one of your supplies to an electrician, and ask him to show you how to connect it. You should be able to do the others by yourself, but make sure you pay attention to the color coding on the wires. Finally, buy an AC power strip, plug it into the wall socket the show people point you at, then plug the power supplies into the strip. You should be all set, and the power strip will have a master switch which will allow you to turn all your boxes on or off.