How do we define the cable size corresponding to different loads,e,g motors,feeders,luminaries?

The cable is sized considering two factors, the load current and the voltage drop. Each manufacturer provides a table for each type of cables ( Copper, Alum., ..) that lists the for each size, the maximum current and the voltage drop given in V/A.Km, therefore you multiply this factor by the current load and the cable length in Km and you simply get the Voltage drop. Voltage drop in general shall not be more than3% but it actually depends on the voltage level at the source and the requested voltage level at the load.

Some correction factors shall be applied to the maximum current load given in the table, such as for:

- The load is single or three phase.

- The location of cable, i.e. in the air, underground, laid on a cable tray...

- How many cables are installed next , above or below the cable, and how much are close and what is the inter-distance...

- The ambient temperature where the cable is installed

One more thing, for large motors, usually >7.5 Horsepower, and unless they have a VFD, they run following a star/ delta configuration, therefore you will have two cables and each cable shall be sized according to load current divided by1.73 ( the square root of3). the same concept is applied to the2-speed Dahlender motors

Regards