Posted by: @jamespa

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However others have said that 5C

The lower the DT the higher the flow rate.

The lower the DT on the heating water side, the hotter the average temperature of the heat emitter, so the the heat emitter can be smaller.  You did mention this. = cheaper.

The higher the flow rate the more noise.

The higher the flow rate the higher the heat transfer coefficient in the plate exchanger in the ASHP so the smaller the plate can be = cheaper.

The higher the flow rate the easier it is to get the flow to split equally at t junctions, because the flow will be be in the turbulent regime at all points in the system.  Which makes the pipework installation easier, in theory, therefore faster to install therefore cheaper.

If the plate exchanger is too small it might not be able to condense all the refrigerant so that could lead to energy being wasted over the depressuring valve.

Just some random thoughts

Bob

(my typing is really bad tonight, i hope my ramblings make some sort of sense)

After mulling this over for a while, I have decided to have another stab at answering the question: do the two samples, setback days and no setback days, come from the same population ie there is no real difference between then, they just appear to be different, or from different populations ie in some material way, they are different.

This is the original plot of all the data:

Visually, the two datasets do appear different. Mean daily energy in (kWh) is also different (stats done in R, df_sb is the setback date, df_nosb is the no setback data):

> mean(df_sb$htg_24h_kWh_in)
[1] 21.89719
> mean(df_nosb$htg_24h_kWh_in)
[1] 37.27308

But there is a problem:

> mean(df_sb$amb_24h_mean)
[1] 10.17582
> mean(df_nosb$amb_24h_mean)
[1] 8.25463

The mean daily ambient temperature was lower during the no setback days. This means we have no way of knowing whether the setback savings happened because (a) the ambient temp was warmer, (b) the setback itself reduced energy use, or (c) a combination of the two (or frankly possibly something else, though that seems unlikely).

The histograms for the mean ambient temps also show they are clearly not the same: 

In an attempt to fix this, I have edited the full data set (the one with both setback and no setback days) to retain only matching pairs, in a manner that might be loosely akin to a matched case control study. I matched on daily mean ambient temperature, keeping only rows where an adjacent opposite setback row had the same daily mean ambient temperature, with a tolerance on 0.1°C. The data ends up looking like this:

2023-12-16T12:01:01	8.1	37.152	0
2023-11-16T12:01:00	8.1	26.957	1
2024-02-28T12:01:01	8.4	33.484	0
2024-03-27T12:01:00	8.4	23.999	1
2023-11-07T12:01:01	8.6	24.874	1
2024-01-04T12:01:00	8.7	33.256	0

The first column is the datetime stamp (days run noon to noon), the second the daily mean ambient temp, the third the total kWh in for the day and the fourth is setback 0 = no, 1 = yes. The first two rows shown are matched on 8.1, the next two rows on 8.4 and the last two rows on 8.6/8.7 (within 0.1°C). This reduced the data set from 199 rows to 85 rows, quite a reduction, but still a usable sample size.

The daily mean ambient temperature are now much closer and the histograms appear pretty much the same (the _m suffix denotes matched data):

> mean(df_sb_m$amb_24h_mean)
[1] 9.685714
> mean(df_nosb_m$amb_24h_mean)
[1] 9.627907

But the difference in mean energy use remains:

> mean(df_sb_m$htg_24h_kWh_in)
[1] 23.62371
> mean(df_nosb_m$htg_24h_kWh_in)
[1] 29.38584

And the scatter plot still suggests samples from different populations:

The net effect of all this is to control for daily mean ambient temperature. Going back to the epidemiological case control study analogy, for each case (a setback day), we have a matched (on daily mean ambient temperature) control (a non-setback day).

We can now run some stats on the matched data set. I have used something called the two sample Kalashnikov-Stalin Kolmogorov–Smirnov test which is a non-parametric (samples do not have to be normally distributed) test for whether two samples came from the same distribution or not. We get a p (probability) value for the null hypothesis that the two samples are drawn from the same population: the lower the p value, the less likely it is that the two samples came from the same population. 

