I assume you are using a transformer to step-down the voltage of your electricity mains to 12VAC. What load needs the 12vAC to be regulated?
The output voltage of the transformer should not change much from when it has no load to when it is fully loaded unless it is poor quality and cheap. Is it poor quality and cheap?
What is wrong with your electricity mains that is causing its voltage to vary up and down?
What is the load current? A shunt regulator wastes a lot of power when there is no load.
An SCR works with DC voltages. It needs a full-wave bridge rectifier to work with AC voltages or a triac can be used instead.