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Building and climate influence on the balance temperature of buildings
Building and Environment 38 (2003) 75 – 81
www.elsevier.com/locate/buildenv
Building and climate in uence on the balance temperature of buildings J. Karlssona; ∗ , A. Roosa , B. Karlssonb a Department
of Materials Science, The Angstr om Laboratory, Uppsala University, P.O. Box 534, S-751 21 Uppsala, Sweden of Construction and Architecture, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden
b Department
Received 19 October 2001; received in revised form 8 January 2002; accepted 10 January 2002
Abstract In this paper, the fact that the balance temperature varies for di.erent types of buildings is evaluated and discussed. An explicit method to add useful hourly solar heat to the degree–hour formalism directly from building and climate data is presented. This also leads to a straightforward de1nition of the solar utilisation factor. Results from taking solar energy into account are compared with results from not taking solar energy into account demonstrating large deviations. The formalism is compared with a dynamic building simulation program (DEROB-LTH). The e.ect on the balance temperature when changing several building parameters is analysed in order to illustrate the errors of using a 1xed balance temperature in the degree–hour methods for di.erent buildings. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Balance temperature; Degree hours; Solar utilisation factor
1. Introduction Considering the whole life cycle of a building, the main part of the total energy use is consumed during the occupational phase of the building rather than for the actual design and construction (including refurbishments, transport, etc.) of the building [1]. In order to predict and reduce this energy consumption, a number of advanced building energy simulation tools have been developed [2–7]. These can be used to calculate the heating and cooling demand and the peak power for a building that is going to be built or refurbished. However, detailed models require detailed input data and a high level of knowledge by the user, which limits their use. For simple studies, as in a pre-design state or for a small project, it is very common to use a simpli1ed building energy model. Most of these simple models are based on, or are in some way related to, what is referred to as the degree–hour (or degree–day) method [2,5]. The degree–hour method estimates the steady-state heat losses through the building envelope by taking the average U -value of the envelope, ventilation losses and the average internal “free” heat gain into account. One problem with the simplest form of the degree– hour method is that it does not explicitly take the useful solar heat into account, which may lead to considerable errors. Useful solar heat gain is the part of the solar energy ∗
Corresponding author. Tel.: +46-18-4713-134; fax: +46-18-500-131. E-mail address: [email protected] (J. Karlsson).
that contributes to heating when heating is needed, which can vary from hour to hour. A few ways of including useful solar heat in this simple formalism have been proposed (see for instance [5,8,9]), but not directly from building and climate data, without the use of empirical parameters. The degree–hour methods are based on the concept of the building’s balance temperature, Tb (sometimes referred to as balance point temperature, or simply base) which is the outside temperature below which the building, on average, requires heating. In many cases, the balance temperature is used as a 1xed value depending on the standard for the speci1c country in which it is used. However, the balance temperature varies greatly depending on the type of building [2] so that using a constant balance temperature can lead to considerable errors. In this paper, it is demonstrated how hourly useful solar energy can be included in the computation of the balance temperature. Knowing the amount of useful solar energy also means that the amount of harmful solar heat is known, which in turn leads to a straightforward de1nition of the solar utilisation factor, normally referred to as . Furthermore, it is illustrated how the balance temperature varies for di.erent types of buildings and building parameters. In the sections below, the simple formulation of the degree– hour method is summarised, after which the method that includes useful solar heat is outlined. In the Results section, the degree–hour method with and without useful solar energy is compared with the results of a dynamic
0360-1323/03/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 1 3 2 3 ( 0 2 ) 0 0 0 2 5 - 2
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
simulation program. Furthermore, a thorough sensitivity analysis of how the balance temperature varies with di.erent changes in building parameters is performed. The purpose of this paper is to demonstrate how the balance temperature varies for di.erent buildings and the importance of acknowledging this variation when using simple degree–hour models. The results can be the base for a methodology of how the balance temperature should be selected in order to increase the accuracy of the simple degree–hour method.
800 N E S (kWh/m2yr)
76
S W 400
0 -10
2. Present formulation
0
10
20
30
Temperature interval (˚C)
In the degree–hour method the required auxiliary heat for a building during a certain period, Jt (e.g. about 720 h for a month), can be de1ned as [2,5]
Fig. 1. Accumulated total solar irradiation, S, on vertical surfaces in four di.erent directions versus temperature interval for Lund, Sweden.
QHaux = Ktot (Tb − Tm )Jt
include useful solar energy in the degree–hour formulation, requiring hourly accumulated solar radiation curves on vertical surfaces versus temperature interval. Such a curve, S, is illustrated in Fig. 1 for a Swedish climate (Lund, 1988), for four di.erent orientations and for a whole year. These curves can be measured or compiled from hourly climate data 1les for a horizontal surface using, for instance, the Hay and Davies method [10]. According to the de1nition of the balance temperature, the useful solar heat impinging on the window is the accumulated solar heat up to Tb , i.e. S(Tb ), which is direction and climate dependent. The corresponding useful solar heat transmitted by the windows is S(Tb ) multiplied by an average g-factor (total solar energy transmittance of the window) for the period Jt, and a shading factor, , if there is any shading. For higher accuracy the S-curves (Fig. 1) can be compiled by calculating the solar incidence angle [10] and taking the corresponding g-factor [11] at each hour into account to obtain what we refer to as Sg -curves. Furthermore, the shading for each hour, , could be included (giving hourly accumulated Sg -curves). Examples of the Sg -curves for an unshaded, uncoated, triple glazed, south- and north-facing window in the Lund climate are shown in Fig. 2. If the window is unshaded (i.e. = 1 for all hours) the useful solar heat during a year is thus de1ned as
∀Tm ¡ Tb ;
(1)
