A light turboprop pilot reported severe turbulence caused a loss of control and generator and communications failures.

Narrative

Flight 1Flight Plan-ZZZ1 to ZZZ2; diverted to ZZZ after requesting ATC assistance.We were flying at FL340 with the autopilot engaged when we encountered severe turbulence. The airplane abruptly dropped to approximately FL300; reaching a 10;000-fpm descent rate and 50 degrees of bank at one point; and the autopilot came offline. Upon exiting the turbulence; we had numerous CAS messages and were in an unusual attitude. Prioritizing aircraft control; I asked the left seat pilot to level the airplane and increase the airspeed; which had been reduced to 122 KIAS. Upon not receiving a prompt response; I took the controls; corrected the aircraft's attitude; obtained flying airspeed; and asked the left seat pilot to run the checklist.I noticed we had a generator failure; and the backup alternator did not come online to pick up the load; so the batteries were in the yellow and being depleted. The left seat pilot ran the checklist for generator failure and successfully reset the generator. I attempted communication with ATC but was unsuccessful on both radios (comm 1& 2); and also tried from both sides and on multiple frequencies to include guard. We turned north towards VMC. During this time; we received a transmission from the center asking us to descend to FL 240 and acknowledge with an Ident if we would hear them; we complied. We continued to try to communicate on both radios and made calls in the blind on guard and the last assigned center frequency. I then attempted to establish wi-fi communication with ATC and pointed the airplane toward an airport that was VFR - ZZZ. The center then asked on guard if we were proceeding to ZZZ; to acknowledge with an Ident; we complied. We then received a descent and asked to acknowledge with another Ident. About that time; the wi-fi connected; and my phone rang with ZZZ3 Center calling. I answered; informed ZZZ3 of our plan regarding ZZZ; and they asked what happened and what assistance we needed. I informed ZZZ3 Center that we experienced severe turbulence; followed by the loss of our generator and lost comms/NORDO even after our generator reset. We were setting up for a left downwind at ZZZ; so I told the center I needed to focus on flying and hung up. We landed uneventfully. ZZZ3 Center called again as soon as we taxied clear and opened the door to exit. ZZZ3 asked if there was any damage to the airplane or injured passengers. I did a walk-around of the airplane; and there was no damage; and everyone was strapped in; so there were no injuries. ZZZ3 asked again for the sequence of events/what happened; and I repeated the same information above. I asked if there was anything further for me to do and was told nothing further since there was no damage or injuries.I was then informed me that someone called and left a number. I called the number; and this time it was ZZZ4 Center. I repeated the same story and informed ZZZ4 that I had just told ZZZ3 everything.After the emergency vehicles cleared; we restarted the engine to taxi to the FBO ramp after shutting down on a taxiway for the emergency vehicles. After the airplane rebooted; all the systems appeared to be working normally. I tested the radios on the ground; and ZZZ4 Center could hear us clearly. We shut down again at the FBO and discussed options. We decided to top off fuel and try another flight since everything seemed to be working. I called the number I was given for ZZZ4 Center and explained our plan after all systems were checked.Flight 2 Flight Plan ZZZ to ZZZ5; divert to ZZZ6We were able to start normally at ZZZ; pick up our clearance over the radio with ZZZ4 Center; and depart without incident. After departure; while passing through about 10;000 ft; comm1 appeared to fail; so I switched to comm 2 and it worked. I had the other pilot try comm 1 on his side; and it did not work either. Passing through about 15;000 ft; comm 2 now failed. We tried both radios; both push-to-talk switches; and the center in addition to the guard; and nobody could hear us. I then connected the wi-fi; and no sooner than it came online; my phone rang with ZZZ3 Center on the line again. It was the same person. I explained that now we had lost comms again and were NORDO. He requested we change our transponder code. I looked for the nearest VFR airfield; which was ZZZ6; and we headed in that direction. As we descended through about 15;000 ft; our radios started working again. We were able to talk with approach control and tower over the radios and landed uneventfully.