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So you have a power supply (PS), and a few hundred meters away, a 12V device (D), and in between, one pair of wires with up to 50 ohms resistance (r). Let the power supply have three states: 1, Waiting for a load; 2, Setting up;
3, Power delivery.1: When PS is in state 1 it supplies 12V at its end of the cable, and the other end is open or attached to a D drawing less than a threshhold, say 10 uA.
2: When D is hooked on and/or switched on, it and PS run some Setup protocol. Perhaps the simplest protocol would be for D to put 12 ohms across line for a millisecond, at the midpoint of which PS would measure current i, then compute r = 12V/i - 12 ohms. Note, i would be at least 12/62 A = 194 mA, and at most 1A. The microcontroller at D could powerdown during the millisecond test period, so its current draw could be say 10 uA, adding less than .01% error in the r calculation. More-complicated protocols could be based on signalling via brief low-current or high-current pulses.3: In the Power delivery phase, PS puts a variable voltage v = 12 + r*i volts (with a max of 12 + r*1) on the line, which for static or slowly varying loads will converge to deliver 12 V at load device. Of course fast-changing load patterns could lead to some over and under voltages at D; eg, with r=10 and D toggling between 12 and 24 ohms of load, PS would toggle a little later between 22 and 17 volts, and at each toggle D voltage would momentarily be 2.73V under or 3.53V over 12V, which might be tolerable. In the same scenario except r=50, PS would toggle between
37 and 62V, and D voltage would be 8.1V low or 4.84V high momentarily at each toggle. Whether this would be tolerable would depend on how quickly PS slews from 37 to 62, it looks like.-jiw