## External Wall Insulation: Day-by-Day analysis

Happy New Year 2021!

• A list of related articles is given at the end
• This article was amended around 12 hours after it was posted to take account of heating effect of the people living in the house!
• Thanks to Ed, Simon and Geoff for noticing. And caring!

At around the time that the External Wall Insulation (EWI) was being applied to my house, I also had my electricity and gas meters upgraded to “Smart Meters”.

This gave me access to daily readings of gas and electricity consumption in kilowatt hours (kWh). I could get these readings in two ways.

• The hand-held readout unit shows daily readings for the last 7 days.
• After 3 days, the readings became available on the EDF web site, either to view directly as histograms, or to download as a spreadsheet.

From analysing this daily data I discovered something so obvious it was surprising!

What does the data look like?

The graph below shows the daily gas consumption (kWh gas consumed) plotted versus day-of-the-year

Click for a larger version. Graph showing daily gas consumption (in kWh) versus day of the year 2020

Initially I did not quite trust this new-fangled technology so I also plotted my weekly gas consumption readings expressed as a daily average. These are shown as solid blue lines on the above graph. Taking parallel overlapping readings showed me that in general I could trust the readings. Also shown are the 7 weeks of the EWI installation.

The daily readings do appear to generally make sense, but there were two days – days 298 and 329 – where gas consumption appears to have been zero: I think these are mis-readings.

To put the vertical scale into context, 24 kWh is the energy used by a 1 kW heater left on all day. So the vertical scale (100 kWh/day) is equivalent to just over 4 kW of continuous heating.

Each kWh of gas consumed results in the release of around 0.2 kg of carbon dioxide. So the full-scale 100 kWh/day would be equivalent to 20 kg per day of carbon dioxide. Total emissions over the period shown are just over 500 kg – more than half a tonne!

Weather

Whether the graph above represents good performance or not depends on how cold the weather was.

Our internal thermostat is set to 19 °C and so I assess the temperature ‘demand’ as being the difference between 19 °C and the average daily external temperature.

Below I have plotted the gas consumption data against the left-hand-axis, and additionally plotted temperature demand data against the right-hand axis.

Click for a larger version. Graph showing daily gas consumption (in kWh : left-hand axis) and temperature demand (in °C :right-hand axis) plotted versus day of the year 2020

The first thing to notice is how closely the curves correlate. Unsurprisingly, gas consumption directly follows temperature ‘demand’.

The second thing to notice is that after day 312, the gas consumption curve is much lower down: – there is a clear ‘gap’ between the temperature demand data and the gas consumption data.

Day 312 marked the point where the kitchen roof was sealed, marking the sealing of the building envelope.

Taking data only from Day 312 onward should allow me to assess the building performance by plotting gas consumption versus temperature demand. This graph is plotted below.

Click for a larger version. Graph showing daily gas consumption (in kWh) versus temperature demand (in °C). Notice that the best-fit line does not go through the origin.

The data make a pleasing straight line, something which is rarely a coincidence. But two things are puzzling.

• The first puzzle is that the graph does not go through zero – or even near it! This implies that when the average daily temperature is 15 °C outside we require no heating!
• The second puzzle is that the slope is 4.6 kWh per day per degree Celsius which is equivalent to 192 W/°C. This is considerably more than the 134 W/°C that appeared to describe the weekly data that I showed in my previous post.

The first puzzling thing

I think the answer to the first point is that I have assumed that the heating inside the house is only due to gas consumption but in fact there are other sources of heating.

The electrical energy used in the house also warms the house. Indeed, in one perspective, one can view all electrical appliances as heaters, each with its own additional functionality as a computer, a light, or a radio etc.

So in the graph below I have plotted daily [gas + electricity] consumption versus demand. The data have the same slope – because electricity consumption is roughly constant day upon day – but the intercept is now closer to zero – indicating zero demand with an external temperature deficit of 2 °C. But this is still not zero.

Click for a larger version. Graph showing daily gas consumption + daily electricity consumption (in kWh) versus temperature demand (in °C). Notice that the best-fit line is closer to the origin.

However there are two more corrections. Over the period plotted, my newly-installed solar panels were generating on average 2.4 kWh per day, 60% of which (1.4 kWh) was used in the house rather than exported.

This 1.4 kWh/day does not show up on the electricity meter. Including this additional term we arrive at the graph below. This suggests zero demand with an external temperature deficit of 1.5 °C.

Click for a larger version. Graph showing daily gas consumption + daily electricity consumption + solar energy (in kWh) versus temperature demand (in °C). Notice that the best-fit line is even closer to the origin.

Finally, (and thanks to Ed, Simon and Geoff for pointing this out) we need to take account of the heating by the two human beings living in the house.

My wife and I each eat a nominal 2000 kilocalories per day (8.4 megajoules per day) and most of that energy ends up as heat. This 8.4 MJ per day corresponds to 2.3 kWh per day each i.e. we are each roughly  equivalent to a 100 W heater. So in a very real sense, our love will keep us warm. Allowing for this effect the best fit line now passes very close to the origin.

Click for a larger version. Graph showing daily gas consumption + daily electricity consumption + solar energy + body heat (in kWh) versus temperature demand (in °C). Notice that the best-fit line is even closer to the origin.

