This was a class project :
COMPRESSOR TEST CORD
I just use a steel (not plastic) 4 inch square electrical box (1900) and a cover with a fuse for mine, with a grounded 14-3 supply cord going in and a length of 14-4 SJ cord coming out with an alligator clip crimped onto each of the wires (white, black, red, and green). And plastic boots on the clips. Also a short piece of 14/2 SJ cord with alligator clips and plastic boots.
I cut holes in the blank cover to accommodate a heavy duty (15A) on/off toggle switch and a momentary contact push button switch. The white neutral supply wire goes straight through to the compressor common alligator clip. The incoming green ground wire attaches to the green wire of the 14/4 SJ cord outgoing line. Using an alligator clip to attach to the frame of the refrigerator.
The 'hot', black side of the supply, feeds first through the on/off toggle switch, and then straight to the 'run' winding alligator clip. From the output side of the toggle switch, a wire 'tail' also feeds the input side of the momentary contact switch.
The output of the momentary contact switch goes to one side of the 14/2 SJ cord the other wire of the 14/2 SJ cord will go to the red wire of the 14/4 SJ cord. The other end of the red wire will go to the compressor start winding alligator clip. The ends of the 14/2 SJ cord with the alligator clips can be clipped together or connected to a start capacitor.
To use, after verifying which compressor terminals are 'common', 'run', and 'start', just remove the relay and overload, and connect the alligator clips directly to the compressor. Plug the test cord into a grounded receptacle.
Turn the on/off switch on (you should hear the run winding's low hum), and hit the momentary switch to briefly energize the start winding just like the start relay does when it's working correctly.
If it starts and runs with a test cord, it *usually* means the compressor's OK. You'll want to test the windings with an ohmmeter, though, to be certain there are no winding shorts causing it to 'short-cycle' and run hot.
One of these cords can be handy for test-running other equipment, too. I often just loop the 'start' alligator clip back out of the way, clipping it to the cord, and use this to quickly attach to small motors, etc, to check them.
Hope that's of some help.