TimeStep Daylighting Calculation[LINK]
A daylighting calculation is performed each time step that the sun is up for each zone that has one or two daylighting reference points specified. The exterior horizontal illuminance from the sun and sky is determined from solar irradiance data from the weather file. The interior illuminance at each reference point is found for each window by interpolating the daylight illuminance factors for the current sun position, then, for skyrelated interior illuminance, multiplying by the exterior horizontal illuminance from the appropriate sky types that time step, and, for sunrelated interior illuminance, multiplying by the exterior horizontal solar illuminance that time step. By summation, the net illuminance and glare due to all of the windows in a zone are found. If glare control has been specified window shading (by movable shading devices or switchable glazing) is deployed to reduce glare. Finally the illuminance at each reference point for the final window and shade configuration is used by the lighting control system simulation to determine the electric lighting power required to meet the illuminance setpoint at each reference point.
Table 27. Variables in
TimeStep Calculations
Mathematical variable

Description

Units

FORTRAN variable

S_{norm,dir}

Direct normal solar irradiance

W/m^{2}

BeamSolarRad

S_{h,dif}

Exterior diffuse horizontal solar irradiance

W/m^{2}

SDIFH, DifSolarRad

S_{h,dir}

Exterior direct horizontal solar irradiance

W/m^{2}

SDIRH

Z

Solar zenith angle

radians

Zeta

m

Relative optical air mass


AirMass

Δ

Sky brightness


SkyBrightness

ε

Sky clearness


SkyClearness

k, k’

Sky type index


ISky

s_{k,k’}

Interpolation factor for skies k and k’


SkyWeight

ψ_{k,k’}

Sky luminance distribution formed from linear interpolation of skies k and k’

