The solar radiation entering the building consists of directly transmitted short wavelength radiation and heat flux from the absorbed radiation in the window. Together with the inter­nal gains, these solar gains may at some times reduce the heating demand to zero. In such periods, the gains lead to temperatures higher than the set temperature. This occurs mostly in summer, but also in shorter periods during winter time. Due to the higher indoor temperature, the transmission and ventilation losses are increased compared to a case without solar gains. This excess of losses represents the part of the gains, which is not utilized. With TRNSYS, the utilized part of solar gains can not be calculated directly. One possibility is to calculate the heating energy demand for two simulations, one with and one without solar gains. The difference in heating energy demand defines the utilized solar

j](m)

(1)

AH(m) ^ Н1(тп) — H0(tn) < 1 AS(m) S0(m) — S1(m)

gains. Note, that the proper time interval for such a study is not arbitrary. If a simulation is run without solar gains for the whole year, the transition period from summer to winter is not modelled correctly. In the summer, the building usually heats up several degrees over the set temperature. The corresponding stored heat can reduce the utilisation of solar gains in the transition period to winter. Without solar gains during summer, this effect is completely suppressed. On the other side, of course, the time interval for the simulation must be considerably longer than the time constant of the buildings, which could be up to several days. Therefore, the utilization of solar gains is calculated on a monthly basis. in this study, the year is divided into 12 months of equal length with 730 hours. This ap­proach requires two subsequent simulations for every analysed month. After simulating a period of several weeks to guarantee independence of initial conditions, the demand of heat energy H0(m) and solar gains S0(m) are calculated for month No. m. In a second simulation over the same period of time, and under exactly the same boundary conditions, the direct and diffuse solar radiation is reduced to a smaller value or zero on all outside window glass surfaces only for month No. m (at the end of the simulation period). The so­lar radiation on the opaque surfaces (including window frames) is not changed. This has been achieved by a simple modification of the subroutine "DWINDOW" within the TRNSYS building model "Type 56". The resulting demand of heat and the solar gains are H1(m) and Si(m), respectively. The utilization factor tj of solar gains through the transparent parts of the building is now given by the results of both simulations:

with m running over all months of the heating period (usually September to May). For a complete suppression of solar radiation with S1(m) = 0, the usable solar gains are given by Su(m) = tj(m)S0(m) = H1(m) — H0(m), which is the saving in heating demand provided by the solar radiation. For the results shown in the next section, S1(m) = 0 was used for all m.

Table 3: Characteristics of the used weather data: Heating degree days (HDD) and global solar radiation on the horizontal. HDD (20/12) total year HDD (20/12) September to May Global radiation on horizontal September to May Stockholm (S) 4586 Kd 4476 Kd 513 kWh/m2 Trier (D) 3505 Kd 3347 Kd 593 kWh/m2 Milan (I) 2756 Kd 2756 Kd 724 kWh/m2

Table 4: Heating energy demand of the four objects with standardized user behaviour and without shading by the surroundings. Object 1 Object 2 Object 3 Object 4 Heating demand in kWh/mF for Sept. to May Stockholm (S) 118.9 99.7 28.1 24.6 Trier (D) 81.4 70.5 15.9 15.1 Milan (I) 61.2 49.8 9.9 8.6

Location: Stockholm (S) Location Milan (I) Fig. 3: Utilisation factor of solar gains in the period September to May for the loca­tions Stockholm (left plot) and Milan (right plot). Results for the buildings with the highest and with the lowest utilisation factors of those analysed here are displayed.

Results

The utilisation factor p, calculated according Eq. 1, is shown in Fig. 3 for the two objects with the highest (object 1) and lowest (object 4) utilisation factor of the four analysed ob­jects. The two plots show results for weather data representing a cold and warm European region, with all other parameters kept constant. Whereas the maximum of the utilization factor within 0.9 < p < 1.0 for the core winter time is quite high for all buildings and both weather conditions, the utilization of solar gains varies significantly in autumn and spring. In these periods, the total gains (internal and solar) can balance the losses (transmission and ventilation), so that the heating demand is zero. This is especially valid for the high performance buildings (objects 3 and 4) and/or in warm climate (Milan), and leads to small utilization factors p or even p = 0.

