Sweden's weather agency (SMHI) issued a class one warning on Saturday for Norrland, forecasting strong winds of up to 24 metres per second. Heavy rain, wet snow and poor visibility were also predicted for other regions in the north.
In Västerbotten and in Östergötland emergency services were called out to remove a number of fallen trees which were blocking the roads. 18 passengers, travelling from Norrbotten to Stockholm, were trapped in a carriage for hours after the train collided with a tree.
They were later rescued and the train was towed to Boden, while the passengers took a bus to Luleå.
At its peak almost 9000 homes in the area were left powerless. By Sunday morning electricity had been restored to several of the affected areas. Supplier Eon said that 2,016 people, from Jämtland, Västerbotten, Västernorrland and Norrbotten were still in the dark.
A spokesperson for electricity generator Vattenfall told the TT news agency that engineers were working round the clock to restore power.
Weather expects said the strong winds were as a result of low pressure from the Norwegian sea crossing over into northern Sweden.
On Sunday SMHI said there were no weather warnings for the entire country. In Kiruna, in the north, it will peak at 6C while in Stockholm there will be sunny spells and patches of cloud, with a temperature of 16C forecast.