The severe cold front passing through the country this week will result in much higher electricity usage, Eskom said on Monday.
"The most critical period within this peak is from 5pm until 7pm as a large number of customers return home from work," it said in a system status bulletin.
Eskom said it had made planned maintenance of its power stations a priority.
"We are making significant progress with our programme of preventative maintenance as we go into winter in an effort to ensure a stable power system."
Total demand on Monday evening was forecast to reach 36,556 megawatts (MW).
Eskom had 37,774MW of capacity available, including from open cycle gas turbines.
Current planned maintenance accounted for 3032MW. Unplanned outages affected 2397MW.
On Sunday, peak demand of 33,710MW was met, with an available capacity of 37,207MW.
On Saturday, peak demand of 33,686MW was met, with an available capacity of 36,649MW.
Demand and capacity figures were similar for Thursday and Friday.
Peak demand for the rest of the week was forecast to reach 35,237MW on Tuesday, 35,207MW on Wednesday, 35,055MW on Thursday, 33,229MW on Friday, 31,548MW on Saturday and 31,721MW on Sunday.
"We urge all South Africans to partner with us to save 10 percent of their electricity usage."
This would make it easier to manage the power system during the planned maintenance, the utility said.