I suspect the answer is somewhere in the middle - maybe two weeks of storage. Though of course prices change all the time so the correct action will change and you need to rerun the numbers as things degrade to decide your next action.
I do say:
> As solar panels increase in efficiency, it might be more sensible to replace the panels on my roof, or add some onto a shed.
Even in the darkest days of winter, they still generate something (unless they're physically covered in snow) - but they'd need to be 20x as efficient to power my typical winter usage.
Our roof is an even East/West split. So one side powers our morning and the other side our afternoon.
We have east and south and our peak production is when the sun is at the south-east, in the middle of the two faces. The east face production drops off from there on out until it's a fraction of what the south face is generating.
My 1.8kWh system at 20% output covers a great percentage of my baseline usage during the day! I'm probably going to add a small battery so I'm not penalized for sending energy back to the grid, but I'm not gonna need much until my kids get older and want new gadgets. The cool part about modern electronics is that we're generally getting more efficient too with newer tech. If I replace the old freezer, my baseline usage drops 20%+.
I don't disagree with your point that sometimes nature is simply just working too hard against your efforts, but I also wrote all this to say that some people need to really do the math and not rely on "common knowledge". Energy efficiency has come an extremely long way in the past decade and much of what was true when residential solar first started popping off is now outdated.
FWIW, a MacBook Pro in active use uses like 45 watts max and an iPhone really like 2-7 depending on the use. I wouldn't worry too much about gadgets.
Way too much to fit on a house though.
My detached house has less space for solar panels than some smaller homes because all faces of the hip roof are triangular; lots of houses nearby that are semi's or terraced actually end up having more roof space because their roof faces are rectangular.
I managed to have 14x 465W panels total added on the east and south faces of my home, but the installer wanted an extra 40% of the total system price to add 5 more panels (and the 15th they couldn't fit on the south face, for 6 total on the west) because they'd have had to erect additional scaffolding and who knows what else. That was an absurd additional cost so we didn't do it, but that additional generation late into the afternoon would have been great for our peak usage at dinner time. My suspicion is they simply didn't want to do it, because the cost just doesn't add up.
On an overcast day at this time of year I can generate nearly enough to power the "baseline" of the house, but currently I receive 24p/kWh to sell the energy back, and I can charge the batteries at 15p/kWh over night, so I can break even if I can generate just enough to export to cover the night-time charge of the batteries.
I haven't had them long enough to run through winter yet so we'll have to wait and see, but based on the end of this summer, I could probably cover the winter usage with export payback through summer at the current tariff rates when we were generating about 100% more than we were using per day.
I suspect the introductory tariff is far more generous than I'll have access to in a year's time when it expires though.
Right now Denmark produces 1724 MW from solar panels even though it is an overcast and rainy day: https://energinet.dk/energisystemet-lige-nu/
Our current usage is relatively high: 5944 MW.
Remaining supply is: 3458 from windmills, 357 from fossils and 434 from import from other countries (mostly hydro/wind).
So if Denmark doubled the amount of windmills (it is a very windy country) and solar panels then Denmark would be able to run of windmills and solar panels even in the autumn.
2024:
May: 2494 kWh
Jun: 2323
Jul: 1915
Aug: 1634
Sep: 1008
Oct: 442
Nov: 185
Dec: 31
2025:
Jan: 43
Feb: 335
Mar: 980
Apr: 1510