The weighted energy demand

All this talk of insulation, but I haven't yet gone over the fundamental point of Minergie which is to reduce the energy demand of buildings, in this case our house. I've mentioned several times that the limiting value for houses is 38 kWh/(m²·a). Then the question is how this energy demand is defined. Different systems of certification (e.g. the German KfW-40) have different ways of calculating this and in the Minergie system under consideration here it is a weighted sum of the energy required to
(i) maintain a comfortable indoor temperature (usually taken to be 20°C), call this Q_H,eff
(ii) to heat water Q_WW and
(iii) to run the ventilation system[1], Q_V.

We have the following relationship (click on the equation to see a larger version):

In Equation 1 the g terms are the weighting factors for the particular type of energy source chosen and the η's (eta) are (or are analogous to) the efficiencies of the devices used. You can see from the inequality that small g's and large η's are good.

More about the η's in the next post, here I'll just say a few words about the weighting factors g. This is where the differences in the different certification systems become apparent[2]. They are basically an attempt to compare the losses associated with the conversion of the energy from different sources to heat (see Table 2 below for the list). Burning fossil fuels to generate heat is taken to have a g of unity. Using the sun directly, as in absorbing the radiation and storing it as heat 'costs' nothing so it is given a weighting of 0. Using electricity, say to run a heat pump or (horror!) a resistance heater is considered least desirable (I imagine because the electricity itself is generated from other sources and there are losses in that chain of production and in the transmission). However, in the case of heat pumps this is mitigated by the ability of these devices to extract energy from the surroundings and this should be clear in tomorrow's post. The energy source to run the ventilation system is almost certainly electricity. A typical value for the Q_V is between 3 kWh/(m²·a) and 4 kWh/(m²·a).

Table 2. Weighting factors for different energy sources. Smaller is better.

	Weighting factor
Source	g
Solar, geothermal, ambient	0
Biomass (Wood, biogas)	0.5
Waste heat	0.6
Fossil fuels	1.0
Electricity	2.0

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[1] A little aside about the ventilation system: The aspect of the building envelope that I've talked about so far, namely the insulation, deals with the loss of heat via conduction through the shell. Another very important mechanism of heat loss is the movement of warm air from (i.e. leakage) and cold air into (i.e. infiltration) the house through gaps in the shell. In a well-insulated house, this can account for upto 50% of the total heat loss. It turns out that it is possible to neutralize this effect and still have good air quality by building a very tight shell and by relying on a high-efficiency mechanical ventilation system with a heat exchanger to capture back more than 80% of the heat of the exhaust air. A topic for other posts.

[2] An entry on the German language Wikipedia compares three systems: Primärenergiebedarf