where Tm represents the average outdoor temperature during the time period Jt. The total loss coeLcient, Ktot (W=K), primarily encompasses heat ow through the envelope and ventilation by Ktot = Utot Atot + VCp Nach ;
(2)
where Utot is the total average U -value of the envelope, Atot is the total envelope area, V is the enclosed volume, Cp is the heat capacity of air (about 0:33 Wh=m3 K) and Nach is the number of air changes (ventilation plus in1ltration) per hour (h−1 ). The studied time period Jt should not be longer than the heating or the cooling season, but a recommended time interval could be a month [2]. The balance temperature, Tb can be de1ned as Qint Tb = Teq − ; (3) Ktot CJt where Teq is the indoor set point temperature, assumed constant, and Qint is the internally produced heat (in Wh) during the period Jt, not including solar heat gain [5]. In ASHRAE [2] Tb is de1ned including solar heat gain but not with hourly useful solar heat. Tb is a characteristic parameter of the building. By knowing Tb and the average temperature, Tm , for the investigated period, Jt, the auxiliary heating can easily be assessed by Eq. (1). The following procedure illustrates how Tb can be explicitly de1ned, containing useful solar heat, that is accumulated hourly from weather and building data. 3. Tb including useful solar energy By introducing the balance temperature it is stipulated that there is an outdoor temperature below which the building needs to be actively heated. When considering solar energy, this de1nition also means that solar heat entering the building at outside temperatures below Tb is useful and solar heat entering the building at outside temperatures above Tb is not useful. This de1nition means that it is possible to
QUsol = Sg (Tb )Aglass ;
(4)
i.e. a point on the Sg -curve multiplied by the area of the glazed part of the building. If the building only has windows facing south, the south Sg -curve is used and if there are windows distributed on all sides of the building, Sg is taken as an area weighted average of the Sg -curves for all directions and glazed areas. Sg can be formed for each time period (e.g. month) or for the whole year, as in Fig. 2. An alternative de1nition of the balance temperature, including useful solar heat, can thus be identi1ed as Tb = Teq −
(Qint + QUsol ) : Ktot Jt
(5)
J. Karlsson et al. / Building and Environment 38 (2003) 75–81 Table 1 Data for the oLce module base-case
500
2
Sg (kWh/m yr)
400 300
S Average N
200 100 0 -10
77
0
10 20 Temperature interval
30
Since QUsol is a function of Tb in itself an iteration procedure through Eqs. (4) and (5) is performed in order to obtain the correct Tb and the corresponding QUsol . Thus, the known building parameters (i.e. Utot ; Atot ; Qint ; Uglass ; Aglass , etc.) and Sg determine which Tb that characterises the building. The highest possible Tb (¡ Teq ) is when no solar radiation is useful (transforming Eq. (5) to Eq. (3)) and at the same time the building has a low Qint and a high Ktot as, for instance, in a hot climate with the Sg -curve shifted to very high temperatures. Buildings with the lowest possible Tb have high Qint and low Ktot . For an extreme building with very high Qint and low Ktot , again no solar heat will be useful. The lowest possible Tb is consequently also described by Eq. (3). Once the balance temperature has been established by the iteration process of Eqs. (4) and (5), the auxiliary heat can be assessed by using Eq. (1) but with a Tb that includes useful solar heat. The illustrated procedure can also be used to assess the cooling demand. Normally a dynamic set point range, Tdyn , ◦ of about 5 C should be used, within which the temperature is allowed to vary without introducing active cooling. With the above de1nitions this means that solar heat entering the building at an outside temperature above Tb + Tdyn is considered negative (leads to overheating). This is given by (6)
where QNUsol is unwanted solar heat gain and Tmax is the maximum temperature during the period. This means that the auxiliary cooling demand for the period can be expressed by QCaux = Ktot (Tm − (Tb + Tdyn ))Jt + QNUsol ∀Tm ¿ Tb + Tdyn :
Lund (Sweden) 2:9 × 2:7 × 4:2 m3 0:18 W=m2 K 1:9 W=m2 K 2:2 W=m2 K 1:2 h−1 30% South 1000 kWh=yr 20 25
2.7 4.2 2.9
(GWAR: glazing-to-wall area ratio.)
Fig. 2. Accumulated total solar irradiation multiplied by the total solar energy transmittance for each hour, Sg , for a south- and north-facing window (uncoated triple glazed window: g(0) = 66%; U = 1:9 W=m2 K, where g(0) means the total solar energy transmittance at normal incidence) in a Lund climate versus temperature interval. The middle curve indicates the Sg -curve averaged over all four cardinal directions.
QNUsol = (Sg (Tmax ) − Sg (Tb + Tdyn ))Aglass ;
OLce module base-case Location Dimension Front wall U -value Glazing U -value Frame U -value Ventilation+in1ltration GWAR Window orientation Free heat, Qint Heating set point Cooling set point
(7)
The formulation with the Sg -curves leads to a simple de1nition of the solar utilisation factor [9] by Sg (Tb ) ; (8) = Sg (Tmax ) which can be evaluated zone by zone for each direction of the windows (using Sg ) or for the whole building (using Sg ). Furthermore, an average annual g-factor, g, can be extracted by the relation Sg (Tmax ) g= : (9) S(Tmax ) Note that this is orientation dependent. For the example in Fig. 2 the average annual incidence angle of direct radiation ◦ ◦ is of the order of 58 for the south-facing window and 72 for the north-facing window. 4. Results 4.1. Comparisons with “DEROB-LTH” For comparison, two di.erent base-cases were de1ned: one commercial oLce module and one residential building, both of a very simple “shoe box” form. The oLce module base-case, described in Table 1, has adiabatic surfaces in all directions except for the outside facing surface. The balance temperature and solar utilisation factor for this case were ◦ 12 C and 45%, respectively, according to Eqs. (5) and (8). The sparsely occupied residential building base-case is described in Table 2. The balance temperature and solar ◦ utilisation factor for this case were 17 C and 66%, respectively, according to Eqs. (5) and (8). For more commonly occupied residential buildings with higher Qint , see Fig. 6c. The heating and cooling demand for both base-cases were calculated for the degree–hour method without solar (“DH no sol”) and for the degree–hour method with useful solar energy (“DH with sol”) as described above. The calculations were performed for the time period of a month at that time and then summed up and presented for a whole year as seen in Figs. 3 and 4. The results were compared with a dynamic simulation program, DEROB-LTH, [7] for four
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
Lund (Sweden) 10 × 2:7 × 10 m3 0:18 W=m2 K 1:9 W=m2 K 2:2 W=m2 K 1:2 h−1 20% Equal to all orientations 1000 kWh=yr 20 25
200
2.7 10 10
QHaux, DEROB QHaux, DH with sol QHaux, DH no sol QCaux, DEROB QCaux, DH with sol QCaux, DH no sol
300
200
100
0
lund
lulea
Denver
Miami
Location Fig. 4. Comparison between the degree–hour method with (“DH with sol”) and without (“DH no sol”) solar heat and a dynamic simulation program (“DEROB-LTH”) for the residential building. The results are given in kWh=m2 oor area and year.
