Auto Switching 12 volt battery under load
There might be better ways to do this but we need more details on the topic.

However one possible way around this is Voltage sensor + high current Mosfet switch. 

Feel free to use a micro-controller of your choice. Make sure it has adc capabilities(almost all have). You job will be simple if it has as many adc pins as the number of batteries you are planning to switch between. If that's not possible, you can always use multiplexers to do the job.

Voltage sensing: Make a voltage divider to bring the charged battery voltage within range that can be measured by your micro-controller (5V, 3.3V or whatever your adc pin allows). Make sure your adc pin never sees a value which is out of range. For ex - If battery has a max voltage of 15V and my adc can accept max voltage of 5V, I can use this circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

This will allow you to sense the battery voltages. You will know which batteries are ready for getting fed into the inverter.

For switching, you need a high current mosfet - one for each battery. Parametric search on digikey will give you some results. If your max current can be 200A, better to select a value higher than that - probably 2-3 times.

Another solution (cheaper) is electromechanical relay but at that current, arcing might kill it very often.

If you are using mosfets, you will have heating issues so you will definitely need to attach massive heatsinks to your mosfets. Having a common heatsink for your mosfets might help because only one mosfet will remain ON at any particular time. Due to the big size, cooling will be more effective as compared to a small detached one. Assume a power dissipation of 150-200 watts in your mosfet while carrying 200A. If that's a concern, you probably shouldn't go this way.