I get power fluctuations here in Houston of generally short duration, usually over-voltage but sometimes total loss of power, and my 1500w UPS covers me very well for that. The Internet stays up so the issues seem to be only local. My UPS load ranges from 100w to 135w which gives me around an hour's running in a worst case scenario and all of my trades have stops in the market. Plus I have my laptop in case it all goes to hell in a handbasket (like a multi-day power outage). Worst, absolute worst, case: phone my broker (who is in another state). Not sure if the Tesla thing could improve on that for me, but probably not. That all said I am all in favor of the solar/battery combination and selling excess back to the utility if that were realistically possible.
My internet goes off all the time, same effect as no power, i just kill wifi and go 3g via tablet /phone, wouldnt not want my tablet and phone backup. sL in place and generally sub $500 before margin is hit if I forget, so no biggy.