cd/m^{2}


f_{k}

Fraction of sky that is type k



E_{h,k}

Horizontal illuminance from sky type k

cd/m^{2}

HorIllSky

E_{h,sky}

Exterior horizontal illuminance from sky

lux

HISKF

E_{h,sun}

Exterior horizontal illuminance from sun

lux

HISUNF

η_{dif}, η_{dir}

Luminous efficacy of diffuse and direct solar radiation

lm/W

DiffLumEff, DirLumEff

I_{win}

Interior illuminance from a window

lux

DaylIllum

S_{win}

Window luminance

cd/m^{2}

SourceLumFromWinAtRefPt

B_{win}

Window background luminance

cd/m^{2}

BACLUM

d_{sun}, d_{sky,k}

Interior illuminance factor for sun, for sky of type k


DaylIllFacSun, DFSUHR, DaylIllFacSky, DFSUHR

w_{sun}, w_{sky,k}

Window luminance factor for sun, for sky of type k


DaylSourceFacSun, SFSUHR, DaylSourceFacSky, SFSKHR

b_{sun}, b_{sky,k}

Window background luminance factor for sun, for sky of type k


DaylBackFacSun, BFSUHR, DaylBackFacSky, BFSKHR

w_{j}

Weighting factor for time step interpolation


WeightNow

i_{L}

Reference point index


IL

i_{S}

Window shade index


IS

I_{tot}

Total daylight illuminance at reference point

lux

DaylIllum

B_{tot}, B

Total window background luminance

cd/m^{2}

BLUM

I_{set}

Illuminance setpoint

lux

ZoneDaylight%IllumSetPoint

f_{L}

Fractional electric lighting output


FL

f_{P}

Fractional electric lighting input power


FP

N_{L}

Number of steps in a stepped control system


LightControlSteps

M_{P}

Lighting power multiplier


ZonePowerReductionFactor

TimeStep Sky Luminance[LINK]
The sky luminance distribution, ψ, for a particular time step is expressed as a linear interpolation of two of the four standard skies — ψ_{cs}, ψ_{ts} , ψ_{is} and ψ_{os} — described above under “Sky Luminance Distributions.” The two sky types that are interpolated depend on the value of the sky clearness. The interpolation factors are a function of sky clearness and sky brightness (Perez et al., 1990). Sky clearness is given by
ε=Sh,dif+Snorm,dirSh,dif+κZ31+κZ3
where S_{h,dif} is the diffuse horizontal solar irradiance, S_{norm,dir}is the direct normal solar irradiance, Z is the solar zenith angle and κ is a constant equal to 1.041 for Z in radians.
Sky brightness is given by
Δ=Sh,difm/Sextnorm,dir
where m is the relative optical air mass and Sextnorm,dir is the extraterrestrial direct normal solar irradiance.
If ε ≤ 1.2
ψis,os=sis,osψis+(1−sis,os)ψos
where ψ_{is} is the intermediate sky luminance distribution, ψ_{os} is the overcast sky luminance distribution, and
sis,os=min{1,max[0,(ε−1)/0.2,(Δ−0.05)/0.4]}
If 1.2<ε ≤ 3
ψts,is=sts,isψts+(1−sts,is)ψis
where ψ_{ts} is the clear turbid sky luminance distribution and
sts,is=(ε−1.2)/1.8
If ε > 3
ψcs,ts=scs,tsψcs+(1−scs,ts)ψts
where ψ_{cs} is the clear sky luminance distribution and
scs,ts=min[1,(ε−3)/3]
Interior Illuminance[LINK]
For each time step the interior illuminance, I_{win}, from a window is calculated as follows by multiplying daylight factors and exterior illuminance.
First, the sun and skyrelated daylight illuminance factors for the time step are determined by interpolation of the hourly factors:
¯dsun(iL,iS)=wjdsun(iL,iS,ih)+(1−wj)dsun(iL,iS,ih+1)
¯dsky,k(iL,iS)=wjdsky,k(iL,iS,ih)+(1−wj)dsky,k(iL,iS,ih+1)
where i_{L} is the reference point index (1 or 2), i_{S} is the window shade index (1 for unshaded window, 2 for shaded window),* i_{h}* is the hour number, and k is the sky type index. For the* j*th time step in an hour, the timestep interpolation weight is given by
wj=1−min[1,j/Nt]
where N_{t} is the number of time steps per hour.
The interior illuminance from a window is calculated as
Iwin(iL,iS)=¯dsunEh,sun+[¯dsky,k(iL,iS)fk+¯dsky,k′(iL,iS)fk′]Eh,sky
where E_{h,sun} and E_{h,sky} are the exterior horizontal illuminance from the sun and sky, respectively, and f_{k} and f_{k’} are the fraction of the exterior horizontal illuminance from the sky that is due to sky type k and k’, respectively.
The horizontal illuminance from sun and sky are given by
Eh,sun=ηdirSnorm,dircosZEh,sky=ηdifSh,dif
where Z is the solar zenith angle, η_{dif} is the luminous efficacy (in lumens/Watt) of diffuse solar radiation from the sky and η_{dir} is the luminous efficacy of direct radiation from the sun. The efficacies are calculated from direct and global solar irradiance using a method described in (Perez et al, 1990).
The fractions f_{k} and f_{k’} are given by
fk=sk,k′Eh,ksk,k′Eh,k+(1−sk,k′)Eh,k′fk′=(1−sk,k′)Eh,k′sk,k′Eh,k+(1−sk,k′)Eh,k′
