Power from 24VAC

I'm not sure what you mean by induced voltage in this context - can you explain?

A small 24V to (say) 6V transformer would do the job, but most transformers are designed for 115V or 230V input.

If you are feeling brave, you could make your own switching regulator using this IC http://uk.farnell.com/allegro-microsystems/a8499slj-t/v-reg-buck-1-5a-50v-smd-soic8/dp/1329622 which has 50V max input voltage. The datasheet gives some typical application circuits. Be sure to get an inductor that can handle the output current without saturating.