2.4 Room Load¶

2.4 Calculation of Room Load¶

The daily integrated room load is calculated by calculating the daily integrated steady-state heat gain per unit floor area based on the envelope configuration of each room and multiplying it by the "factor for converting steady-state heat gain to room load".

The inputs and outputs shown in this entire section are listed in the table below.

Table 22. Input (entire section 2.4)
Variable Name	Description	Unit	Reference
\(A_{room,i}\)	Area of room	m²	Form 2-1: (1) Floor Area
\(D_{env,i,j}\)	Orientation of the envelope j belonging to room	-	Form 2-4: (2) Orientation
\(γ_{wind,c,i,j}\)	Sunshade effect coefficient of window, etc. j belonging to room i (cooling)	-	Form 2-4: (3) Sunshade Effect Coefficient (Cooling)
\(γ_{wind,h,i,j}\)	Sunshade effect coefficient of window, etc. j belonging to room i (heating)	-	Form 2-4: (3) Sunshade Effect Coefficient (Heating)
\(A_{env,i,j}\)	Area of the envelope j belonging to room	m²	Form 2-4: (5) Envelope Area (including windows)
\(A_{wind,i,j}\)	Area of window, etc. j belonging to room	m²	Form 2-4: (7) Openings Window Area
\(S_{dsr,d,t}\)	Direct Normal Irradiance at date \(d\), time \(t\)	W/m²	2.2.1
\(S_{isr,d,t}\)	Horizontal sky solar radiation at date \(d\), time \(t\)	W/m²	2.2.1
\(S_{nsr,d,t}\)	Horizontal Long-wavelength Radiation at date \(d\), time \(t\)	W/m²	2.2.1
\(Season_{d}\)	Cooling/heating season (cooling, intermediate, or heating seasons) on date \(d\)	-	2.2.2
\(\theta_{AC,oa,d}\)	Daily average outside air temperature on date \(d\)	℃	2.2.3
\(\theta_{AC,oa,ave}\)	Annual average outside air temperature	℃	2.2.3
\(\theta_{AC,room,i,d}\)	Temperature setting of room i on date \(d\)	℃	2.3.1
\(O_{AC,room,i,d}\)	Operating status of the air conditioner in room i on date \(d\)	Boolean value	2.3.3
\(Q_{AC,room,light,i,d}\)	Daily integrated value of lighting heat generation density in room i on date \(d\)	Wh/(m²・d)	2.3.4
\(Q_{AC,room,human,i,d}\)	Daily integrated value of heat generation density of occupants in room i on date \(d\)	Wh/(m²・d)	2.3.4
\(Q_{AC,room,app,i,d}\)	Daily integrated value of equipment heat generation density in room i on date \(d\)	Wh/(m²・d)	2.3.4
\(U_{wall,i,j}\)	Thermal transmittance of exterior walls, etc. j belonging to room	W/(m²・K)	A.1
\(U_{wind,i,j}\)	Thermal transmittance of windows, etc. j belonging to room	W/(m²・K)	A.2
\(\eta_{i,j}\)	Solar heat gain coefficient of windows, etc. j belonging to room	-	A.2
\(a_{tc1,d}, a_{tc2,d}\)	Coefficient for converting steady-state heat gain caused by temperature difference on date \(d\) to room load (cooling)	-	A.3
\(a_{th1,d}, a_{th2,d}\)	Coefficient for converting steady-state heat gain caused by temperature difference on date \(d\) to room load (heating)	-	A.3
\(a_{sc1,d}, a_{sc2,d}\)	Coefficient for converting steady-state heat gain due to solar radiation on date \(d\) to room load (cooling)	-	A.3

Table 23. Output (Section 2.4)
Variable Name	Description	Unit	References
\(Q_{AC,room,c,i,d}\)	Daily integrated room load (cooling) for room i on date \(d\)	Wh/(m²・d)	2.5.1
\(Q_{AC,room,h,i,d}\)	Daily integrated room load (heating) of room i on date \(d\)	Wh/(m²・d)	2.5.1

2.4.1 Incident Solar Radiation to Envelope¶

Table 24. Input
Variable Name	Description	Unit	Reference
\(D_{env,i,j}\)	Orientation of envelope, etc. j belonging to room	-	Form 2-4: (2) Orientation
\(S_{dsr,d,t}\)	Direct normal irradiance at date \(d\), time t	W/m²	2.2.1
\(S_{isr,d,t}\)	Horizontal sky solar radiation at date \(d\), time t	W/m²	2.2.1
\(S_{nsr,d,t}\)	Horizontal long-wavelength radiation at date \(d\), time t	W/m²	2.2.1
\(lati\)	Latitude	rad	2.2.1
\(longi\)	Longitude	rad	2.2.1

