B737 Captain reported the loss of both electrical systems in cruise. Flight crew landed at the nearest suitable airport and passengers deplaned.

Narrative

We were at FL340 and had just requested climb to FL380. We were cleared to FL380 and had just started a climb when we got a Caution Light for ELEC. We looked up and the initial light was T/R (Transformer Rectifier) Unit. I had just started to use the DC selector to determine the faulty T/R Unit when that light extinguished and the Source Off light for the Left Generator illuminated. My FO was the PF; so I pulled out the QRH and started to accomplish the checklist. The Left Generator would not come back online. I continued with the checklist and started the APU. After the APU stabilized I connected the APU Generator to the Left Bus. The checklist was complete and we continued on our way. After about 5-10 minutes we received another Caution Light for ELEC. The Source Off light was on again. The APU Low Oil Pressure light was also so and the APU had Auto Shutdown. At this point I pulled out the QRH checklist and it said to land at the nearest suitable airport. The closest airport in our ND (Navigation Display) was ZZZ. I informed ATC that we would need to divert to ZZZ due to a loss of dual electrical systems. They inquired if I wanted to (have priority handling) and I told them yes. I sent Dispatch a Message to call me. When they responded; I handed off ATC communications to my FO. I informed Dispatch of the situation; and they concurred that ZZZ was a prudent option. They said they would line up everything we needed on arrival. I signed off with Dispatch and reconnected with my FO. She informed me of the instructions that ATC had given us and we verified the status of the aircraft. I then handed communications back to her while I conducted a Brief with our Purser. After finishing that brief; I gave a quick PA to the passengers to explain our situation and what we would be doing. I then reconnected with my FO. She filled me in on our status and clearance. We then conducted an Approach/Descent Brief. After completing the brief and the appropriate checklists; we continued into ZZZ for an uneventful Approach and Landing. We were very light so the Overweight landing was not a consideration. After landing we pulled off of the runway and were instructed to stop so the CFR (crash fire rescue) trucks could approach to check us out quick. They soon called with the report that everything looked normal; and we taxied into our gate. As we were taxiing in I was concerned with the ground crews' safety with trying to install Ground Power with the Number 2 engine running. The alternative would have been to shut down both engines and have the airplane go dark while the power was connected. I asked my FO. To call Operations; and let them know the situation. They said they were aware and the crew would connect the power with Number 2 engine still running. I was not thrilled with that option; so I chose to attempt to restart the APU. It started on the first attempt; and we powered the Busses and shut the engines down normally. They quickly established ground power; and we then shut down the APU. After running the Parking checklist; I informed the Passengers that we would be deboarding the aircraft so that they should gather all belongings and the agents inside would have more information on the options. I then debriefed with my FO. We made the appropriate logbook entries and gave the local Maintenance personnel a verbal brief of what we had experienced. After debriefing ; and consulting with the Chief Pilot and my FO; we determined that we were OK to continue to ZZZ1. The rest of the night went without any further disruptions.