Heating & power usage...

Heating - how much do we use / need in our house?

A simple question, but there are many ways to look at it. I've taken a fairly simplistic. I've used linear models to estimate the effect of temperature on energy usage. The graphical representation of the relation between temperature and energy usage is below... 
Some key take aways for people not used to reading graphs:
  1. The vertical (y-axis) is daily energy consumption in kilowatts.
  2. The horizontal (x-axis) is temperature (in this case it is the running mean operating temperature [RMOT] recorded by the HRV).
  3. The dots are 160 individual days - each with a corresponding RMOT and energy consumption reading.
  4. The black line is straight and declining - indicating that energy use decreases as temperature increases. In fact for every degree colder we use an extra 0.5kW (this is the slope of the black line).
  5. The grey area encompasses 95% of the variation and there is considerable variation. Temperature explains ~ 39% of the total variation in usage. I looked at using other temperature measurements including daily mean temperature but the RMOT explains more of the variation which makes sense since the house with have some thermal inertia as well.
  6. I added other things to the model like how much power we produced (electrical power production should be a good proxy for the amount of solar gain or passive solar heating), but none of these improved the model much. Power production only explains an extra ~ 1.5% of the variability.
  7. Statistically this relationship in the figure above is highly significant, and even more importantly this is quite a meaningful and intuitive result.
  8. While 39% of the total variance is not as much as one might want to predict, but it is worth considering the magnitude of the power usage - at 20 °C we use 11.3kW on average. 
    • About 4.5 kW of that is what I would consider as unavoidable base usage. That is the power between midnight and 5am extrapolated over 24 hours. That is the HRV, the refrigerator, clocks on the microwave/oven, router and all the other things that don't ever get turned off. 
    • We average about 2.5kW a day in hot water based on examining the change in power usage during the period when the hot water heating system is active. 
    • The rest of the power usage is complicated by people. Each time the dish washer runs is about 1.5kW, a load of clothes in a cold wash is barely even detectable. Cooking energy use is highly variable - with the oven being used more often on the weekends and in colder weather as well. 
    • So the an extra load of dishes or a meal in the oven - easily explains the variability in the consumed electricity.
  9. Below is the quarter hourly electricity consumption. The black line is the median usage, with increasing shades of grey from 95th, 75th, 50th, 25th, 5th, and 0th percentiles.


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