Processing the output

Job no. Units Sec. par. Model

04.10.01,02 A_ext – (4.25)

04.10.27,01 mroof,r – (4.25) 04.10.31,08-11 V_roof τ_roof (4.26)

04.25.17 Aext – (4.25)

04.25.31 A_ext d_r,i (4.26)

Table 4.8: Parameters and price models used for calculating the cost of constructing the roof.

by:

Qh = 1 1000

8760

X

i=1

(Q⁰_h)i·∆t (4.96)

Qc = 1 1000

8760

X

i=1

(Q⁰_c)i·∆t, (4.97)

where ∆t= 1 h is the sample rate. The effect of internal loads and solar gains are included inQh andQc.

The energy efficiency of the district heating unit is not considered. The energy efficiency of the cooling system must be considered in order to find the amount of electric energy Q_c,el it requires. Q_c and Q_c,el are related through the coefficient of performance (COP) for the cooling system. The COP-valueηc for the cooling system is given by:

η_c= Qc

Q_c,el ⇔ Q_c,el=Qc

η_c. (4.98)

The energyQ_wrequired for producing domestic hot water is calculated by assuming that the total volume of the hot water is proportional with the heated floor area A_tot. For non-residential buildings, the Danish building regulations [13] assume that 100 liters of hot water is required annually for every m² of heated floor area.

Therefore, the annual volumeVw of hot water required is

V_w =A_tot·100 l/m², (4.99)

and the massm_w of the water is

mw =%w·Atot·100 l/m², (4.100)

where%_w is the density of water. The annual amount of energyQ_w required for heating the domestic hot water is:

Q_w =C_w·∆T_w=m_w·c_w·∆T_w=%_w·A_tot·c_w·∆T_w·100 l/m², (4.101) whereC_wandc_w are the heat capacity and the specific heat capacity, respectively, for the hot water, and where ∆Tw is the temperature difference required for heating the water.

The specific fan power (SFP-value)εvfor the ventilation fan is defined as the ratio between the electrical powerQ⁰_vrequired by the fan and the volume air flowV⁰:

ε_v=Q⁰_v

V⁰ ⇔ Q⁰_v=V⁰·ε_v. (4.102)

The annual amount of electric energyQ_v for ventilating the building is thus given by:

Qv= 1 1000

8760

X

i=1

(Q⁰_v)i·∆t. (4.103)

The annual amount of energyQ_l required for artificial lighting is calculated in a similar way as by Nielsen [47], except that the average daylight factor DFavg is assumed to be constant, and thereby independent of the window area. A small value is used in order to provide a conservative estimate ofQl.

Nielsen propose that 2 W of power is used per m²of internal floor area when the average internal illumination levelIavgis between 100 and 500 lux, and that 5 W of power is used per m²whenI_avg is below 100 lux, that is:

Q⁰_l=







0 W for Iavg≥500 lux

2 W/m²·A_int for 100 lux≤I_avg<500 lux 5 W/m²·Aint for Iavg<100 lux

, (4.104)

whereQ⁰_lis the power required for lighting. I_avgis related toDF_avg in the following way:

I_avg=DF_avg·I_h, (4.105)

where I_h is the global illuminance, which can be found in DRY climate data sets. It is assumed that electric lighting is only used when the building is used. Given the DRY data, the daylight factor, and the periods where the building is used, the following parameters can be calculated:

ϕ1 : annual number of hours where 100 lux≤Iavg<500 lux (4.106) ϕ₂ : annual number of hours where I_avg<100 lux (4.107) The parametersϕ₁andϕ₂ only include periods where the building is used.

The following expression is used in order to calculate the annual amount of energy Q_l that is required for lighting:

Ql= A_int

1000 2 W/m²·ϕ1+ 5 W/m²·ϕ2

(4.108)

The annual amount of energyQtot required by the building is thus expressed in terms of the output from the performance calculation methods, as well as constants.

Given Q_tot, the performance measures EF₃, EF₂ and EF₁ can be calculated using the expressions (4.16), (4.17) and (4.18).