Table 25. Output
Variable Name	Description	Unit	Reference
\(I_{dsr,j,d}\)	Integrated direct solar radiation on orientation j on date \(d\)	Wh/(m²・d)	2.4.2.6, 2.4.2.7
\(I'_{dsr,j,d}\)	Integrated direct solar radiation on orientation j on date \(d\) (with angle-of-incidence characteristic)	Wh/(m²・d)	2.4.2.6, 2.4.2.7
\(I_{isr,j,d}\)	Integrated sky solar radiation on orientation j on date \(d\)	Wh/(m²・d)	2.4.2.6, 2.4.2.7
\(I_{nsr,j,d}\)	Integrated long-wavelength radiation to orientation j on date \(d\)	Wh/(m²・d)	2.4.2.4, 2.4.2.5
\(\eta_{max}\)	Maximum angle-of-incidence characteristic	-	2.4.2.7

First, the inclination angle \(\theta_{env,slp,j}\) [°] and the azimuth angle \(\theta_{env,drct,j}\) [°] are specified according to the orientation of the envelope, etc. j belonging to room i \(D_{env,i,j}\), as in the following table.

Table 26. Azimuth and tilt angles relative to the orientation of the envelope
Orientation \(D_{env,i,j}\)	Inclination angle \(\theta_{env,slp,j}\)	Azimuth \(\theta_{env,drct,j}\)
South	90	0
Southwest	90	45
West	90	90
Northwest	90	135
North	90	180
Northeast	90	225
East	90	270
Southeast	90	315
Horizontal	0	0

The integrated direct solar radiation \(I_{dsr,j,d}\), the integrated sky solar radiation \(I_{isr,j,d}\), and the integrated long-wavelength radiation \(I_{nsr,j,d}\) to the envelope j on date \(d\) are calculated according to the azimuth and tilt angle of the envelope j as follows. Note that 0.5 in the formula is the sky view factor from a vertical surface, and 0.1 is the solar reflectance at the ground surface. Also, \(\theta_{j,d,t}\) is the angle between the normal of envelope j and the sun direction at date \(d\) time t, \(h_{sun,d,t}\) is the sun altitude at date \(d\) time t, and \(\theta_{sun,d,t}\) is the sun azimuth angle at date \(d\) time t. \(\eta_{j,d,t}\) is the angle-of-incidence characteristic of the envelope j at date \(d\) time t, which should be obtained by the following formula. \(\eta_{max}\) is the maximum value of \(\eta_{j,d,t}\), which is 0.89.

\[ I_{dsr,j,d} = \sum_{t=1}^{24} \left( S_{dsr,d,t} \times \cos \theta_{j,d,t} \right) \]

\[ I'_{dsr,j,d} = \sum_{t=1}^{24} \left( S_{dsr,d,t} \times \cos \theta_{j,d,t} \times \eta_{j,d,t} \right) \]

\[ I_{isr,j,d} = \begin{cases} \sum_{t=1}^{24} \left( 0.5 \times S_{isr,d,t} + 0.1 \times 0.5 \times \left( S_{isr,d,t} + S_{dsr,d,t} \times \sin h_{sun,d,t} \right) \right) , & (\theta_{env,slp,j} = 90) \\ \sum_{t=1}^{24} S_{isr,d,t} , & (\theta_{env,slp,j} = 0) \end{cases} \]

\[ I_{nsr,j,d} = \begin{cases} \sum_{t=1}^{24} \left( 0.5 \times S_{nsr,d,t} \right), & (\theta_{wall,slp,j} = 90) \\ \sum_{t=1}^{24} S_{nsr,d,t}, & (\theta_{wall,slp,j} = 0) \end{cases} \]

\[ \eta_{j,d,t} = \frac{ 2.3920 \times \cos \theta_{j,d,t} - 3.8636 \times \cos^{3} \theta_{j,d,t} + 3.7568 \times \cos^{5} \theta_{j,d,t} - 1.3952 \times \cos^{7} \theta_{j,d,t} }{ \eta_{max} } \]

\[ \cos \theta_{j,d,t} = \max \left\{ 0,\ \cos h_{sun,d,t} \times \left( \cos \theta_{sun,d,t} \times \cos \theta_{env,drct,j} + \sin \theta_{sun,d,t} \times \sin \theta_{env,drct,j} \right) \right\} \]

