Isn't there a way to sell the unused solar power to the grid in summers and during winters the grid sends back the power needed to you at a discounted price?
Well, until '27, I'm allowed to use the grid as a free battery, basically, this is a kind of government subsidy. But that will end, and the contracts available will be fixed price with a feed in tariff or dynamic (realtime) market price, but then prices can and have been negative during peak solar hours. A battery can solve this only for a bit, and maybe with smart algorithms it can be trading on the electricity market full time, I'm not sure if that makes enough money for the grid power in winter.. it's nice to think about though.
or you get a battery. Is just great. I have 3.5kw solar power witha 9kwh battery. Very very seldom it switches to power line. And this is in south Germany, maybe a bit sunnier than north but still - it rains a lot/cloudy, sun is sparse.
It seems like that works for daily cycles, but isn't that very expensive storage for one cycle a year, which is what you need to save energy for winter?
Depends how close to the poles you are. A lot of the world can do this fine by sizing the PV for winter; too close to the poles and there's not going to work — you either need to diversify power generation by kind (wind, wave, hydro, geothermal all work too, but again geographically constrained) or by distance (the maths says we can build an adequate and literally global power grid for an affordable quantity of aluminium, shame about the politics).
If every household did this we would have massive problems. We would still need a base load amount in the winter, and in the summer there would be an over abundance. The price of electricity would swing between essentially free in the summer to higher than normal in the winter, because the cost of operating base grid power would be about same but they would need to cover all operating costs during the winter.
Utilities should charge a separate connection fee and per-kWh rate if that's what matches the economic reality of their business. I don't see the summer abundance as an issue. It means we get to shut off the fossil fuels 8 months out of the year. The remaining 4 months, everyone pays a little more per kWh, averaging out to the same cost over a full year. What's not to like?