Sorry I don't have exact numbers for you, but there do exist some very long HVDC lines [1]. The longest as of writing is in Brazil at 2385 km. There is a fairly long one in the US at 1360 km between the Columbia River Gorge and the Los Angeles basin [2].
But given that the solar terminator moves at about cos(latitude) * 1668 km / h (so slower towards the poles), even at a generous mid-Europe latitude of 45° N it'd be moving at 1180 km / h, giving you only a 2-hour window to make use of such a scheme with the HDVC lengths we have now. But hours before sunset, you're probably not at peak solar production anyway.
But given that the solar terminator moves at about cos(latitude) * 1668 km / h (so slower towards the poles), even at a generous mid-Europe latitude of 45° N it'd be moving at 1180 km / h, giving you only a 2-hour window to make use of such a scheme with the HDVC lengths we have now. But hours before sunset, you're probably not at peak solar production anyway.
[1] http://www.power-technology.com/features/featurethe-worlds-l...
[2] http://new.abb.com/systems/hvdc/references/pacific-intertie