The sine and cosine values of the solar altitude \(h_{sun,d,t}\) [rad] and the solar azimuth angle \(\theta_{sun,d,t}\) [rad] at date \(d\), time \(t\)are calculated as follows. Note that the unit of angle in obtaining the sine and cosine is radian.

\[ \sin h_{sun,d,t} = \sin(lati) \sin (del_{d}) + \cos (lati) \cos (del_{d}) + \cos (Tim_{d,t}) \]

\[ \cos h_{sun,d,t} = \sqrt{1 - \sin^2 (h_{sun,d,t})} \]

\[ \sin \theta_{sun,d,t} = \frac{ \cos (del_{d}) \sin (Tim_{d,t}) }{ \cos h_{sun,d,t} } \]

\[ \cos \theta_{sun,d,t} = \frac{ \sin h_{sun,d,t} \sin(lati) - \sin(del_{d}) } { \cos h_{sun,d,t} \cos (lati) } \]

where \(del_{d}\) [rad] is the solar declination of date \(d\) and \(e_{d}\) [rad] is the equation of time on date \(d\), which is obtained from the following formula. The daynum(d) in the formula is the function to find the day of year of the date \(d\).

\[ \begin{aligned} del_{d} &= 0.006322 \\ &\quad - 0.405748 \times \cos(w + 0.153231) \\ &\quad - 0.005880 \times \cos(2w - 0.207099) \\ &\quad - 0.003233 \times \cos(3w + 0.620129) \end{aligned} \]

\[ \begin{aligned} e_{d} &= -0.0002786409 \\ &\quad + 0.1227715 \times \cos(w + 1.498311) \\ &\quad - 0.1654575 \times \cos(2w - 1.261546) \\ &\quad - 0.00535383 \times \cos(3w - 1.1571) \end{aligned} \]

\[ w = \begin{cases} \frac{2\pi} {366} \times daynum(d), & (daynum(d) \leqq 59) \\ \frac{2\pi} {366} \times \{daynum(d) + 1\}, & (\mbox{otherwise}) \end{cases} \]

\(Tim_{d,t}\) [rad] is the hour angle at date \(d\) time t, which is obtained from the following formula. Where, time t is from 1 to 24.

\[ Tim_{d,t} = \frac{\pi}{12} \times (t + e_{d} -12) + longi - \frac{3\pi}{4} \]

2.4.2 Steady-State Heat Gain from Envelope¶

Steady-state heat gain from the envelope is calculated separately for "steady-state heat gain due to temperature difference" and "steady-state heat gain due to solar radiation".

Table 27. Input
Variable Name	Description	Unit	Reference
\(Q_{wall,t,i,d}\)	Steady-state heat gain through transmission due to temperature differences, etc. from exterior walls, etc. of room i on date \(d\)	Wh/d	2.4.2.2
\(Q_{wind,t,i,d}\)	Steady-state heat gain through transmission due to temperature differences from windows, etc. of room i on date \(d\)	Wh/d	2.4.2.3
\(Q_{wall,n,i,d}\)	Steady-state heat loss through transmission due to long-wavelength radiation from exterior walls, etc. of room i on date \(d\)	Wh/d	2.4.2.4
\(Q_{wind,n,i,d}\)	Steady-state heat loss through transmission due to long-wavelength radiation from windows, etc. of room i on date \(d\)	Wh/d	2.4.2.5
\(Q_{wall,s,i,d}\)	Steady-state heat gain due to solar radiation from exterior walls, etc. of room i on date \(d\)	Wh/d	2.4.2.6
\(Q_{wind,s,i,d}\)	Steady-state heat gain due to solar radiation from windows, etc. in room i on date \(d\)	Wh/d	2.4.2.7
\(A_{room,i}\)	Floor area of room	m²	Form 2-1: (1) Room Area
\(AirConditioning_{i}\)	Whether room i is an air-conditioned room or not	Boolean value	Form 2-4: (1) True if there is a room name in the air conditioned zone name. False otherwise.

