Internal heat gains from lights, people, and equipment of
various types are often significant elements in the zone
thermal balance. EnergyPlus allows the user to specify heat
gains for several equipment types including people, lights,
gas/electric equipment, and several other types. The total
heat gain is comprised of convective, radiant and latent gains
in various proportions from these sources. Convective gains
are instantaneous additions of heat to the zone air. Radiant
gains are distributed on the surfaces of the zone, where they
are first absorbed and then released back into the room (with
some fraction conducted through the surface) according to the
surface heat balances. {See Surface Heat Balance Manager /
Processes in this document}. Latent gains must be handled by
ventilation or air conditioning equipment. Recommended heat
gains are given by ASHRAE [1]. These recommendations include
the sensible (convective plus radiative) and latent
proportions. Sensible gains from equipment are primarily
radiant. The user can specify the heat gains and proportions
for any type of equipment. Determining the gains from lights,
people and baseboard heat are slightly more complicated.
The input object Lights
provides a model for internal gains from lights. Radiant gains
from lights must be handled differently from other radiant
gains for reasons described here (long wavelength
description). The total radiant gains from lights must be
divided into visible and thermal portions. For example, the
total electric input to typical incandescent lights is
converted to 10% visible radiation, 80% thermal radiation, and
10% convective gain. In contrast, the electric input to
typical fluorescent lights is converted to 20% visible
radiation, 20% thermal radiation, and 60% convective gain [2].
These percentage splits are under user control with the Lights
input object.
The input object People
provides a model for internal gains from occupants. Heat is
generated in the human body by oxidation at a rate called the
metabolic rate (see Thermal Comfort discussion for more
details). This heat is dissipated from the body surface and
respiratory tract by a combination of radiation, convection,
and evaporation. The relative proportions of sensible
(radiation plus convection) and latent (evaporation) heat from
people is a complex function of the metabolic rate and the
environmental conditions. EnergyPlus uses a polynomial
function to divide the total metabolic heat gain into sensible
and latent portions. That function is based on a fit to data
[3] at average adjusted metabolic rates of 350, 400, 450, 500,
750, 850, 1000 and 1450 Btu/h each at temperatures of 70, 75,
78, 80, 82 degrees Fahrenheit. Sensible gains of 0 at 96 F and
sensible gains equal to the metabolic rate at 30 F were
assumed in order to give reasonable values beyond the reported
temperature range.
Average adjusted metabolic rate [3] is the metabolic rate
to be applied to a mixed group of people with a typical
percent composition based on the following factors:
Metabolic rate, adult female=Metabolic rate, adult male X
0.85
Metabolic rate, children = Metabolic rate, adult male X
0.75
The original data was in I-P (Inch-Pound) units, but the
following correlation is in SI (Systems-International)
units.
Latent Gain is simply the total gain (metabolic rate) -
sensible gain:
\[LatentGain = MetabolicRate -
SensibleGain\]
Sensible Heat Gain from People
Correlation
The function for sensible gain calculation is compared to
the original data points in the following figure. The radiant
fraction of the sensible gain is a user input on the People
object.
The input object ElectricEquipment:ITE:AirCooled describes
air-cooled electric information technology equipment (ITE)
which has variable power consumption as a function of loading
and temperature. The calculations are described below.
PDesign = Design power input when fully loaded and
entering air temperature is at the user-specified design inlet
temperature [W]
PFanFracDesign = Design fan power input fraction of total
power input when fully loaded and entering air temperature is
at the user-specified design inlet temperature
SchDesignLevel = Scheduled fraction of this equipment
which is powered up
SchCPULoading = Scheduled fraction of CPU loading
TAirInDesign = Air inlet temperature at design condition
[C]
VAirDesign = Air volume flow rate at design condition
[m3/s]
VAirfLoadTAir = Air volume flow rate modifier function of
TAirIn and SchCPULoading
PCPUfLoadTAir = CPU power input modifier function of
TAirIn and SchCPULoading
PFanfFlowFrac = Fan power input modifier function of air
flow fraction
RecircFracDesign = Recirculation Fraction at design
condition [C]
RecircfLoadTAir = Recirculation Fraction modifier function
of TAirSupply and SchCPULoading
UPSEfficDesign = Design electric power supply
efficiency
UPSEfficfPLR = Electric power supply efficiency function
of part load ratio
UPSLossFracToZone = Fraction of electric power supply
losses to zone
The convective heat gain to the zone and the air outlet
temperature are then calculated. The user specified fration of
power supply losses are always added to the general zone heat
balace convective heat gain. For air node connection types
AdjustedSupply and ZoneAirNode, the CPU and fan power
consumption are also added to the zone convective heat gain.
