Electricity is generated by various means, but the type of energy produced and methods of distribution are the same regardless of the method of generation. The electricity produced by wind farms is the same as the electricity produced by less eco-friendly means like coal and nuclear plants, and is distributed in exactly the same way, so the existing grids are fine to carry wind energy.
Wind energy can power electric grids, so long as batteries exist for days when there isn't enough wind to generate electricity at the turbines. Green energy is just as reliable as coal or nuclear, the dynamics of such energy usage are just different. Homes and appliances should be more efficient to use less power. Batteries must be maintained. Overall, electricity is the same no matter what the source of power.