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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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ChickenBig

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16/09/2023 8:54 am

Posted by: @cathoderay

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I suppose one way to do it might be to have five column grid and a pencil, and mark off on a scale of 1 to 5 how comfortable one felt every hour.

Perhaps this is what the Octopus 'Cosy Pods' room sensors are all about; gather data on air (and IR) temperatures and humidity and ask for feedback (or in the absence of feedback interpret that as approval for the current operating conditions). Combine that with a bit of server-driven experimentation and you've got yourself a way of determining personalised human comfort levels. I feel there is a startup in there.

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cathodeRay

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16/09/2023 7:27 pm

Posted by: @derek-m

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Do you go out among the 'sick' people?

I did, before I retired. But then so too did Jesus, before he got retired. Minister: 'CMG?' Civil Servant: 'Call Me God. And KCMG is Kindly Call Me God.' Minister: 'What about GCMG?' Civil Servant: 'God Calls Me God.'

Midea 14kW (for now...) ASHP heating both building and DHW

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newhouse87

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18/09/2023 6:16 pm

does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

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Fazel

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18/09/2023 6:31 pm

Posted by: @newhouse87

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does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

2000 joules/m3 air/degree C

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newhouse87

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18/09/2023 6:34 pm

Posted by: @fazel

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Posted by: @newhouse87

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does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

2000 joules/m3 air/degree C

for a far less knowledgeable poster like me, in plain language as a %?

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Derek M

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18/09/2023 7:22 pm

Posted by: @newhouse87

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does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

It mainly depends upon the outside temperature and how hard your heat pump is working, but will probably be in the 5% to 6% range.

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JamesPa

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Topic starter 18/09/2023 7:24 pm

Posted by: @newhouse87

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does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

A deceptively simple and important question but not actually that easy to calculate (for the avoidance of doubt I don't think the previous answer was correct).

To get a good answer you would need to compare degree days (see degreedays.net) when the house is at 21, with degreedays when the house is at 22, in both cases for your location.

To do this you need to know the 'base temperature' for the house (at 21), which is (in essence) the outside temperature at which the house is warm enough to switch off the heating. This depends on comfort, other sources of heating in the house, including electrical equipment, cooking and of course people, and degree of insulation. Its often said to be 15.5 for the UK, based on a house temperature of 20, but this is a broad brush average.

So for example with a house temp of 21 its likely that the base temperature is around 16.5. Based on a location in the South East of England there were on average 2289 degree days on average each year for the past 3 years. If the base temperature is increased to 17.5 (for a house temperature of 22) then the average number of degree days over the same period is 2591, a 13% increase.

Thats very probably in the right ballpark unless you live in an exceptionally well insulated or an exceptionally poorly insulated house, or in a location where the climate is very different from South East England.

This post was modified 2 years ago 2 times by JamesPa

4kW peak of solar PV since 2011; EV and a 1930s house which has been partially renovated to improve its efficiency. 7kW Vaillant heat pump.

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Derek M

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18/09/2023 8:11 pm

Posted by: @newhouse87

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does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

Are you referring to instantaneous electrical energy increase or the increase over a year, since the two will probably be different.

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JamesPa

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Topic starter 18/09/2023 8:22 pm

Posted by: @derek-m

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Posted by: @newhouse87

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does anybody have idea how much extra electricity is used from having house at 22 instead of 21. Women are cold creatures. 10%?

Are you referring to instantaneous electrical energy increase or the increase over a year, since the two will probably be different.

Good question!

The total used over the year will be the sum (mathematically the integral) of the instantaneous, so on this interpretation they are same.

The _peak_ instantaneous (and thus the required system capacity) will be different though. The peak will increase much less than the total as it's proportional to inside temp - outside temp at the design OAT. Based again on South east of England, this is roughly 5% as opposed to roughly 13%

This post was modified 2 years ago by JamesPa

4kW peak of solar PV since 2011; EV and a 1930s house which has been partially renovated to improve its efficiency. 7kW Vaillant heat pump.

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Fazel

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18/09/2023 8:24 pm

10% could be a real ballpark

https://energy-stats.uk/vaillant-arotherm-weather-curve-information/

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newhouse87

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19/09/2023 8:57 am

@derek-m suppose instantaneous as in ever over a day period to keep house at 22 from 7am to 10pm, difference between 21 and 22 for the day kwh?

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newhouse87

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19/09/2023 9:01 am

@jamespa hmm, was thinking it was simple question with maybe not so simple answer. House newly built very well insulated. Monitoring the house at 21 and 22 on 2 different similar cold days would tell me as you said.

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