First, lets compare the daily mean ambient temperatures (using R again):

> ks.test(df_sb_m$amb_24h_mean, df_nosb_m$amb_24h_mean)

Exact two-sample Kolmogorov-Smirnov test

data: df_sb_m$amb_24h_mean and df_nosb_m$amb_24h_mean
D = 0.043743, p-value = 1
alternative hypothesis: two-sided

That's encouraging, the matching seems to have worked (p-value = 1, the two data sets have matched ambient temperatures distributions).

Now the daily kWh use:

> ks.test(df_sb_m$htg_24h_kWh_in, df_nosb_m$htg_24h_kWh_in)

Exact two-sample Kolmogorov-Smirnov test

data: df_sb_m$htg_24h_kWh_in and df_nosb_m$htg_24h_kWh_in
D = 0.40975, p-value = 0.001152
alternative hypothesis: two-sided

This is a very low p-value (way way below the conventional 0.05 value, or even the tighter 0.01 value) which tells us that it is extremely unlikely that the samples come from the same population, or, in plain English, they are different.

And in the means (as above) mean anything (these are not normally distributed samples), the difference is not trivial (20%, 23.6kWh with setback vs 29.4kWh with no setback) between the samples looked at. Perhaps we should also look at the median:

> median(df_sb_m$htg_24h_kWh_in)
[1] 20.464

> median(df_nosb_m$htg_24h_kWh_in)
[1] 26.473

Difference 23%, 20.5kWh with setback, 26.5kWh without setback.

The setback running as recorded in this data set appears to use about 20-23% less energy compared to no setback running.

@jamespa - I think this is a fairly robust analysis. If any statisticians out there think otherwise, please do comment!      

@cathoderay 

Im not a statistician but note with interest that the error bands (I presume they are error bands) overlap at OAT>13.  Thats going to mean something at some point in the evolution of this discussion. 

THH I have not doubted for some while that there is a difference in your system between the setback population and the non-setback population, so Im not surprised at further confirmation that this is the case.  Although always very mindful that correlation does not equal causality, presuming that there is a link, albeit possibly indirect/multi-facetted, the question for me is now why?

There are still some known differences between the two sets of conditions for which you haven't, in the most recent analysis, corrected namely the effect of the AIT/OAT sensor and the interior temperature outside setback hours (however that is defined).  Once these are taken out it may well still be the case that the differences exceed that attributable to savings in energy lost from the house, and if so then we need to understand how the balance is made up in order to predict the impact on any system other than yours.

I dont know if your latest technique provides a way to take out the two known differences remaining, if it does then it would be good to do it and if not perhaps we can work on finding another way to do it in the source data and then apply the technique to the result.  This would then give a residual in which the only known effect is the difference in energy lost due to setback and, if the population difference still exceeds that 9which I have a hunch it will) we can think about what else might explain it and the extent to which these other factors may apply elsewhere.

I favour the moving window way to deal with the AIT/OAT sensor.  i was thinking we could apply this to the 'minute' data, but as the figures from the Midea are integers, I dont think we can so will have to rely on the hour data.  The fairly sharp steps when the heat pump switches on/off should still give us a pretty good figure, and from other data we can deduce the 'sign' of the correction to apply.  I will give some more thought to how this could be calculated, but you may well have some ideas

Posted by: @jamespa

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Im not a statistician but note with interest that the error bands (I presume they are error bands) overlap at OAT>13.  Thats going to mean something at some point in the evolution of this discussion. 

I'm not a statistician, but I have had to use statistics, mainly but not exclusively in medicine. Yes, they are the 95% confidence intervals, assuming I have understood R's default plotting behaviour correctly. I think the overlap may just be an artefact caused by the fact there are very few data points in that area, sort of a local low (statistical) power means wide confidence intervals.

Posted by: @jamespa

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I dont know if your latest technique provides a way to take out the two known differences remaining, if it does then it would be good to do it and if not perhaps we can work on finding another way to do it in the source data and then apply the technique to the result.

I'll see what I can come up with. The essence of the latest analysis is matched controls, if we can find a way of matching on the other variables then progress but inevitably the tighter the matching the fewer the data points remaining, but arguably the more useful they are. That said, I will soon have a whole new data set I can add, from the current 2024/25 heating season, but we will have to bear in mind there have been significant changes, notably opening up all the valves, in the current season.