No, you don't need 40 amps. But if you wanted that, it takes #8 gauge wire.
Just because each controller can handle 12 amps, does not mean you need to have a source for that capacity.
In order to actually help you, I need more particulars. You sound like you might be a Restaurateur.
Your 15 amp circuit can give you 1800 watts. Each of your smokers appears to be a 500 watt* load rating. So, at the most, 1500 watts, on a circuit good for 1800 watts. ;) (*=
Page 8, item G) Good to go, as you already know.
So, theoretically, you should be able to connect each smoker to it's independent PID controller. No problems, the PID controllers will function the 500 watt heating element. ...Theoretically...
Here's the problem... Bradley never designed their puck poopers to be "cord controlled". You unplug the cord, then plug it back in, at the very least, the puck timer is going to be reset. You could test that by starting one up, then unplug it, and plug it back in to see if it resumes. If it does, you may be golden.
(If it's any consolation MES smokers aren't either. Except possibly the 1500 watt dial (analog) controlled type.)
If you want to actually have some control over the Bradley Smokers
internal temperature, you will need to separate the smoke generator, from the smoker/oven box. With
a Bradley Cold Smoker attachment. Then, put a heating source in the Bradley Smoker box that the PID controls. (A simple hot plate comes to mind. You could choose a more powerful hotplate, 1000 watts, 1200 watts. As long as it is Analog in function, not digital.)
That way, the Smoke Generator runs independently of the Smoker Oven's temperature being controlled by the PID.
Following me here? We are separating the smoke generator, from the Smoker/Oven, and controlling the Smoker/Oven temperature with the PID and an independent heat source.
There is another catch to this... You will exceed your 15 amp circuit capacity. You will need a 15 amp circuit for each Smoker/Oven configured this way. If you need to run all 3 at the same time, this is required.
So, is it really worth so many revisions to be able to revise the 3 Bradley's to PID control? You could do one, then decide. But I would say you are looking at hundreds per each if electrical work gets involved. (A Bradley Cold smoker modification is $99. Then add in hot plate to heat the Smoker/Oven.)
Figure 1500 watts for each one. (Bradley unit + additional heat source.)
So you see, to every solution, there is a problem. :(
If you would like to simply add a PID heat source in addition,
a hot plate controlled by the PID could be used. But the Bradley Smoke generator itself, along with the disintegrating pucks will remain to be a considerable source of heat.
Clear as mud, huh....
I decided to abandon my Bradley Smoke generator for several reasons. The foremost was the price of the pucks. But my use of my Bradley was in a UDS, with a separate 1500 watt heating element. I decided I wanted to use pellets, but electric heat and control.
So I invested in a
Masterbuilt unit, and modified it to work my way. Including being able to choose regular, or a
bypassed mode that gives me cord control over my smoker. And I separated the smoke generation from the oven function.