Please correct me if I am misinterpreting the graphs, but the upper one appears to indicate that the Energy In would appear to be reduced, by NOT initiating a 6 hour setback.
The two charts together are intended to compare the energy in predictions from your model (upper chart) and my regression equation (lower chart) against actual energy use. The charts are identical except for the red prediction lines, with my regression equation predictions (lower chart) getting closer in this (limited time frame) chart to the actual energy use (the blue line, CR Calc means my calculated actual use, as calculated from volts times amps in). Here's the chart again for ease of reference:
What I find rather difficult to understand is the need for a 1.18 correction factor.
Why would a heat pump manufacturer, even a Chinese one, spend the time, effort and expense of designing and building a system, to which it is then necessary to apply a correction factor?
Taking the December data you supplied, the 1.18 correction factor is not consistently 1.18, but varies from 1.09 to 1.27. Could you please explain why?
I think that if you were to apply the 1.18 correction factor to the spreadsheet predictions, or remove the 1.18 correction factor from your predictions, the two traces would not be too far apart.
My method of calculating savings is as follows: (1) Measure energy consumption actuals with a setback. (2) Estimate energy consumption without a setback. (3) Subtract (1) from (2).
We are in effect using the same method, observed with setback vs expected without setback. The general method of comparing observed vs expected is widely used in epidemiology, and despite the fact biological systems are probably far more complicated than physical systems, the generally method works well, provided the necessary precautions (usually standardisation) are taken, to ensure apples are being compared with apples not oranges, and unjustified extrapolation is avoided. This last point is why we have to repeat time and again the caveat that my results only apply to my heating system in my house.
The only difference between our methods is that I have 'refined' the method used to determine the estimated/expected energy use by plotting the energy use against the OAT, and fitting a regression line/equation, and then using that equation to generate the expected values. These plots (see posts passim) have high R squared values, meaning the variation in OAT explains most of the variation in energy use, and while I have great admiration for and welcome @derek-m's and @jamespa's sterling efforts to derive a model, I do think - and this is critical - all of the necessary variables are baked into that regression equation. What I am suggesting is that the empirical result necessarily includes all of the variables, even if we don't know what they are, or how they work. This observational approach - observing an outcome without yet knowing every detail of the underlying variables and equations - has served medicine well, and I see no fundamental reason why a similar approach cannot be applied to a physical system. The key point is that all the key variables are baked into the observed result, even if that process happens invisibly.
Here is the last week's minute data for my system in my house, running without setbacks:
This is useful, insofar as it shows at least two periods of relatively stable OATs that correspond with relatively stable energy in values, again suggesting that it is not unreasonable to use the OAT to predict the expected energy use. Note also the generally stable IAT - the house is in 'energy balance'. It will be interesting to see what happens over the next few days, given the forecast is for significantly lower OATs. I suspect the IAT may dip a little (heat pump can't quite cope), and energy use will almost certainly rise sharply, partly because lower OATs need more energy in to maintain IAT, but also because lower OAT means higher LWT and that in turn means lower COP, and then of course there are those devilish defrost cycles. The lower OATs also mean I will not use setbacks, as previous experience shows the IAT struggles to recover, at lower OATs. That's OK, I just make a point of avoiding setbacks in cold weather, but that doesn't mean I can't use them to save some energy/cost in milder weather. I only have to move one slider one notch to turn setbacks on or off (change the main room stat from manual (no setback) to program (with setback) mode and back again).
Lastly, I do find it interesting that both of our observation based findings suggest saving of the order of 20%. Is this just mere coincidence, or is it in fact the tip of an unseen iceberg of more general findings? I don't know the answer, and that is why I have tried to encourage, unfortunately without much success, others who have the data to post their findings. All the more thanks to you for posting yours!
I did use OAT to predict energy use up to a point; in order to estimate the energy use without setback I looked at other days with the same OAT to obtain a baseline then arithmetically tweaked it to match the OAT profile on my sample day. Not very rigorous but maybe accurate enough.
