When you plug-in a cable into the Power Generator it often unplugs again on my client, but when I try to plug it back in as shown in the interaction prompt of the generator, it would not work. Rejoining or (un-)plugging a different cable seems to also update the system.
However it is not intuitive and most certainly not working as intended.
Plug something's cable into a Power generator
Try to position the item around the area, maybe climb a small ladder
Listen for the clicking sound indicating something happened with the plugged-in cable
Watch closely on the model whether the cable is rolled-up or going into the direction of the power generator
Unplug something from the power generator and see some other cable (dis-)appear