QHaux, DEROB QHaux, DH with sol QHaux, DH no sol QCaux, DEROB QCaux, DH with sol QCaux, DH no sol
2
Heating/Cooling demand (kWh/m yr)
Residential base-case Location Dimension Wall U -value Glazing U -value Frame U -value Ventilation+in1ltration GWAR Window orientation Free heat, Qint Heating set point Cooling set point
2
Table 2 Data for the residential base-case. Heat loss to the ground is calculated according to the Swedish norm [12] (no time delay and heat loss is multiplied with 0.75 to account for storage in the ground)
Heating/Cooling demand (kWh/m yr)
78
100
0
lund
lulea
Denver
Miami
Location Fig. 3. Comparison between the degree–hour method with (“DH with sol”) and without (“DH no sol”) solar heat and a dynamic simulation program (“DEROB”) for the oLce module. QHaux represents the heating demand and QCaux represents the cooling demand. The three bars on the left give the heating demand and the three bars on the right give the cooling demand (if any) for the four di.erent climates, respectively. The results are given in kWh=m2 oor area and year and the heating and cooling plant eLciency is set to unity.
very di.erent types of climates: Lund, SWE (lat. 56, long. 13), Lulea, SWE (lat. 66, long. 22), Denver, US (lat. 40, long. −105), Miami, US (lat. 26, long. −80). In Figs. 3 and 4 it is seen that if solar energy is taken into account in the described way the deviations from the dynamic simulation program can be highly reduced, but still not completely eliminated. Latent heat is omitted in both models. In Fig. 5 the hourly heating and cooling power is plotted versus outside temperature for the base-case oLce module in Lund. The data are simulated with DEROB-LTH and it is seen that one can identify a certain outdoor temperature, the balance temperature, below which heating is needed. The solid square illustrates the balance temperature as computed with useful solar energy as described above, and the solid triangle illustrates the balance temperature as computed without useful solar energy. It is seen that the balance temperature is more accurately de1ned (the building requires
Fig. 5. Hourly heating and cooling power for the base-case oLce module in Lund versus outside temperature. The heating power is plotted on the positive side of the y-axis and the cooling power is plotted on the negative side of the y-axis. The solid square indicates the balance temperature, Tb , calculated including useful solar energy and the solid triangle indicates the balance temperature, Tb , calculated not including useful solar energy.
heating below Tb and not above Tb ) when hourly useful solar heat gain is included, than when it is not included. 4.2. Di
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
10
10 Tb (˚C)
15
Tb (˚C)
15
DH with sol DH no sol
5
0 0.0
0.5
1.0
(a)
DH with sol DH no sol
5
1.5
0 0.0
2.0
2
0.2
0.4
(b)
U-wall (W/m K)
79
0.6
0.8
GWAR (%)
20 DH with sol DH no sol
15
15
Tb (˚C)
Tb (˚C)
10 5
10
DH with sol DH no sol
0 0
(c)
1000
2000
3000
4000 5
-5
Q int (kWh/yr)
0
1
2
3
-1
Nach (h )
(d) 15
10
10 DH with sol DH no sol
5
Tb (˚C)
Tb (˚C)
15
DH with sol, S DH with sol, N DH no sol
5
0 0
1
2
(e)
3
4
5
0
6
(f)
2
Uglass (W/m K)
Lund
Denver
Miami
Location
15
Tb (˚C)
10 DH with sol, South DH with sol, North DH no sol
5
0 20
30
(g)
40
50
60
70
g (%) ◦
Fig. 6. (a–g) The balance temperature, Tb ( C) of an oLce module versus wall U -value (Uwall ), the glazing-to-wall area ratio (GWAR), the internally produced heat (Qint ), the ventilation (Nach ), the glazing U -value (Uglass ), the location and the g-factor.
balance temperature is quite insensitive to changes in wall U -value, glazing-to-wall area ratio, and the total solar energy transmittance. Even extreme changes in GWAR only ◦ change Tb within ±1 C. Extreme changes (0.2–2 W=m2 K) ◦ in Uwall changes Tb at most by ±2 C. The balance temperature is also insensitive to extreme changes in the g-factor for the south-facing window and even less for a north-facing window. The balance temperature is relatively insensitive to changes in the glazing U -value and the location (Figs. 6e and f), although more sensitive than for GWAR, Uwall and g. An extreme change in Uglass (single glazed to triple with two low-e coatings and gas 1ll) can change Tb by about ◦ 3–4 C. However, small changes in Uglass (less than about ±0:5 W=m2 K) are negligible. The location can also a.ect
◦
the balance temperature by up to about 5 C depending on the amount of useful solar heat at each location. In Miami no solar heat is useful which means that Tb is given by Eq. (3). In the cold but sunny climate of Denver, a large amount of solar heat can be utilised and thus reducing Tb as given by Eq. (5). The di.erence in Tb for a north- and a south-facing window at the same location can be signi1cant: ◦ about 3 C for the Denver climate. The balance temperature is strongly a.ected by changes in the ventilation rate as seen in Fig. 6d. A change from 0.5 to 1 air change per hour in the ventilation rate can notably ◦ change the balance temperature by more than 2 C. Tb is very sensitive to changes in the internal free heat. The di.erence between an oLce module that is occupied by one person and that has energy eLcient lighting (Qint ≈ 400 kWh=yr)
J. Karlsson et al. / Building and Environment 38 (2003) 75–81 20
20
15
15
10
Tb (˚C)
Tb (˚C)
80
DH with sol DH no sol
10
0 0.0
0.5
1.0
0 0.0
2.0
20
15
15
10 DH with sol DH no sol
0.4
0.6
0.8
GWAR (%)
20
5
0.2
(b)
Uwall (W/m K)
Tb (˚C)
Tb (˚C)
1.5 2
(a)
10 DH with sol DH no sol
5
0
0 0
5000
10000
Q int(kWh/yr)
(c)
0
20
15
15
10 DH with sol DH no sol
1
2
3
4
5
(h )
10 DH with sol DH no sol
0
6
Lund
2
Uglass(W/m K)
(e)
3
-1
ach
5
0 0
2 N
20
5
1
(d)
Tb (˚C)
Tb (˚C)
DH with sol DH no sol
5
5
(f)
Denver
Miami
Location
20
Tb (˚C)
15
10 DH with sol DH no sol
5
0 20
30
(g)
40
50
60
70
g (%) ◦
Fig. 7. (a–g) The balance temperature, Tb ( C) of a residential building versus wall U -value (Uwall ), the glazing-to-wall area ratio (GWAR), the internally produced heat (Qint ), the ventilation (Nach ), the glazing U -value (Uglass ), the location and the g-factor.