Yes it is interesting we get the same answer, especially when we have completely different systems. Yours (by your own admission) an old leaky cottage with an ASPH that struggles to produce sufficient power and mine a modern house with an ASHP that has more than enough power. More data would be good.
What I find rather difficult to understand is the need for a 1.18 correction factor.
Why would a heat pump manufacturer, even a Chinese one, spend the time, effort and expense of designing and building a system, to which it is then necessary to apply a correction factor?
Taking the December data you supplied, the 1.18 correction factor is not consistently 1.18, but varies from 1.09 to 1.27. Could you please explain why?
I think that if you were to apply the 1.18 correction factor to the spreadsheet predictions, or remove the 1.18 correction factor from your predictions, the two traces would not be too far apart.
I agree with most of the points, but the 1.18 factor is there, as the average difference between the Midea volts x amps value and the external kWh meter value. It is an average value because it varies, as you have observed. I have no idea why it varies. It is far from perfect having to use it, but it is, providing it is declared as it has been, better than using the uncorrected values which are definitely wrong. I'm using the best available estimation of actual values, which means having to apply the correction factor.
I suspect most of the correction factor arises because of loads that are not metered by the heat pump. Despite going over the Midea manuals with a tooth comb, I haven't found anything that says how and where the amps/volts are measured. I think it is possible, though obviously I can't prove it, that it measures what goes to the compressor, meaning the volts are probably right, as they appear to be in the raw data, but the amps misses the ancillary equipment (one or both circulating pumps, fan) and standing loads. If I can find a period when the heating was on, but the thermostat was not calling for heat, things might become clearer; failing that, seeing what the Midea vs external meter use is in the summer is when the heating is off might suggest something.
The ultimate fix would be to get a modbus enabled external kWh meter, and ditch the Midea amps/volts values altogether. At the moment, the only way of reading the external kWh meter is manual, and I am defo not going to sit by it recording values for hours on end!
I would assume that the data within the manufacturers data tables was obtained using more precise, and correctly calibrated, test equipment than any heat pump owner is likely to possess, so this has been used as the basis of the simulation spreadsheet.
I am also not surprised that your 1.18 correction factor varies quite considerably, because just using OAT values for power input predictions is inherently flawed. Whilst OAT does provide an approximation of likely power input values, I would not deem it accurate enough to make predictions of likely electrical energy usage. There are too many other factors that are not being taken into account.
I would assume that the data within the manufacturers data tables was obtained using more precise, and correctly calibrated, test equipment than any heat pump owner is likely to possess, so this has been used as the basis of the simulation spreadsheet.
I am sure the first point is correct, but the second relies on the correct inclusion and processing of the many variables. As I have said before, I don't doubt the laws of physics/thermodynamics for a moment, but I can ask whether they have been applied correctly. The ultimate test is how well the spreadsheet (model) predicts the real world.
At the moment, both your spreadsheet and my regression based method are about on a par when setbacks are not in use. However, when setbacks are in use, in the limited sample in the chart posted above, the regression method gives better predictions than the spreadsheet method.
Whilst OAT does provide an approximation of likely power input values, I would not deem it accurate enough to make predictions of likely electrical energy usage. There are too many other factors that are not being taken into account.
It seems I am not making my thinking clear enough. Firstly, the high 2 squared value (93%) for the regression means that, regardless of causality, and for whatever reason, the OAT does go a long way (93% of the way) towards predicting the energy in. Here again are the results from the regression (based on 1205 observations, note that I added an OAT (ambient) squared column, and then did a regression that included both the ambient and ambient squared columns as independent (predictor) variables):
In the main plot, apart from at the highest ambients, when something does happen, the actual values look reasonably well spread about the prediction line, suggesting they are normally distributed. This is further confirmed by the residual plots, which are reasonably well spread around zero, again apart from at the highest ambients. This is good enough to suggest to me the actual values are normally distributed, which means that, while individual values will be out, the sums over longer periods will be reasonable estimates for that total sum (and for that matter average) for that period. More specifically, taking a 24 hour period, some predictions will be over, and some under, but when the 24 hourly values are summed the over and under values in effect cancel each other out, and one is left with a passable estimate of the sum (and average) for the 24 hour period, though not for the individual hours in the period. Recall that we only get the hour values so we can determine the 24 hour values (for observed vs expected method), ie it is the 24 hour value that matters for this purpose.