where E_{h,k} and E_{h,k’} are the horizontal illuminances from skies k and k’, respectively (see “Exterior Horizontal Luminance,” above), and s_{k,k’} is the interpolation factor for skies kand k’(see “TimeStep Sky Luminance,” above). For example, if ε > 3, k = cs (clear sky), k’ = ts (clear turbid sky) and
sk,k′=scs,ts=min[1,(ε−3)/3]
Similarly, the window source luminance, S_{win}, and window background luminance, B_{win}, for a window are calculated from
Swin(iL,iS)=¯wsunEh,sun+[¯wsky,k(iL,iS)fk+¯wsky,k′(iL,iS)fk′]Eh,sky
Bwin(iL,iS)=¯bsunEh,sun+[¯bsky,k(iL,iS)fk+¯bsky,k′(iL,iS)fk′]Eh,sky
The total illuminance at a reference point from all of the exterior windows in a zone is
Itot(iL)=∑windowsinzoneIwin(is,iL)
where* i_{S}* = 1 if the window is unshaded and i_{S} = 2 if the window is shaded that time step. (Before the illuminance calculation is done the window shading control will have been simulated to determine whether or not the window is shaded.)
Similarly, the total background luminance is calculated:
Btot(iL)=∑windowsinzoneBwin(is,iL)
The net glare index at each reference point is calculated as
GI(iL)=10log10∑windowsinzoneSwin(iL,iS)1.6Ω(iL)0.8B(iL)+0.07ω(iL)0.5Swin(iL,iS)
where
B(iL)=max(Bwin(iL),ρbIset(iL))
In the last relationship, the background luminance is approximated as the larger of the background luminance from daylight and the average background luminance that would be produced by the electric lighting at full power if the illuminance on the room surfaces were equal to the setpoint illuminance. In a more detailed calculation, where the luminance of each room surface is separately determined, B(i_{L}) would be better approximated as an areaweighted luminance of the surfaces surrounding a window, taking into account the luminance contribution from the electric lights.
Glare Control Logic[LINK]
If glare control has been specified and the glare index at either reference point exceeds a userspecified maximum value, G_{I,max}, then the windows in the zone are shaded one by one in attempt to bring the glare at both points below G_{I,max}. (Each time a window is shaded the glare and illuminance at each reference point is recalculated.) The following logic is used:
5) If there is only one reference point, shade a window if it is unshaded and shading it decreases the glare, even if it does not decrease the glare below G_{I,max}. Note that if a window has already been shaded, say to control solar gain, it will be left in the shaded state.
6) If there are two reference points, then:
* If glare is too high at both points, shade the window if it decreases glare at both points.
If glare is too high only at the first point, shade the window if the glare at the first point decreases, and the glare at the second point stays belowG_{I,max}*.
 If glare is too high only at the second point, shade the window if the glare at the second point decreases, and the glare at the first point stays below G_{I,max}.
7) Shades are closed in the order of window input until glare at both points is below G_{I,max}, or until there are no more windows left to shade.
Lighting Control System Simulation[LINK]
Once the final daylight illuminance value at each reference point has been determined, the electric lighting control is simulated. The fractional electric lighting output, f_{L}, required to meet the setpoint at reference point i_{L} is given by
fL(iL)=max[0,Iset(iL)−Itot(iL)Iset(iL)]
Here, I_{set} is the illuminance setpoint and I_{tot} is the daylight illuminance at the reference point. This relationship assumes that the electric lights at full power produce an illuminance equal to I_{set} at the reference point.
The fractional electric lighting input power, f_{P}, corresponding to f_{L} is then calculated. The relationship between f_{P} and f_{L} depends on the lighting control type.
Continuous Dimming Control[LINK]
For a continuouslydimmable control system, it is assumed that f_{P} is constant and equal to f_{P,min}for f_{L}<f_{L,min} and that f_{P} increases linearly from f_{P,min} to 1.0 as f_{L} increases from f_{L,min} to 1.0 (Figure 60). This gives
fP=⎧⎨⎩fP,minforfL<fL,minfL+(1−fL)fP,min−fL,min1−fL,minforfL,min≤fL≤1
Figure 60. Control action for a continuous dimming system.
Continuous/Off Dimming Control[LINK]
A “continuous/off” dimming system has the same behavior as a continuous dimming system except that the lights switch off for f_{L} < f_{L,min} rather than staying at f_{P,min}.
Stepped Control[LINK]
