House Thermal Inertia and Roomstat Setback (some cautionary notes)

Hardware Heatpump
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It may surprise heat pump owners just how much energy is required to reheat a house after any night-time setback, and what effect this has on heat demand from the HP.

To illustrate this, here’s a worked example, based on the following simplifying conditions (you can amend/refine the calculations below to suit your own situation):

  • Your average required indoor temperature = 20degC (some rooms warmer, some rooms cooler)
  • The outside temperature = 0degC (assumed constant in this example)
  • Your estimated house heat loss at these temperatures = 5kW (this may be from a survey, or from your own operating experience)
  • You have an 8kW heat pump
  • Your emitters are capable of transferring 100% of the heat pump output at the weather compensated (WC) target LWT

First, you have to estimate the house thermal inertia (measured in kJ/K). This is the heat content of the entire house, including the boundaries (walls/floor/ceilings etc.), and furnishings and other house contents (including occupants, and even the air). You can do this with a once-off test in which you measure the fall in house temperature over a known time period without any heating, at a known (preferably constant) outdoor temperature. For this example let us assume that you establish one night that with the heating switched off, your house cools from 20degC average to 16degC average over 8 hours when the outside temperature is 0degC for the whole of the test.

You can estimate your thermal inertia from (m.Cp) = Q / DT where Q is the house heat loss (in kWh) and DT is the house temperature difference between the start and end of the test (in degC). Actually, the heat loss reduces proportionately as the house-to-ambient temperature difference falls. If this is 5kW when the house is at 20degC average, it will be 16 / 20 * 5 = 4kW when the house reaches 16degC at the end of the test. This gives an average heat loss of (5 + 4) / 2 = 4.5kW, and so the calculated (m.Cp) is 8h x 4.5kW / (20 – 16)degC x 3600s/h = 32400kJ/K. (Strictly, DT does not vary linearly with time as the house cools, but the assumption of linearity gives a good approximation.)

After setback finishes each morning, your heat pump will have to supply not only the ongoing heat loss, but also the “sensible heat” needed to re-warm the house fabric from your night-time setback – let’s assume that this is 2degC for this study (i.e. 18degC average house temperature) – back to 20degC in a reasonable time (occupant comfort considerations).

Assuming that your heat pump delivers exactly 8kW – not always true in practice of course – and that the outside temperature remains at 0degC, you can calculate how fast the house will warm up using the thermal inertia calculated above:

  • With the house at 18degC, heat loss = 5 x (18 / 20) = 4.5kW, leaving 3.5kW available from the heat pump for house warming. At (m.Cp) = 32400kJ/K, the house temperature will rise at 3.5kW / 32400kJ/K x 3600s/h = 0.39degC/h.
  • With the house at 20degC house, heat loss will have risen to 5kW, so only 3kW is available for sensible heat, and the house temperature will rise at 3 / 32400 x 3600 = 0.33degC/h.
  • The average house temperature rise rate is thus (0.39 + 0.33) / 2 = 0.36degC/h (the above comments on non-linearity apply here too, but this figure would be a good approximation).
  • So to recover the 2degC temperature setback it will take roughly 2 / 0.36 = 5.5h of heat pump operation at maximum output. If you start your heat pump at 06:00, your house won’t be back up to your required temperature until 11:30 if it is 0degC outside.

If there is less margin between heat pump duty and house heat loss than in the above example, the capacity for overcoming setback will be even less. For example, if your normal heat loss is 6kW (rather than the 5kW used above), but you still install an 8kW heat pump, it will take 7.7h to reheat your house from setback, again at full heat pump output.

Note that the above calculation assumed that your heat pump would be able to run continuously at full output during house reheating. If your weather compensator setup causes heat pump cycling, you will obviously get less total heat and thus even longer reheat times. (Cycling may occur if your WC target LWT is too low for your emitters to transfer the necessary heat, in which case LWT will reach WC setpoint and the compressor will slow down or even stop – not what you want if you are trying to extract maximum heat to reheat the house.)

To summarise, installing a heat pump where the nameplate capacity is well-matched to the maximum house heat loss may minimise the inefficiencies of cycling, but may limit your scope to operate a setback (timing and magnitude) at cold ambient conditions.