They key thing I am relying on is the error (variation) being normally distributed. If that is not the case, then the above is not valid. But I think, for the reasons given above, there is good enough evidence that the individual hourly errors are normally distributed, and as a result the above logic is valid.
Midea 14kW (for now...) ASHP heating both building and DHW
However, when setbacks are in use, in the limited sample in the chart posted above, the regression method gives better predictions than the spreadsheet method.
So how do you know that the regression method gives better predictions? Your appear to be taking the desired result and then using a correction factor to achieve it.
It seems I am not making my thinking clear enough. Firstly, the high 2 squared value (93%) for the regression means that, regardless of causality, and for whatever reason, the OAT does go a long way (93% of the way) towards predicting the energy in. Here again are the results from the regression (based on 1205 observations, note that I added an OAT (ambient) squared column, and then did a regression that included both the ambient and ambient squared columns as independent (predictor) variables):
In the main plot, apart from at the highest ambients, when something does happen, the actual values look reasonably well spread about the prediction line, suggesting they are normally distributed. This is further confirmed by the residual plots, which are reasonably well spread around zero, again apart from at the highest ambients. This is good enough to suggest to me the actual values are normally distributed, which means that, while individual values will be out, the sums over longer periods will be reasonable estimates for that total sum (and for that matter average) for that period. More specifically, taking a 24 hour period, some predictions will be over, and some under, but when the 24 hourly values are summed the over and under values in effect cancel each other out, and one is left with a passable estimate of the sum (and average) for the 24 hour period, though not for the individual hours in the period. Recall that we only get the hour values so we can determine the 24 hour values (for observed vs expected method), ie it is the 24 hour value that matters for this purpose.
They key thing I am relying on is the error (variation) being normally distributed. If that is not the case, then the above is not valid. But I think, for the reasons given above, there is good enough evidence that the individual hourly errors are normally distributed, and as a result the above logic is valid.
I don't dispute the fact that the electrical energy input is highly dependent upon the heat loss, which in turn is dependent upon the OAT, but you appear to be relying upon too many averages and assumptions for it to be used with any degree of confidence.
The probable reason why your results change at higher ambient temperatures is because the Midea OAT sensor is providing a more believable ambient air temperature reading.
For me this discussion risks going the wrong way again.
I think that we know that for one human being (heat pump system) giving a drug (setback) appears to have a short term benefit (energy saving) increasing life expectancy (inverse cost) by 20%, albeit with a small degradation in quality of life (IAT at peak hours) for reasons (causes) we cant explain because the observed saving either violates our understanding of biochemistry ( the laws of physics) or is due in part to one or more secondary effects of the drug, not the primary effect of the drug which, in this case, happens to be known and which we do know is likely to vary from human to human.
On that basis the human being in question may well choose to continue taking the drug, and may be well justified in doing so.
We also know that multiple experiments on the same human (heat pump syatem) are not the same as experiments on multiple humans.
Taking all of the above together, other human beings might be a little more cautious and want some more evidence and/ or wish to quantify the life quality degradation and/or possible scenarios where their life expectancy reduces before taking the drug, and NICE would probably not recommend that the drug be available on the nhs.
That's about as close as I can get to a biological analogy and roughly how much we know from experiment so far
The result with Mr smith is interesting, but for me far more interesting is: is it true (or even likely on balance of probability) that the majority of human beings will experience a positive effect on life expectancy with side effects (degradation in quality of life/reduction in peak hours iat) that is tolerable.
Unfortunately few people are coming forward to participate in the drug trial, because it disrupts their life too much , takes too long, and they aren't being paid enough, so currently my only possible way forward to answer the interesting question is to try to work out the likely causes of the effect of the drug on Mr Smith and infer the general from the specific.
