You are bit on track now Dr. Smith.I think I get you.
look at the output first. you have 250 volts AC.
what are the steps you have on the auto transformer ?
if you have say 10 volts between taps on the output , then the most you need is to resolve the input to say 5v.
The number of relays is irrelivant,
if you only need to detect within 5v , then the number of levels you need in the ADC is 250 / 5, i.e 50 levels.
a 6 bit ADC would give you the resolution you need , with spare.
hence the reason a few of us have been asking, but not getting answers to
a) what are the voltage steps on the auto transformer you want to use ? this sets the ADC resolution needed.
b) how often do you wish to switch the relays ?
this sets do you need relays or solid state solution
get on back to this please with clear answers .
The paper did not tell anything about it.
a) Did you see the transformer design that I showed in a post ? Let's say 10 step.
b It depends on the relay. But they usually take around 10ms (milliseconds) to switch on, or off. So about 100 flips per second (50 Hz).