For a stepped control system, f_{P} takes on discrete values depending on the range of f_{L}and the number of steps, N_{L}_{ } (Figure 61). This gives
fP=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩0,iffL=0int(NLfL)+1NL,for0<fL<11,iffL=1
If a lighting control probability,* p_{L}, is specified, f_{P}* is set one level higher a fraction of the time equal to 1p_{L}. Specifically, if* f_{P}* <1,* f_{P}à f_{P}+ 1/N_{L}* if a random number between 0 and 1 exceeds p_{L}. This can be used to simulate the uncertainty associated with manual switching of lights.
Figure 61. Stepped lighting control with three steps.
Lighting Power Reduction[LINK]
Using the value of f_{P}at each reference point and the fraction f_{Z} of the zone controlled by the reference point, the net lighting power multiplier, M_{P}, for the entire zone is calculated; this value multiplies the lighting power output without daylighting.
MP=2∑iL=1fP(iL)fZ(iL)+⎛⎝1−2∑iL=1fZ(iL)⎞⎠
In this expression, the term to the right in the parentheses corresponds to the fraction of the zone not controlled by either reference point. For this fraction the electric lighting is unaffected and the power multiplier is 1.0.
CIE Technical Committee 4.2. 1973. Standardization of the Luminance Distribution on Clear Skies. CIE Pub. No. 22, Commission Internationale d’Eclairage, Paris.
Hopkinson, R.G., J. Longmore and P. Petherbridge. 1954. An Empirical Formula for the Computation of the Indirect Component of Daylight Factors. Trans. Illum. Eng. Soc. (London) 19, 201.
Hopkinson, R.G., P. Petherbridge and J. Longmore. 1966. Daylighting. Heinnemann, London, p. 322.
Hopkinson, R.G. 1970. Glare from Windows. Construction Research and Development Journal 2, 98.
Hopkinson, R.G. 1972. Glare from Daylighting in Buildings. Applied Ergonomics 3, 206.
Kittler, R. 1965. Standardization of Outdoor Conditions for the Calculation of the Daylight Factor with Clear Skies. Proc. CIE InterSession Meeting on Sunlight, NewcastleUponTyne.
Lynes, J.A. 1968. Principles of Natural Lighting. Applied Science Publishers, Ltd., London, p. 129.
Matsuura, K. 1987. Luminance Distributions of Various Reference Skies. CIE Technical Report of TC 309.
Moon, P. and D. Spencer. 1942. Illumination from a Nonuniform Sky. Illuminating Engineering 37, 707726.
[1] For beam incident on an exterior window we have the following: For transparent glass with no shade or blind there is only beamtobeam transmission. For diffusing glass, or if a window shade is in place, there is only beamtodiffuse transmission. If a window blind is in place there is beamtodiffuse transmission, and, depending on slat angle, solar profile angle, etc., there can also be beamtobeam transmission.
[2] See “Beam Solar Reflection from Window Reveal Surfaces.”
[3] If Solar Distribution = FullInteriorAndExterior in the Building object, the program calculates where beam solar from exterior windows falls inside the zone. Otherwise, all beam solar is assumed to fall on the floor.
[4] For the purposes of the surface heat balance calculation, any beam solar radiation absorbed by a surface is assumed to be uniformly distributed over the surface even though in reality it is likely to be concentrated in one or more discrete patches on the surface.
[5] TBm_{i}_{}is zero if the window has diffusing glass or a shade. TBm_{i} can be > 0 if a blind is present and the slat angle, solar profile angle, etc., are such that some beam passes between the slats.
[6] A different method from that described here is used for calculating reflections from daylighting shelves (see “Daylighting Shelves”).
[7] The ground surface is assumed to be diffusely reflecting so there is no specular reflection from the ground. The program could be improved by adding a ground surface specular component, which could be important for snowcover conditions.
[8] The sun positions for which the daylight factors are calculated are the same as those for which the solar shadowing calculations are done.
Perez, R., P. Ineichen, R. Seals, J. Michalsky and R. Stewart. 1990. Modeling Daylight Availability and Irradiance Components from Direct and Global Irradiance. Solar Energy 44, 271289.
Petherbridge, P. and J. Longmore. 1954. Solid Angles Applied to Visual Comfort Problems. Light and Lighting 47,173.
Winkelmann, F.C. 1983. Daylighting Calculation in DOE2. Lawrence Berkeley Laboratory report no. LBL11353, January 1983.
Winkelmann, F.C. and S. Selkowitz. 1985. Daylighting Simulation in the DOE2 Building Energy Analysis Program. Energy and Buildings 8, 271286.
