Never do your turn when up for 26 hours

[Fyron]

Not exactly. Resource Converters convert resources in storage from one type to another, in the amounts and types that you specify. They bear no relation to the planet on which they are located. You have to issue the order from that planet, but it uses the global stores of resources. You only get automated conversion if you use repeat orders, which can be quite dangerous with converters. There is a limit of something around 1 million resources converted per turn, but that only comes into play for truly massive empires.