SA Power Networks has confirmed the mass blackout via Twitter saying the outage was caused by an "upstream supply" failure.

"No upstream supply from the transmission network. State currently w/out power," the company said.

"Do not report outages. We will provide updates when avail.

"Drive safely and if you come across any downed powerlines pull over and call 13 13 66."

Thirty nine DFES personnel, including SES volunteers from the Perth metropolitan area and the South West are being deployed to South Australia on Wednesday to assist with the severe weather and floods.

Traffic lights are down, the roads are choked and building fire alarms are blaring across the city, according to local media reports.

Police have called on all South Australians to avoid travel if possible.

Two storm fronts swept across SA on Wednesday, the first hitting Adelaide around lunchtime and the second about 3.30pm.

The power went out across the state about 3.45pm, when there was heavy rain, lightning and thunder over the capital.

The town of Cleve, on the central Eyre Peninsula, was among the hardest hit. Other towns including Gawler, Kapunda, Clare and Balaklava were also hammered by the storm, which dumped large hail over the region.