Table 28. Output
Variable Name	Description	Unit	References
\(Q_{AC,room,tin,i,d}\)	Steady-state heat gain due to temperature difference in room i on date \(d\)	Wh/(m²・d)	2.4.4
\(Q_{AC,room,sin,i,d}\)	Steady-state heat gain due to solar radiation in room i on date \(d\)	Wh/(m²・d)	2.4.4

The steady-state heat gain per unit floor area due to temperature difference and long-wavelength radiation in room i on date \(d\) \(Q_{AC,room,tin,i,d}\) is determined by the following formula.

a) If room i is a room to be air-conditioned (\(AirConditioning_{i}={\mathrm{True}}\)),

\[ Q_{AC,room,tin,i,d} = \begin{cases} \frac{ Q_{wall,t,i,d} + Q_{wind,t,i,d} + Q_{wall,n,i,d} + Q_{wind,n,i,d} }{A_{room,i}}, & (A_{room,i} > 0) \\ 0, & (A_{room,i} = 0) \end{cases} \]

b) If room i is a non-air-conditioned room (only when calculating PAL*) (\(AirCondioning_{i}={\mathrm{False}}\)),

\[ Q_{AC,room,tin,i,d} = \begin{cases} \frac{1}{2} \times \frac{ Q_{wall,t,i,d} + Q_{wind,t,i,d} + Q_{wall,n,i,d} + Q_{wind,n,i,d} }{A_{room,i}}, & (A_{room,i} > 0) \\ 0, & (A_{room,i} = 0) \end{cases} \]

The daily integrated steady-state heat gain due to solar radiation in room i on date \(d\), \(Q_{AC,room,sin,i,d}\) is obtained by the following formula.

a) If room i is a room to be air-conditioned (\(AirConditioning_{i}={\mathrm{True}}\)),

\[ Q_{AC,room,sin,i,d} = \begin{cases} \frac{ Q_{wall,s,i,d} + Q_{wind,s,i,d} }{ A_{room,i}}, & (A_{room,i} > 0) \\ 0, & (A_{room,i} = 0) \end{cases} \]

b) If room i is a non-air-conditioned room (only when calculating PAL*) (\(AirCondioning_{i}={\mathrm{False}}\)),

\[ Q_{AC,room,sin,i,d} = \begin{cases} \frac{1}{2} \times \frac{ Q_{wall,s,i,d} + Q_{wind,s,i,d} }{ A_{room,i} }, & (A_{room,i} > 0) \\ 0, & (A_{room,i} = 0) \end{cases} \]

2.4.2.1 Area of Exterior Walls¶

The exterior wall area is calculated by subtracting the window area from the entered envelope area.

Table 29. Input
Variable Name	Description	Unit	Reference
\(A_{env,i,j}\)	Area of the envelope j belonging to room	m²	Form 2-4: (5) Envelope Area (including windows)
\(A_{wind,i,j}\)	Area of window, etc. j belonging to room	m²	Form 2-4: (7) Openings Window Area

Table 30. Output
Variable Name	Description	Unit	References
\(A_{wall,i,j}\)	Area of exterior walls, etc. j belonging to room	m²	2.4.2.2, 2.4.2.4, 2.4.2.6

The area of exterior walls, etc. is calculated by the following formula.

\[ A_{wall,i,j} = A_{env,i,j} - A_{wind,i,j} \]

2.4.2.2 Steady-state Heat Gain Through Transmission due to Temperature Differences in Exterior Walls, etc.¶

Calculate the steady-state heat gain through transmission due to temperature differences in exterior walls, etc.

Table 31. Input
Variable Name	Description	Unit	Reference
\(A_{wall,i,j}\)	Area of exterior walls, etc. j belonging to room	m²	2.4.2.1
\(WallType_{i,j}\)	Type of exterior walls, etc. j belonging to room	-	Form 2-2: (2) Wall Type
\(U_{wall,i,j}\)	Thermal transmittance of exterior walls, etc. j belonging to room	W/(m²・K)	A.1
\(\theta_{AC,room,i,d}\)	Temperature setting of room i on date \(d\)	℃	2.3.1
\(\theta_{AC,oa,d}\)	Daily average outside air temperature on date \(d\)	℃	2.2.3
\(\theta_{AC,oa,ave}\)	Annual average outside air temperature	℃	2.2.3

Table 32. Output
Variable Name	Description	Unit	References
\(Q_{wall,t,i,d}\)	Steady-state heat gain through transmission due to temperature differences from exterior walls, etc. of room i on date \(d\)	Wh/d	2.4.2

Steady-state heat gain through transmission due to temperature differences from exterior walls, etc. of room i on date \(d\) \(Q_{wall,t,i,d}\) is calculated by the following method a) when the exterior wall, etc. is in contact with the outside air, and by the following method b) when the exterior wall, etc. is in contact with the ground. The subscript j in each formula should represent the exterior wall, etc. of room i that corresponds to the conditions in a) and b), respectively.

