"Best to leave heat constant" is a convenient untruth
Convenient because it means always coming home to a warm house, and shrugging off the heating bill as "just what it costs".
I am having trouble finding the actual data that would support this conclusion.
Because it's horsepuckey.
Heat transfer is pretty simple here: What is the difference in temperature between inside and outside wall? 20F? 40F? 60F difference? Your heat losses will be proportional to that number. You'll lose twice as much heat at a 40F difference than a 20F difference, and therefore require twice the make-up heating. (or A/C if that's what we're doing today).
That means if you allow interior temperature to move closer to outside temp while you're not around, you will spend less on HVAC costs. That's a hard fact. Some people have some arm-waving rationalization for why it's equal either way because the unit will have to work harder when you turn it back on; no, that's not true. Closing the temperature gap indoor vs outdoor for that time results in real and proportionate savings.
But there are a couple of wrinkles to this.
HVAC does NOT run most efficient at full power.
This calculation runs counter to the prevailing wisdom surrounding mini splits, leading me to conclude either (1) the prevailing wisdom is just wrong or (2) something is wrong with this analysis.
Both are true.
Historically, Americans have used dog-simple "BANG-BANG" thermostatic controls: At a setpoint BANG! the system turns on and runs at 100% max power. At the limit point BANG! it shuts off. It's cheap, it's easy to understand, and it's not efficient. Take furnaces.
- Dumb old bang-bang furnaces deliberately keep the end of the heat exchange hot enough to assure condensation does not happen and the exhaust remains plenty hot - so it will carry itself up the flue on the "hot air rises" principle.
- Modern 95% gas furnaces throttle-adjust to a fraction of max power, and run continuously. That means instead of their heat exchanger being right-sized, it's massively oversized for the low power they're running at. The direct result is the heat exchanger does a much better job extracting heat energy from the exhaust - even to the point of condensing the water vapor in the exhaust - that's 1000 free BTUs per pound of water condensed!
The downside is the exhaust is barely warm - cool enough it can use a PVC exhaust pipe! Hot air rises but this doesn't - and that means it must use a blower to push the exhaust up the stack. That blower only takes a few watts of electricity, but buys you thousands of free BTUs that you were blowing up the stack before.
With heat pumps, if you run at max power, you need to pull a lot of heat through that outside unit. That means you're running at a much sharper temperature difference from outside - in heating mode, that means much cooler, and that means more icing, and that means more defrost cycles, which are a total loss. You are better off running it at low power, keeping your outside coils above 32F so you don't get icing.
I am having trouble finding the actual data that would support this conclusion. For example, I saw that the coefficient of performance of a mini split varies by about a factor of 2 from "full throttle" to "low throttle". If we assume that is true then that would suggest that if the mini split is expected to be on 25% of the time at full throttle and off 75% of the time as opposed to being at minimum throttle the entire time the total energy consumption would still be lower cycling, as opposed to remaining continuously on.
That's where you messed up the math. You presumed the heat pump draws the exact same amount of power at full throttle as low throttle. Say your laptop has a 140W power supply. No doubt if you plug in with a battery at 20% and then load up a high-demand game at 120 FPS, it's pulling 140W. But what about when it's at 100% charge and you're checking email? Far less than 140W. 20W perhaps.
In similar fashion, the power draw of the mini-split varies. It's more at 100% obviously. Let's say it's a 4000W unit with A COP of 3 at 100% power, so 40,000* BTU/hr on the hour you run it, and 25% duty cycle so only running 1 out of 4 hours. Your average HVAC load is 10,000 BTU/hr. You run 4000W 1/4 the time, so 1000W average. Agree?
But instead, you run the unit continuously - 1/4 BTU/hr, and 100% duty cycle. At this low power, you have a COP of 6. So 10,000 BTU only requires 500 watts**. So you have 500W average power. Double the efficiency, just like the COP data said.
* 4000 watts x 3.4 BTU/hr per watt x 3.0 COP = ~40,000 BTU/hr.
** 500 watts x 3.4 BTU/hr per watt x 6.0 COP = ~10,000 BTU.
And utility time-of-day rates throw a wrench into it
Thanks, Alec from Technology Connections for completely confounding all the above logic.
Alec says if our house insulation is tight, maybe we're barking up the wrong tree here. We've been holding out that there's some sort of "win" for holding the house at a CONSTANT temperature*. What if that whole concept is just dumb? What if it's smarter to gamify the temperature we keep it at, to best exploit utility rates or locally generated solar, or just our personal comfort?
Solar: Suppose you have 1000W of grid-tied solar, and you don't have a net-metering tariff. That means you're selling all your solar from 7AM-4PM to the power company for 2 cents a KWH, then at 4PM when your air conditioner really has to start working at the same time as everyone else's, hence the peak-hour demand rates of 32 cents a kWH - or 60 cents in California, no joke! Wouldn't it be better to recapture that solar power locally by running the heat pump at 1000W speed and say, 5.5 COP when you'd otherwise nearly waste that solar? Yes, you're overcooling the house and so what? IT'S FREE - you're saving 30 cents a kWH on the power used!
So anyway, questions like COP, while still important, pale in comparison to considerations like efficiency at low power, and the benefit of time-shifting and using the house as a thermal storage battery.
