Hi

I have a question. On an automotive 48V system that the phase current is 200A is there a way to calculate the size of the ground cable you need to use?

 

Of course, it's not guess work.
You determine how much voltage drop you can tolerate for the resistance of that length of cable and then look in a wire table to determine what wire size has a resistance no higher than that for that length.

 

So, for example, 3℅ is considered a reasonable but fairly low voltage drop. A car is maybe a 20' circuit, #3 wire probably won't get too hot, unless that ampacity is pretty constant, and the resistance for 20' is 0.00508 (0.254 per 1000), and your voltage drop is close to 1V - close to 2%.

I'm uncertain of your application, but suspect that conductor heating may be a larger concern than voltage drop. I also work more with higher voltages and greater distances typically, but I can't imagine why considering a smaller conductor would be defensible for the small quantity of wire needed.

Best of luck!