To analyse the major influences on the utilization factor, variations of the construction type of the walls, of window size and distribution and of total heat loss have been studied. The results are presented in form of the total and utilized solar gains in the heating period, i. e. in September to May. The integration of these monthly simulation results over the heating period in Trier is shown in Fig. 4 (left side). The ratio of utilized solar gains to total solar gains is given in the figure as a percentage. The left graph shows the solar gains for the buildings in their original construction. The right graph shows the solar gains for the same buildings, but with a modified construction type of the outer opaque envelope. The origi­nally massive buildings were changed to a light construction and vice versa. All values given in Table 2 are hereby not changed, for example the sizes and U-values of walls and windows remain constant. Only the type of constructions for walls, roof and ground floor (see Table 1) were interchanged between objects 1 and 2, and between objects 3 and 4. A comparison of the left and right graph in Fig. 4 shows, that the utilized solar gains do not depend strongly on the type of construction. The differences in utilized solar gains be­tween the massive and the light construction type of otherwise the same building is less than 10% for all four objects and for weather data from Trier (as shown in Fig. 4), Milan and Stockholm. In general, buildings with massive construction have slightly higher utiliza­tion factor than those with light construction. The putative exemption from this rule for ob­ject 3 (see Fig. 4) is due to the shading strategy against overheating (above 24 °C). With-

Fig. 4: Total and usable solar gains in the period September to May. The percentage in the columns is the fraction of usable solar gains during this period. The left graph shows the solar gains for the 4 objects in their original construction. The right graph shows results for modified simulation models, where the type of wall construction has been changed from massive to light and from light to massive, respectively. Thereby, the U-values for the building envelopes were not modified.

50

40-

0

Original construction

10 СО

E5SI Usable solar gains □□ Total solar gains

Object 1 Object 2 Object 3 Object 4 massive light massive light

30

20

Modified construction: massive ^ light

Object 1 Object 2 Object 3 Object 4 light massive light massive

50

0

40

30

20

10

out active shading, the utilisation factor for the massive version is p = 55%, somewhat higher than for the light version, which in this case is only p = 53%.

Object 1 Object 4

Regardless of construction type, the houses with the lowest heating demand (objects 3 and 4) take advantage of significantly lower utilised solar gains than the "standard" low — energy buildings (objects 1 and 2). Note, that also the amounts of not-utilized solar gains are quite different for the buildings. The amount of such not-utilized solar gains gives an indication of possible overheating problems in the building. For example, object 1 requires roughly 5 times more heating than object 4, but object 4 has even more total solar gains than object 1. This results in a very low utilisation factor for object 4 and at the same time a much more significant potential overheating problem in summer. The simulation presented here, without ambitious shading and cooling, reveals such overheating problems. Only additional ventilation of 1 ach/h and shading of 50% is applied, if the temperature exceeds 24 °C and lasts until the temperature falls below 22 °C. A user (or an advanced sophisti­cated system) might be able to perform much better cooling strategies (e. g. night cooling

Hours Hours

Fig. 5: Number of hours with mean indoor air temperature above certain limits, for ob­ject 1 (left) and object 4 (right). The mean indoor temperatures are averages weighted by the volumes of the living spaces inside the buildings.

and cooling in anticipation of hot days), however this is not always possible. In figure 5, the number of hours during one complete year with mean indoor temperature within certain temperature bands are presented for the objects 1 and 4. The object 4 exhibits signifi­cantly more overheating hours between 22 °C and 24 °C than object 1, even if its type of construction is changed from lightweight to massive.

Besides from the building mass, the major constructional differences between the 4 ob­jects are total heat loss and window distribution. Whereas objects 2 and 4 are predomi­nantly oriented towards south, the windows of the objects 1 and 3 are distributed equally to all directions. The influence of window size and distribution can be determined with varia­tions of the simulation model. Exemplary results are presented in Table 5 for variations of object 3, which has originally the lowest amount of utilized solar gains compared with the other objects. In variation 1, the windows are more concentrated to the south. Variation 2 includes windows whose size is increased up to a still reasonable maximum. In variation 3, the window area is reduced to the smallest size, which is required according to the legal regulations in Germany. The results show, that the utilized solar gains for this building could be increased by about 15% (variation 2). However, due to the losses through the larger window area, the heating demand for this variation is higher than in the original case. The distribution of windows towards south (variation 1) leads to a slightly lower heat­ing demand compared to the original construction, but this may entail drawbacks for the outside view and lighting in some zones of the building.

To emphasize the relationship between the total heat loss of the building and its utilisation of solar gains, variations of object 1 with different heat loss were simulated. The total heat loss is influenced by the thickness of the insulation layer and by the efficiency of the venti­lation system to recover heat. Variations of these parameters lead to a yearly heating de­mand for object 1 between 124 kWh/m2 to 18 kWh/m2 for the period September to May and for the weather of Trier. This band of results for the heating demand is represented by 7 individual simulations, and the corresponding solar gains are shown in Fig. 6. The total solar gain is, of course, equal for these simulations, because the windows and the bound­ary conditions are not changed. However, the utilized solar gains decrease for decreasing heat loss, or heating demand, respectively. An additional simulation was performed for a case with heating demand as low as 9 kWh/mPa. For this case, high performance windows had to be used. These windows exhibit a lower g-value, which leads to lower total solar gains. Fig. 6 shows clearly, that the utilised solar gains depend strongly on the heating demand. Whereas the building with poor energy performance has used solar gains of