TimeStep Daylighting Calculation[LINK]
Overview[LINK]
A daylighting calculation is performed each time step that the sun is up for each zone that has one or two daylighting reference points specified. The exterior horizontal illuminance from the sun and sky is determined from solar irradiance data from the weather file. The interior illuminance at each reference point is found for each window by interpolating the daylight illuminance factors for the current sun position, then, for skyrelated interior illuminance, multiplying by the exterior horizontal illuminance from the appropriate sky types that time step, and, for sunrelated interior illuminance, multiplying by the exterior horizontal solar illuminance that time step. By summation, the net illuminance and glare due to all of the windows in a zone are found. If glare control has been specified window shading (by movable shading devices or switchable glazing) is deployed to reduce glare. Finally the illuminance at each reference point for the final window and shade configuration is used by the lighting control system simulation to determine the electric lighting power required to meet the illuminance setpoint at each reference point.
Table 27. Variables in TimeStep CalculationsTimeStep Sky Luminance[LINK]
The sky luminance distribution, ψ, for a particular time step is expressed as a linear interpolation of two of the four standard skies — ψ_{cs}, ψ_{ts} , ψ_{is} and ψ_{os} — described above under “Sky Luminance Distributions.” The two sky types that are interpolated depend on the value of the sky clearness. The interpolation factors are a function of sky clearness and sky brightness (Perez et al., 1990). Sky clearness is given by
ε=Sh,dif+Snorm,dirSh,dif+κZ31+κZ3
where S_{h,dif} is the diffuse horizontal solar irradiance, S_{norm,dir}is the direct normal solar irradiance, Z is the solar zenith angle and κ is a constant equal to 1.041 for Z in radians.
Sky brightness is given by
Δ=Sh,difm/Sextnorm,dir
where m is the relative optical air mass and Sextnorm,dir is the extraterrestrial direct normal solar irradiance.
If ε ≤ 1.2
ψis,os=sis,osψis+(1−sis,os)ψos
where ψ_{is} is the intermediate sky luminance distribution, ψ_{os} is the overcast sky luminance distribution, and
sis,os=min{1,max[0,(ε−1)/0.2,(Δ−0.05)/0.4]}
If 1.2<ε ≤ 3
ψts,is=sts,isψts+(1−sts,is)ψis
where ψ_{ts} is the clear turbid sky luminance distribution and
sts,is=(ε−1.2)/1.8
If ε > 3
ψcs,ts=scs,tsψcs+(1−scs,ts)ψts
where ψ_{cs} is the clear sky luminance distribution and
scs,ts=min[1,(ε−3)/3]
Interior Illuminance[LINK]
For each time step the interior illuminance, I_{win}, from a window is calculated as follows by multiplying daylight factors and exterior illuminance.
First, the sun and skyrelated daylight illuminance factors for the time step are determined by interpolation of the hourly factors:
¯dsun(iL,iS)=wjdsun(iL,iS,ih)+(1−wj)dsun(iL,iS,ih+1)
¯dsky,k(iL,iS)=wjdsky,k(iL,iS,ih)+(1−wj)dsky,k(iL,iS,ih+1)
where i_{L} is the reference point index (1 or 2), i_{S} is the window shade index (1 for unshaded window, 2 for shaded window),* i_{h}* is the hour number, and k is the sky type index. For the* j*th time step in an hour, the timestep interpolation weight is given by
wj=1−min[1,j/Nt]
where N_{t} is the number of time steps per hour.
The interior illuminance from a window is calculated as
Iwin(iL,iS)=¯dsunEh,sun+[¯dsky,k(iL,iS)fk+¯dsky,k′(iL,iS)fk′]Eh,sky
where E_{h,sun} and E_{h,sky} are the exterior horizontal illuminance from the sun and sky, respectively, and f_{k} and f_{k’} are the fraction of the exterior horizontal illuminance from the sky that is due to sky type k and k’, respectively.
The horizontal illuminance from sun and sky are given by
Eh,sun=ηdirSnorm,dircosZEh,sky=ηdifSh,dif
where Z is the solar zenith angle, η_{dif} is the luminous efficacy (in lumens/Watt) of diffuse solar radiation from the sky and η_{dir} is the luminous efficacy of direct radiation from the sun. The efficacies are calculated from direct and global solar irradiance using a method described in (Perez et al, 1990).
The fractions f_{k} and f_{k’} are given by
fk=sk,k′Eh,ksk,k′Eh,k+(1−sk,k′)Eh,k′fk′=(1−sk,k′)Eh,k′sk,k′Eh,k+(1−sk,k′)Eh,k′
where E_{h,k} and E_{h,k’} are the horizontal illuminances from skies k and k’, respectively (see “Exterior Horizontal Luminance,” above), and s_{k,k’} is the interpolation factor for skies kand k’(see “TimeStep Sky Luminance,” above). For example, if ε > 3, k = cs (clear sky), k’ = ts (clear turbid sky) and
