Citation 560 pilot reported during cruise in an area with thunderstorm activity both generators malfunctioned and could not be reset. The flight crew diverted and used battery power to extend landing gear and flaps for landing.

Narrative

It was an IFR flight from ZZZ to ZZZ1. Both of us [are] typed in the C560 Ultra and on this leg I was the pilot monitoring or SIC. A preflight check of both generators was verified. We also briefed about the consecutive weather in State X running from the border down to State Y. The southern area had tops to 60;000 and the north was around 40;000. Our initial altitude was FL380 after about an hour went to FL430 followed later to FL450. I had asked ZZZ Center about deviating around the thunderstorms and if other aircraft had been through the same area. He said a Cessna (I'm unsure of the type of altitude) and a BE40 at FL450 and gone through the area. I asked for a heading change to the north of the build up on my radar and was given the change. We experienced some light turbulence and with occasional moderate. The pilot flying also noticed a fluctuation in airspeed of 10 knots. As we were about to turn back on course; we saw the RED Warning Lights flash followed by both RH and LH generator lights on the annunciator panel illuminated. I reached for the checklist as the pilot tried to reset the generators but was unable to do so. Due to our concern of limited battery and following the checklist; the pilot selected EMER BAT and asked me to get a lower altitude with ZZZ Center. I was given an initial descent to FL240 then to 17000 FT; with the next controller then shortly later down to 4000 FT. I also requested a VFR airport and was told the best one was ZZZ2. We broke out of the clouds about 40 miles northeast of ZZZ2 and landed normally using the main battery to put the landing gear and the flaps down. I have learned that at FL450 near thunderstorms can have a negative effect on the generators. I don't believe we were hit by lightning; but maintenance replaced the nosecone strips and one static wick. I have always felt I have been a conservative pilot over the last few years of flying; but this was an experience I will never forget and it will never happen again.