The calculation is quite simple.
I consume 5000 kWh of electricity per year. Thanks to the electricity price cap, the kWh now costs 40 cents. So I have to pay 2000 euros annually for the electricity consumed. Clear so far. One person has a little more, another a little less consumption.
A photovoltaic system 10 kWP with storage for 15,000 euros means that I can reduce my electricity purchase from the energy supplier by about 70 percent with some planning. Thus, my annual savings amount to 1400 euros plus possible feed-in compensation. That won’t be much, maybe 200 euros per year.
So the system will have paid for itself after 10 years. The difference is, I do not pay the 1600 euros to the energy supplier but to myself. I do not care whether I have the 15k now in the bank or on the roof.
For me, the electricity supplier now debits only 35 euros per month instead of 120 euros. And any electricity price increases basically don’t affect me at all.