Power was restored to Dobsonville and Mmesi Park, Soweto, on Wednesday, Eskom said.
The utility's Gauteng spokeswoman Reneiloe Semenya said it was monitoring the situation.
"Our network is currently constrained due to overloading. The cold weather conditions aggravate the situation, as the demand for electricity increases significantly during the peak period between 5pm and 9pm."
She urged people to use electricity sparingly.
Eskom had not planned any maintenance work. Therefore there were no planned outages.
If the power tripped, people could call Eskom on 08600-37566. A response team was on standby to attend to any power disruptions.
Semenya pleaded with people affected by outages not to protest and to allow the utility's technicians to do their jobs.
Klipsruit residents barricaded roads and burnt 15 vehicles during a power outage in the area last week.
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