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

Question	Estimate 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.

Welcome back to our series of footnotes about US taxes. We explained how a tax deduction would have worked, but Solar is a tax credit, which is much better than a deduction. A tax credit cuts your total income tax by the full amount of the credit. That money is effectively refunded^א. Income tax rates don’t matter for credits. The US offers a $2000 tax credit for each child^ב, so if you have three kids and owe $20,000 in taxes, you actually owe $14,000 in taxes. If you paid $20,000 through payroll deductions^ג throughout the year, then you would get a refund^ד of $6000 after you filed your tax return. The Solar Investment Tax Credit is a credit, of 30%, so we paid $20,510 for the system, and then paid $6153 less tax than we otherwise would have. With a 100% tax credit, the system would have been free, except for the detail of having to cough up $20k and wait up to a year to get it back^ה. ↩︎
IRS. Credits and deductions under the Inflation Reduction Act of 2022. 2024-06-17. irs.gov. ↩︎
Heat pumps are more than 100% efficient for cooling as well as heating, but that’s not a breakthrough because a heat pump in cooling mode is an air conditioner, and we already have those, though I would hope most heat pumps are especially efficient air conditioners. Interestingly, a heat pump can never be as efficient a cooler as a heater because the inevitable waste of friction and noise and engineering compromises and such all turns to … heat^ו., which is a bonus when heating but a demerit when cooling. ↩︎
Heat only moves from hotter things to colder things. Burn propane, and the heat in the flame will move into the air or water you pass over it, and then you can push that air or water wherever you want heat. If we want to heat the inside of our house, presumably the outside is colder, so we need to move heat from a colder thing to a hotter thing, which is impossible. So we cheat. Take some refrigerant fluid and stretch it out (within some contraption involving pipes, so you don’t lose it). It will get colder, just as an aerosol can gets colder when you spray it. Stretch it out enough and it’s colder than outside. With good engineering, this will work even if outside is well below freezing^ז. Bring it back inside and squeeze it back together, and it will hotter than when you started. Do this for a while, and maybe you put 1 kW·h of of energy into the heat pump to run fans and (literal, mechanical) pumps, and added 2 or 3 kW·h of heat to the inside room. No perpetual motion here, you—meaning your heat pump—just sucked some heat from the colder air outside. ↩︎
A Watt is a measure of power, not energy, and we pay PG&E to delivery energy. A Hyundai Ioniq has 78kW motor; the same power could light 780 100W incandescent bulbs^ח. But for how long? The Joule is the unit for energy, defined as one Watt for one second. But the joule is too small things the scale of a car or house: a kilojoule is only one watt for an hour, or a kilowatt for about 28 seconds. So everything is measured and priced as thousands of watts per hour, or kW·h, to make the math easier. If you drive your Ioniq full throttle for an hour, you’ve liberated 78kW·h from your batteries, converting it to a mix of wind, joy, and police helicopters in pursuit. ↩︎
All respect to Aten the sun aspect of the mighty Ra! All hail Ra and also other many gods! Don’t make the same mistake as Pharaoh Akhnaten!

Akhnaten · Hymn to the Sun. ↩︎
Technically, the plans call for an azimuth of 175°. ↩︎
This is a joke. Most of California lies on the North American Plate. Even our house, for all its ocean-driven fog, is a mile or two inland of the San Andreas fault^ט. And any land that remains on the Pacific Plate is going to go north.

↩︎
The Gripping Hand ↩︎

So a 100% tax credit will always be better than a 100% tax deduction. Any tax credit with a rate higher than your tax bracket will be worth more than a deduction. The highest bracket is 37%, so a 38% credit will be better, for anyone, than a 100% tax deduction.
some restrictions apply. Usually these credits start tapering for incomes over about $100,000, and drop to zeroby $400,000. So whereas deductions are regressive (help lower incomes less), income-capped credits are progressive (help lower incomes more).
At this point, if you have never calculated US taxes before, you are undoubtedly staring at the screen dumbfounded. No doubt you are thinking, this tax stuff is so simple, I can't believe I didn't already know all of this. Before you offer to do your American friends' taxes for them, let me expose you to just a few complications. First: payroll deductions is not the same thing as tax deductions. The US requires employees to pay taxes with every paycheck. The employer is required take the money out of each paycheck before it reaches the employee. (Note that paychecks are usually weekly or bi-weekly, but the employer only has to pass the money on to the government every quarter, after collecting an average of six weeks of interest on … a over a trillion dollars a year … say 5% … about $6 billion a year‽ Add in the $50 billion employers steal from employees annually, and the $150 billion the wealthiest American illegally underpay, and you can see that waging class warfare is very profitable for the winners.) Everything coming out of the paycheck is a payroll deduction, but most aren't tax deductions.
If you paid more in taxes than you ended up owing, the IRS sends you the extra money as a tax refund. This is true even if you ended up owing less because of a non-refundable tax credit. This is because refundable means something different for taxes than it does for tax credits. If you think this is confusing, you are wrong. For tax credits, refundable means that you will get the money 'back' even if you didn't pay that much tax. If your annual tax bill is $2000, and you have a $6000 credit, your annual tax bill is now negative $4000. If you already paid the $2000, such as by payroll deductions, you'll get a check for $6000. And if you didn't pay your taxes yet, you don't have to, and you'll still get a check for 4000. But if the credit is non-refundable, which most of them are, then the rest of the credit is worthless to you. You owe 0, so anything you already paid will be refunded, but that's it. This is of course regressive, so the credits really ought to all be refundable, but anyway tax refunds are a terrible mechanism to distribute government incentives, but that's another topic.
Probably why even people who can afford to pay all at once usually still finance.
You shouldn't dwell too long on heat pump efficiency lest it lead you to think about entropy and the inevitable heat death of the universe. Unless you like that sort of thing.
It won't work as well, because the refrigerant won't be that much colder, but efficiency over 200% is still possible in sub-freezing weather.
But of course you don't have any incandescent light bulbs … because of woke.
U.S. Geological Survey. Is a Powerful Quake Likely to Strike in the Next 30 Years?. 2023-04-17. pubs.usgs.gov.