Would a global cooling event disable solar energy usage? Imagine that we've improved the level quality, affordability, and ease of use of photo-voltaic solar, and it's use is widely distributed in the USA.  We've improved the grid for power distribution, we increase wind, hydro, geothermal sources for 24-hour generation and create a storage network to the point where fossil fuel generation is only needed for, say, 20% of our energy needs, and peak/backup needs.

Everyone is happy, bliss abounds.

Would such a system be vulnerable to a natural disaster?  If there was another Krakatoa event, with an equivalent amount of ash thrown into the atmosphere, how much, percentage-wise, of a reduction in solar intensity would we see, and for how long?
I am not sure about the size of Krakatoa eruption but the eruption of Mt. Pinatubo in Indonesia around 12th June 1991 is considered as the largest eruption in the past 100 years. Global average of decrease in solar radiation after 4 months of eruption was about 2.7 +/- 1 W/m^2. Global average surface reaching solar radiation is about 198 W/m^2. In other words, Mt. Pinatubo eruption caused about 1.3% decrease. 

The number 2.7 W/m^2 is a global average, so the decrease might have been more in tropical regions and less at high latitudes. It took about three years for stratospheric aerosol amount to return to the background level. 

Reference: 


Minnis et al., 1993, "Radiative climate forcing by the Mt. Pinatubo eruption", Science, vol. 259, 1411-1415, doi: 10.1126/science.259.5100.1411 
Kremser et al., 2016, "Stratospheric aerosol - observations, processes and impact on climate, Review of Geophysics, vol. 54, 278-335, doi:10.1002/2015rg000511