ASHRAE Journal - December 2011 - 40

where qin = qout = a = b =

input rate, Btu/h (kW) output rate, Btu/h (kW) slope of the input/output line idle loss rate or intercept of the input/output line, Btu/h (kW) This input/output relationship can be used to evaluate annual fuel requirements and efﬁciency in different ways. Either a bin-type analysis or an hourly heat load analysis using, for example, a building load simulation program can be used. Here a simple bin analysis has been used. For the building and location the design day outdoor temperature and heat load are set. For the selected location, the distribution of heating season hours in 5°F (2.8°C) bins are obtained from published weather data.10 For any bin the average hourly heat load is calculated as: (65 − Ti ) qout i = ×q (2) (65 − Tdd ) out dd

100 90 80 Annual Efﬁciency (%) 70 Efﬁciency (%) 60 50 40 30 20 10 0 0 2 Idle Loss (%) 4 Annual Efﬁciency DHW Efﬁciency

90 88 86 84 82 80 78 76 1 Idle Loss = 0.15% Idle Loss = 2% 1.5 2 Oversize Factor 2.5

Figure 3: Example results of the impact of idle loss. (Assumed thermal efficiency is 88%; location is Albany, N.Y.; design day heat load is 40,000 Btu/h [11.7 kW], system maximum output is 110,000 Btu/h [32.2 kW], domestic hot water load is 64.3 gallons/day [243 L].)

Figure 4: Example results. Effect of system oversize on annual efficiency at two different idle loss levels. (Assumed thermal efficiency is 86%; location is Albany, N.Y.; design day heat load is 40,000 Btu/h [11.7 kW]; domestic hot water load is 64.3 galllons/day [243 L].)

where qout i = heat output rate required for heating in bin i, Btu/h (kW) Ti = average outdoor temperature in bin i, °F Tdd = design day outdoor temperature, °F qout dd = design day building heat load, Btu/h (kW) Assuming the system also meets a domestic hot water load, an average value of q out for this would also be added to qout i. For each bin the integrated system input rate required, q in i can then be determined from the linear relationship above. For the entire year, the total energy input and output is determined by adding all q in i and q out i values. Annual efficiency is simply determined from the ratio:
Annual Efficiency = 100 × ∑ qout i

∑ qin i
i

(3)

To illustrate the application of this approach, energy use with a range of example systems has been calculated and results presented in Tables 1 to 4, Page 39. For all of these cases, daily domestic hot water use has been assumed to be 64.3 gallons (243 L). One of the points illustrated by these tables is that the annual efﬁciency can be much lower than the steady state thermal efﬁciency. This is consistent with discussion in the recent article by Durkin.9 Note that, in going from a poorly performing system to a better system with lower idle loss, the improvement in annual efﬁciency is considerably greater than that which would be predicted by thermal efﬁciency alone.
40 ASHRAE Journal

In a similar way, just a ﬂue loss “combustion efﬁciency” does not fully predict the savings associated with replacing an older system with a high performance system. The ﬁrst row in Table 4 is notable because of the very low efﬁciency for both heating and DHW. This is a result of the use of a large, oversized combination system with a high idle loss. During the non-heating season, with DHW load only, this unit is operating at the extreme low end of its range. Figure 3 highlights the impact of idle loss through an analysis of one speciﬁc case. This is a home located in Albany, N.Y. with a design day heat load of 40,000 Btu/h (11.7 kW). The combination system is assumed to have a rated maximum output of 110,000 Btu/h (32.2 kW) with a full load thermal efﬁciency of 88%. Idle loss is varied in this analysis from 0.15% (lowest measured in this work) to 4%. The DHW efﬁciency is the efﬁciency with which this system would meet the domestic hot water load during the non-heating season. This result clearly demonstrates the importance of minimizing idle losses. Figure 4 illustrates another interesting result of the analysis. Again a speciﬁc example is assumed: Albany, 88% thermal efﬁciency. Two levels of system idle loss, 0.15% and 2% are assumed and annual efﬁciency is shown as a function of system oversize. Oversize here is based only on heating load and is the rated output of the system divided by the design day heat load. This analysis shows that the annual performance of a system with high idle losses is much more dependent on the oversize factor than a system with low idle losses.
ashrae.org December 2011

ASHRAE Journal - December 2011

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