The best-fit line still describes the trend of the data well, but is now (within plausible experimental uncertainty) consistent with my belief that there should not be an offset.

Overall, I take this data as evidence for the validity of the obvious: that the heat from all the electrical appliances and the people in the house really does heat the house. I have known this intellectually, but this is the first time I have ever seen specific evidence that this is the case.

So I find this both completely obvious, but also somehow surprising – because I wasn’t looking for it!

The second puzzling thing

• So taking account of the first puzzling thing, I conclude – from analysing around 50 days of data – that the house takes 4.6 kWh/day/°C [192 W/°C] to maintain 19 °C.
• But in the previous blog I concluded – from analysing two year’s worth of weekly data – that the house performed better, requiring less than 3.2 kWh/day/°C [134 W/°C] to maintain 19 °C.

Which of these do I believe? Sadly, I believe the worse of these two estimates.

The model in the previous blog article took no account of roughly 10 kWh/day of electrical heating or the 2 x 2.4 kWh/day of body heating by my wife and I. While this may not have been significant a couple of winters ago when we used almost 100 kWh/day in winter, it is significant now that daily gas consumption is only (roughly) 35 kWh/day.

Thermal Models #1 and #2

So I have now made a new thermal model Model#2 – which incorporates the electrical heating.

The graph below compares the two models #1 (- – -) and #2 (- – -). They both predict the gas consumption in terms of the weather, and a parameter that describes the house insulation. But Model #2 takes account of the fact that electrical power dissipation and human bodies also heat the house.

Average Daily gas consumption in KWh per day for the last two years. Also shown are two models. Model#1  (- – -) predicts gas consumption based on the average temperature ‘demand’. Model#2  (- – -) predicts the same thing but takes account of the heating of the house by (a) electrical appliances estimated at 400 W continuously or 9.6 4.8 kWh/day. The constants of proportionality for each model are changed to allow the model to match the gas consumption in the winters of 2018/19 and 2019/20. Click for a larger version.

Overall Model#2 is slightly better than Model #1 at matching the gas consumption data – but more importantly it is based on the basic reality that electrical appliances and body heat really do heat the house!

The models differ in the constants of proportionality that they require to describe the thermal insulation. In the graph above I have changed the constant of proportionality around Day 250 – when most windows were triple-glazed – and around Day 660 – when the EWI commenced.

• In the winter of 2018/2019 model#1 suggests it took 280 W ( 6.7 kWh/day) of continuous power for each 1 °C above the external temperature.
• Using model#2 the data is better described by a figure of 350 W ( 8.4 kWh/day) per °C
• In the winter of 2019/2020 model#1 suggests it took 240 W of continuous power (5.7 kWh/day) for each 1 °C above the external temperature
• Using model#2 the data is better described by a figure of 300 W ( 7.2 kWh/day) per °C
• In this winter of 2020/2021 I had hoped the EWI would mean I needed only 134 W (3.2 kWh/day) of continuous power for each 1 °C above the external temperature.
• Using model#2 the data is better described by a figure of 192 W ( 4.6 kWh/day) per °C

Summary

Looking at daily data, I found that a graph of gas consumption versus temperature demand did not go near the origin unless I took account of the heating due to the electrical appliances and the people living in the house.

• Although this is obvious, this is the first time I have ever seen data which demonstrated this to be the case.
• Essentially, I have turned my house into a calorimeter!

Taking account of this suggests that my house currently requires 192 W to heat it 1 °C above external temperature. This is 43% higher than 134 W/°C I had hoped for.

I will consider the impact of this effect, and other possible explanations in another article – watch this space!

Previous articles on this topic

2020

2019

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### 9 Responses to “External Wall Insulation: Day-by-Day analysis”

1. Simon Says:

Hi Michael (and happy New year!)
Have you reached the point in the modelling where it helps to allow for the other source of heat – people digesting their dinner, etc?
I vaguely recall that this is of the order 100W (or more).
Best wishes
Simon

• Simon Says:

PS another thought – gas boiler efficiency isn’t 100% (I read that A-rated only means over 90%) I suppose the wasted heat goes out the flue. Might this account for some of the discrepancy between actual 167W and hoped-for 134W?

• protonsforbreakfast Says:

Another good thought. This will alter the slope and bias it in the ‘right’ direction because I am using around 10% less heating power than I allowed for.

• protonsforbreakfast Says:

Simon

Happy New Year. Yes – of course – why did I not think of that. I was aware of teh effect in labs but I have been incorrectly think of my home as a domicile rather than a quasi-adiabatic laboratory. I will add a correction to the article.

M

2. Edmond Hui Says:

From memory when we were designing the school, human beings act as 100W heaters. Have you taken these into account? We were told in 2010 that there was hope that new building management systems could track human movements and adjust heating to compensate- full classrooms need less heating than under capacity ones. There may also be pets, bacterial metabolism, etc. You might get that line of best fit to go naturally through the origin. Happy New Year.

• protonsforbreakfast Says:

Good Morning Ed. Happy New Year.

It is a measure of the obviousness of my omission that you are the third person to point it out this morning – I will amend the original article.

M
: Thank you. I have updated the post.

3. Ross Mason Says:

It’s good that you finally have become significant in your household. I am still waiting…..