and an oLce module with two persons, ineLcient lighting and two computers that are left on during night (Qint ≈ ◦ 4000 kWh=yr) is more than 15 C, Fig. 6c. When comparing the “improved” model with the “old” degree–hour model it is seen that the variations follow the same trends except for the GWAR, g and the location. For the GWAR the trend is the opposite for the two models depending on the fact that the old model only considers an increased GWAR as an increased heat loss and no increased solar gain. The di.erences at di.erent locations and for di.erent g-factors of the window originate from the fact that the old model does not consider solar at all.
In Figs. 7a–g the corresponding variations for the residential building are illustrated. These changes basically follow the same pattern as for the oLce module, except for a lower sensitivity to Qint and ventilation rate because of the larger volume. The balance temperature for the non-solar case is high because of the very low Qint . 5. Conclusion and discussion An explicit method to include hourly useful solar energy in the simple degree–hour method for the heating and cooling demand in buildings has been presented. Apart from
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
the common requirements of the degree–hour method, this method requires hourly accumulated solar irradiation curves for vertical surfaces. The formalism shows acceptable results for annual heating and cooling demand when compared with a dynamic simulation program. A possible source of error when using the traditional degree–hour method, apart from not correctly taking useful solar heat gain into account, is probably that the balance temperature is not correctly chosen. The variation of balance temperatures in Section 4.2 indicates highly di.erent balance temperatures for di.erent types of buildings in some cases. The balance temperature decreases with increased internally produced heat, insulation and with reduced ventilation. Note that even though the balance temperature may vary only slightly for a certain building component change, the heating demand can change considerably because the total loss coeLcient also changes (see Eq. (1)). The variation of the balance temperature depending on building components is important to acknowledge if the energy consumption is compared between, for instance, a “passive solar house” versus a “standard” house. A highly insulated passive solar house has a lower Tb and thus lower heat losses and a lower heating demand. It also has a lower contribution of useful solar heat per square metre of glazed area, which might increase the (or create a) cooling need. An oLce module with a very high level of internally produced heat and low heat losses can experience very low ◦ balance temperatures, even below 0 C. This means that the module requires cooling even at very low outdoor temperatures if no countermeasures are taken, such as shading. The balance temperature and the total loss coeLcient can be used as characteristic parameters of buildings and maybe for energy rating of buildings. Furthermore, it can be a useful parameter when considering the energy eLciency of certain building components such as, for instance windows [13]. Another example could be energy eLcient lighting. If a building has a high Tb in a cold climate so that the outside temperature most of the time is below Tb , the free heat from the (otherwise ineLcient) lamps is “useful” heat. But if a building has a low Tb and if the outside temperature most of the time is above Tb it will be more energy eLcient to install energy eLcient lighting since most of the excess energy is not useful. Although the presented formulation illustrates an improvement of the degree–hour model, it still shows quite large deviations in some cases compared to the dynamic simulation program. This comes from the fact that it does not take into account heat storage (thermal inertia), solar absorbance in the walls, temperature dependence of the
81
U -value and other common di.erences between a dynamic simulation program and a steady-state model. Furthermore, since simulation is required the use of such a model may be questionable considering that other detailed simulation tools o.er more information. However, the outline and Figs. 6 and 7 in this paper can be of help when choosing the balance temperature for a building, instead of using the same Tb for all buildings. This would improve the accuracy and increase the understanding of simple degree–hour methods and building energy demand. Acknowledgements Helena Below HSube and Kurt KSallblad, Department of Construction and Architecture, Lund University are acknowledged for sharing their knowledge about DEROB-LTH. This work was supported by the Swedish Foundation for Strategic Research through the Graduate School Energy Systems, and by Carl Trygger’s Foundation. References [1] Adalberth K. Energy use and environmental impact of new residential buildings. Report TVBH-1012, 2000, Lund, SE. [2] ASHRAE. Fundamentals handbook, US: ISBN 1-883413-88-5, 2001. [3] Lomas KJ, Eppel H, Martin CJ, Bloom1eld DP. Empirical validation of building energy simulation programs. Energy and Buildings 1997;26:253–75. [4] Clarke AJ. Energy simulation in building design. Bristol, UK: Adam Hilger, 1985. [5] Balcomb JD. Passive solar buildings. Cambridge, MA, US: MIT Press, 1992. [6] Hong T, Chou SK, Bong TY. Building simulation: an overview of developments and information sources. Building and Environment 2000;35:347–61. [7] KSallblad K. Thermal models of buildings. Determination of temperatures, heating and cooling loads, theories, models and computer programs. Report TABK—98=1015, Building Science, Lund, SE, 1998. [8] European standard, EN 832, 1998. [9] Yohanis YG, Norton B. Utilization factor for building solar-heat gain for use in a simpli1ed energy model. Applied Energy 1999;63: 227–39. [10] DuLe JA, Beckman WA. Solar energy of thermal processes, 2nd ed. USA: Wiley, 1991. [11] Karlsson J, Roos A. Modelling the angular behaviour of the total solar energy transmittance of windows. Solar Energy 2000;69(4): 321–9. [12] Boverket, Boverkets Bygg Regler, www.boverket.se, ISBN: 91-7147-454-4, 1998. [13] Karlsson J, Karlsson B, Roos A. A simple model for assessing the energy eLciency of windows. Energy and Buildings 2000;33(7): 641–51.