For air connection type RoomAirModel, the gains from the CPU
and fan power consumption are added to the outlet room air
model node.
QAir = PCPU + PFan
QUPS = PUPS * UPSLossFracToZone
QConv:
If Air Node Connection Type = AdjustedSupply OR
ZoneAirNode
QConv = QAir + QUPS
If Air Node Connection Type = RoomAirModel
QConv = QUPS
TAirOut = TAirIn + QAir / (VAir * RhoAir * CpAir)
The individual ITE supply heat index is calculated as shown
below.
SHI = (TAirIn – TAirSupply) / (TAirOut - TAirSupply)
The zone average ITE supply heat index is weighted by the
air flow rate of each ITE object.
The input object ZoneBaseboard:OutdoorTemperatureControlled
provides a model for an outdoor temperature controlled
baseboard heater that adds energy to the zone according a
control profile as shown in the following figure. At TA = T2,
the baseboard heat gain is Q2. For TA > T2, there is no
heat gain. For TA < T1, a maximum amount of energy, Q1, is
added to the zone. There is proportional control between those
two temperatures:
Control of Outdoor Temperature
Controlled Baseboard Heat
These temperature and capacity fields can be autosized
based upon envelope, infiltration, and ventilation loads. To
autosize these fields, users may set a design zone heating
temperature that is assumed to be 20°C if blank.
The capacity at low temperature is the maximum capacity of
the unit. It includes external envelope conduction load,
infiltration load, and ventilation load in a space where the
unit serves. The model first finds the lowest outdoor air
temperature throughout design days included in the simulation,
and determines the conduction load through external envelop
as:
\[q_{Cond} = UA \left( T_{Htg} -
T_L \right)\]
where
qCond is conduction load through
external envelope, W
U is heat transfer coefficient of external wall,
W/m2K
A is area of external wall, m2
THtg is baseboard zone heating setpoint
temperature, °C
TL is low temperature, °C
The capacity at low temperature that is the maximum
capacity of the unit is thus expressed as:
\[Cap_{T_L} = q_{Cond} + q_{I} +
q_{V}\]
where
\(Cap_{T_L}\) is capacity
at low temperature, W
\(q_{I}\) is design
infiltration sensible load, W
\(q_{V}\) = design
ventilation sensible load, W
The capacity at high temperature is then prorated against
the reference low and high temperatures as:
It is useful to consider the distribution of short
wavelength (including visible) radiant energy separate from
long wavelength (thermal) radiant energy because many
materials have different optical properties at different
wavelengths. An extreme example is glass that is opaque to the
long wavelengths and transparent to the short. Properties of
materials vary across the entire spectrum of wavelengths. In
EnergyPlus, all radiant interactions are represented in terms
of only two wavelengths: “short” and “long”. Short wavelength
refers to the distribution given by a ~6000K black body source
such as the sun. Long wavelengths refer to radiation from
~300K sources such as walls or people. There is negligible
overlap between these two distributions. Some sources, such as
lights, must be considered as emitting both long and short
wavelength radiation in proportions that approximate their
actual effects on room surfaces.
Long wavelength radiation from all internal sources, such
as people, lights and equipment, is combined and then
distributed over surfaces. (see Internal Long-Wave Radiation
Exchange).
