Selected references with regard to the gap between theoretical

Sunikka-Blank and Galvin [29] made a comprehensive literature review on the gap between real energy use for heating and theoretical values from regulatory energy assessment calculations. They defined what they called the ‘prebound’

factor as Eq.(6.1), which equals what was defined by Hens et al. [31,45] as the

‘direct rebound’ factor. The names ‘direct rebound’ and ‘prebound’ might thus be considered misleading in their reference to ‘rebound’ because what this factor accounts for is the average prediction gap between theoretical and real consumption values expressed as a percentage of the theoretical value. It can thus account for any modelling error or simplification, regarding user profiles, building or system characteristics etc. and is not necessarily related to changes in

user behaviour being associated in building performance. They showed that not only in Germany, where most of the data they analysed came from (incl. data on over 3400 houses), but also in other countries (Belgium, France, the UK, the Netherlands) large overestimation errors occurred at poor theoretical performance (an estimated 60% at theoretical values of 500kWh/(m².year)) while small overestimations were found at better performance levels (around 17% at 150kWh/(m².year)) shifting even further to underestimation at high performance levels (below 100kWh/(m².year)). This was also discussed in Chapters 2, 3, with the data on the old and new neighbourhoods from Chapter 3 showing comparable overestimations for the not insulated houses (an overestimation by on average 53% at 321kWh/(m².year)). However, the overestimation in the new neighbourhood was still 30% at theoretical values of 97kWh/(m².year). When comparing such values, the differences between the datasets should be considered. Obviously, the dataset analysed in Chapter 3 was a specific case-study, much smaller and more homogeneous than the large dataset and thus less representative for average values at building stock level. Furthermore, different countries have different climates, building traditions etc. Another important difference is the calculation method used as a reference value in the different studies, being mostly the regulatory assessment methods from the respective counties. As was discussed in Chapter 5 and will be further illustrated in this chapter, the modelling approaches used in different countries show significant differences, making a direct comparison between the values from different countries difficult and mainly illustrative of the fact that ‘similar’ relations are found between prediction errors and performance levels.

Because of these differences between calculation methods, findings only from two studies are discussed here and will be used for comparison with the simulation results. These two studies are also selected because, instead of giving an average percentage of overestimation at one or two performance levels, they present a correlation defining the values of Eq.(6.1) at different performance levels. When such empirical correlation has been defined statistically, it can be used at different performance levels to find a more accurate or probable estimation of the real energy use based on a theoretical calculation by reversing Eq.(6.1). This of course gives a result that should be considered as an average value considering large numbers of cases and not as a value to be considered accurate for each specific household. Having such correlations also allows analysing their trends (e.g. are they linear, exponential etc.) and comparing those.

The first study is one by Loga et al.[44] based on data from Germany. Therefore, comparing their correlation between real and theoretical values with our correlations between results from more detailed models and results from standard approaches should be considered solely as indicative. Using as a reference model our model that includes the German correction approaches and user profiles from DIN 18599 would not make a quantitative comparison more valid, because another (seasonal) calculation method was considered in the data analysed by Loga et al. [44,182]. The second study is one by Hens et al. [31,45]

based on data from Belgium.

𝑃 = 𝑄_{ℎ,𝑡ℎ𝑒𝑜𝑟𝑦}− 𝑄_{ℎ,𝑟𝑒𝑎𝑙}

𝑄_{ℎ,𝑡ℎ𝑒𝑜𝑟𝑦} ^(6.1)

With

P = dimensionless ‘prebound’ factor

Qh,theory = theoretical final energy use for space heating Qh,real = real final energy use for space heating

The correction factor found by Loga et al. [44] is formulated in function of the theoretical energy use (Qh,theory) normalized per floor area, expressed in kWh/(m².year) and equals Eq. (6.2). It was derived from data on energy use in houses with a central heating system. Based on ‘(subjective) experience’, they state this factor should be corrected for houses with local stoves to take into account the lower temperatures found in these houses, an experience that corroborates the findings from Chapter 3 comparing the old houses with local gas stoves with the new houses with central heating systems. Since the necessary quantitative evidence was not available for defining this value empirically, they propose increasing the value from Eq. (6.2) with a flat rate of 10 percent points, at all performance levels. Using Eq. (6.2) and Eq.(6.1), Figure 6.1 shows the corresponding empirical relation between real and theoretical energy use and illustratively includes the real and theoretical energy use of the old houses analysed in Chapter 3 (‘cs1).

𝑃_{𝐿𝑜𝑔𝑎2013}= 1.2 − 1.30 (1 +𝑄ℎ,𝑡ℎ𝑒𝑜𝑟𝑦,𝑝𝑠𝑓𝑙

500 )

(6.2)

With

Qh,theory,psfl = theoretical final energy use for space heating per floor area [kWh/(m².year)]

Figure 6.1: The gap between real and theoretical energy use for space heating according to Loga et al. [44] (‘c.h.’: original correlation based on houses with central heating;

‘local h.’: correlationcorrection for local heating) with real and theoretical final energy use of the old houses of cs1 from Chapter 3.

Hens et.al [31,45] did not define their correlation directly in function of the theoretical energy use calculated using a standard performance assessment model. They started from the observation that the energy use for space heating can be expressed in function of the transmission heat transfer coefficient after a normalization per cubic meter of volume (Eq.(6.3)). Considering the theoretical energy use based on simulations with the equivalent set-point temperature of 18°C in the EPB-methods in Belgium, this function was found to be linear (b=1 in Eq.(6.3)). In a first paper [31], the linear coefficient (‘a’ in Eq.(6.3)) was reported to be 311, while in a second paper [45] discussing the same approach it was reported to be 363. In both cases, these values were compared with the same dataset on real consumption data which proved that, in reality, the relation was not linear but following a power function, with for Eq.(6.3) a=229.6 and b=0.84.Figure 6.2 shows these correlations and illustratively includes the real and theoretical values of the old houses analysed in Chapter 3 (‘cs1’). Based on these correlations and on Eq.(6.1), the ‘direct rebound’ or ‘prebound’ factor corresponding to the theoretical linear correlations can be formulated as Eq.(6.4) and Eq. (6.5), respectively. These can be used according to Hens et al. as an average correction factor on the results from official EPB-calculations. Eq. (6.4) differs from the equation reported in the original paper [31] (and copied in [29]) because it was found that the theoretical and real values had been mixed up in that paper when using Eq.(6.1).

𝑄_ℎ,∗∗

𝑉 = 𝑎 (𝐻_𝑡

𝑉)

𝑏

(6.3)

With

Qh** = the final energy use for space heating, theoretical or real [MJ]

a, b = regression coefficients defined based on simulations or real data Ht = the transmission heat transfer coefficient [W/K]

V= the volume of the building [m³]

𝑃_{𝐻𝑒𝑛𝑠2010}= 1 − 0.633 (𝐻_𝑡

𝑉)

−0.16

(6.4)

𝑃_{𝐻𝑒𝑛𝑠2013}= 1 − 0.738 (𝐻_𝑡

𝑉)

−0.16

(6.5)

Figure 6.2: the gap between real and theoretical energy use for space heating according to Hens et al.2010 [31] and Hens et al.2013[45], with real and theoretical final energy

use of the old houses of cs1 from Chapter 3.