sk,k′=scs,ts=min[1,(ε−3)/3]
Similarly, the window source luminance, S_{win}, and window background luminance, B_{win}, for a window are calculated from
Swin(iL,iS)=¯wsunEh,sun+[¯wsky,k(iL,iS)fk+¯wsky,k′(iL,iS)fk′]Eh,sky
Bwin(iL,iS)=¯bsunEh,sun+[¯bsky,k(iL,iS)fk+¯bsky,k′(iL,iS)fk′]Eh,sky
The total illuminance at a reference point from all of the exterior windows in a zone is
Itot(iL)=∑windowsinzoneIwin(is,iL)
where* i_{S}* = 1 if the window is unshaded and i_{S} = 2 if the window is shaded that time step. (Before the illuminance calculation is done the window shading control will have been simulated to determine whether or not the window is shaded.)
Similarly, the total background luminance is calculated:
Btot(iL)=∑windowsinzoneBwin(is,iL)
Glare Index[LINK]
The net glare index at each reference point is calculated as
GI(iL)=10log10∑windowsinzoneSwin(iL,iS)1.6Ω(iL)0.8B(iL)+0.07ω(iL)0.5Swin(iL,iS)
where
B(iL)=max(Bwin(iL),ρbIset(iL))
In the last relationship, the background luminance is approximated as the larger of the background luminance from daylight and the average background luminance that would be produced by the electric lighting at full power if the illuminance on the room surfaces were equal to the setpoint illuminance. In a more detailed calculation, where the luminance of each room surface is separately determined, B(i_{L}) would be better approximated as an areaweighted luminance of the surfaces surrounding a window, taking into account the luminance contribution from the electric lights.
Glare Control Logic[LINK]
If glare control has been specified and the glare index at either reference point exceeds a userspecified maximum value, G_{I,max}, then the windows in the zone are shaded one by one in attempt to bring the glare at both points below G_{I,max}. (Each time a window is shaded the glare and illuminance at each reference point is recalculated.) The following logic is used:
5) If there is only one reference point, shade a window if it is unshaded and shading it decreases the glare, even if it does not decrease the glare below G_{I,max}. Note that if a window has already been shaded, say to control solar gain, it will be left in the shaded state.
6) If there are two reference points, then:
* If glare is too high at both points, shade the window if it decreases glare at both points.
If glare is too high only at the first point, shade the window if the glare at the first point decreases, and the glare at the second point stays belowG_{I,max}*.
7) Shades are closed in the order of window input until glare at both points is below G_{I,max}, or until there are no more windows left to shade.
Lighting Control System Simulation[LINK]
Once the final daylight illuminance value at each reference point has been determined, the electric lighting control is simulated. The fractional electric lighting output, f_{L}, required to meet the setpoint at reference point i_{L} is given by
fL(iL)=max[0,Iset(iL)−Itot(iL)Iset(iL)]
Here, I_{set} is the illuminance setpoint and I_{tot} is the daylight illuminance at the reference point. This relationship assumes that the electric lights at full power produce an illuminance equal to I_{set} at the reference point.
The fractional electric lighting input power, f_{P}, corresponding to f_{L} is then calculated. The relationship between f_{P} and f_{L} depends on the lighting control type.
Continuous Dimming Control[LINK]
For a continuouslydimmable control system, it is assumed that f_{P} is constant and equal to f_{P,min}for f_{L}<f_{L,min} and that f_{P} increases linearly from f_{P,min} to 1.0 as f_{L} increases from f_{L,min} to 1.0 (Figure 60). This gives
fP=⎧⎨⎩fP,minforfL<fL,minfL+(1−fL)fP,min−fL,min1−fL,minforfL,min≤fL≤1
Figure 60. Control action for a continuous dimming system.
Continuous/Off Dimming Control[LINK]
A “continuous/off” dimming system has the same behavior as a continuous dimming system except that the lights switch off for f_{L} < f_{L,min} rather than staying at f_{P,min}.
Stepped Control[LINK]
For a stepped control system, f_{P} takes on discrete values depending on the range of f_{L}and the number of steps, N_{L}_{ } (Figure 61). This gives
fP=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩0,iffL=0int(NLfL)+1NL,for0<fL<11,iffL=1
If a lighting control probability,* p_{L}, is specified, f_{P}* is set one level higher a fraction of the time equal to 1p_{L}. Specifically, if* f_{P}* <1,* f_{P}à f_{P}+ 1/N_{L}* if a random number between 0 and 1 exceeds p_{L}. This can be used to simulate the uncertainty associated with manual switching of lights.
