If I were in your shoes, what I might do is; to leave the PV array at 24 volts nominal, leave the battery bank at 24 volts nominal, then tap into the battery bank "halfway" to get 12 volts nominal for the 12 volt nominal inverter. Do you or do you not have batteries wired in series? What is the nominal voltage of each one of the batteries? 2, 4, 6, 8, 12, 24?
At the very least you either have;
1 - 24 volt battery by its self or,
12 - 2 volt batteries in series or,
6 - 4 volt batteries in series or,
4 - 6 volt batteries in series or,
3 - 8 volt batteries in series or,
2 - 12 volt batteries.
If its any but the first in this list or 3 - 8's you can tap into them "halfway" and get 12 volts nominal.
Take your multimeter and hold the black lead at the negative end of the battery bank, then take the red lead and move from battery terminal to battery terminal until your meter reads 12 volts.
Now do you get it?
Think about it this way: if I had 2 - 12 volt batteries wired in series I would have a wire from the positive lead of one to the negative lead of the other. Now when I measure the voltage at the other pos. and neg. terminals I have 24 volts, BUT!!! if I measure the pos. and neg. on just one of those batteries I still can get 12 volts. This works weather its; 12 -2's, 2 - 12's, 6 - 4's, or 4 -6's but not if its 1 -24, or 3 - 8's.
Its all in the math.
