The cables would run from Denny, west of Falkirk, along the Atlantic, to Deeside in Wales and from Peterhead, underneath the North Sea, to Hawthorn Pit, in the north-east of England.

They would be crucial in harnessing the huge potential Scotland has to develop renewable power.

National Grid’s chief executive Steve Holliday said the proposal was part of the company’s strategic forecast for 2020-30: “I do see a world in which we are more interconnected and with greater flexibility so we can import power when we need it and export when we don’t.”

The cables would link existing and planned onshore windfarms in Scotland as well as proposed offshore wind and tidal generation.

Designing the cable system would cost about £200m, he said, and each would cost about £1.5bn to build.  Holliday said he saw no problem in attracting the private investment that the National Grid would require to undertake the projects.

The key will be in getting the UK Government to back the concept as part of its ambition to substantially raise the amount of renewables generated. Asked about the chances of winning its support, Holliday said: “I have to persuade them.”