I hope that the above makes sense.

Thanks for such a detailed description in words. It really does help my understanding of what you are doing. 

How can this be a coincidence?

It is certainly interesting that the numbers should be so similar. Looking at the last week's use, to 0700 yesterday (Monday), it is still in the same ball park, 1.13. I am currently taking daily readings from the external meter, and will post results once I have a weeks data. It will be interesting to see how the current cold weather affects things.  

I've had success with this £6 sensor attached to a Raspberry Pi

Yes, I came across Raspberry Pi solutions, but it means adding a whole new layer of complexity which I think I could manage technically (can solder without burning holes in things), but I do like simplicity. The modbus setup I have is one cat5e cable connected via a RS485 to USB adaptor to a USB port which also supplies the voltage needed to run the XY-MD02 sensor, with the Midea wired controller (and any other sensors I may add) daisy chained to the modbus cable. Python's minimalmodbus module then collects the data. It is simple robust and reliable.

The XY-MD02 sensor (paid £11 on ebay) is about 3" x 2" x 1" and looks like this: 

As you can see, it is clearly not weatherproof, and even direct sunlight could I suspect cause false readings. I did think about some sort of cowl for it, but again it may lead to aberrant readings if there isn't enough free flow of air. Finally, after yet another search online, I have come across a couple of 5V modbus enabled temperature/humidity sensors that claim they are waterproof to IP67. They are either obviously from China, or likely from China, given the delivery times, but one way or another I'll get one and hook it up. I will then - hopefully - have the true OAT.

If you wish I will post a copy after I have updated for the OHS capability.

Oumefar Digital Temperature Sensor Module Board Kit DS18B20 Electronic Components with Waterproof Stainless Steel Probe for Raspberry Pi https://amzn.eu/d/hzGTum7

The Pi of course has to be indoors (and you need a Pi or similar GPIO device to attach it to), but if you have a garage or shed with power you can put the Pi inside and run the probe outside under the garage door or whatever. That's if you enjoy DIY'ing this stuff and would rather not spend £££ on a waterproof temperature logger.

@derek-m I think I've used your spreadsheet in the (long) past but haven't seen a recent version. I'll go have a look when I get some time this week.

Re the 1.18 correction figure. I have a completely different pump (Viessmann) and have a well insulated property with underfloor throughout. I have a meter that records the heating and hot water, including all circulation pumps, in addition the heat pump has its own meter. All my data is from manually recording the values on a daily basis. For the entire year (2023) my total use is 4033 Kwh, the heat pump meter gives 3410 Kwh, the difference is 1.1826. How can this be a coincidence? if i take a 2 month figure in the heating season, Nov and Dec 23 i get 1128 and 993, a difference of 1.1359, a 5 month figure in summer with no heating is 347 and 276 a difference of 1.26. So with me the hot water gives a bigger difference maybe because the pump has to work hard to get to the higher temperatures, however in summer the heating circulation pumps are all off.

Well done. It looks like you are getting there.

If I am understanding your formulas correctly, they should produce somewhat similar results to those from the spreadsheet simulator, though there appears to be some differences, since I could only achieve an energy saving over 20% by failing to fully recover the heat balance over the 24 hour period.

I don't know if you have looked at the spreadsheet, but it may be useful to do a comparison, to see if my philosophies are missing something, or you need to further develop your work, or possibly both.

The spreadsheet tries to simulate both the home and the heating system, so it requires some initial information about the home. The calculated heat loss needs to be entered along with the relevant OAT and IAT. Next is the total capacity of the heat emitters at the standard reference temperature. Followed by a desired heat pump Delta T. The final parameter is an estimation of the thermal capacity of the building, which dictates how long it takes to warm up and how quickly it is likely to cool down.

I have tried to develop a type of universal simulation spreadsheet, that is not limited to one specific home, or one make or model of heat pump, but can be used with any, provided that manufacturer's data tables are available, and the required information about the home is also available.

Obviously all the above initial parameters can be changed by the user, which enables experimentation (or as CR likes to call it, 'whatiffery', which I think is a good description) to be performed, such as what would be the effect of increasing insulation levels to reduce the calculated heat loss, or what would happen if larger heat emitters are installed. It should even be possible to simulate the effect of changing to UFH with a large concrete slab, and thereby increasing the thermal mass of the building.

The main limiting factor will be how accurate is this initial data.

The main work is done within the sheet I named 'playroom', which is where the hourly values such as OAT and WC Offset can be entered, to produce the predictive results. The playroom is also where the WC curve settings are entered and can be varied to see the effect. Specifically for CR's system I also added a PHE DT parameter, which can be disabled by entering a value of zero. I have also added a Other Heat Source (OHS), which is to account for human activity within the home such as cooking etc. The WC curve settings are straightforward, with the problem areas being a measurement of the temperature drop across a PHE, if one is installed, and quantifying the effect of human activity, which in milder weather conditions could be providing 10% or more of the required thermal energy to keep the home warm. I have suggested removing the 'human infestation', for scientific purposes of course, but have not had much success in convincing anyone. 😋 

I don't have time to go into great detail, so I will give you a quick overview and you can then ask any questions you wish.

I have tried to simulate, as closely as possible, how I presume a heat pump operating in WC mode would perform. Calculations are made at hourly time intervals, with the ending values of the previous hour being the starting parameters for the present hour.

From the OAT value for each hour and the WC curve settings, the required LWT for each hour is calculated. The WC Offset can then be added to or subtracted from this value.

Using this LWT value and the OAT value, the predicted COP value is extrapolated from the manufacturer's data tables.

The Energy Supply value is where I think that our approaches differ, with this value being calculated from the LWT, any temperature drop across the PHE, the average water temperature at the heat emitters, the average IAT during the hour, with reference to the total capacity of the heat emitters. In basic terms, the maximum thermal energy that the heat emitters can emit under those operating conditions.

The Power Input (PI) is a simple Energy Supply divided by COP calculation, which matches quite closely the PI value extrapolated from the manufacturer's data tables. It would appear that this value is virtually the V x I value without any auxiliary power included.

This discussion has been very useful, because the addition of the OHS parameter now means that I will need to re-assess the Energy Supply equation to account for the reduction of thermal energy required from the heat pump and its effect upon PI.

The Energy Demand is the standard IAT minus OAT times the heat loss per 1C from the calculated heat loss. 

The Energy Balance is the difference between Energy Supply and Energy Demand.

The Energy Balance value is added to, or subtracted from, the Thermal Capacity value, from which is derived the new IAT value.

The process is then repeated for the next hourly period, but because there are circular references, it is necessary to enable iteration, which recalculates the whole worksheet until a stable result is obtained, or the present limit of 100 iterations has been reached.

I hope that the above makes sense.

If you are able to take temperature measurements independently of the heat pump itself, from a different side of the building, away from the cold well

I have thought about how to do this a few times. The problem is finding a modbus enabled sensor that can run off USB voltages and is weatherproof. The indoor sensor I have works fine, and I could get another one - but it isn't waterproof, very far from it, and making it waterproof will inevitably insulate it from the environment, and compromise it's ability to get an accurate OAT reading. So far, I haven't come up with an answer!