That's the situation in which we find ourselves so far as I can see.
@derek-m - it seems the quotes/new comment in your post have got mixed up, making it hard to follow. I think you rather than I wrote:
"So how do you know that the regression method gives better predictions? Your appear to be taking the desired result and then using a correction factor to achieve it."
to which I would point out that I developed and applied the correction factor long before I did the comparison, meaning your suggestion simply doesn't make sense. The correction factor was established long before the comparison was done. Nor do I understand why you would think that i would attempt to cook the books in such a way. The Midea amps x volts adjusted by the correction factor gives the best/least bad estimate of actual energy in as verified by the external kWh meter, and that is why I use it.
I don't dispute the fact that the electrical energy input is highly dependent upon the heat loss, which in turn is dependent upon the OAT, but you appear to be relying upon too many averages and assumptions for it to be used with any degree of confidence.
The probable reason why your results change at higher ambient temperatures is because the Midea OAT sensor is providing a more believable ambient air temperature reading.
I am not relying on rafts of assumptions that lack justification. The whole process from start to end is very simple, and far more transparent than your spreadsheet based approach. The steps are:
(1) run the system and collect data (no assumptions or averages involved)
(2) do a regression of the energy in on OAT. This sort of assumes normailty of the data, but that is not a problem because I can test for normality, which i did, with the result that the data does, unsurprisingly, appear to be normally distributed (one assumption, tested and confirmed)
(3) the R squared value shows the OAT predicts 93% of the variation in energy in (fact, no assumption involved)
(4) use the regression equation to predict energy in based on OAT (no assumption involved, because of (3) above; results are an an average, but that is OK, see below for why it is OK)
(5) because the regression equation predicts the mean energy out for a given OAT, in reality actual values will vary about that mean (fact of life, no assumption involved)
(6) however, because the prediction is for the mean, and the actual values are normally distributed, over time the means will sum to a value that gets ever closer to the actual value (this is the way normal distributions behave, no assumptions involved). It is in a way a sort of example of regression to the mean, only the actual number I use (for the observed vs expected comparison, which is what this is all about) is the sum over 24 hours, although the mean (24 hour value / 24) is hiding in plain sight.
I suppose you could argue I am assuming the characteristics of the normal distribution apply to the normal distribution, but that is the whole point of a normal distribution, it has certain characteristics, eg the mean has meaning (it reflects the central tendency well), and individual values will be equally distributed about that mean (the bell shaped curve), and the more samples you take, the closer your sample mean gets to the population mean (regression to the mean). It's the way the world works (95% of the time).
I don't think the OAT sensor providing a more believable (odd choice of word, I would use accurate) OAT reading at higher ambients explains the change seen at higher ambients. To suggest such a thing doesn't even reach the dizzy heights of an assumption, it is instead speculation based on your prejudice against the Midea OAT sensor. Given it is visibly a step change, and the energy in values are consistently lower, and it happens at about the OAT that the heat pump will turn itself off, I suspect (but it is only a guess) that that is what is happening: the heat pump stops putting out energy, and as a result, the energy in falls. But more important that that speculation, I think it is a red herring: it only affects a small number of values at one extreme of the operating range. The vast majority of the values in the rest of the operating range are normally distributed.
Which leaves us with the chart, which shows beyond doubt the regression method better predicts the actual energy use during setbacks. Here it is again with some notes added (and I accept it is a small sample, but it is the only one I have for the spreadsheet predictions, meaning that for now, it is all we have):
All the usual caveats about one system in one house apply, forever and ever, world without end.
Midea 14kW (for now...) ASHP heating both building and DHW
The result with Mr smith is interesting, but for me far more interesting is: is it true (or even likely on balance of probability) that the majority of human beings will experience a positive effect on life expectancy with side effects (degradation in quality of life/reduction in peak hours iat) that is tolerable.
