Great data.  I look forward to being able to generate some like it myself one day.

Posted by: @mike-patrick

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I've also shown the best fit line but in fact I think the distribution of results would be better explained by a curve.

I might be getting carried away in my excitement, but it looks from the plotted data like there's a non-zero lower asymptotic value (which makes sense as there will be a non-zero lower limit on the energy consumption), so an exponential with an offset (y=a+c*exp(b*x)) would probably give a good fit.  Polynomials aren't so useful for this type of response.

You can select an exponential fit in Excel after adding the trend line, which should increase the R-squared value a bit, but this doesn't include the offset, so it won't be a perfect fit.  Unless you have access to some more capable non-linear curve-fitting software, a quick fix would be to estimate the lower limit (say, from the mean of the values above 15C) and subtract this from all of the values before refitting the curve.

I'll be quiet now.

You are perfectly correct, there is a non-zero element which needs to be considered. It is due the the 'human infestation' along with their toys and gizmo's which often tend to produce thermal energy inside the thermal envelope of the home.

@mattc Here's the same chart with the Excel exponential line added.

I could subtract the background 8-10 kWh per day that is used when the ASHP is off and we are away but wouldn't that just drop the whole curve by that number of units. As we don't have separate metering of the pump, yes there is also some daily variation in total kWh due to daily activities, with cooking probably being the major one. Anecdotally I'd say that also varies seasonally - with more baking during the winter (hot meals) than the summer (mostly salads).

It's interesting how these exercises answer some questions but produce more as well. Having just acquired a weather station, with the ability to monitor the outside humidity, I wish I had been collecting that data too over the last 3 years. I've seen during the recent cold spells what a big difference it makes to the kWh. On low humidity cold days the ASHP is much less likely to go into a defrost cycle, with the resultant lower kWh - maybe as much as 20kWh compared with similar temperatures on a high humidity day.

Mike

This is precisely why it is not possible to predict Power Input or Power Output, with any degree of accuracy by merely using outside air temperature variations. There are many more variables that need to be taken into account.

Posted by: @mike-patrick

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I could subtract the background 8-10 kWh per day that is used when the ASHP is off and we are away but wouldn't that just drop the whole curve by that number of units

Yes.  That would just drop the curve on the graph, so you'd have to re-label the axis to compensate. The idea of subtracting a constant from the results is just a sneaky trick that I hoped would fool the software into producing a better-fitting curve.  However, after trying it out, it turns out that Excel won't fit the exponential curve in the presence of negative or zero values, so unfortunately it won't help us (I suspect it's just log-transforming the y variable and using linear regression, rather than using a proper non-linear algorithm).  The best option would be to fit the appropriate curve using some more capable software - I'd be happy to give it a go if you don't mind sending me the data - or I could point you to some software if you prefer to do it yourself.

To all Forum members and others.

Could I please ask any forum members or guest who have received advice to spend a little time and report back upon the quality and helpfulness of the advice received.

Many thanks in anticipation.