The SDREA says getting to downed poles and power lines has been difficult in some areas, with crews having to travel to sites on snowmobiles.
Repair crews are seeing ice and frost accumulations the size of softballs.
Power companies from Minnesota are helping South Dakota crews.
The SDREA has even received offers of help from contractors as far away as Utah.
The South Dakota Rural Electric Association says the number of people without power grew to about 9,300 overnight.