More than 5,000 properties are without electricity due to high winds bringing down powerlines in Adelaide's north-eastern suburbs, part of the Adelaide Hills and on the Fleurieu Peninsula.
Extra crews are on duty but some people are expected to face more than a day without power.
SA Power Networks official Paul Roberts said poor weather was still hampering efforts to restore services.
"People need to really plan for the fact that they're likely to have quite extensive outages," he said.
"We're doing everything we can, pulling out all stops to get people back tonight who were out yesterday.
"We can't guarantee it at this stage, we're still working through a large number of outages with extensive damage and trees to be moved and cut."
The weather bureau and State Emergency Service are warning of more possible problems over the weekend, with significant rain forecast and a chance of flash flooding.
By Monday, rainfall of up to 80 mm is forecast over southern coasts and in the Mount Lofty Ranges.
The bureau said there might be weekend snow on the higher peaks of the Mount Lofty Ranges and in the mid-north and Flinders districts.
© ABC 2013
14:24 EDT Thunderstorms are due to develop daily across New South Wales and Queensland for almost two weeks.