\[ Q_{wall,t,i,d} = \sum_{j=1} Q_{wall,t,i,j,d} \]

a) If it is an exterior wall in contact with the outside air (\(WallType_{i,j}=\mbox{exterior wall}\)),

\[ Q_{wall,t,i,j,d} = 24 \times U_{wall,i,j} \times A_{wall,i,j} \times (\theta_{AC,oa,d} - \theta_{AC,room,i,d}) \]

b) If it is a grounded wall (wall in contact with the ground) (\(WallType_{i,j}=\mbox{grounded wall}\)),

\[ Q_{wall,t,i,j,d} = 24 \times U_{wall,i,j} \times A_{wall,i,j} \times (\theta_{AC,oa,ave} - \theta_{AC,room,i,d}) \]

2.4.2.3 Steady-State Heat Gain Through Transmission due to Temperature Differences at Windows, etc.¶

Calculate the steady-state heat gain through transmission due to temperature differences at windows, etc.

Table 33. Input
Variable Name	Description	Unit	Reference
\(A_{wind,i,j}\)	Area of window, etc. j belonging to room	m²	Form 2-4: (7) Openings Window Area
\(D_{env,i,j}\)	Orientation of envelope, etc. j belonging to room	-	Form 2-4: (2) Orientation
\(U_{wind,i,j}\)	Thermal transmittance of windows, etc. j belonging to room	W/(m²・K)	A.2
\(\theta_{AC,room,i,d}\)	Temperature setting of room i on date \(d\)	℃	2.3.1
\(\theta_{AC,oa,d}\)	Daily average outside air temperature on date \(d\)	℃	2.2.3

Table 34. Output
Variable Name	Description	Unit	References
\(Q_{wind,t,i,d}\)	Steady-state heat gain through transmission due to temperature differences from windows, etc. of room i on date \(d\)	Wh/d	2.4.2

The steady-state heat gain through transmission due to temperature differences from windows, etc. of room i on date \(d\) \(Q_{wind,t,i,d}\) is calculated by the following formula.

\[ Q_{wind,t,i,d} = \sum_{j=1} Q_{wind,t,i,j,d} \]

a) If the orientation of the window, etc. j is not "in shade",

\[ Q_{wind,t,i,j,d} = 24 \times U_{wind,i,j} \times A_{wind,i,j} \times (\theta_{AC,oa,d} - \theta_{AC,room,i,d}) \]

b) If the orientation of the window, etc. j is "in shade",

\[ Q_{wind,t,i,j,d} = 0 \]

2.4.2.4 Steady-state Heat Loss Through Transmission due to Long-wavelength Radiation from Exterior Walls, etc.¶

Calculate the steady-state heat loss through transmission due to long-wavelength radiation from exterior walls, etc.

Table 35. Input
Variable Name	Description	Unit	Reference
\(U_{wall,i,j}\)	Thermal transmittance of exterior walls, etc. j belonging to room	W/(m²・K)	A.1
\(A_{wall,i,j}\)	Area of exterior walls, etc. j belonging to room	m²	2.4.2.1
\(I_{nsr,i,j,d}\)	Integrated long-wavelength radiation to the envelope j belonging to room i on date \(d\)	Wh/(m²・d)	2.4.1

Table 36. Output
Variable Name	Description	Unit	References
\(Q_{wall,n,i,d}\)	Steady-state heat loss through transmission due to long-wavelength radiation from exterior walls, etc. of room i on date \(d\)	Wh/d	2.4.2

The steady-state heat loss through transmission due to long-wavelength radiation from exterior walls, etc. of room i on date \(d\) \(Q_{wall,n,i,d}\) is calculated by the following method a) for exterior walls, etc. in contact with the outside air, and by the following method b) for exterior walls in contact with the ground. Multiply by -1 because the loss is a negative value.

\[ Q_{wall,n,i,d} = \sum_{j=1} Q_{wall,n,i,j,d} \]

\[ Q_{wall,n,i,j,d} = -1 \times \frac{ 0.9 \times U_{wall,i,j} \times A_{wall,i,j} \times I_{nsr,i,j,d} }{\alpha_{o}} \]

The "0.9" in the formula is the longwave emissivity at the wall, etc.

2.4.2.5 Steady-State Heat Loss through Transmission due to Long-Wavelength Radiation from Windows, etc.¶

Calculate the steady-state heat loss through transmission due to long-wavelength radiation from windows, etc.

