Friends, in the last article I explained how the concept of Heating Degree Days (HDDs) allowed one to estimate the Heat Transfer Coefficient (HTC) for a house (a.k.a. its ‘thermal leakiness’) in a simple way.
- Find out how many kWh per year it takes to keep a dwelling warm.
- For gas users, use the number of kWh of gas consumed each year
- For oil users, multiply the volume of oil used annually (in litres) by 10.
- Find the number of HDDs for your locale,
- or use 2,150±150 °C-days per year as a guess for most of the southern UK
- or use 2,350 ± 150 °C-days per year as a guess for most of the northern UK.
- And then divide, the number of kWh/year by the number of HDDs per year to yield the overall HTC for your dwelling.
In this article I want to explain how I checked this calculation using a much more complicated process. Read on if you want to know the gory details!
Basic Observations
The reason I love the idea of HDDs so much is because I spent such a long time – several years! – trying to work out the heat transfer coefficient (HTC) for my home the long way.
For me it all started back in late 2018 when I bought a weather station. Fired by ‘new toy’ enthusiasm, I recorded the average daily and weekly temperatures, and wondered whether the gas consumption increased as the outside temperature fell. I started to read the gas meter, at first daily, but then settled down to reading it weekly.
Although it is completely obvious, I felt surprised to ‘discover’ that gas consumption did indeed increase as the outside temperature fell.
On the graph above I have plotted temperature ‘demand‘ (the difference between the inside and outside temperatures) and gas consumption (kWh/day) on the same graph. The data on this has been smoothed, plotting the average of ±2 weeks around each data point.
You can see quite clearly that gas consumption follows temperature demand. The Heat Transfer Coefficient (HTC) is the constant of proportionality between these two quantities. But you can see that (as a result of the new glazing and insulation) the HTC changes through the years.
For example, the graph below shows the same data as in the graph above but highlights the effect of the new glazing and insulation. The heating demand in Jan/Feb 2021 was greater than in Jan/Feb 2019 but the gas consumption was only about half that in Jan/Feb 2019. In other words. In other words, I had reduced the HTC by about half.
The four phases
The graphs above cover 4 distinct phases of the work on the house.
- Phase#1 is the period before works began.
- Phase#2 is the period after the main Triple-Glazing work was done
- Phase#3 is the period after the final Triple-Glazing was done and the External Wall Insulation was applied.
In each of these phases, we should expect a distinctly different proportionality between heating demand and gas consumption – i.e. they each have a distinct HTC.
In Phase 3 we have data for both gas consumption (Phase#3A) and for heat pump use (Phase#3B). These should both have the same HTC – the insulation was the same – but the data is acquired in quite different ways.
I took the data in each of the phases and plotted average daily gas consumption versus temperature demand. The graphs for phases 1, 2 and 3A are plotted below.
The graphs all have the same vertical and horizontal scales and you can see that as the works progressed, the slope of the data has decreased. In other words, as the re-furbishment progressed, it took fewer kWh of gas per day to keep the house warm.
These graphs are fascinating. Firstly we note that graphs consist of two regions:
- At low heating demand, there is no temperature-dependence of the heating demand – the graph is flat at about 5 kWh/day. This is because during the summer, the heating is used for domestic hot water and cooking only.
- At high heating demand the data fit plausibly to a straight line, but not one that goes through the origin. The slope intercepts the 5 kWh line at roughly 3.5±0.5 °C of demand. This slope is just the HTC that we are looking for. It tells us how many extra kWh/day it takes to warm the house for each extra °C of temperature demand
The fact that the gas consumption doesn’t start to increase immediately the outside temperature falls below the thermostat set-temperature is because there are other sources of heat in the house.
- All the electrical items in our house typically consume around 200 W continuously – or 4.8 kWh/day.
- And each person in the house contributes around 100 W continuously, so my wife and I contribute another 4.8 kWh/day.
I investigated this phenomenon in quite some detail in these articles (1, 2), but the upshot is that the heating in my home doesn’t switch itself on until the external temperature falls about 3.5±0.5 °C below the thermostat temperature.
Looking at the slopes of the graphs, I can plot them to show how the Heat Transfer Coefficient has been reduced as a result of my refurbishments.
