4.2 The performance calculations
4.2.1 Energy and indoor environment
TheU-value requirements can be addressed by specifying upper limits on the performance measuresUg,Uwall,Ur,Uwin(1) andUwin(2).
The Danish building regulations furthermore establish an upper bound on the heat loss through the building envelope, not including windows and doors. The heat lossQe per m2 of the building envelope is required to be less than 6 W, that is:
Qe Ae ≤6W
m2 ⇔ 6 W
m2·Ae−Qe≥0, (4.20)
whereAeis the area of the building envelope, not including windows and doors. The left hand side of (4.20) is used as a performance measure:
BE= 6W
m2·Ae−Qe. (4.21)
The Danish building regulations also specify upper limits on the linear thermal trans-mittances for the interaction between various parts of the building envelope. However, calculating the linear thermal transmittance for the interaction between two building com-ponents requires numerical methods for solving partial differential equations. This could make the performance calculations more time-consuming, and thereby increase the time needed for solving the optimization problem (3.8).
All linear thermal transmittances are therefore assumed to be constant, and close to or equal to the upper limits specified by the building regulations, in order to provide a conservative estimate of the design decisions. Developing methods for performing fast and reliable calculations for the linear thermal transmittance is a possible topic for further research. Methods similar to the one described in the paper included in Appendix B might be useful for this purpose; however, this has not been investigated as part of this study.
1. A node representing the external environment, with temperatureText. 2. A node representing the internal air, with temperatureTa.
3. A node representing the internal surfaces, with temperatureTs. 4. A node representing the thermal mass, with temperatureTw.
Ta Text
Ts Ki Kw
C i
C w Tw
Text
UA Q's Q'a Kr
Ta Text Tw Ts
C w C i
Kw Ki UA
Q'a Q's
Text
Text Ta Tw Ts
C w
C i
Kw Ki UA
Q's Q'a
Kg Ta Text Tw Ts
C w C i
Kw Ki UA
Q'a Q's
floors N
Figure 4.5: The thermal networks used for estimating the energy performance for each of the two zones.
The networks consists of the thermal conductance between the thermal mass and the surface Kw, the conductance between the surface and the internal airKi, and the con-ductance between the internal air and the external environment U A, which is used for calculating the heat loss through the external walls and windows. The heat loss through the roof construction and the ground slab are calculated using the conductancesKr and Kg, respectively. The effective heat capacity of the constructions is represented byCw, and the heat capacity of the internal air and property contents is represented byCi.
The heat sourcesQ0sandQ0a are given by:
Q0s=S wsQ0sun, (4.22)
and
Q0a=S waQ0sun+Q0l+Q0h−Q0c, (4.23) whereQ0sun is the transmitted solar energy, andS is the shading factor for the shading device, which is assumed to be variable. The factorsws andwa are the fractions of the solar energy absorbed by the internal surfaces and the internal air, respectively. The contribution from internal loads is represented by Q0l, and the contributions from the heating and cooling systems are represented byQ0handQ0c, respectively.
The only difference between the networks used for representing the thermal zones is that the first floor and the top floor have additional heat losses due to the heat losses through the roof construction and the ground slab. The networks representing the intermediate floors are all identical.
In order to simplify the calculations, the additional heat losses are distributed equally among all floors. All networks thereby become identical with the network proposed by Nielsen [50]. The thermal conductance between the internal and external air is denoted dU A, which is given by:
dU A=U A+Kr
N +bg·Kg
N . (4.24)
This means that the energy performance of the building can be estimated using only one simulation for each thermal zone. The network used for estimating the energy performance of a single floor for each of the two thermal zones is shown in Figure 4.6.
The factorbg in (4.24) is a temperature factor that compensates for smaller temperature differences for some building components, where
1. the external temperature of the component is not the same as the external air temperature, or
2. the internal temperature of the component is not the same as the internal air tem-perature.
Given the network parameters, information about the internal loads, settings for the HVAC systems, active solar shading devices and variable insulation system, as well as weather data and information about the location of the building, the method by Nielsen [50] provides, among others, hourly values of the required energy for heating and cooling the building, the internal air temperature, as well as ventilations rates for natural and mechanical ventilation systems.
The method furthermore provides evaluations of the thermal indoor environment, ex-pressed in terms of the number of hours with overheating, based on a user-defined maxi-mum allowed indoor air temperature. Finally, the method provides hourly values of the predicted mean vote (PMV), and the predicted percentage of dissatisfied (PPD).
ÛUA
Ta Text
Ts Kw Ki
C i C w
Tw
Q's Q'a
Figure 4.6: The thermal network resulting from distributing the additional heat losses equally among the floors. The network is used for estimating the performance of a single floor for each of the two thermal zones.
The current version of the building optimization method does not use the PMV and PPD values as performance measures. The number of hours with overheating is calculated using linear interpolation between hourly values of the indoor air temperature. This method is described in Section 4.4.2.
Furthermore, active solar shading devices are not used, and the windows have no overhang.
Parameter Unit Description
Ta∈R8760 ◦C Vector with hourly values of the internal air temperature.
Q0h∈R8760 W Vector with hourly values of the required power for heating the building.
Q0c∈R8760 W Vector with hourly values of the required power for cooling the building.
V0∈R8760 m3/s Vector with hourly values of the mechan-ical ventilation rate.
Table 4.1: The output from the method by Nielsen [50], which is used for calculating the performance measures.
The output from the method by Nielsen [50], which is used for calculating the performance measures, is shown in Table 4.1.
Section 4.3.3 concerns calculations of the network parameters, and other parameters re-quired by the performance calculation method, based on decision variables and constant parameters.