Table 37. Input
Variable Name	Description	Unit	Reference
\(A_{wind,i,j}\)	Area of window, etc. j belonging to room	m²	Form 2-4: (7) Openings Window Area
\(U_{wind,i,j}\)	Thermal transmittance of windows, etc. j belonging to room	W/(m²・K)	A.2
\(I_{nsr,i,j,d}\)	Integrated long-wavelength radiation to envelope j on date \(d\)	Wh/(m²・d)	2.4.1

Table 38. Output
Variable Name	Description	Unit	References
\(Q_{wind,n,i,d}\)	Steady-state heat loss through transmission due to long-wavelength radiation from windows, etc. of room i on date \(d\)	Wh/d	2.4.2

Steady-state heat loss through transmission due to long-wavelength radiation from windows, etc. of room i on date \(d\) \(Q_{wind,n,i,d}\) is calculated by the following formula. Multiply by -1 because the loss is a negative value.

\[ Q_{wind,n,i,d} = \sum_{j=1} Q_{wind,n,i,j,d} \]

\[ Q_{wind,n,i,j,d} = -1 \times \frac{ 0.9 \times U_{wind,i,j} \times A_{wind,i,j} \times I_{nsr,i,j,d} }{\alpha_{o}} \]

The "0.9" in the formula is the longwave emissivity at the wall, etc.

2.4.2.6 Steady-State Heat Gain due to Solar Radiation to Exterior Walls, etc.¶

Calculate the steady-state heat gain due to solar radiation to exterior walls, etc.

Table 39. Input
Variable Name	Description	Unit	Reference
\(D_{env,i,j}\)	Orientation of envelope, etc. j belonging to room	-	Form 2-4: (2) Orientation
\(U_{wall,i,j}\)	Thermal transmittance of exterior walls, etc. j belonging to room	W/(m²・K)	A.1
\(A_{wall,i,j}\)	Area of exterior walls, etc. j belonging to room	m²	2.4.2.1
\(I_{dsr,i,j,d}\)	Integrated direct solar radiation to the envelope j belonging to room i on date \(d\)	Wh/(m²・d)	2.4.1
\(I_{isr,i,j,d}\)	Integrated sky solar radiation and reflected solar radiation to the envelope j belonging to room i on date \(d\)	Wh/(m²・d)	2.4.1

Table 40. Output
Variable Name	Description	Unit	References
\(Q_{wall,s,i,d}\)	Steady-state heat gain due to solar radiation from exterior walls, etc. of room i on date \(d\)	Wh/d	2.4.2

The steady-state heat gain due to solar radiation from exterior walls \(Q_{wall,s,i,d}\) is calculated by the method a) for exterior walls, etc. exposed to the sun, and by the method b) for exterior walls, etc. not exposed to the sun.

\[ Q_{wall,s,i,d} = \sum_{j=1} Q_{wall,s,i,j,d} \]

a) If the orientation of the envelope, etc. j is not "in shade",

\[ Q_{wall,s,i,j,d} = \frac{ 0.8 \times U_{wall,i,j} \times A_{wall,i,j} \times ( I_{dsr,i,j,d} + I_{isr,i,j,d} ) }{\alpha_{o}} \]

b) If the orientation of the envelope, etc. j is "in shade",

\[ Q_{wall,s,i,j,d} = 0 \]

The "0.8" in the formula is the solar absorptance at the wall, etc.

2.4.2.7 Steady-State Heat Gain due to Solar Radiation from Windows, etc.¶

Calculate the steady-state heat gain from solar radiation from windows, etc.

Table 41. Input
Variable Name	Description	Unit	Reference
\(D_{env,i,j}\)	Orientation of envelope, etc. j belonging to room	-	Form 2-4: (2) Orientation
\(\gamma_{wind,c,i,j}\)	Sunshade effect coefficient of window, etc. j belonging to room i (cooling)	-	Form 2-4: (3) Sunshade Effect Coefficient (Cooling)
\(\gamma_{wind,h,i,j}\)	Sunshade effect coefficient of window, etc. j belonging to room i (heating)	-	Form 2-4: (3) Sunshade Effect Coefficient (Heating)
\(A_{wind,i,j}\)	Area of window, etc. j belonging to room	m²	Form 2-4: (7) Openings Window Area
\(\eta_{i,j}\)	Solar heat gain coefficient of windows, etc. j belonging to room	-	A.2
\(Season_{d}\)	Cooling/heating season (cooling, intermediate, or heating seasons) on date \(d\)	-	2.2.2
\(I'_{dsr,i,j,d}\)	Integrated direct solar radiation to the envelope j belonging to room i on date \(d\) (with angle of incidence characteristic)	Wh/(m²・d)	2.4.1
\(I_{isr,i,j,d}\)	Integrated sky solar radiation and reflected solar radiation to the envelope j belonging to room i on date \(d\)	Wh/(m²・d)	2.4.1
\(\eta_{max}\)	Maximum angle-of-incidence characteristic	-	2.4.1

