Parameters when choosing a relay
When switching large inductive loads like an air conditioner, it is important to use the right kind of relay. Inductive loads like motors are more damaging to relay contacts than resistive loads. Damage come from arcing during opening and closing. I would not trust those little relay boards you find for a few dollars on ebay. I would question their ability to handle multiple on-off cycles of a motor load.

With that in mind, if you choose to use a standard electromechanical relay, select one that is rated for a higher current than your air conditioner. My advice is to select one that handles 20+ amps and 250 volts AC. Your next problem is switching them on with a microcontroller. Coil currents for smaller 5V relays can be quite high, in many cases 100mA or more. An arduino and similar micros can't source that much current from a gpio pin. The solution is to drive the relay with a transistor. Check out this schematic:







simulate this circuit &ndash; Schematic created using CircuitLab
The diode dissipates the spike from the relay coil when it is powered off. That spike can damage the transistor and is shorted by the diode. The 1N4004 is a slower diode but should be enough to protect the relay. A fast rectifier diode might be a better alternative. And FYI, +V can be 5V or, if you want to use a higher voltage relay, say 12 or 24V, you can use the same circuit. Just be sure that the ground of the power supply for the relay is tied to the ground of the micro. Another tip is you can also use a 3.3V micro with this circuit.

Another route to go is to buy a motor contactor. They are nothing more than relays with a dual contact setup. Dual contact meaning that instead of a moving contact connecting to a stationary contact you have two stationary contacts that have a moving contact that connects the two together. This dual contact arrangement helps extinguish arcs from an inductive load by creating two air gaps. The only issue is most contactors are designed for industrial systems and typically have AC coils that accept line voltages like 120 or 230VAC. Though, there are contactors with 12 and 24V DC coils. 24VDC is a standard voltage used in industrial control systems. You could use the above transistor circuit to switch a 12 or 24V contactor. To switch an AC contactor you can use a smaller relay to switch mains AC to the contactor.
PROS:
-Robust design and long life.
-Middle of the road cost (Check out Automationdirect if in the USA)
CONS:
-They are loud when they switch on and off. They make a loud snap or bang sound when actuating.
-No coil voltages below 12V.

SSR's are another alternative, though you have to be careful when selecting them and they cost a lot of money. Check out Crydom, their CWD2425 can handle a 1HP motor or 25 amps resistive load and up to 280VAC. They also have a relay selector tool to help select the right SSR.
PROS:
-Silent switching
-Can be directly driven by microcontroller gpio pin.
CONS
-Costly: you are looking to spend about $45+ USD for an SSR.
-They will dissipate power. Depending on the load, you may need to mount it on a metal plate or heatsink.