The whole of the Western Isles was left without power after the outage just before 7am on Wednesday. Scottish Hydro Electric Power Distribution said its engineers were working to restore supplies.
Elsewhere a rescue operation has been launched to help a Spanish fishing vessel in difficulties off Orkney. Shetland Coastguard said the coastguard rescue helicopter and Stromness Lifeboat had been sent to the scene.
People around the UK are facing disruption with 80mph winds and huge coastal waves predicted for some areas on Wednesday.
In Scotland several ferry and train services have been cancelled while some bridges have been closed due to high winds.
Fifteen flood warnings and 12 flood alerts have been issued by the Scottish Environment Protection Agency (Sepa).
The process behind the storm - rapid cyclogenesis, known colloquially as a weather bomb - is a deep low pressure system moving between Scotland and Iceland.
For the west coast of Scotland, the Highlands and Islands, Orkney, Shetland and Northern Ireland, the Met Office has upgraded its warning to amber ‘’be prepared’’ status.
People have been warned to expect dangerous conditions, especially along causeways and coastal roads exposed to the west.
High winds are also set to hit northern parts of England and Wales, with yellow “be aware” warnings in place.
Steve Willington, chief meteorologist at the Met Office, said: “Very strong winds are likely to affect northern and central parts of the UK from early Wednesday and last through until early Thursday as a very deep low pressure system moves slowly eastwards between Scotland and Iceland.
“A period of severe gales is likely over northern and central Britain, as well as the potential for storm force winds over north-western coastal areas of Scotland.”
Traffic Scotland said gusts of 70mph had been recorded on the Forth and Tay road bridges while the Met Office recorded a 59mph gust in Lerwick, Shetland, and a 55mph gust in Glasgow.
Police warned that travel conditions in the worst-hit areas of Scotland could be “hazardous”, with disruption also expected on ferries, rail services, roads and bridges.
Many ferry services operated by Caledonian MacBrayne, which operates in the west of Scotland, have been cancelled or disrupted, while the Argyll Ferries service between Gourock and Dunoon has been suspended.
There were also disruptions and cancellations on NorthLink Ferries services between Orkney, Shetland and the mainland, while P&O ferries said its Larne and Cairnryan sailings were operating with delays of up to at least two hours, with further disruption expected throughout the day.
Several train services will be cancelled as a safety precaution, Network Rail and train operator ScotRail announced. On the roads the Skye Bridge and Forth Road Bridge were closed to high-sided vehicles while the Tay Bridge was only open to cars.
Western Isles Council said all its schools and nurseries will be closed as police have advised the public not to travel unless it is absolutely necessary. All depots, libraries, museums and sports facilities in the Western Isles will also be shut.
Scotland’s Deputy First Minister John Swinney has urged people across the country to be on the lookout for travel and safety advice. He said: ‘’I am confident we are well-placed to cope.”
Councils south of the border insisted they are prepared for the plunge in temperatures, with gritters ‘’out in force’’ and depots filled with about 1.3 million tonnes of salt.
The Met Office warnings for wind run through Wednesday and into Thursday morning, extending by that stage to cover the whole of the UK.
Mr Swinney said the Scottish Government’s Resilience Committee would meet again later to discuss the situation.
He told BBC Radio Scotland: “It is important to keep this in context. It’s not a surprise that Scotland faces severe winter weather, we face it to a greater or lesser extent every year. This morning we’re wrestling with a number of different issues.
“We’re wrestling with very high wind speeds, which are not that uncommon in the Western Isles for example, but they are still severe and need to be prepared for.
“We’re wrestling with the possibility of coastal flooding because of the sea surges and strength of waves that are likely to come, and in other parts of the country we’re wrestling with the issues of snow on the A9 and M74 and we also will, I suspect, be dealing with a bit of flooding on some of the river systems in Scotland but mainly on agricultural land.
“I think it’s important to remember that this is weather which is characteristic of winter weather in Scotland and what’s important is that we take the necessary steps to prepare for it.
“That involves the public authorities preparing for it but also members of the public being aware of the circumstances as well.”