Heat pumps and on/off working - starting to quantify it

JamesPa · 2023-09-13T17:14:43Z

There has been much discussion on on/off working/nighttime setback in relation to heat pumps, but not much that is quantitative. @fazel and @derek-m have made some helpful comments in another thread and I have now started to think about it more quantitatively. I present an example of how one might assess the effect, it needs development and discussion but is a 'starter for 10' Worked example: Lets consider a 10kW heat pump fitted to a house which consumes 8kW when the OAT is 0C and the target IDT is 20C. Lets also assume that the emitters are radiators with a FT of 45C at 0C, and furthermore that we wish save energy by setting back/switching off for a maximum period of 9 hours (overnight) - eg from 10pm-7am. Lets consider what happens when the OAT is 10C. Lets further assume that the temperature drops by 5C during an 'off' period of 4.5 hours, when we switch it back on to get the house warmed up in time for 7am. Once we have worked through this example it will be relatively easy to change the assumptions. At OAT of 10C and IDT of 20C the load will be 4kW and the flow temperature required to deliver this will be 34.7C (applying the rule that emission from radiators is proportional to (deltaT rad-room)^1.3. At this FT and OAT we can typically expect to achieve a COP of 4 (as will become evident later it doesn't matter what the exact COP is for the calculation, but it does matter roughly what it is). During the on/off cycle the average IDT will be approximately 17.5C, so instead of losing 4kW the house will lose (on average) 3kW. Thus over the 9 hour cycle the house will lose 9x3=27kWh instead of 9*4=36kWh had we left the heat pump on. More importantly during the 4.5hour cool down period we will lose approximately half of this amount, 13.5kWh , and this is lost from the fabric so will have to be replaced to return to the state we started with. We will return to this shortly. However we don't pay for energy lost from the house, we pay for energy consumed by the heat pump. This is where it gets interesting as the amount of energy consumed by the heat pump depends on the control strategy during the recovery period. Control strategy 1 - forced recovery In this strategy we attempt, during the recovery period, to get the house back to the state it was when we first switched off the heat pump. This means bringing the house back up to 20C and replacing the 12.5kW we have lost from the fabric. To do this we will have to supply to the house, in addition to the heat loss during the recovery period (average 3kW), an additional 13.5kWh to replace the heat lost from the fabric. thus we need to supply on average 3+13.5/4.5 = 6kW to the house. The heat pump is perfectly capable of doing this, but the only way the radiators can emit that amount of energy is by raising the flow temperature during the recovery period to about 40C (40.04C to be precise). A heat pump that has a fixed WC curve wont do this but one that has room compensation might. This causes the efficiency of the heat pump to drop by about 10% (2% per degree is a good rule of thumb). So a heat pump which was operating at a COP of 4 will instead operate, during the recovery period, at a COP of 3.6. If we work through all of these numbers we find that the heat pump would have consumed 9kWh to deliver the 36kWh that would have been lost had we left the heating on, and 7.5kWh to deliver the 27kWh that is lost if we switch the heat pump off, a saving of only 16% in energy consumed as opposed to the saving of 25% in energy delivered/lost. With these figures its still a saving so still worthwhile, but with other figures, particularly as the OAT drops, the saving becomes much smaller. Some exploration of the 'space' with an excel model is indicated (my next step). Control Strategy 2 - natural recovery In this strategy we don't alter the flow temperature during the recovery, it remains at 34.7C. Heat pumps operating pure WC will do this. However the rads will still deliver to the house more energy than that needed to maintain the steady state and this the temperature will still recover, albeit more slowly because a) the rad-room delta T is higher (but gets smaller as the house starts to heat up) and b) the house to OAT delta T is lower (but gets larger as the house starts to heat up) I dont have a formula for this (I think its logarithmic/exponential) but its easy to work out in a spreadsheet, which I have done. Putting all of the above assumptions in the house will reach about 18.9C after 4.5 hours, and will get to 19.8 after 10 hrs. The saving in energy is 27/4 vs 36/4, 25% but at the expense of a bit of a loss in comfort, because the house is roughly 1C under temp at the end of the recovery period. This may be tolerable or alternatively after experiencing it for some days the owner might nudge the WC curve up to compensate, increasing FT by about 1-1.5C, causing a 2-3% penalty on efficiency for the entirety of the day. However thats a ...

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guthrie

(@guthrie)

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28/12/2023 12:23 pm

Posted by: @cathoderay

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The modellers are determined to settle this question using models, in much the same way that alchemists sought to turn base metals into gold by using dark magic, but my own inclination is that the only satisfactory answer will be an empirical one, even if such an approach has the problem that no two days are the same, in other words, I can't do a controlled experiment, instead I have to rely on observations.

I was browsing older threads and found this, seeing as it is the quite holiday time between holidays and it is horribly wet and windy out there, I have nothing better to do.

Basically alchemists did not use dark magic. There's no evidence they did or tried to; surviving texts don't say that. The main accusation of using demons came from a Spanish Inquisitor in the late 14th century, but even at the time they thought he was a bit of an extremist.

The aim usually was to use knowledge of natural processes to change the constituents of the metals in question in order to make them into gold or silver. Of course one of the reasons alchemy never quite made it as a serious university topic was that people greatly disagreed on whether it was possible or not in the first place and there were arguments for and against it. Ultimately it failed to do what was promised so was gradually abandoned in favour of it's offspring, chemistry.

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Derek M

(@derek-m)

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28/12/2023 1:41 pm

Posted by: @guthrie

↑

Posted by: @cathoderay

↑

The modellers are determined to settle this question using models, in much the same way that alchemists sought to turn base metals into gold by using dark magic, but my own inclination is that the only satisfactory answer will be an empirical one, even if such an approach has the problem that no two days are the same, in other words, I can't do a controlled experiment, instead I have to rely on observations.

I was browsing older threads and found this, seeing as it is the quite holiday time between holidays and it is horribly wet and windy out there, I have nothing better to do.

Basically alchemists did not use dark magic. There's no evidence they did or tried to; surviving texts don't say that. The main accusation of using demons came from a Spanish Inquisitor in the late 14th century, but even at the time they thought he was a bit of an extremist.

The aim usually was to use knowledge of natural processes to change the constituents of the metals in question in order to make them into gold or silver. Of course one of the reasons alchemy never quite made it as a serious university topic was that people greatly disagreed on whether it was possible or not in the first place and there were arguments for and against it. Ultimately it failed to do what was promised so was gradually abandoned in favour of it's offspring, chemistry.

You are indeed correct, while Alchemy may have received a bad press, probably because it was feared by the then church hierarchy, Chemistry is now fully accepted by modern society.

The main problem with using any form of simulation is first identifying the main variables which affect the process, and then measuring them with the required precision for the end results to be accurate and meaningful.

I believe that the first objective has been achieved, although I do keep adding more capability to the spreadsheet as more knowledge becomes available. The second part of the requirement is gradually improving, but does need more data from different sources.

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