No more arequirement than for a system with a Mechanical HDD.
In fact many of the newer SSD use a capacitor like a battery. Has enough energy so that if power is removed it can write what is in the write buffer.
Personnaly I do recommend an ups as it allows an ORDERLY shut down when power goes out - HDD or SSD makes no difference. Does not happen often, but just once can make it worth the cost.
The other day we had some bad weather move in. at on point the power went out, back in 4 or 5 times within 10 Sec before going for a couple of hours. That can really play havoc with a computer system.