I've not sure if has changed in the last few years, but one issue Denmark has run into is that our tariffs on CO2 actually harms the use of surplus green energy.
Most of Denmark (at least in the cities) are heats using hot water from remote heating plants, either surplus heat from power generation or garbage incineration, with auxiliary gas and coal plants. 15 years ago many of the smaller gas powered heating plants offered to install the equipment needed to convert excess electrical power to heat. The idea being that they would save money, compared to buying gas, the only caveat: They didn't want to pay the CO2 tariffs, which made sense, given that the power would mostly be from wind anyway. Paying the tariff would completely negate any cost savings, compared to buying the gas.
This solution was refused by politicians for years, so instead the heating plants would burn gas, generation CO2, and the excess wind power would be sold to Germany for almost nothing, and in many cases for free. That this point Germany wasn't closing down its nuclear power plants, so the electricity the Danish windfarms replaced was also CO2 free.