Table 42. Output
Variable Name	Description	Unit	References
\(Q_{wind,s,i,d}\)	Steady-state heat gain due to solar radiation from windows, etc. in room i on date \(d\)	Wh/d	2.4.2

The steady-state heat gain due to solar radiation from windows, etc. in room i on date \(d\) \(Q_{wind,s,i,d}\) is calculated by the following method a) for a window, etc. exposed to the sun, and by the following method b) for a window, etc. not exposed to the sun. For the sunshade effect coefficient on date \(d\), either the sunshade effect coefficient (cooling) or the sunshade effect coefficient (heating) should be applied, depending on the cooling/heating season on date \(d\).

\[ Q_{wind,s,i,d} = \sum_{j=1} Q_{wind,s,i,j,d} \]

a) If the orientation of the envelope, etc. j is not "in shade",

\[ Q_{wind,s,i,j,d} = \left( \gamma_{wind,i,j,d} \times A_{wind,i,j} \times \frac{\eta_{i,j}}{0.88} \times (\eta_{max} \times I'_{dsr,i,j,d} + 0.808 \times I_{isr,i,j,d}) \right) \]

\[ \gamma_{wind,i,j,d} = \begin{cases} \gamma_{wind,c,i,j}, & (\mbox{cooling/heating season is "cooling season" or "intermediate season"}) \\ \gamma_{wind,h,i,j}, & (\mbox{cooling/heating season is "heating season"}) \end{cases} \]

b) If the orientation of the envelope, etc. j is "in shade",

\[ Q_{wind,s,i,j,d} = 0 \]

The "0.88" in the formula is the solar heat gain for standard glass, and the "0.808" is the angle-of-incidence characteristic for sky solar radiation and reflected solar radiation.

2.4.3 Heat Gain due to Internal Heat Generation¶

Calculate the heat gain due to internal heat generation.

Table 43. Input
Variable Name	Description	Unit	Reference
\(O_{AC,room,i,d}\)	Operating status of the air conditioner in room i on date \(d\)	Boolean value	2.3.3
\(Q_{AC,room,light,i,d}\)	Daily integrated value of lighting heat generation density in room i on date \(d\)	Wh/(m²・d)	2.3.4
\(Q_{AC,room,human,i,d}\)	Daily integrated value of heat generation density of occupants in room i on date \(d\)	Wh/(m²・d)	2.3.4
\(Q_{AC,room,app,i,d}\)	Daily integrated value of equipment heat generation density in room i on date \(d\)	Wh/(m²・d)	2.3.4

Table 44. Output
Variable Name	Description	Unit	References
\(Q_{AC,room,in,i,d}\)	Load due to internal heat generation in room i on date \(d\)	Wh/(m²・d)	2.4.4

In this calculation method, for simplicity, heat generations from room lighting, human body and equipment are treated as steady-state heat gain with no time delay. However, if date \(d\) is not air-conditioned day, both of these should be set to 0. Whether a day is air-conditioned day or not is defined by the standard room use conditions for each room use.

a) If the air conditioning is ON on date \(d\) for room i (\(O_{AC,room,i,d}={\mathrm{True}}\)),

\[ Q_{AC,room,in,i,d} = (Q_{AC,room,light,i,d} + Q_{AC,room,human,i,d} + Q_{AC,room,app,i,d}) \]

b) If the air conditioning is OFF on date \(d\) for room i (\(O_{AC,room,i,d}={\mathrm{False}}\)),

\[ Q_{AC,room,in,i,d} = 0 \]

2.4.4 Daily Integrated Room Load¶

The daily integrated room load is calculated by calculating the daily integrated steady-state heat gain per unit floor area based on the envelope configuration of each room and multiplying it by the "factor for converting steady-state heat gain to room load".