www.elsevier.com/locate/buildenv
Building and climate in uence on the balance temperature of buildings J. Karlssona; ∗ , A. Roosa , B. Karlssonb a Department
of Materials Science, The Angstr om Laboratory, Uppsala University, P.O. Box 534, S-751 21 Uppsala, Sweden of Construction and Architecture, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden
b Department
Received 19 October 2001; received in revised form 8 January 2002; accepted 10 January 2002
Abstract In this paper, the fact that the balance temperature varies for di.erent types of buildings is evaluated and discussed. An explicit method to add useful hourly solar heat to the degree–hour formalism directly from building and climate data is presented. This also leads to a straightforward de1nition of the solar utilisation factor. Results from taking solar energy into account are compared with results from not taking solar energy into account demonstrating large deviations. The formalism is compared with a dynamic building simulation program (DEROB-LTH). The e.ect on the balance temperature when changing several building parameters is analysed in order to illustrate the errors of using a 1xed balance temperature in the degree–hour methods for di.erent buildings. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Balance temperature; Degree hours; Solar utilisation factor
1. Introduction Considering the whole life cycle of a building, the main part of the total energy use is consumed during the occupational phase of the building rather than for the actual design and construction (including refurbishments, transport, etc.) of the building [1]. In order to predict and reduce this energy consumption, a number of advanced building energy simulation tools have been developed [2–7]. These can be used to calculate the heating and cooling demand and the peak power for a building that is going to be built or refurbished. However, detailed models require detailed input data and a high level of knowledge by the user, which limits their use. For simple studies, as in a pre-design state or for a small project, it is very common to use a simpli1ed building energy model. Most of these simple models are based on, or are in some way related to, what is referred to as the degree–hour (or degree–day) method [2,5]. The degree–hour method estimates the steady-state heat losses through the building envelope by taking the average U -value of the envelope, ventilation losses and the average internal “free” heat gain into account. One problem with the simplest form of the degree– hour method is that it does not explicitly take the useful solar heat into account, which may lead to considerable errors. Useful solar heat gain is the part of the solar energy ∗
Corresponding author. Tel.: +46-18-4713-134; fax: +46-18-500-131. E-mail address: [email protected] (J. Karlsson).
that contributes to heating when heating is needed, which can vary from hour to hour. A few ways of including useful solar heat in this simple formalism have been proposed (see for instance [5,8,9]), but not directly from building and climate data, without the use of empirical parameters. The degree–hour methods are based on the concept of the building’s balance temperature, Tb (sometimes referred to as balance point temperature, or simply base) which is the outside temperature below which the building, on average, requires heating. In many cases, the balance temperature is used as a 1xed value depending on the standard for the speci1c country in which it is used. However, the balance temperature varies greatly depending on the type of building [2] so that using a constant balance temperature can lead to considerable errors. In this paper, it is demonstrated how hourly useful solar energy can be included in the computation of the balance temperature. Knowing the amount of useful solar energy also means that the amount of harmful solar heat is known, which in turn leads to a straightforward de1nition of the solar utilisation factor, normally referred to as . Furthermore, it is illustrated how the balance temperature varies for di.erent types of buildings and building parameters. In the sections below, the simple formulation of the degree– hour method is summarised, after which the method that includes useful solar heat is outlined. In the Results section, the degree–hour method with and without useful solar energy is compared with the results of a dynamic
0360-1323/03/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 1 3 2 3 ( 0 2 ) 0 0 0 2 5 - 2
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
simulation program. Furthermore, a thorough sensitivity analysis of how the balance temperature varies with di.erent changes in building parameters is performed. The purpose of this paper is to demonstrate how the balance temperature varies for di.erent buildings and the importance of acknowledging this variation when using simple degree–hour models. The results can be the base for a methodology of how the balance temperature should be selected in order to increase the accuracy of the simple degree–hour method.
800 N E S (kWh/m2yr)
76
S W 400
0 -10
2. Present formulation
0
10
20
30
Temperature interval (˚C)
In the degree–hour method the required auxiliary heat for a building during a certain period, Jt (e.g. about 720 h for a month), can be de1ned as [2,5]
Fig. 1. Accumulated total solar irradiation, S, on vertical surfaces in four di.erent directions versus temperature interval for Lund, Sweden.
QHaux = Ktot (Tb − Tm )Jt
include useful solar energy in the degree–hour formulation, requiring hourly accumulated solar radiation curves on vertical surfaces versus temperature interval. Such a curve, S, is illustrated in Fig. 1 for a Swedish climate (Lund, 1988), for four di.erent orientations and for a whole year. These curves can be measured or compiled from hourly climate data 1les for a horizontal surface using, for instance, the Hay and Davies method [10]. According to the de1nition of the balance temperature, the useful solar heat impinging on the window is the accumulated solar heat up to Tb , i.e. S(Tb ), which is direction and climate dependent. The corresponding useful solar heat transmitted by the windows is S(Tb ) multiplied by an average g-factor (total solar energy transmittance of the window) for the period Jt, and a shading factor, , if there is any shading. For higher accuracy the S-curves (Fig. 1) can be compiled by calculating the solar incidence angle [10] and taking the corresponding g-factor [11] at each hour into account to obtain what we refer to as Sg -curves. Furthermore, the shading for each hour, , could be included (giving hourly accumulated Sg -curves). Examples of the Sg -curves for an unshaded, uncoated, triple glazed, south- and north-facing window in the Lund climate are shown in Fig. 2. If the window is unshaded (i.e. = 1 for all hours) the useful solar heat during a year is thus de1ned as
∀Tm ¡ Tb ;
(1)
where Tm represents the average outdoor temperature during the time period Jt. The total loss coeLcient, Ktot (W=K), primarily encompasses heat ow through the envelope and ventilation by Ktot = Utot Atot + VCp Nach ;
