The weighted energy demand, part II

Yesterday's post was about the calculation of the energy demand of a house and the weighting factors assigned to different energy sources. Another factor that must be taken into account is the efficiency of the particular device, e.g. a furnace, used to produce the heat energy. A note on terminology: In the case of heat pumps, the word efficiency is not accurate and the phrase coefficient of performance[1] is used instead.

It is important to note that these are the "standard" values accepted in the Minergie system. There are heat pumps which beat these numbers and our architects have recommended one of the best performing models on the market. The COPs for the air-source heat pumps made by this company[2] are claimed to range from 3.56 to 4.2, depending on the particular model. I plan to write a post about these systems before too long. Update 23 August 2009: Instead of a heat pump we will probably use district heating. Please see post 038.

Table 3. Efficiencies or coefficient of performance (COP) for a selection of different heat generating systems. Larger is better.

	Heating	Warm (hot) water
Source	ηH	ηWW
Oil or gas furnace	0.85	0.85
Oil, condensing furnace	0.91	0.88
Wood-fired furnace	0.75	0.75
Wood pellet furnace	0.85	0.85
Waste (district) heat	1.0	1.0
Electricity	1.0	0.9
Heat pump, outside air	2.3	2.3
Heat pump, ground source	3.1	2.7
Heat pump, ground water	3.2	2.9
Photovoltaic	0	0
Solar collector	0	0

The effect of this weighting system can be seen in figure 8 below. The standard values for the weighting factors for the different energy sources have been used here to compare the different results for the same house. I've left off the numbers on the graph because I just want to give an idea of the relative differences. A process of optimization leads to the the best solution for a particular house.

Figure 8. The weighted energy demand calculated using different energy sources.

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[1] Read about COP at this Wikipedia page → Coefficient of performance

[2] The company is Heliotherm → Heliotherm air-source heat pump

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