My guess is 15A comes from the breaker in the main box, or the outlet and wiring ratings. Or maybe the rectifier diodes if using one rated for that or less, so that "hopefully" one of those things will fail just before the battery gets hot enough to explode.
Also, I missed the part about "constant current source" in there before...I see nothing that will regulate the current to a constant level (which would require changing the voltage upward as the battery charges, in a matching curve). I'd be interested in seeing a chart of real-world voltage and current measurements while this is being used to charge something (but not in *my* house!).
If you have a Cycle Analyst, you could use it along with a serial port on a computer to log the data it outputs, and have it between the load and the charger. Just make sure that whatever voltage is being output by this charger is not higher than the 100V the standard CA can take, or use the HV CA version instead. Or modify the CA's input wiring so it does not take it's power from the shunt input, and use a separate external power source for it.