(2)
where Utot is the total average U -value of the envelope, Atot is the total envelope area, V is the enclosed volume, Cp is the heat capacity of air (about 0:33 Wh=m3 K) and Nach is the number of air changes (ventilation plus in1ltration) per hour (h−1 ). The studied time period Jt should not be longer than the heating or the cooling season, but a recommended time interval could be a month [2]. The balance temperature, Tb can be de1ned as Qint Tb = Teq − ; (3) Ktot CJt where Teq is the indoor set point temperature, assumed constant, and Qint is the internally produced heat (in Wh) during the period Jt, not including solar heat gain [5]. In ASHRAE [2] Tb is de1ned including solar heat gain but not with hourly useful solar heat. Tb is a characteristic parameter of the building. By knowing Tb and the average temperature, Tm , for the investigated period, Jt, the auxiliary heating can easily be assessed by Eq. (1). The following procedure illustrates how Tb can be explicitly de1ned, containing useful solar heat, that is accumulated hourly from weather and building data. 3. Tb including useful solar energy By introducing the balance temperature it is stipulated that there is an outdoor temperature below which the building needs to be actively heated. When considering solar energy, this de1nition also means that solar heat entering the building at outside temperatures below Tb is useful and solar heat entering the building at outside temperatures above Tb is not useful. This de1nition means that it is possible to
QUsol = Sg (Tb )Aglass ;
(4)
i.e. a point on the Sg -curve multiplied by the area of the glazed part of the building. If the building only has windows facing south, the south Sg -curve is used and if there are windows distributed on all sides of the building, Sg is taken as an area weighted average of the Sg -curves for all directions and glazed areas. Sg can be formed for each time period (e.g. month) or for the whole year, as in Fig. 2. An alternative de1nition of the balance temperature, including useful solar heat, can thus be identi1ed as Tb = Teq −
(Qint + QUsol ) : Ktot Jt
(5)
J. Karlsson et al. / Building and Environment 38 (2003) 75–81 Table 1 Data for the oLce module base-case
500
2
Sg (kWh/m yr)
400 300
S Average N
200 100 0 -10
77
0
10 20 Temperature interval
30
Since QUsol is a function of Tb in itself an iteration procedure through Eqs. (4) and (5) is performed in order to obtain the correct Tb and the corresponding QUsol . Thus, the known building parameters (i.e. Utot ; Atot ; Qint ; Uglass ; Aglass , etc.) and Sg determine which Tb that characterises the building. The highest possible Tb (¡ Teq ) is when no solar radiation is useful (transforming Eq. (5) to Eq. (3)) and at the same time the building has a low Qint and a high Ktot as, for instance, in a hot climate with the Sg -curve shifted to very high temperatures. Buildings with the lowest possible Tb have high Qint and low Ktot . For an extreme building with very high Qint and low Ktot , again no solar heat will be useful. The lowest possible Tb is consequently also described by Eq. (3). Once the balance temperature has been established by the iteration process of Eqs. (4) and (5), the auxiliary heat can be assessed by using Eq. (1) but with a Tb that includes useful solar heat. The illustrated procedure can also be used to assess the cooling demand. Normally a dynamic set point range, Tdyn , ◦ of about 5 C should be used, within which the temperature is allowed to vary without introducing active cooling. With the above de1nitions this means that solar heat entering the building at an outside temperature above Tb + Tdyn is considered negative (leads to overheating). This is given by (6)
where QNUsol is unwanted solar heat gain and Tmax is the maximum temperature during the period. This means that the auxiliary cooling demand for the period can be expressed by QCaux = Ktot (Tm − (Tb + Tdyn ))Jt + QNUsol ∀Tm ¿ Tb + Tdyn :
Lund (Sweden) 2:9 × 2:7 × 4:2 m3 0:18 W=m2 K 1:9 W=m2 K 2:2 W=m2 K 1:2 h−1 30% South 1000 kWh=yr 20 25
2.7 4.2 2.9
(GWAR: glazing-to-wall area ratio.)
Fig. 2. Accumulated total solar irradiation multiplied by the total solar energy transmittance for each hour, Sg , for a south- and north-facing window (uncoated triple glazed window: g(0) = 66%; U = 1:9 W=m2 K, where g(0) means the total solar energy transmittance at normal incidence) in a Lund climate versus temperature interval. The middle curve indicates the Sg -curve averaged over all four cardinal directions.
QNUsol = (Sg (Tmax ) − Sg (Tb + Tdyn ))Aglass ;
OLce module base-case Location Dimension Front wall U -value Glazing U -value Frame U -value Ventilation+in1ltration GWAR Window orientation Free heat, Qint Heating set point Cooling set point
(7)
The formulation with the Sg -curves leads to a simple de1nition of the solar utilisation factor [9] by Sg (Tb ) ; (8) = Sg (Tmax ) which can be evaluated zone by zone for each direction of the windows (using Sg ) or for the whole building (using Sg ). Furthermore, an average annual g-factor, g, can be extracted by the relation Sg (Tmax ) g= : (9) S(Tmax ) Note that this is orientation dependent. For the example in Fig. 2 the average annual incidence angle of direct radiation ◦ ◦ is of the order of 58 for the south-facing window and 72 for the north-facing window. 4. Results 4.1. Comparisons with “DEROB-LTH” For comparison, two di.erent base-cases were de1ned: one commercial oLce module and one residential building, both of a very simple “shoe box” form. The oLce module base-case, described in Table 1, has adiabatic surfaces in all directions except for the outside facing surface. The balance temperature and solar utilisation factor for this case were ◦ 12 C and 45%, respectively, according to Eqs. (5) and (8). The sparsely occupied residential building base-case is described in Table 2. The balance temperature and solar ◦ utilisation factor for this case were 17 C and 66%, respectively, according to Eqs. (5) and (8). For more commonly occupied residential buildings with higher Qint , see Fig. 6c. The heating and cooling demand for both base-cases were calculated for the degree–hour method without solar (“DH no sol”) and for the degree–hour method with useful solar energy (“DH with sol”) as described above. The calculations were performed for the time period of a month at that time and then summed up and presented for a whole year as seen in Figs. 3 and 4. The results were compared with a dynamic simulation program, DEROB-LTH, [7] for four
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
Lund (Sweden) 10 × 2:7 × 10 m3 0:18 W=m2 K 1:9 W=m2 K 2:2 W=m2 K 1:2 h−1 20% Equal to all orientations 1000 kWh=yr 20 25
200
2.7 10 10
QHaux, DEROB QHaux, DH with sol QHaux, DH no sol QCaux, DEROB QCaux, DH with sol QCaux, DH no sol
300
200
100
0
lund
lulea
Denver
Miami
Location Fig. 4. Comparison between the degree–hour method with (“DH with sol”) and without (“DH no sol”) solar heat and a dynamic simulation program (“DEROB-LTH”) for the residential building. The results are given in kWh=m2 oor area and year.
