House Energy Budget

An Eccentric Anomaly: Ed Davies's Blog

I'm quite confident of having plenty of energy for most of the year in my house. The two months or so of the worst bit of the winter are a bit tricker.

Summary version on the Green Building Forum.

It's difficult to work out what to expect from the house's performance. I don't know of any other houses with the active management of the somewhat-seasonal heat store that I plan. Otherwise similar houses tend to use a more passive approach to getting heat into and out of the store and few report in much detail how the house performs in practice.

Still, a number of houses seem to mostly work without extra heating. Examples include the Hockerton Housing Project where many of the houses are not heated most winters and Tony's House which was essentially unheated for the first few winters but has used UFH heating (direct heating of the water by electricity) at a low level more recently because of changes to the temperatures needed by occupants. Viking House in Ireland have also had some success with houses with no external heating but I, for one, am not sure quite which of their projects achieve this in which way.

As I hope my systems will be a bit better than theirs I'm reasonably hopeful it can be made to work in the long run.

However, it's difficult to know exactly what's needed and what energy sources will work best so I intend to take an incremental approach - first implementing a basic system which I'm fairly confident will come close, though it might get a bit chilly for a few weeks, then see how much extra is needed and what is likely to work well.

This does not play well with the building control system which rather assumes that a building will be finished on a certain date and that the plans for what will be there on that day should provably be sufficient for the purposes.

Anyway, this is my most recent run through the numbers.

Heat Losses

My previous Heatloss Calculation post described some code to work out the heatloss from the house. I've since tweaked that to deal with the lofts separately: reducing the temperature of the closed-off parts of the loft from 21 to 18 °C reduces the overall heatloss of the house in cold conditions by about 100 W. In addition, I've changed it to be able to easily calculate for different external temperatures. Here's the new version:

A new module,, does overall energy calculations based on and other data.

A basic assumption for these calculations is that internal temperatures will never drop below 15.5 °C but external temperatures will never rise above that level. Calculation is done with an basic heat loss set to what it would be at that external temperature plus an incremental heat loss for every degree the outside temperature is lower.

The heat loss is calculated for each of the four worst months using the output from Degree for EGPC (Wick) averaged over 5 years with a base temperature of 15.5 °C. This gives average heat loss rates:

Heat loss at base temperature: 261.39042616005383 W
Incremental loss: 62.89855126402148 W/K

Heat losses:
Nov 835.8638610381166 W
Dec 1018.2020268529575 W
Jan 997.9121716064989 W
Feb 989.4550726497891 W

Heat Gains

There are various sources of heat gain: the photovoltaic panels, solar thermal panels, windows and metabolism of the occupant(s). For these calculations I've assumed a single occupant giving off 100 W.


Output of the PV is calculated using data from the PVGIS web site for 6 kW of panels on the house site at an angle of 60°, oriented 10° east of south with 14% system losses.

With figures for each month in kWh/day for the PV array output and kWh/(m²·day) for the raw insolation of the roof surface this gives:

    ('Nov', 5.23, 1.05),
    ('Dec', 2.76, 0.54),
    ('Jan', 3.99, 0.79),
    ('Feb', 9.00, 1.83))

Dividing those kWh/day figures across a day length (24 hours) gives average outputs of the PV (in watts):

PV output:
Nov 217.91666666666666
Dec 115.0
Jan 166.25
Feb 375.0

Solar Thermal

The output of the solar thermal panels is a bit harder to calculate as it depends on more than just the sunlight available. The temperature of the surrounding air is a lot more significant than it is for PV and the assumed output temperature also matters a lot. Normally solar thermal is used for domestic hot water so getting an idea of performance at the “wrong” time of year for low temperature operation for space heating is difficult.

For these purposes I've assumed 300 W/m² insolation as typical decent winter weather and divided up the daily heat input per m² reported by PVGIS on this basis. Under these conditions, with the panel temperature 20 °C above ambient, my calculator gives an output of 235 W/panel so 1880 W for the 8 panels I have.

Using the insolation/m² data from PVGIS shown above I get the following equivalent number of hours of 300 W/m² insolation and average outputs in watts:

Solar thermal output:
Nov 3.5 274.1666666666667
Dec 1.8 141.0
Jan 2.6333333333333333 206.2777777777778
Feb 6.1 477.8333333333333

Window Heat Gain

Similarly, assuming that 60% of the sunlight arriving on the windows gets into the house as heat the heat gains through the windows comes out as:

Window heat gain:
Nov 171.74429999999998
Dec 88.32564
Jan 129.21714
Feb 299.32578

Total Heat Gains

Adding together the body, PV, solar thermal and window heat gains gives the following average gains, in watts:
Total gains:
Nov 763.8276333333333
Dec 444.32564
Jan 601.7449177777778
Feb 1252.1591133333334

Net Heat Losses

For November the heat gains are a bit less than the losses, for December and January considerably so but come February there's a net heat gain.

For each month the following are the net loss in watts, the total amount of energy lost over the month (in megajoules) and the temperature drop in the 10 tonnes of water in the thermal store needed to supply that energy.

Net losses:
Nov 72.0362277047833 186.7179022107983 4.462664966797282
Dec 573.8763868529575 1537.0705145469612 36.73686698247995
Jan 396.1672538287211 1061.0943726548464 25.360764164790787
Feb -262.70404068354424 -641.2080225003948 -15.32523954350848

A net loss in temperature in the thermal store over Nov, Dec and January of some 65 °C is much too large.

However, it's not all impossibly so. Slightly more heat gain or slightly less heat loss might well make things a bit more sensible.

For example, a 1 kW wind turbine (such as a Futurenergy FE1048) might reasonably be expected to operate at a capacity factor of somewhat better than 30% in these months. Assuming an additional input of 350 W from one of these devices changes the figures to:

Net losses:
Nov -277.9637722952167 -720.4820977892017 -17.219935415611896
Dec 223.87638685295747 599.6305145469613 14.33151325399047
Jan 46.16725382872107 123.6543726548465 2.9554104363013027
Feb -612.7040406835442 -1495.488022500395 -35.74302157027712

Now the total temperature drop in the store over the months which now have net losses is only 18 °C which is entirely sensible, in my humble opinion.


I have low confidence in these figures as they are so dependent on the assumptions made though my hunch, based mostly on the performance of some existing houses, are that they are pessimistic in much the way that official SAP figures seem to be. What they do show is that the design of the house and its associated energy systems are in the right general area and that the house should be reasonably habitable and, perhaps with some extra energy input, quite comfortable to live in.