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In operation, it will be similar to the relay based one. So, you can just use the triacs and control them by keeping them on or off. Best way to drive them would be using zero-crossing opto-triac such as MOC3041:
Problem is, it will get hot as it has a voltage drop. So, if it has a voltage drop of 1.5V, and 10A current passes through, the triac will dissipate 15W power! You need a way of cooling the triacs. So, heatsink is a must. Cooling fan is optional.
Yes, I think relay is better in this regard, but triac is advantageous in the sense that it is solid-state. So, you can use triacs in the voltage stablizer, in place of relays and use MOC304x to drive them, but just take care that there is heatsinking and enough cooling.
About 20 years ago, I designed two types of mains stabilizers using relays and triacs.
At that time I sold about 300 pcs of the relay type and 3 pcs of the triac one (and kept one for my house that works till today).
Using relays gave me the chance to buy my first car But I won't install at home a stabilizer by relays.
My old circuit uses many digital ICs (as of 7400 series) so the board is relatively big and complex. I didn't design a better one using MCUs since even now the relay type is the best seller