Unfortunately few people are coming forward to participate in the drug trial, because it disrupts their life too much , takes too long, and they aren't being paid enough, so currently my only possible way forward to answer the interesting question is to try to work out the likely causes of the effect of the drug on Mr Smith and infer the general from the specific.
That's the situation in which we find ourselves so far as I can see.
I agree. In medicine (as elsewhere), we call it N=1. It's a single case report, an anecdote. The next step up is a case series (maybe N=10 or something like that). But we have only got as far a N=2 (and a bit, if we include the various other reported findings), and of course NICE would never recommend something on the basis of N=2. But that is as you say where we are. It is indeed unfortunate no one else has come forward, and I fear, as I have said before, it may well be at least partly because potential contributors can see all too plainly that they are likely to be hit by a ton of bricks thrown at them for making (absurd - not always said, but clearly implied) claims that defy the laws of physics if they do come forward. I have myself been fairly battered in this thread...
I am sure I have asked this before, but I still don't think I have a clear answer: given a house has a steady average IAT (ie no net energy gain/loss over time) how and why does a saving of XX% (substitute random number of choice for XX) as suggested by empirical data violate the laws of thermodynamics/physics. I'm hoping for answer with specific hows and whys, in plain English.
I'm going to end this post with a snippet from the Lancet (1991 - how little things change! Though perhaps we wouldn't be quite so open about getting tanked up these days). It is about another common clash, this time between medicine (in that notorious branch called psychiatry) and the law, and while not all of it applies, the gist is clear, and I think it is rather well written. But then I would, because I am a doctor:
In England Now
We were seven judges and seven psychiatrists week-ending in Cambridge at a contrived get-together designed to bring about mutual understanding by considering matters of common concern. Friday evening found us in our dark suits in my old college, enjoying a stiff camaraderie before the serious matters of the morrow.
By then differences were obvious. The judges had all changed into their heather mixture. They were articulate; we were hesitant. They reasoned precisely; we were discursive. We were wordy and repetitive; they marshalled their arguments succinctly and eloquently. Against men thoroughly versed in the adversarial approach we made a poor showing. During the afternoon the odds against us lengthened. One of our side, a neurologist included by mistake, decided to defect and become a quasi-jurist.
The evening provided a welcome interlude. The Master gave us an excellent dinner and the judges could afford to be charitable. The defector subsequently redeemed himself by inviting the psychiatrists back to his room and producing whisky in quantity. He was an entertaining man and it was a long and convivial night.
The final round began on Sunday morning. The judges, sober-suited once more, had about them the air of having been to early Communion. The psychiatrists’ only satisfaction lay in not having hangovers; technical know-how counted for something. One of our number was wearing a scarlet polo-necked sweater and tartan trews. We felt let down by this sartorial breaking of ranks but we had no inkling then of what we were to owe to him. In mid-morning, when the oldest of the judges was prosing on mellifluously, our champion sprang to his feet and silenced him with this interruption: "It’s all right for you lot, because you only have to practise something you’ve invented, while we have to deal with something that actually exists".
It was a knock-out blow. We had been up against the ropes and suddenly the tables were turned. The judges were left with no effective response. Their few remaining speeches were halting, laden with concession and defeat. Victory was ours without a doubt. There was no need even for a summing-up.
We returned to London in very cheerful mood. We knew then that patients seek our advice and help when struggling against natural adversities, not man-made ones, which is why we adopt cooperative rather than adversarial procedures. Medicine is exacting as a profession because doctors do not create its rules and because we are constantly required to make decisions based on incomplete information. We have to proceed despite uncertainty. Not for us the luxury of adjourning the case. As Lord Cohen once put it, a patient would much rather be a live problem than a dead certainty.
