What it means
Once I could price any battery on a real year of data, I could ask what actually changes the answer. Buying a bigger battery does not. This page is the part of the project you could use even if you never care what a qubit is.
First finding
And that turns out to be the useful part.
On the summer weekday there is not one best plan. There are 2,448 of them, all costing exactly the same. I counted them rather than guessing, and then asked which decisions every one of them agrees on.
The answer is four: run the house off the battery in all four peak hours. That is it. All twenty other hours are a free choice. Whether you charge at midnight or at two in the afternoon changes nothing, because every off-peak hour costs the same.
So the value here is not in clever timing. A hardware timer captures all of it. On a tariff with two price levels there is nothing for smart scheduling to be smart about, which is worth knowing before paying for it.
The surprise
Savings climb with capacity, then stop dead.
How much it holds, at 2 kWh/hr
2 kWh
$0.48
4 kWh
$0.97
6 kWh
$1.45
8 kWh
$1.93
10 kWh
$1.93
12 kWh
$1.93
16 kWh
$1.93
20 kWh
$1.93
How fast it empties, at 10 kWh
0.5 kWh/hr
$0.48
1.0 kWh/hr
$0.97
2.0 kWh/hr
$1.93
2.5 kWh/hr
$2.42
5.0 kWh/hr
$2.42
Savings rise in a straight line to 8 kWh and then go flat. 10 kWh, 12, 16 and 20 all save exactly the same $1.93 a day. Every point was re-solved from scratch, not read off a curve.
The reason is the first finding again. The expensive hours last four, and the battery can only push out 2 kWh in each of them, so 8 kWh is everything it can physically deliver before the window closes. The last 2 kWh of a 10 kWh battery never moves.
Speed runs out in exactly the same way. Look at the second table: going from 2.5 to 5.0 kWh an hour earns nothing at all. Once a battery can empty itself inside the expensive window, going faster has nothing left to move. Whichever number you increase, it stops mattering as soon as it passes the other one.
What actually earns anything
the smaller of what it holds
and what it can push out
A 10 kWh battery that pushes out 2 kWh an hour, over four expensive hours, can only deliver 8 kWh. The other 2 kWh may as well not be there.
Does it hold elsewhere?
Colorado's four-hour peak was the only real one available, so I built the others.
| Peak length | Window | Rule predicts | Measured knee | Daily ceiling |
|---|---|---|---|---|
| 3 hours | 6 to 9 PM | 6 kWh | 6 kWh | $1.45 |
| 4 hours | 5 to 9 PM | 8 kWh | 8 kWh | $1.93 |
| 5 hours | 4 to 9 PM | 10 kWh | 10 kWh | $2.42 |
| 6 hours | 3 to 9 PM | 12 kWh | 12 kWh | $2.90 |
The knee lands exactly where the rule says every time. Across 56 separately solved cases there were zero mismatches. So this is a property of how two-price tariffs are shaped, not a quirk of one Colorado bill. Count the expensive hours on your own bill and multiply by how much the battery pushes out in an hour.
The practical part
Both of these are upgrades to the same battery, priced over a full year on the real tariff.
A battery that empties 25% faster
Same size, quicker out. 2 to 2.5 kWh an hour.
+$113.93/yr
A battery twice the size
Twice the storage, same speed. 10 kWh to 20 kWh.
+$0.00/yr
Doubling the size earns nothing, and going 25% faster earns 25% more. But that second half only holds up to a point. Speed is worth buying only while the battery still cannot empty itself during the expensive hours, and past that it is as dead as extra size. On this battery that limit arrives at 2.5 kWh an hour, and the table above shows 5.0 earning exactly the same.
So neither number is the right one to shop on. They only mean something together, and what you want is them matched: a battery that can just empty itself over the expensive hours, and no more of either. Count the expensive hours on your bill, divide the size by that, and you have the speed worth paying for. Ten kWh over four hours wants 2.5 kWh an hour. Buying past the match on either side is buying something that will not show up on your bill.
The uncomfortable part
$455.72 a year against what these systems cost installed.
| Installed cost | Standard speed | 25% faster | Inside a 10-year warranty? |
|---|---|---|---|
| $5,000 | 11.0 yr | 8.8 yr | Only at 2.5 kWh/hr |
| $7,000 | 15.4 yr | 12.3 yr | No |
| $9,000 | 19.7 yr | 15.8 yr | No |
| $11,500 | 25.2 yr | 20.2 yr | No |
| $14,000 | 30.7 yr | 24.6 yr | No |
At a typical installed cost of about $11,500, the battery pays for itself in roughly 25 years against a 10-year warranty. It would have to outlive its guarantee two and a half times over. Only the cheapest install with the faster battery, at 8.8 years, clears the warranty at all.
Right-sizing moves you up this table, which is the practical use of everything above. An 8 kWh battery earns the same $455.72 a year as a 20 kWh one, so the smaller one should cost less for identical savings, and a cheaper install is a shorter payback. The rows are not fixed points; the sizing rule tells you which row you can shop into.
What these figures assume
The fair conclusion
On a two-price tariff, moving power from cheap hours to expensive ones does not pay for the hardware within the life it is guaranteed for. That is what the arithmetic says and I am not going to dress it up.
But capacity past the knee is not wasted, it is just not buying savings. Every extra kWh is more hours of power in the house when the grid is down. A cost-minimizing schedule has no term for the lights staying on, so this model cannot price that, and not being able to price something is not the same as it being worth nothing.
So the savings have a ceiling, and I can state it exactly. What backup is worth is yours to decide. The two get sold together as one number, and they are different purchases.
Limits
One house, one tariff, one year. The shape should carry to any two-price tariff, because it follows from how those tariffs are built. The dollar figures should not be carried anywhere.
Weekend days on this tariff have one flat price and save $0 at any size or speed. No amount of battery helps when there is no price gap to work with.
Where these numbers come from
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