I recently had occasion to think about sizing a solar energy system. Let me say up front that I do not advocate using solar as a significant part of the energy grid. We have a lot of cheap coal and gas and we should burn it over the next several years, while we convert the grid to nuclear. I am only looking at home solar as a way to avoid power outages and utility price spikes that are occurring precisely because there isn't enough fossil and nuclear power being generated.
My situation is new construction of an average-sized residence in a place where it can optionally be tied into the grid, so you can offset your electric bill through net-metering. I also assumed gas heating, cooking and clothes drying, but the latter two may not make a big difference. That doesn't cover every situation but it's probably one of the commonest. If this fits you, then read on.
I'm an engineer, and as often happens when I look at fields I'm not an expert in, I did a lot of calculations and ended up arriving at the same conclusions that experts in the field already know.
The first thing I considered was a totally off-grid system. Because this is new construction, I thought if I could avoid the upfront cost of a grid tie-in (something like $15,000) then I could put the savings toward a solar system that would let me be free of the grid forever.
This did not work out. The simple reason is that the insolation (fancy word I learned meaning the sunlight available to run your solar panels) is cut by about 3/4 when it's cloudy. If you live anywhere except the Desert Southwest, you are going to run into a string of cloudy days a few times a year. Furthermore, the insolation in winter even on a perfectly clear day is about 3/4 less than on a summer day, and that occurs everywhere in the US because in winter the days are shorter and the sun doesn't rise as high. So you could be looking at a 10 to 1 variation in the daily insolation over a year.
This means that, to cover cloudy stretches, it takes an off-grid system bigger than what is needed for an average day. Not a few percent bigger, several times bigger. Buying a big battery does not help much, because your panels have to produce a surplus for several days to fill the battery. It takes a lot of panels to be able to do that in the dead of winter - so many panels that there may not be room on your property. The fact that you don't have to run your air conditioning in the winter (AC is a huge energy hog) helps, but doesn't compensate for the lack of sun.
Overall, to go off-grid will cost you something like 50% more over the life of your system than using the grid alone, even accounting for the $15,000 you saved in avoiding the grid tie-in cost. If you're a hardcore survivalist in a cabin far from a grid connection, off-grid is your only choice, and you may be willing to live with some outages in the winter. But for most people, it's not worth it.
The other option is to connect to the grid to cover those cloudy days, but to build a solar system to offset the cost, through net-metering. With this type of system, the lowest-cost option is the system that exactly meets the average energy usage of your house. This is probably 20-30 standard 300-watt panels for the average house. And you probably don't need a battery, because you can draw from the grid any time you need, whether it's at night or on an overcast day. I don't recommend buying a battery for the sole purpose of getting through that rare week when the grid is down and you don't have enough sun to meet your usage. It takes a very big, expensive battery to do that. An emergency generator will do that job at lower cost.
Why is the lowest-cost system the one that exactly meets your average usage? It has to do with how net metering normally works. Net metering lets you accumulate credits when you generate more energy than you use in a month. Then you can use those credits to offset the cost of energy you may have to buy during the winter --- partially, because they only credit you for the supply cost, not the distribution cost or any fixed fees on your bill. It is a little complicated.
The way it works is, in the summer you are producing more than you're consuming, so your electric bill is nearly zero (except for fixed fees) and you build up a bunch of credits. Then in the winter, your solar panels aren't able to meet your usage, so you draw from the grid and spend down your credits to offset the cost. Your electric bill is still low because of the offsets.
But the thing is, the utility will not give you a cash payment for credits. You can only use them as offsets. Therefore, any credits over and above what you need to cover the winter will just represent energy you gave the utility for free. (This may be why they agreed to net metering in the first place.) So you want to size your system to meet your average usage over the year. Anything more is wasted investment, at least from your own perspective.
The average-size grid-connected system doesn't get you totally off-grid, but it gives you a lot of independence, costs less in the long run based on current electric rates, and insulates you from future rate hikes. You can buy a modest battery if you want to be independent of the grid during summer nights. Even if you have electrically powered whole-house air conditioning, you will produce a surplus in the summer and always have power even during a thunderstorm grid outage. Weather outages always seem to happen in the summer, at least in the places I've lived.
Having said all this, I am sure there are weird net metering rules somewhere that lead to a different conclusion, or no net metering at all in your state, so you still have to do a little homework.
A clever person probably could have figured this out without all the analysis, but I'm not clever, just willing to grind through a pile of numbers with a computer and try to learn from it.