QHaux, DEROB QHaux, DH with sol QHaux, DH no sol QCaux, DEROB QCaux, DH with sol QCaux, DH no sol
2
Heating/Cooling demand (kWh/m yr)
Residential base-case Location Dimension Wall U -value Glazing U -value Frame U -value Ventilation+in1ltration GWAR Window orientation Free heat, Qint Heating set point Cooling set point
2
Table 2 Data for the residential base-case. Heat loss to the ground is calculated according to the Swedish norm [12] (no time delay and heat loss is multiplied with 0.75 to account for storage in the ground)
Heating/Cooling demand (kWh/m yr)
78
100
0
lund
lulea
Denver
Miami
Location Fig. 3. Comparison between the degree–hour method with (“DH with sol”) and without (“DH no sol”) solar heat and a dynamic simulation program (“DEROB”) for the oLce module. QHaux represents the heating demand and QCaux represents the cooling demand. The three bars on the left give the heating demand and the three bars on the right give the cooling demand (if any) for the four di.erent climates, respectively. The results are given in kWh=m2 oor area and year and the heating and cooling plant eLciency is set to unity.
very di.erent types of climates: Lund, SWE (lat. 56, long. 13), Lulea, SWE (lat. 66, long. 22), Denver, US (lat. 40, long. −105), Miami, US (lat. 26, long. −80). In Figs. 3 and 4 it is seen that if solar energy is taken into account in the described way the deviations from the dynamic simulation program can be highly reduced, but still not completely eliminated. Latent heat is omitted in both models. In Fig. 5 the hourly heating and cooling power is plotted versus outside temperature for the base-case oLce module in Lund. The data are simulated with DEROB-LTH and it is seen that one can identify a certain outdoor temperature, the balance temperature, below which heating is needed. The solid square illustrates the balance temperature as computed with useful solar energy as described above, and the solid triangle illustrates the balance temperature as computed without useful solar energy. It is seen that the balance temperature is more accurately de1ned (the building requires
Fig. 5. Hourly heating and cooling power for the base-case oLce module in Lund versus outside temperature. The heating power is plotted on the positive side of the y-axis and the cooling power is plotted on the negative side of the y-axis. The solid square indicates the balance temperature, Tb , calculated including useful solar energy and the solid triangle indicates the balance temperature, Tb , calculated not including useful solar energy.
heating below Tb and not above Tb ) when hourly useful solar heat gain is included, than when it is not included. 4.2. Di
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
10
10 Tb (˚C)
15
Tb (˚C)
15
DH with sol DH no sol
5
0 0.0
0.5
1.0
(a)
DH with sol DH no sol
5
1.5
0 0.0
2.0
2
0.2
0.4
(b)
U-wall (W/m K)
79
0.6
0.8
GWAR (%)
20 DH with sol DH no sol
15
15
Tb (˚C)
Tb (˚C)
10 5
10
DH with sol DH no sol
0 0
(c)
1000
2000
3000
4000 5
-5
Q int (kWh/yr)
0
1
2
3
-1
Nach (h )
(d) 15
10
10 DH with sol DH no sol
5
Tb (˚C)
Tb (˚C)
15
DH with sol, S DH with sol, N DH no sol
5
0 0
1
2
(e)
3
4
5
0
6
(f)
2
Uglass (W/m K)
Lund
Denver
Miami
Location
15
Tb (˚C)
10 DH with sol, South DH with sol, North DH no sol
5
0 20
30
(g)
40
50
60
70
g (%) ◦
Fig. 6. (a–g) The balance temperature, Tb ( C) of an oLce module versus wall U -value (Uwall ), the glazing-to-wall area ratio (GWAR), the internally produced heat (Qint ), the ventilation (Nach ), the glazing U -value (Uglass ), the location and the g-factor.
balance temperature is quite insensitive to changes in wall U -value, glazing-to-wall area ratio, and the total solar energy transmittance. Even extreme changes in GWAR only ◦ change Tb within ±1 C. Extreme changes (0.2–2 W=m2 K) ◦ in Uwall changes Tb at most by ±2 C. The balance temperature is also insensitive to extreme changes in the g-factor for the south-facing window and even less for a north-facing window. The balance temperature is relatively insensitive to changes in the glazing U -value and the location (Figs. 6e and f), although more sensitive than for GWAR, Uwall and g. An extreme change in Uglass (single glazed to triple with two low-e coatings and gas 1ll) can change Tb by about ◦ 3–4 C. However, small changes in Uglass (less than about ±0:5 W=m2 K) are negligible. The location can also a.ect
◦
the balance temperature by up to about 5 C depending on the amount of useful solar heat at each location. In Miami no solar heat is useful which means that Tb is given by Eq. (3). In the cold but sunny climate of Denver, a large amount of solar heat can be utilised and thus reducing Tb as given by Eq. (5). The di.erence in Tb for a north- and a south-facing window at the same location can be signi1cant: ◦ about 3 C for the Denver climate. The balance temperature is strongly a.ected by changes in the ventilation rate as seen in Fig. 6d. A change from 0.5 to 1 air change per hour in the ventilation rate can notably ◦ change the balance temperature by more than 2 C. Tb is very sensitive to changes in the internal free heat. The di.erence between an oLce module that is occupied by one person and that has energy eLcient lighting (Qint ≈ 400 kWh=yr)
J. Karlsson et al. / Building and Environment 38 (2003) 75–81 20
20
15
15
10
Tb (˚C)
Tb (˚C)
80
DH with sol DH no sol
10
0 0.0
0.5
1.0
0 0.0
2.0
20
15
15
10 DH with sol DH no sol
0.4
0.6
0.8
GWAR (%)
20
5
0.2
(b)
Uwall (W/m K)
Tb (˚C)
Tb (˚C)
1.5 2
(a)
10 DH with sol DH no sol
5
0
0 0
5000
10000
Q int(kWh/yr)
(c)
0
20
15
15
10 DH with sol DH no sol
1
2
3
4
5
(h )
10 DH with sol DH no sol
0
6
Lund
2
Uglass(W/m K)
(e)
3
-1
ach
5
0 0
2 N
20
5
1
(d)
Tb (˚C)
Tb (˚C)
DH with sol DH no sol
5
5
(f)
Denver
Miami
Location
20
Tb (˚C)
15
10 DH with sol DH no sol
5
0 20
30
(g)
40
50
60
70
g (%) ◦
Fig. 7. (a–g) The balance temperature, Tb ( C) of a residential building versus wall U -value (Uwall ), the glazing-to-wall area ratio (GWAR), the internally produced heat (Qint ), the ventilation (Nach ), the glazing U -value (Uglass ), the location and the g-factor.