The performance measure Q_be is calculated using the expression (4.21), which requires the heat lossQ⁰_eand the areaAeof the building envelope. The heat lossQ⁰_ethrough the building envelope, not including windows and doors, is given by:

Q⁰_e=

Uwall·(A⁽¹⁾_wall+A⁽²⁾_wall) +Ur·Aext+Ug·Aext+ Ψf w·Oext

·∆Thl, (4.109) where ∆T_hl is the design temperature difference. The area of the building envelopeA_e, not including windows and doors, is given by:

Ae=A⁽¹⁾_wall+A⁽²⁾_wall+ 2·Aext. (4.110)

The expressions required for calculating U_g, U_wall, U_r, U_win⁽¹⁾ and U_win⁽²⁾, are provided in Section 4.3.3. The expressions required for calculatingA⁽¹⁾_wall,A⁽²⁾_wall andA_ext are provided in Section 4.3.1.

4.4.2 Performance measures for the indoor environment

The annual number of hours with overheating is calculated by making linear interpolation between the internal air temperaturesTa for the time steps ti, i= 1, . . . ,8760, as illus-trated in Figure 4.12. Overheating occur whenT_aexceeds the maximum allowed internal air temperatureTmax.

Only time periods where the building is occupied contribute to the annual number of hours with overheating.

Rounding errors occur when calculatingTa. This must be taken into consideration when calculating time periods with overheating, since T_max is often used as set point for the cooling system. The effect of rounding errors is that when the cooling system is active, T_a is not exactly equal toT_max, as indicated in Figure 4.12.

Ta

Tmax Tmax +ε

Time step ti ti+1

ti-1 Time period with overheating

Time period where cooling system is active

Figure 4.12: An illustration of the method used for calculating the annual number of hours with overheating.

The time periods where overheating occur is therefore not calculated by comparingT_a withTmax, but by comparingTawith ˆTmax=Tmax+ε, whereεis a tolerance level. Using ε'10⁻³K usually provides satisfactory results.

The contribution ∆t_i to the annual number of hours with overheating, from the time period ranging fromtitoti+1, is calculated using the following linear interpolation:

Tˆ_a(∆t) =T_i(1−∆t) +T_i+1∆t. (4.111)

The time ∆t^∗, where the interpolated internal air temperature becomes equal to ˆTmax, is given by:

Ti(1−∆t^∗) +Ti+1∆t^∗= ˆTmax ⇔ ∆t^∗=

Tˆ_max−T_i Ti+1−Ti

. (4.112)

The following scheme is used for calculating ∆t_i:

∆ti=















0 if the building is empty

0 if Ti <Tˆmax and Ti+1<Tˆmax

1−∆t^∗ if Ti <Tˆmax and Ti+1≥Tˆmax

∆t^∗ if Ti ≥Tˆmax and Ti+1<Tˆmax

1 if Ti ≥Tˆmax and Ti+1≥Tˆmax

, for i= 1, . . . ,8759. (4.113)

This approach is applied to the simulation results from both thermal zones, which provides the contributions ∆t⁽¹⁾_i and ∆t⁽²⁾_i , i = 1, . . . ,8759. The annual number of hours with overheating for the two thermal zones, denotedOH⁽¹⁾ andOH⁽²⁾, respectively, can thus be calculated using the following expressions:

OH⁽¹⁾=

8759

X

i=1

∆t⁽¹⁾_i (4.114)

OH⁽²⁾=

8759

X

i=1

∆t⁽²⁾_i (4.115)

The performance measuresDH⁽¹⁾andDH⁽²⁾, which are used as very simple measures for the utilization level of natural light, are given by:

DH⁽¹⁾= wint

h⁽¹⁾_win (4.116)

DH⁽²⁾= w_int

h⁽²⁾_win, (4.117)

wherewintis given by the expression (4.47), and whereh⁽¹⁾_win andh⁽²⁾_win are given by (4.52) and (4.53), respectively.

4.4.3 Performance measures for the economy

Given the unit pricesP ∈R^njobsfor the construction jobs, the construction costsCconfor the building is given by the following expression:

C_con=

njobs

X

i=1

u_i·P_i, (4.118)

whereu_i is the number of units required for construction jobi. The number of units for the required construction jobs are provided in Tables 4.4, 4.5, 4.6, 4.7 and 4.8.

Only the cost of energy is considered when calculating the annual costCop of operating the building. C_op is therefore given by:

C_op=p_el·Q_el+p_dh·Q_dh, (4.119)

wherep_elandp_dhare energy prices for electrical energy and energy supplied by the district heating system, respectively.

In document A method for optimizingthe performance of buildings (Sider 73-77)