During our severe heat wave a couple weeks back in which local temps were in the 110-120 range, my local utility warned of possibly brownouts and even blackouts (due to overloading causing transformers and other infrastructure to fail) if we don't manage our daytime electricity use wisely, to include setting thermostats higher and putting off using major appliances until after 9 PM. An EVSE especially a 240 volt one is going to use more electricity than just about any other major appliance in the home with central A/C the possible exception.
One time during this period I was forced to charge my car during the day, but opted to use the 120 volt cord instead, that way at least I'm only drawing 1440 watts and not the 4800 it would normally draw. It also kept the battery at the full mark for the least amount of time since it took a lot longer to charge.
Unless they're willing to build more infrastructure particularly generation plants, charging off-peak and encouraging more solar adoption is the only way to manage the growing number of EV's.
Blue Ocean 2012 Leaf SV, lost that 1st bar at 34 months/26,435 miles. Lease returned 2 months later. Final LeafStat figures: 225 Gids, 17.44 kWH, SOC 91.89%, SOH 82.36%, 69.49% HX, 54.57 Ahr, battery temp 61.8 F.
Now driving a 2015 VW eGolf SEL.