(The above notes do not address the economics of setback. Running a heat pump at maximum output for several hours per day to re-heat a house may or may not cost less than the savings from not operating it during the setback period, a matter further complicated by attractive off-peak TOU tariffs. You would need to assess the best operating strategy for your own situation and cost control strategy – some folk aim for a maximised CoP, others for a minimised electricity bill. These are not the same thing, of course.)

Any comments, please?

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You are very smart Sarah, smarter than me.

I have always found that running my heat pump continuously at the minimum required to keep my house at a relatively constant temperature uses not only the least amount of electricity but also gives me the best efficiency.

Not very scientific, but then I don’t think science works that well with what are pretty crude machines.

Cliche, but I have always found low and slow is best in all aspects for a heat pump in my house.

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This is a very good summary. I never looked at the setback from the feasibility standpoint before, so thanks for that. For reference, I’m also putting Michael de Podesta’s excellent article on setback here:

He specifically looks at the efficiency of using a setback, which complements your post nicely.

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Thanks @matt-drummer, but…

  1. …not so. You see what is really there, I see what ought to be there, based on what I learned 50 years ago :face_with_diagonal_mouth:.
  2. As you often say, Daikins are not like other HPs (so much so, you make me wonder if they even obey the 2nd Law of Thermodynamics…) and it doesn’t surprise me that “low and slow” suits them - and you - perfectly.
  3. Just to throw in one more curved ball. I’ve calculated that on my HP (an 8kW Samsung) that the best efficiency point (BEP - where you get the most compressor kW energy output per kW compressor power requirement) occurs at or near synchronous speed (50Hz inverter frequency) which corresponds to nameplate Outdoor Unit heat duty. At lower (or higher) speeds, the efficiency drops off. So - perhaps counterintuitively - I get more bangs for my buck when the compressor runs flat out, and running at a lower speed (as it would do if I ran “low and slow”) would actually cost me more electricity in 1 hour than would flat out for half an hour followed by stopped for the other half hour.

Life is so complicated…just hand me those headache pills…

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I still think you are pretty smart Sarah :slight_smile:

I too worked on what I thought would be there, but it isn’t.

And that is where the monitoring really helped along with @ColinS, @Marko_Cosic and @TrystanLea

And any others I forgot, sounds like an award acceptance speech, sorry!

I made the mistake of thinking that a 9kW heat pump had a reasonably wide operating range, little did I know that it wasn’t really a 9kW heat pump but a hobbled 16kW heat pump.

I then made another mistake in thinking that if I lower my flow temperature enough I will get the best efficiency, failed again!

Sadly , these things are a bit suck it and see, they are not entirely predictable.

But, we make the most of what we have and I can see, even comparing to others, that I use the same amount of electricity to generate more heat just by leaving it running.

Despite some issues, my heat pump is pretty efficient and could be much better.

However, I started with an aim of a SCOP between 3 and 4 and have nearly 5 so nothing to complain about.

On your topic though, it is pretty frustrating how these heat pumps are marketed and sold, it is not honest and transparent and there really isn’t enough information provided to make the correct choice.

I firmly believe that there is an ideal heat pump for every property but they won’t all come from one manufacturer as their ranges have limitations.

And that is the problem with Octopus who have chosen only to use Daikin up until now, a company that only really makes two sizes of heat pump.

The key, as you are saying, is finding out what gives the most heat for the least electricity.

And that is what I have always felt, a high SCOP and low energy consumption go hand in hand and are not mutually exclusive.

You write some great posts and are admirably smart in my eyes, so thank you.

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This is a really good summary.

It links well with the recent topic on oversized heat loss:
https://community.openenergymonitor.org/t/over-sized-heat-loss-over-estimated-design-temperatures/27795

If we have a truly accurate heat loss and design systems around that then there is very little flexibility for setbacks and heating back up. Most of these discussions centre on the cost/value of electricity as being static. But as we move to a more electric powered society and more renewable generation it seems very unlikely that will be the case.

