The implication that I read is that the existing electrical system in whatever it is that you're modifying has a generator or alternator to charge your battery. The OPs suggestion to start with a lawnmower belies this implication, but the OP didn't write the contents of the link. Presumably, anyways.
So if you put this system on a car, for example, it would run off of the car battery, which would be charged by the alternator on the engine as per normal. It has been suggested that the energy required to crack the water would be more than the generator would produce, but the original content claims that the energy required is quite reasonable. To quote:
"In the BIG picture, your Free Energy is coming from the tap water, in an open system, as the latent energy in the water is enough to power the engine, and hence drive the alternator and whatever belt-driven accessories; AND the alternator is efficient enough to run the various electrical loads (10-20 amps), including the additional low current to run this vapour reaction. No extra batteries are required."
If they are correct (don't you just
love starting sentences like that?) then this system should work like gangbusters. 8-)
Here's an interesting and quite recent link about the cost of cracking hydrogen, and using hydrogen to power vehicles:
http://www.popularmechanics.com/blog/science/2936846.html
There is some good info in there. One thing that is repeatably stressed is that all the electrolysis does is break apart the H20 into H2 and O. If you then use that to power an engine that just puts the H2 and O back together again, how can you gain energy? Something has to be
consumed to produce power. If a litre of water goes in and a litre of water comes out the tailpipe then where is the power coming from? It is very, very possible that I am missing something here. I'm no expert, I'm just telling it as I see it.
The existing system where grid electricity or some other power source
external to the vehicle is used to crack the water, and the hydrogen is burned in an engine back into water, then the hydrogen is being used kind of as a 'battery' to store the energy that was used to crack it in the first place. Some suggest that this is enough... that hydrogen is useful as it is simply because it avoids batteries, and batteries are inherantly inefficient. I don't like big batteries, so I like the sound of that argument. That's not to say that it's *correct*, though...