Some fraction of the beam solar radiation transmitted into
the zone is directly absorbed by the interior surfaces
according to the solar distribution algorithm (see Solar
Distribution) selected by the user. The beam radiation not
directly absorbed, plus the diffuse sky and ground-reflected
radiation, plus the short wavelength radiation from lights are
combined and distributed over the surfaces of the zone
according to:
If all surfaces in the room are opaque, the radiation is
distributed in proportion to the area*absorptance product of
each surface. For surfaces which are transparent,
\[{\rho _i} = 1 - {\alpha _i} -
{\tau _i}\]
That fraction of radiation represented by \({\tau _i}\) is lost from the
zone.
The transmittance and absorptance of transparent surfaces
(windows or glass doors) are calculated as in section Window
Calculation Module based on the optical properties of the
window material layers. The total absorptance of the window is
computed for the interior shading device, the inside surface,
and the outside surface for diffuse solar radiation incident
from outside the zone. Those absorptances are used for short
wavelength radiation incident from inside the zone. In most
cases, this should not cause significant error. When movable
insulation covers the window, the radiation that would have
been transmitted is absorbed at the outer surface of the
window (thermally equal to the inside surface of the
insulation).
Zone Internal Gains[LINK]
Sources and Types of Gains[LINK]
Internal heat gains from lights, people, and equipment of various types are often significant elements in the zone thermal balance. EnergyPlus allows the user to specify heat gains for several equipment types including people, lights, gas/electric equipment, and several other types. The total heat gain is comprised of convective, radiant and latent gains in various proportions from these sources. Convective gains are instantaneous additions of heat to the zone air. Radiant gains are distributed on the surfaces of the zone, where they are first absorbed and then released back into the room (with some fraction conducted through the surface) according to the surface heat balances. {See Surface Heat Balance Manager / Processes in this document}. Latent gains must be handled by ventilation or air conditioning equipment. Recommended heat gains are given by ASHRAE [1]. These recommendations include the sensible (convective plus radiative) and latent proportions. Sensible gains from equipment are primarily radiant. The user can specify the heat gains and proportions for any type of equipment. Determining the gains from lights, people and baseboard heat are slightly more complicated.
Heat Gain from Lights[LINK]
The input object Lights provides a model for internal gains from lights. Radiant gains from lights must be handled differently from other radiant gains for reasons described here (long wavelength description). The total radiant gains from lights must be divided into visible and thermal portions. For example, the total electric input to typical incandescent lights is converted to 10% visible radiation, 80% thermal radiation, and 10% convective gain. In contrast, the electric input to typical fluorescent lights is converted to 20% visible radiation, 20% thermal radiation, and 60% convective gain [2]. These percentage splits are under user control with the Lights input object.
Heat Gain from People[LINK]
The input object People provides a model for internal gains from occupants. Heat is generated in the human body by oxidation at a rate called the metabolic rate (see Thermal Comfort discussion for more details). This heat is dissipated from the body surface and respiratory tract by a combination of radiation, convection, and evaporation. The relative proportions of sensible (radiation plus convection) and latent (evaporation) heat from people is a complex function of the metabolic rate and the environmental conditions. EnergyPlus uses a polynomial function to divide the total metabolic heat gain into sensible and latent portions. That function is based on a fit to data [3] at average adjusted metabolic rates of 350, 400, 450, 500, 750, 850, 1000 and 1450 Btu/h each at temperatures of 70, 75, 78, 80, 82 degrees Fahrenheit. Sensible gains of 0 at 96 F and sensible gains equal to the metabolic rate at 30 F were assumed in order to give reasonable values beyond the reported temperature range.
The original data was in I-P (Inch-Pound) units, but the following correlation is in SI (Systems-International) units.
\[\begin{array}{c}S = 6.461927 + .946892M + .0000255737{M^2}\ + 7.139322T - .0627909TM + .0000589172T{M^2}\ - .198550{T^2} + .000940018{T^2}M - .00000149532{T^2}{M^2}\end{array}\]
where
M=Metabolic Rate (W)
T=Air Temperature (C)
S=Sensible Gain (W)
Latent Gain is simply the total gain (metabolic rate) - sensible gain:
\[LatentGain = MetabolicRate - SensibleGain\]
The function for sensible gain calculation is compared to the original data points in the following figure. The radiant fraction of the sensible gain is a user input on the People object.
