If you do a search over the last 15 years on Kzrider you will find the largest number of low-voltage complaints on Kz650's have to do with the 78 and 79 years of Kz650 when they use a Dyna S ignition.
For whatever reason the 78 and 79 1-phase charging system, with no brown wire on the reg/rec was made slightly on the weaker side. It would work fine with a stock electrical system. The Dyna S nearly doubles the dwell which nearly doubles the current draw on the system and this tips the scales so the marginal charging system can't quite keep up. Sometimes it will seem ok, but usually it's just a little lower than it should be to the point that the battery does not keep a full charge.
The solution is usually pretty simple. Install a 3-phase stator from a later Kz650 or Kz750-four. Then install a 3-phase reg/rec from a much more recent Kawasaki Ninja 250, 500 etc. They can be had used for $10 or $15 and they work fine.
If you have money to throw at it, you can install a high-output, aftermarket, 3-phase stator and then make sure to use a heavy duty reg/rec or a Shindengen Sh775. A high-output stator will rob extra crankshaft power if you use a shunting reg/rec, so the Sh775 would be a better choice in that case, but make sure it's a real one. There are plenty of counterfeits out there.
Most people report success with retrofitting used parts from later models, which is much less expensive.
This problem has come up so many times I have created a graphic and a video to address one possible reason why only some 78/79 Kz650's have this problem. It's not all of them either. It is just some percentage of those models. Some 78/79 Kz650's have no problem with a Dyna S and stock charging system, but when the problem comes up, 90% of the time it's a 78 or 79 650.
I have speculated that some 78 /79 Kz650 had one of the flywheel magnets flipped at the factory, but I haven't been able to look into it any further to rule it out. The factory originally used a design that could potentially end up with one magnet reversed. Then they changed the design to a type where the magnet would work the same no matter how it was installed.