In general, continuously running an air conditioner with the compressor going on and off periodically is likely to consume less power than switching it on and off every half an hour.
When you turn on an air conditioner, the compressor needs to work harder initially to bring the room temperature down to the desired level. Once the desired temperature is reached, the compressor will cycle on and off to maintain that temperature. This cycling process is more efficient than constantly starting and stopping the compressor.
When you switch the AC off every half an hour, the compressor has to work harder each time you turn it back on to cool down the room again. The frequent on/off cycling consumes more power during the startup phase, and it also doesn't allow the AC to reach its maximum efficiency during continuous operation.
Additionally, modern air conditioners often have a feature called "sleep mode" or "energy-saving mode" that allows them to adjust their cooling output and run more efficiently during continuous operation.
In conclusion, it's generally more energy-efficient to keep the air conditioner on continuously (with compressor cycling on and off) rather than frequently switching it on and off. However, the actual energy consumption may vary depending on the efficiency of the AC unit, the insulation of the room, the outside temperature, and the desired indoor temperature.