The Red Circles on the graph below show estimates assuming that the gas boiler is 100% efficient i.e. all the energy of burning the gas is retained within my home. A more realistic estimate is that only 90% of the heat is retained within the house. The estimate of the HTC using this assumption is showing blue.
I have gone through this calculation of the HTC in some detail to show just how difficult it is. Now let’s look and see how much easier it is using degree days.
Calculation Using Degree Days
To calculate the same estimates for HTC I need to do the following:
- Look up my records to find out how many kWh of gas I used in each of the three phases. All it requires is a single reading of the gas meter at the start and end of each phase. To gain extra accuracy one can assume that at best 90% of these kWh of gas consumed resulting in heating kWh.
- Look up the Degree Days Website to find out the number of heating degree days in each of the three phases.
- Divide the gas consumption by the number of HDDs.
During Phases #1, #2 and #3A, our thermostat was set to 19.0 °C, and so I used HDDs with a base temperature of 15.5 °C i.e. 3.5 °C lower than 19.0 °C.
The Calculational Steps outlined in the bullet points are summarised in the table below.
Phase | Gas Consumption (kWh) | Heating (kWh) at 90% Efficiency | HDD15.5s
(°C-days) |
HTC (kWh/day/°C) |
HTC (W/°C) |
1 | 13,323 | 11,991 | 1,430 | 8.4 | 349 |
2 | 13,756 | 12,380 | 1,787 | 6.9 | 288 |
3A | 6,902 | 6,212 | 1,773 | 3.5 | 146 |
The resulting HTC estimates are compared with those previously calculated using the long-winded method in the Graph below.
The agreement between the two methods of calculating the HTC is striking.
What this means is that instead of having to record external temperatures and gas consumption week-by-week as I did for three years, one can get equivalent results by using HDDs and just one or two gas meter records.
A final test: Phase#3B
I can check the calculational method and some of my assumptions by comparing the HTC in Phases 3A and 3B. There were no changes to the insulation in these phases: what changed was that I switched from heating using a gas boiler to heating with a heat pump.
So HTC should be the same in Phases 3A and 3B.
However there was one change that arose from etc heat pump switch. As I learned to use the controls of the heat pump, I eventually stuck with settings that resulted in the house being warmer (~20.5 °C) than it had been previously (~19 °C).
For this reason I calculated the number of degree-days in Phase#3B using a base temperature of 17.0 °C rather than 15.5 °C. The result is plotted in purple on the graph below.
All three calculations of the HTC in Phase#3 agree within a range of 10%, which is pretty much as good as any calculation or measurement of HTC can hope for.
This gives me confidence that the HDD method does indeed work, and that the likely boiler efficiency in Phases #1, #2 and #3A was probably not very different from 90%.
Summary
Apologies for this very long article. You may be asking, as I am, “Why did I write this?”
The answer is that being able to calculate the HTC for a dwelling is important. And if using HDDs makes the calculation simpler, then maybe more people will do the calculation.
And this should enable more people to rationally plan their home refurbishment and estimate the size of the heat pump they require.
And it’s all thanks to the kind people over at Heating Degree Days.
In the next article I’ll look at how HDD’s vary with:
- choice of base temperature,
- location in the UK, and
- from year-to-year.
November 2, 2022 at 12:52 pm |
This is fascinating – thank you so much for posting. I am puzzled by the heat pump calculations, though. It looks like you used as many kWh electricity per degree-day with the heat pump as you used kWh of gas in phase 3A. But, we expect heat pumps to have >100% efficiency. Am I missing something? Kind Regards . .
November 2, 2022 at 1:00 pm |
David. Good Afternoon. I guess you are talking about the figure above. The quantity plotted in dark blue is heat pump *output* i.e. how much heat it produces. The average COP over that winter was 3.6 so electrical *consumption* was a factor 3.6 less than the heat output.
The point about the graph was that the estimate of heat output when using the gas boiler looked to be about right.
I use a heat meter to measure the output of the heat pump. It measures the temperature difference between the inlet and outlet of the heat pump, and the flow rate of water through the pump. From these measurements it calculates the amount of heat produced.
Best wishes. M
November 2, 2022 at 1:41 pm
Dear Michael,
Thank you for prompt and clear reply – I am reassured to know that the heat pump is doing its job.
Very much appreciate your articles.
Kind Regards,
David