Midea 14kW (for now...) ASHP heating both building and DHW
I agree. In medicine (as elsewhere), we call it N=1. It's a single case report, an anecdote. The next step up is a case series (maybe N=10 or something like that). But we have only got as far a N=2 (and a bit, if we include the various other reported findings), and of course NICE would never recommend something on the basis of N=2. But that is as you say where we are. It is indeed unfortunate no one else has come forward,
Fair enough, we currently have 2 patients in the trial. One of the patients has suspected breathing difficulties (intake in a bit of a well) and suspected high blood pressure and poor circulation (the PHE) and we are worried that the results we are seeing on that patient may be linked, at least in part, to these underlying conditions, and thus not directly applicable to 'healthy' patients. We cant even measure blood pressure (temperature across the PHE) reliably because the monitor wont fit properly. We think the medicine is worth pursuing. We are in a bind.
I am sure I have asked this before, but I still don't think I have a clear answer: given a house has a steady average IAT (ie no net energy gain/loss over time) how and why does a saving of XX% (substitute random number of choice for XX) as suggested by empirical data violate the laws of thermodynamics/physics. I'm hoping for answer with specific hows and whys, in plain English.
I presume you mean 'if the house returns to a steady IAT after setback' not 'if the house (remains) at a steady IAT.
Here is the simple explanation using only O level physics and primary school maths:
The loss from the house is proportional to IAT-OAT, lets call the proportionality constant L. This is just a fact.
So if the house is at IAT1 the loss is L(IAT1-OAT).
If IAT is reduced to IAT2 then the loss is L(IAT2-OAT)
The difference between the losses in L (IAT1-IAT2), and the % difference is (IAT1-IAT2)/(IAT1-OAT)
I hope thats clear enough so far
If the house is at IAT1 for 18 hrs of the day and IAT2 for 6 hrs of the day the percentage reduction in loss from the house is 0.25*(IAT1-IAT2)/(IAT1-OAT)
If we are seeing an energy saving which is different to this then the excess saving (or deficit in saving) must be coming from somewhere, because the first law of thermodynamics says that energy is conserved (we aren't doing fission or fusion so can forget e=mc^2 in this case).
In a nutshell thats the important physics.
From here we can start thinking about what we might actually be seeing (going beyond your question initially but then returning to it). In the cases you post the apparent excess saving is about half the total. There are various possible reasons for this
a) Some of it can be accounted for if OAT rises during recovery
because the HP is more efficient at higher OATs so, whilst the loss is a linear function of OAT the input energy is not.
b) Some of it is accounted for (in some of your plots) by the failure of the house fully to recover to IAT1. This has two effects namely
The loss never quite makes it to the original figure
Heat energy is released from the fabric to the house/outside world. This happens only once (if things subsequently stabilise), but its quite significant in scale and confuses readings in the first and possibly second day of setback. Unfortunately with changing OATs its all to easy for this confusion to get swept up in changes in OAT and thus this side effect ignored and attributed to setback
c) Some of it might be due to other effects including (reduction in cycling, change in in penalty due to the 'well', change in penalty due to the PHE etc.
a and b are pretty possible to model, the various contributions in c less so, because their magnitude is due to engineering detail that wwe dont know well (or at all).
a) is systematic, can be expected to apply to all systems (but with the limitation that it depends on the timing of setback and recovery), and is legitimately including in 'saving due to setback'
b) is clearly not legitimately included in 'saving due to setback'. Its a separate saving due to reducing IAT at peak hours.
c) the various elements of c may be legitimately included in saving due to setback for the specific system only
So if setback appears to save x% and x is greater than the amount you get from the basic equation plus an allowance for a) (all of which is readily calculable), then we cannot yet infer that setback in general will save x% because to make that inference would violate the laws of physics. We do of course know that the system itself does not violate the laws of physics, so we know that there must be additional factors at work. What we don't know is in what circumstances these factors exist and how they affect systems other than the one in question in the circumstances in question.
I presume you mean 'if the house returns to a steady IAT after setback' not 'if the house (remains) at a steady IAT.
Yes, we are saying the same thing here using different words. I said "steady average IAT (ie no net energy gain/loss over time)", average being over 24 hours, and the important bit is in brackets: overall, the house remains in net energy balance (no net gain/loss over time), ie an overall steady state (though there may be variations within the 24 hours).