Figure 61. Stepped lighting control with three steps.
Lighting Power Reduction[LINK]
Using the value of f_{P}at each reference point and the fraction f_{Z} of the zone controlled by the reference point, the net lighting power multiplier, M_{P}, for the entire zone is calculated; this value multiplies the lighting power output without daylighting.
MP=2∑iL=1fP(iL)fZ(iL)+⎛⎝1−2∑iL=1fZ(iL)⎞⎠
In this expression, the term to the right in the parentheses corresponds to the fraction of the zone not controlled by either reference point. For this fraction the electric lighting is unaffected and the power multiplier is 1.0.
References[LINK]
CIE Technical Committee 4.2. 1973. Standardization of the Luminance Distribution on Clear Skies. CIE Pub. No. 22, Commission Internationale d’Eclairage, Paris.
Hopkinson, R.G., J. Longmore and P. Petherbridge. 1954. An Empirical Formula for the Computation of the Indirect Component of Daylight Factors. Trans. Illum. Eng. Soc. (London) 19, 201.
Hopkinson, R.G., P. Petherbridge and J. Longmore. 1966. Daylighting. Heinnemann, London, p. 322.
Hopkinson, R.G. 1970. Glare from Windows. Construction Research and Development Journal 2, 98.
Hopkinson, R.G. 1972. Glare from Daylighting in Buildings. Applied Ergonomics 3, 206.
Kittler, R. 1965. Standardization of Outdoor Conditions for the Calculation of the Daylight Factor with Clear Skies. Proc. CIE InterSession Meeting on Sunlight, NewcastleUponTyne.
Lynes, J.A. 1968. Principles of Natural Lighting. Applied Science Publishers, Ltd., London, p. 129.
Matsuura, K. 1987. Luminance Distributions of Various Reference Skies. CIE Technical Report of TC 309.
Moon, P. and D. Spencer. 1942. Illumination from a Nonuniform Sky. Illuminating Engineering 37, 707726.
[1] For beam incident on an exterior window we have the following: For transparent glass with no shade or blind there is only beamtobeam transmission. For diffusing glass, or if a window shade is in place, there is only beamtodiffuse transmission. If a window blind is in place there is beamtodiffuse transmission, and, depending on slat angle, solar profile angle, etc., there can also be beamtobeam transmission.
[2] See “Beam Solar Reflection from Window Reveal Surfaces.”
[3] If Solar Distribution = FullInteriorAndExterior in the Building object, the program calculates where beam solar from exterior windows falls inside the zone. Otherwise, all beam solar is assumed to fall on the floor.
[4] For the purposes of the surface heat balance calculation, any beam solar radiation absorbed by a surface is assumed to be uniformly distributed over the surface even though in reality it is likely to be concentrated in one or more discrete patches on the surface.
[5] TBm_{i}_{}is zero if the window has diffusing glass or a shade. TBm_{i} can be > 0 if a blind is present and the slat angle, solar profile angle, etc., are such that some beam passes between the slats.
[6] A different method from that described here is used for calculating reflections from daylighting shelves (see “Daylighting Shelves”).
[7] The ground surface is assumed to be diffusely reflecting so there is no specular reflection from the ground. The program could be improved by adding a ground surface specular component, which could be important for snowcover conditions.
[8] The sun positions for which the daylight factors are calculated are the same as those for which the solar shadowing calculations are done.
Perez, R., P. Ineichen, R. Seals, J. Michalsky and R. Stewart. 1990. Modeling Daylight Availability and Irradiance Components from Direct and Global Irradiance. Solar Energy 44, 271289.
Petherbridge, P. and J. Longmore. 1954. Solid Angles Applied to Visual Comfort Problems. Light and Lighting 47,173.
Winkelmann, F.C. 1983. Daylighting Calculation in DOE2. Lawrence Berkeley Laboratory report no. LBL11353, January 1983.
Winkelmann, F.C. and S. Selkowitz. 1985. Daylighting Simulation in the DOE2 Building Energy Analysis Program. Energy and Buildings 8, 271286.
Documentation content copyright © 19962015 The Board of Trustees of the University of Illinois and the Regents of the University of California through the Ernest Orlando Lawrence Berkeley National Laboratory. All rights reserved. EnergyPlus is a trademark of the US Department of Energy.
This documentation is made available under the EnergyPlus Open Source License v1.0.