We have Solar at Home Part 3: How Much Electricity …?

Next: We have Solar at Home Part 4.
Previously: We have Solar at Home Part 2.

Last week we finished pricing the system1, the third of four answers we need to make the forecasts. Before we move on: if the tax discussion in the footnotes has grabbed your attention, which it should have, and you file with the IRS, and live in your own home in the US, you should know that the Inflation Reduction Act provides or extends federal income tax credits—not deductions, these are better, read the footnotes if you don’t know why—for buying more efficient air conditioning, heat pumps, furnaces, doors and windows, and other things, and for new solar power, solar water heating, fuel cells, and batteries2. The IRA—no, not that one—also funds state-level subsidies you can get in addition to the federal tax credits. Some of the credits are capped at $1200 or $2000 per year or per category or lifetime; it’s not all that well explained, which is a policy execution disaster so you may have to do some more digging, or wait until we buy a heat pump water heater and I blog about it.

By the way, if you are wondering what a heat pump is and why there’s so much fuss about them: it’s air conditioning that can run “backwards”. While air conditioning your backyard might seem unwise, the point is that when you do so, you are heating your home. Heat pumps are energy-saving because they are more energy-efficient than any other heating methods because, while gas heating can be 90% efficient, and electric heating 100% efficient, heat pumps are more than 100% efficient3. How is that possible? They use the sorcery of thermodynamics to steal energy from elsewhere4. Very cool. Or hot! Let’s move on.

How much electricity will the system generate?

We don’t know. 12 380W panels = 4.56 kW5. That’s peak; what will we actually get over the course of a day? Sanity check, we think we will need up to 5835 kW·h per year, that’s about 16 kW·h per day, which is the equivalent of three hours a day with the sun directly over the panels. This is literally impossible. The earth’s axis is tilted at 22.5° with respect to the sun6, and we live at 37.75°N but even with the panels mounted at a tilt we—meaning the contractor—calculated as year-round optimal, which is 10° southward7, so the sun will never be directly head-on to the panels unless California finally escapes the North American Plate8. On the other hand, the sun does shine for more than three hours a day, so these numbers seem to be in the ballpark. On the gripping hand9, there’s the fog, the seasons, rainy days ….

We—meaning the vendor—calculated that 9 panels would generate 3915 kW·h per year, and 12 panels, 6934 kW·h per year. Or at least that’s what I put in the spreadsheet, though the numbers don’t look quite right. I also saw somewhere (the proposal? the internet? the CPUC utiliganda? don’t remember which) that that would drop one percent per year.

Final assumptions

QuestionEstimate from April 2022
How much electricity will we use between 2023 and 2032?between 3217 and 5835 kW·h per year
How much will PG&E charge for that electricity?$0.43 per kW·h, increasing 7.6 percent per year
How much will the system cost to install and operate?$17,000 or $20,000
How much electricity will the system generate?3915 kW·h or 6934 kW·h, decreasing 1% per year.

Next: We have Solar at Home Part 4.