Around 31,000 customers of Ellevio, Vattenfall, Eon and other regional and local network companies in southern and western Sweden are without power, says the state-owned utility Svenska kraftnät.
At present, the forecast is that some customers will have to wait overnight before power is restored on Monday.
Svenska kraftnät says strong winds and the onset of darkness are making repair work more difficult and delaying it.
In previous outages, power has also tended to come and go when switched back on.
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