Your post touches on the fact a night time setback may save power at a time when power is at its cheapest. An alternative would be a setback at peak time (say 4-7pm) when power is at its most expensive, do we need to be designing systems that have the headroom to be able to deliver their heating power is something less than 24h and have the ability to warm back up after a setback (or maybe do half of it beforehand by heating up a bit before the setback).

My anecdotal evidence from living with a system that has a bit more “sensible heat” capacity than your example (say 10kW heat pump for 5kW heat loss) is that the days with the heating switched off at night use less total energy than keeping a steady low and slow. The cost element however is complicated by 1/4 price electricity at night, and a battery which can cover some level of daytime usage. That combination can make the low and slow cheaper, even though it uses more total energy.

I’ve suspected this to be the case but have never seen hard facts about it. Do you have more?? I think many people’s intuition is that running things gently produces the most efficient results, perhaps from our experiences of driving. But in many industrial applications things are designed to be run at full power for extended periods of time.

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I played around with a set back of just 1°C via the Madoka schedule at midnight to the 4am cheap tariff start (Cosy).
That is enough to shut the heat pump off.
The house did not lose much in those 4 hours.
Around 0.7°C from our ideal downstairs temp.

Quite right, it took a very long time to build back up to the ideal temperature.

The consumption figures were not better for us with the set back.
The long burn to regain temp goes way beyond the 3 hours of cheap tariff and at seemingly quite high W usage.

Concluded that keeping the fabric of the building at a steady state is a much better thing for our property.
I could drop the flow temps quite a bit and that improves COP.
The bill decrease or increase is harder to spot (will take more data) what with different outside temps, what we do in the house playing in too - oven on for roasts, wood burner occasionally cos’ it’s nice etc.

Turning off avoiding the highest tariff period for 3 hrs 4pm to 7pm, well the jury is out on that one.

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Another point worth highlighting here is that when the solid mass of the building is warm, it emits heat into the interior, and feels warmer to the occupants. The rooms will remain warm for longer, and take less time to warm up if the temperature drops.

Whereas if the heating is only on periodically, it heats up just the air and the walls will remain cool and continue to suck heat out, requiring frequent bursts of heat during the “on” periods to keep the air warm.

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Another way to say this is: in order to get the full power out of the heatpump, the radiators will need to run hot enough to emit that power, which means a higher flow temperature, which means lower COP, which means higher cost per unit of heat.

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Hello that’s interesting, I have stone built house where the night setback is great due to poor insulation. Is it better possibly to have two small heat pumps rather than one large one, so the second one can only come in use to help with the setback? And reduces cycling
David

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In my experience, it’s cheaper and more comfortable to not have any kind of setback whatsoever.

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Picking up on this point…

Up until a week ago, I had been operating my heat pump flexibly on Octopus Agile, finding the most expensive 6 x 30min periods in the morning and afternoon and turning off for those, as well as pre-heating before as a function of ambient temperature. Invariably in the afternoon that period is 4pm to 7pm, but that may well not be the case in a world of lots of renewables, when there may well be afternoon peak periods when wind output can readily meet demand, then, flexibility will become key and a slightly oversized heat pump should give benefits (I’ve just been having this debate with some folk at DESNZ).

Why have I changed? As many of you will know, Agile has been super expensive for the last 2-3 months. When the price outside of that 4-7pm window was typically ~1/2 the tariff cap, it was clear that sacrificing some efficiency for flexibility was beneficial - there is no way that my heat pump was operating at half the CoP flexibly - in fact, I think only about 10% less efficient. Now that that the agile price outside of the expensive periods is only a few p/kWh less than the tariff cap, it no longer makes sense to be flexible (especially as I have an EV which can be charged much more cost-effectively now on an EV tariff, and I can reimplement my ‘low CO2’ charging algorithm :slight_smile: ).

