lyvia:

My short answer, no. My environment has much more light in winter than yours but I suspect that for greens in winter it's not light that stops growth as much as temperature. If you can get the days in winter into the 50s and 60s by day your greens will grow.

The cost to duplicate the light we get from the sun would be outrageous. In my 1700 sq ft greenhouse probably $20 per day in winter won't come close.

If you can increase/concentrate light and temperature in winter you are getting somewhere. In my sunroom I've done that via reflectors on the ground, outside, on the south side. It could be done in a greenhouse via reflectors inside or outside on the north side. This raises light inside and temperature inside if reflectors are outside.

You might want to check out some of the winter GH books. "Four-season Harvest" by Coleman talks about winter growing in a far more northern area than you and may give you some ideas.

I'd agree with the other reply regarding heat vs light. I have a small (8x18') solar GH and have successfully grown vegies over the winter without supplemental light (still harvesting 1qt of cherry tomatoes per week from one plant), but growth slows way down during Dec-Jan. More light will help, but only if heating requirements for faster growth are present as well.

You do have the option of adding supplemental light, but an led rope is not going to do it. A larger HPS or MH grow light could be used for a small bed, but would likely add significantly to your electric bill.

For greens in the winter, a more economical option might be to increase the size of the bed, so that it supplies you with enough even with the slow growth rates.