To determine the size of the inverter you need to power your air conditioner, you first need to consider the inverter's continuous power rating. The continuous power rating of the inverter should be greater than the cooling input power of the air conditioner to ensure it operates smoothly without overloading the inverter.
Given that your air conditioner has a cooling input power of 1500 watts, you would need an inverter with a continuous power rating of at least 1500 watts to run the air conditioner. However, it's advisable to add some margin to handle possible power surges and efficiency losses.
Considering that air conditioners can have a higher starting surge current, you should choose an inverter with a higher continuous power rating. A good rule of thumb is to choose an inverter with a capacity of at least 1.5 to 2 times the cooling input power of the air conditioner. So, for a 1500-watt air conditioner, you would want an inverter with a continuous power rating of 2250 to 3000 watts.
Additionally, when selecting the inverter, make sure it's compatible with a 24V battery system, as some inverters are designed for different voltage setups. Always check the specifications and compatibility information provided by the inverter manufacturer before making a purchase.
Keep in mind that running an air conditioner for an extended period can consume a significant amount of battery capacity. Make sure your 200Ah 24V battery bank is adequately sized to handle the air conditioner's power consumption without draining the batteries too quickly or damaging them.