and an oLce module with two persons, ineLcient lighting and two computers that are left on during night (Qint ≈ ◦ 4000 kWh=yr) is more than 15 C, Fig. 6c. When comparing the “improved” model with the “old” degree–hour model it is seen that the variations follow the same trends except for the GWAR, g and the location. For the GWAR the trend is the opposite for the two models depending on the fact that the old model only considers an increased GWAR as an increased heat loss and no increased solar gain. The di.erences at di.erent locations and for di.erent g-factors of the window originate from the fact that the old model does not consider solar at all.
In Figs. 7a–g the corresponding variations for the residential building are illustrated. These changes basically follow the same pattern as for the oLce module, except for a lower sensitivity to Qint and ventilation rate because of the larger volume. The balance temperature for the non-solar case is high because of the very low Qint . 5. Conclusion and discussion An explicit method to include hourly useful solar energy in the simple degree–hour method for the heating and cooling demand in buildings has been presented. Apart from
J. Karlsson et al. / Building and Environment 38 (2003) 75–81
the common requirements of the degree–hour method, this method requires hourly accumulated solar irradiation curves for vertical surfaces. The formalism shows acceptable results for annual heating and cooling demand when compared with a dynamic simulation program. A possible source of error when using the traditional degree–hour method, apart from not correctly taking useful solar heat gain into account, is probably that the balance temperature is not correctly chosen. The variation of balance temperatures in Section 4.2 indicates highly di.erent balance temperatures for di.erent types of buildings in some cases. The balance temperature decreases with increased internally produced heat, insulation and with reduced ventilation. Note that even though the balance temperature may vary only slightly for a certain building component change, the heating demand can change considerably because the total loss coeLcient also changes (see Eq. (1)). The variation of the balance temperature depending on building components is important to acknowledge if the energy consumption is compared between, for instance, a “passive solar house” versus a “standard” house. A highly insulated passive solar house has a lower Tb and thus lower heat losses and a lower heating demand. It also has a lower contribution of useful solar heat per square metre of glazed area, which might increase the (or create a) cooling need. An oLce module with a very high level of internally produced heat and low heat losses can experience very low ◦ balance temperatures, even below 0 C. This means that the module requires cooling even at very low outdoor temperatures if no countermeasures are taken, such as shading. The balance temperature and the total loss coeLcient can be used as characteristic parameters of buildings and maybe for energy rating of buildings. Furthermore, it can be a useful parameter when considering the energy eLciency of certain building components such as, for instance windows [13]. Another example could be energy eLcient lighting. If a building has a high Tb in a cold climate so that the outside temperature most of the time is below Tb , the free heat from the (otherwise ineLcient) lamps is “useful” heat. But if a building has a low Tb and if the outside temperature most of the time is above Tb it will be more energy eLcient to install energy eLcient lighting since most of the excess energy is not useful. Although the presented formulation illustrates an improvement of the degree–hour model, it still shows quite large deviations in some cases compared to the dynamic simulation program. This comes from the fact that it does not take into account heat storage (thermal inertia), solar absorbance in the walls, temperature dependence of the
81
U -value and other common di.erences between a dynamic simulation program and a steady-state model. Furthermore, since simulation is required the use of such a model may be questionable considering that other detailed simulation tools o.er more information. However, the outline and Figs. 6 and 7 in this paper can be of help when choosing the balance temperature for a building, instead of using the same Tb for all buildings. This would improve the accuracy and increase the understanding of simple degree–hour methods and building energy demand. Acknowledgements Helena Below HSube and Kurt KSallblad, Department of Construction and Architecture, Lund University are acknowledged for sharing their knowledge about DEROB-LTH. This work was supported by the Swedish Foundation for Strategic Research through the Graduate School Energy Systems, and by Carl Trygger’s Foundation. References [1] Adalberth K. Energy use and environmental impact of new residential buildings. Report TVBH-1012, 2000, Lund, SE. [2] ASHRAE. Fundamentals handbook, US: ISBN 1-883413-88-5, 2001. [3] Lomas KJ, Eppel H, Martin CJ, Bloom1eld DP. Empirical validation of building energy simulation programs. Energy and Buildings 1997;26:253–75. [4] Clarke AJ. Energy simulation in building design. Bristol, UK: Adam Hilger, 1985. [5] Balcomb JD. Passive solar buildings. Cambridge, MA, US: MIT Press, 1992. [6] Hong T, Chou SK, Bong TY. Building simulation: an overview of developments and information sources. Building and Environment 2000;35:347–61. [7] KSallblad K. Thermal models of buildings. Determination of temperatures, heating and cooling loads, theories, models and computer programs. Report TABK—98=1015, Building Science, Lund, SE, 1998. [8] European standard, EN 832, 1998. [9] Yohanis YG, Norton B. Utilization factor for building solar-heat gain for use in a simpli1ed energy model. Applied Energy 1999;63: 227–39. [10] DuLe JA, Beckman WA. Solar energy of thermal processes, 2nd ed. USA: Wiley, 1991. [11] Karlsson J, Roos A. Modelling the angular behaviour of the total solar energy transmittance of windows. Solar Energy 2000;69(4): 321–9. [12] Boverket, Boverkets Bygg Regler, www.boverket.se, ISBN: 91-7147-454-4, 1998. [13] Karlsson J, Karlsson B, Roos A. A simple model for assessing the energy eLciency of windows. Energy and Buildings 2000;33(7): 641–51.