Table 45. Input
Variable Name	Description	Unit	Reference
\(Q_{AC,room,tin,i,d}\)	Steady-state heat gain due to temperature difference in room i on date \(d\)	Wh/(m²・d)	2.4.2
\(Q_{AC,room,sin,i,d}\)	Steady-state heat gain due to solar radiation in room i on date \(d\)	Wh/(m²・d)	2.4.2
\(Q_{AC,room,in,i,d}\)	Internal heat generation in room i on date \(d\)	Wh/(m²・d)	2.4.3
\(a_{tc1,d}, a_{tc2,d}\)	Coefficient for converting steady-state heat gain caused by temperature difference on date \(d\) to room load (cooling)	-	A.3
\(a_{th1,d}, a_{th2,d}\)	Coefficient for converting steady-state heat gain caused by temperature difference on date \(d\) to room load (heating)	-	A.3
\(a_{sc1,d}, a_{sc2,d}\)	Coefficient for converting steady-state heat gain due to solar radiation on date \(d\) to room load (cooling)	-	A.3
\(O_{AC,room,i,d}\)	Operating status of the air conditioner in room i on date \(d\)	Boolean value	2.3.3

Table 46. Output
Variable Name	Description	Unit	References
\(Q_{AC,room,c,i,d}\)	Daily integrated room load (cooling) for room i on date \(d\)	Wh/(m²・d)	2.5.1
\(Q_{AC,room,h,i,d}\)	Daily integrated room load (heating) for room i on date \(d\)	Wh/(m²・d)	2.5.1

First, calculate the cooling load due to temperature difference \(Q_{AC,room,tc,i,d}\)[Wh/(m²・d)], heating load due to temperature difference \(Q_{AC,room,th,i,d}\)[Wh/(m²・d)], cooling load due to solar radiation \(Q_{AC,room,sc,i,d }\)[Wh/(m²・d)], respectively. For convenience, the cooling load is expressed as a positive value and the heating load as a negative value, and \(Q_{AC,room,tc,i,d}≥0\), \(Q_{AC,room,th,i,d}≤0\), \(Q_{AC,room,sc,i,d}≥0\).

a) If the air conditioning is ON on date \(d\) for room i,

\[ Q_{AC,room,tc,i,d} = \max⁡(a_{tc1,d} \times Q_{AC,room,tin,i,d} + a_{tc2,d},\, 0) \]

\[ Q_{AC,room,th,i,d} = \min⁡(a_{th1,d} \times Q_{AC,room,tin,i,d} + a_{th2,d},\, 0) \]

\[ Q_{AC,room,sc,i,d} = \max⁡(a_{sc1,d} \times Q_{AC,room,sin,i,d} + a_{sc2,d},\, 0) \]

b) If the air conditioning is OFF on date \(d\) for room i,

\[ Q_{AC,room,tc,i,d} = 0 \]

\[ Q_{AC,room,th,i,d} = 0 \]

\[ Q_{AC,room,sc,i,d} = 0 \]

The coefficients for converting steady-state heat gain to room load \(\{a_{tc1,d},a_{tc2,d}\}\), \(\{a_{th1,d},a_{th2,d}\}\), and \(\{a_{sc1,d},a_{sc2,d}\}\) are defined by region, room use, cooling/heating season (cooling season, intermediate season, heating season), and the previous day’s air conditioning operation status.

Based on these loads \(Q_{AC,room,tc,i,d}\), \(Q_{AC,room,th,i,d}\), \(Q_{AC,room,sc,i,d}\) and the load due to internal heat generation \(Q_{AC,room,in,i,d}\), the daily integrated room load is calculated by following procedure.

Step 1) Find the following A and B.

a) If \(Q_{AC,room,th,i,d} + Q_{AC,room,sc,i,d}＜0\),

\[ A = Q_{AC,room,tc,i,d} \]

\[ B = Q_{AC,room,th,i,d} + Q_{AC,room,sc,i,d} \]

b) If \(Q_{AC,room,th,i,d} + Q_{AC,room,sc,i,d}≥0\),

\[ A = Q_{AC,room,tc,i,d} + Q_{AC,room,th,i,d} + Q_{AC,room,sc,i,d}\]

\[ B = 0 \]

Step 2) Find the following C and D.

(a) If \(B + Q_{AC,room,in,i,d}＜0\),

\[ C = A \]

\[ D = B + Q_{AC,room,in,i,d} \]

(b) If \(B + Q_{AC,room,in,i,d}≥0\),

\[ C = A + B + Q_{AC,room,in,i,d} \]

\[ D = 0 \]

The calculated C is the daily integrated room load (cooling) for room i \(Q_{AC,room,c,i,d}\)[Wh/( m²・d )] , and D is the daily integrated room load (heating) for room i \(Q_{AC,room,h,i,d}\)[Wh/( m²・d )]. However, if date \(d\) is not a air-conditioned day, these will both be 0. Whether a day is air-conditioned day or not is defined by the standard room use conditions for each room use.