2001 Saturn SL1 Total System Shutdown

The car totally shutdown while my daughter was driveing down a city street about 15 miles from home. After a series of being powerless and having power, she was able to restart the car and drive it home. The problem appears to be intermittent. What happens is a total loss of electrical. With ignition key on, there are no dash lights, no accessory electrical, and nothing to the starter circuit - totally dead. Then, for no obvious reason, everything will work: the car will start without difficulty and run for who knows how long. Yesterday afternoon, with the engine warm and no apparent power, I checked under the hood and smelled hot electrical insulation (like Bakelite); this may be normal. As I lingered under the hood, I heard a click (like a relay) and turned the ignition key on and had full electrical. I started the car and it ran for about 30 seconds and everything went dead. I have not traced circuitry to see where all the relays related to the ignition circuit are located but wonder if the problem could be in the ignition switch or if there is a relay anywhere outside the starting circuit (alternator, perhaps?) That could shut power off to everything if it is acting up. Any suggestions? I have basic mechanics tools and volt-ohm meters. I do have a fault code reader which I cannot find! If I found it, is there a fault code to be aware of for ignition switch problems? Thank you for your input.