Table 5: Simulation results for a variation of window size and window distribution for object 3 and weather data of Trier. The window fraction is related to the fagade area. Total window area Total window fraction Southern window area Southern window fraction Heating demand Total solar gains Utilised solar gains in kWh/m2 for Sept. to May Original Construction 51.45 m2 19% 19.24 m2 28% 15.9 18.2 10.1 Variation 1 south dominant 50.00 m2 18% 26.81 m2 39% 14.5 19.6 10.8 Variation 2 large windows 60.00 m2 22% 20.62 m2 30% 17.0 20.8 11.6 Variation 3 small windows 30.00 m2 11% 9.14 m2 13% 14.1 10.2 5.8

20.0 kWh/m2 this value drops for the high performance case down to 7.5 kWh/m2. The reason for this is the reduced length of the heating period for high performance buildings. In such buildings, the solar gains in the transition period between winter and summer are not utilised for heating, because the heating demand tends to zero.

Heat loss variation for object 1 ESM Usable solar gains I I Total solar gains 124 106 91 63 40 27 18 9 Heating energy demand in kWh/(m2 a)

25

<4

;§ 20

JZ

§

15

V)

c

’ro

10

s—

03

0

Fig. 6: Solar gains for variations of the insulation level of object 1. For each variation, the heating energy demand is given. For the case with heating demand of 9 kWh/(m2 a), high performance glazing (U = 0.7 W/m2K, g = 0.54) have been used. The lower g-value leads to reduced total solar gains compared to the other 7 considered cases (U = 1.4 W/m2K, g = 0.62). The simulations are performed with weather data for Trier.

Table 6: Heating demand and utilised solar gains for the analysed objects and varia­tions thereof. The heating demand is roughly 15 kWh/(m2a) for typical German weather conditions. All these variations represent "passive houses". The weather used for the shown cases is that of Trier, if not denoted otherwise.____________________________________________ Heating demand Utilised solar gains (Su) in kWh/m2 for Sept. to May Object 3, original construction 15.9 10.1 Object 3, variation 1 (see Table 5) 14.5 10.8 Object 3, variation 2 (see Table 5) 17.0 11.6 Object 3, original construction, weather: Milan 9.9 7.8 Object 1, variation 7 (see Fig. 6) 18.2 12.0 Object 1, variation 8 (see Fig. 6) 9.2 7.5 Object 4, original construction 15.1 12.4 Object 4, original construction, weather: Milan 8.6 11.2

For passive houses, the overall variation of the utilized solar gains is rather small. In Table 6, the heating demand and the utilised solar gains of some analysed variations of the four objects are shown. These variations represent passive houses, with a heating demand of roughly 15 kWh/(m2a) for German weather conditions. The values for the utilised solar gains Su shown in Table 6 can be summarised as Su = (10 ± 2) kWh/(m2 a). This range is valid for passive houses with a reasonable window fraction of about 20%. For buildings with extremely small windows or a window distribution oriented towards north, the total and usable solar gains could, of course, be smaller (e. g. variation 3 in Table 5). On the other side, in very cold climates, the utilized solar gains are larger, because of the extended heating period. In the climate of Stockholm, the utilised solar gains (and the heating de­mand) are up to 50% larger than for the weather of Trier. However, the dependence on construction type and window distribution is equally small for all considered climates.

Conclusions

The analysed buildings with a heating demand of about 15 kWh/(m2 a) for standard Ger­man weather conditions ("passive houses") in un-shaded locations exhibit utilized solar gains of Su = (10 ± 2) kWh/(m2 a) in this climate. These solar gains do not depend strongly on type of construction (heavy or light) or windows, as long as the windows are reasonably in size and orientation. However, the overheating hours can increase with the window size and also depend on window orientation, especially for light-weight constructions.

Particularly for passive houses, the glazed area is extremely expensive. In conclusion, the results indicate, that for such buildings the window area towards south should not be maxi­mised. Windows can be distributed over all directions and should be limited in size to provide appropriate day lighting, outside view, summer comfort and to provoke lowest costs.

Acknowledgements

The authors thank the Ministry for Science and Research of North-Rhine Westphalia (NRW), Germany, for funding this study within the project of the AG Solar NRW "Bewer — tung der Energieeffizienz verschiedener MaRnahmen fur Gebaude mit sehr geringem En- ergiebedarf" under No. 262 104 99.

References

Gieseler, U. D.J., Heidt, F. D. and Bier, W., 2003: Combined thermal measurement and simulation for the detailed analysis of four occupied low-energy buildings, Proceedings of the 8th Intern. IBPSA Conf., Building Simulation, Eindhoven (2003), vol. 1, pp. 391-398.

Klein, S. A., Duffie, J. A. and Beckman, W. A., 1976: TRNSYS — A Transient Simulation Pro­gram. ASHRAE Trans 82, p. 623, Version 14.2 (1998), http://sel. me. wisc. edu/trnsys/.

Meteotest, 2000: METEONORM, Edition 2000, Global Meteorological Database for Solar Energy and Applied Meteorology, Version 4.0, Bern, http://www. meteotest. ch.