Strongest electrical wire at AWG 24
Since you are using 5V ("5V and the current 0.5A" from a comment), you probably have two limitations, one based on heating and one based on voltage drop. The second may well be the long pole in the tent. 

Incidentally, your 0.22 mm diameter number is wrong for AWG24 wire diameter (it's actually a bit over 0.5mm diameter), so it's not clear to me whether you are keying off the gauge or the diameter. 

In any case, you might be able to kill two birds with one stone by using a switchmode regulator along with a relatively high voltage such as 24VDC.

Assuming, say, 85% efficiency, 2.5W at the destination will require about 3W input or 125mA at 24VDC. The loop resistance of 0.255 mm (AWG 30) steel wire 1m long (x2 for return path) would be around  8 ohms, so it would drop about 1V, costing about 5% in efficiency. Not too bad. One watt spread over 2m of wire is not too much either.