Typically they produce tens of billions of watts of electrical power, but there is no known way to harness this energy because of the vast scales over which it is produced, and the very low density of this power. It would be like trying to harness the mechanical energy of a flock of mosquitoes. If you want to keep up with the actual daily/hourly power output of aurora, have a look at the NOAA/POES satellite website. They produce plots like the one above which give the total equivalent power of auroral activity in the north and south hemisphere. The numbers in their archive show a range from 4 to over 300 billion watts of power in the northern hemisphere alone. The total world production would be about twice this amount because there are nearly identical aurora in the southern hemisphere too.
All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY project.