I’ve actually switched from Octopus to Eon Next Drive as neither my charger (OpenEVSE) or car (Kia e-Niro) are compatible with Intelligent Go. The Next Drive tariff is ~25p/kWh 7.00am to midnight and 6.7p for 7 hours from midnight to 7.00am. I’ve now set up my heat pump to set back at 10.00pm (but only to 18C) and pick up again to 19C from 2am and 20.5C from 4.30am. At 7.00am I’m dropping the setpoint back to 19C (my normal daytime temp). So not much variation, but sufficient house thermal mass to mean that I avoid 4-5 hours of peak tariff operation in the evening and morning. (And by 9.00-9.30am when the heat pump typically kicks in again, I might have some solar gain or PV output). So in effect, I have up to 7 hours (my DHW starts at midnight and typically the heat pump stays on after to maintain 18C room temp) of 6.7p/kWh (including the period the heat pump is working hardest to pre-warm the house) and 7 hours of peak. If the heat pump were were working at constant power input over the whole period, my average tariff would be 15.85p/kWh, which is 4p/kWh better than I’ve been doing on Agile for the last few months.

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This response is not a quantitive analysis so I’ve appreciated your analysis. We have a 7kW Vaillant and a reference heat loss about 6->6.5kW (by various measures). We set back by just 1C from 22:30 and put back on @4am. It’s marginal on reduced total electrical consumption at 0C but makes the house cooler overnight. We’re onCosy so that makes sense for us. Usually it takes about 5hrs from 4am to recover the temperature when it’s ~0C outside, but the day is warming too.
Your analysis looks right to me (Physics degree but too lazy to calculate it).
I

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Shame there is not an easy way to remove set backs etc when outside conditions are making it hard for the heatpump to cope. (Also automatically enable emerson to heat dwh on cheaprate to free up heatpump for CH.)

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I expect with Cosy Tariff better to overheat by 1c or 2c in the afternoon cheaprate.

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Actually, I could do that. I’m using Home Assistant to change the setpoint on my Mitsi Ecodan because you can’t have it in autoadapt and have a schedule, so I could just override the setting if particularly cold outside, but I only ever let the temperature drop to 18C, and it’s never failed to regain 1C even when it was -6C outside last year.

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Thanks Sarah for another clear and well-reasoned post.

You’ve reminded me it’s not safe to assume a heat pump only ever needs to compensate for the heat loss from an already-warm building. The worst case scenario is re-heating from rather less than 18 degrees - e.g. after a winter storm brings down overhead power lines which take a few days to repair. Properties which are vulnerable to such power outages should take this into account when sizing their heat pump system.

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I suspect I’ve misinterpreted this but I definitely have schedules set for my two zones auto adapt setup. No setback for downstairs, two degrees for upstairs.

I’ve also flipped to EON from Octopus Go - same EV charger, not a compatible car and three extra hours overnight at a cheaper rate to charge the car and batteries. My FIT has been with EON since 2010 - super efficient these days - get paid about four days after submitting the quarterly reading.

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Interesting - I just looked at mine and see you can now have different temperatures at different times - that must be a firmware update I think. When I first had mine 3 years ago, I’m sure autoadapt was just on/off control. Even so, I wouldn’t have been able to do the Agile trickery without remotely setting setpoints!

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My Vaillant 7kwh just, or maybe not quite, meets the needs of our house at -3deg. 10kwh was marginal and large for where sited. Cop is not quite what I wanted, even after various tweaks. Better cop would clearly have given more output and so flexibility.

I tried time of use tariffs but found a noticeable cold point when sitting down during 4-7pm high price period - likely as outside temperatures also dropping.

Now switched to OVO heat pump plus so can run system continuously throughout 24 hours. The heating plan allows for slightly lower night (18.5) and then daytime (19) temps wiith higher in evening (20).

It’s early days but see that efficiency (cop) is very slightly improved but cost per day is significantly lower. Analysing last year’s usage suggests that OVO HP+ will be more expensive during summer, due to only applying to heat pump usage - rest of house on standard variable tariff. As heat pump use rises as a percentage then it becomes cheaper on a daily basis in mid October and on a cumulative basis in early February, ending year around 8% cheaper. This is calculated so we will see what true life brings.

Main conclusion is that each system and house needs is different. Lack of spare heat capacity on cold days and house demands means this analysis and conclusion works for me but maybe not others. Spare heating capacity on cold days gives flexibility where TOU tariffs may be appropriate.

My other measure is that on a very cold day if system were turned off and house cooled down then it would take 2-3 days to get back to temperature - so that’s not going to happen deliberately.

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