Yes, I get the physics explanation, thanks. Putting some numbers into the last equation, let's say the average (because it is easier than integrating the individual hourly values which change) IAT during the setback is 2 degrees less: 17 instead of 19 degrees, and the OAT is a steady 10 degrees (does sort of happen every now and then, and keeps the sums simple again). We then have:
0.25*(19-17)/(19-10) = 0.25*2/9 = 0.0555 (or 5.5% - I think your formula gives the ratio to 1, so we need to multiply by 100 to get percent).
At a lower OAT of 5 degrees (any lower and we will start to get defrost cycles confusing the picture), we get:
0.25*(19-17)/(19-5) = 0.25*2/14 = 2.6%
from which I observe
(a) the formula predicts that halving the OAT from 10 to 5 degrees all but halves the savings (may or may not be consistent, we suspect setbacks do better in milder conditions, but I don't think anyone has actually done the analysis on observed data to show this is the case)
(b) the formula (based on the physics) predicts savings considerably less than those apparently observed. That is the discrepancy.
Yes, like you, observation (b) forces me to conclude that something else is in play. Put another way, 0.25*(IAT1-IAT2)/(IAT1-OAT) isn't the whole story. As I have said many times, of course the laws of physics always apply, but that doesn't necessarily mean they have been fully and correctly applied in this particular case. Taking your suggestions in order:
(a) the OAT rises during the recovery period (say 0300 to 0900): sometimes it does, sometimes it doesn't. Over the last week, it has only clearly risen once by about 3 to 4 degrees (5 to 8-9 degrees); during the last setback trial, it happened only once during the seven day trial:
The COP will improve when it does happen, but it doesn't appear to happen very often, and when it does, is it enough to explain a two to four fold or more discrepancy? I haven't done the sums, but I doubt it.
(b) failure to recover to IAT1: this may be worthy of further investigation (see above chart): although the net energy balance requirement is met overall (the average of all IATs stays constant, or near enough constant), there are days when the IAT hadn't recovered by 0900 (the target time for the purposes of this discussion). But the effect of that is to lower the average IAT1 (ie the non setback period average is is a bit lower than it should be), and the equation then becomes (for example):
0.25*(18-17)/(18-10) = 0.25*1/8 = 3.1% (compared to 5.5% with full recovery)
ie not fully recovering (to a lower IAT1) makes less of a saving than fully recovering - something isn't right here! Furthermore, overall, the house is in energy balance when considered over 24 hour and longer periods, with just one exception in the above chart (20th Dec, when the IAT only reached 18.5 degrees in the evening). But by and large, IAT1 is recovered, meaning surely failure to reach IAT1 can't be the explanation.
(c) various speculations: these are indeed the ghosts in the machine that we can't see. On the Holmes principle, when you have eliminated everything else, then these ghosts must indeed be the explanation, however improbable. Perhaps we need a ghost buster not a scientist to fix this one.
That said, there is yet another possibility: my observed and/or predicted values (and for that matter @kev-m's, given his similar findings) are wrong. None of my measurements are gold standard, and furthermore my predicted values are absolutely and exclusively based on the observed values, meaning if the observed values are out, then the predicted values will be out, albeit in the same direction. I do worry about this: have I built my case on the sands of shifted and shifting values? Against this, the only other broadly comparable evidence we have (@kev-m's) gets broadly similar results (and vice versa) - but maybe his data has the same invisible flaw? I simply don't know the detail, but what I do know is that the energy in values I have do correspond well with the longer interval (days/weeks) external kWh meter readings, and that suggest to me there is at least a prima facie case for saying they can't be that far out.
Thus I am left with the enigma of the ghost in the machine, a conclusion you also came to (bold added) in more prosaic language:
We do of course know that the system itself does not violate the laws of physics, so we know that there must be additional factors at work. What we don't know is in what circumstances these factors exist and how they affect systems other than the one in question in the circumstances in question.
Midea 14kW (for now...) ASHP heating both building and DHW