Heat Gain from IT Equipment[LINK]
The input object ElectricEquipment:ITE:AirCooled describes air-cooled electric information technology equipment (ITE) which has variable power consumption as a function of loading and temperature. The calculations are described below.
Variable Definitions – User Inputs:[LINK]
Variable Definitions – Simulation Inputs:[LINK]
Variable Definitions – Intermediate Calculations:[LINK]
Variable Definitions – Outputs:[LINK]
Calculations[LINK]
The design power input is first split into portions for the CPU (everything in the equipment except the cooling fans) and the fan(s).
PCPUDesign = PDesign * (1 - PFanFracDesign)
PFanDesign = PDesign * PFanFracDesign
For each time step, the air inlet temperature is calculated depending on the type of air node connection.
TAirIn:
Using the air inlet temperature, the CPU power consumption, air flow rate, fan power consumption, and power supply power consumption are calculated.
PCPU = PCPUDesign * SchDesignLevel * PfLoadTAir(SchCPULoading, TAirIn)
FlowFrac = VAirfLoadTAir(SchCPULoading, TAirIn)
VAir = VAirDesign * FlowFrac
PFan = PFanDesign * SchDesignLevel * PFanfFlowFrac(FlowFrac)
UPSPLR = (PCPU + PFan) / (PCPUDesign + PFanDesign)
PUPS = (PCPU + PFan) * (1 - UPSEfficDesign * UPSEfficfPLR (UPSPLR))
The convective heat gain to the zone and the air outlet temperature are then calculated. The user specified fration of power supply losses are always added to the general zone heat balace convective heat gain. For air node connection types AdjustedSupply and ZoneAirNode, the CPU and fan power consumption are also added to the zone convective heat gain. For air connection type RoomAirModel, the gains from the CPU and fan power consumption are added to the outlet room air model node.
QAir = PCPU + PFan
QUPS = PUPS * UPSLossFracToZone
QConv:
TAirOut = TAirIn + QAir / (VAir * RhoAir * CpAir)
The individual ITE supply heat index is calculated as shown below.
SHI = (TAirIn – TAirSupply) / (TAirOut - TAirSupply)
The zone average ITE supply heat index is weighted by the air flow rate of each ITE object.
SHIZone = ∑ [VAir * (TAirIn – TAirSupply)] / ∑ [VAir * (TAirOut - TAirSupply)]
Heat Gain from Baseboard Heat[LINK]
The input object ZoneBaseboard:OutdoorTemperatureControlled provides a model for an outdoor temperature controlled baseboard heater that adds energy to the zone according a control profile as shown in the following figure. At TA = T2, the baseboard heat gain is Q2. For TA > T2, there is no heat gain. For TA < T1, a maximum amount of energy, Q1, is added to the zone. There is proportional control between those two temperatures:
\[Q = Q2 - \frac{{(Q2 - Q1)(T2 - TA)}}{{(T2 - T1)}}\]
These temperature and capacity fields can be autosized based upon envelope, infiltration, and ventilation loads. To autosize these fields, users may set a design zone heating temperature that is assumed to be 20°C if blank.
The capacity at low temperature is the maximum capacity of the unit. It includes external envelope conduction load, infiltration load, and ventilation load in a space where the unit serves. The model first finds the lowest outdoor air temperature throughout design days included in the simulation, and determines the conduction load through external envelop as:
\[q_{Cond} = UA \left( T_{Htg} - T_L \right)\]
where
qCond is conduction load through external envelope, W
U is heat transfer coefficient of external wall, W/m2K
A is area of external wall, m2
THtg is baseboard zone heating setpoint temperature, °C
TL is low temperature, °C
The capacity at low temperature that is the maximum capacity of the unit is thus expressed as:
\[Cap_{T_L} = q_{Cond} + q_{I} + q_{V}\]
where
\(Cap_{T_L}\) is capacity at low temperature, W
\(q_{I}\) is design infiltration sensible load, W
\(q_{V}\) = design ventilation sensible load, W
The capacity at high temperature is then prorated against the reference low and high temperatures as:
\[Cap_{T_H} = Cap_{T_L} \frac{\left( T_{Htg} - T_H \right)}{\left( T_{Htg} - T_L \right)}\]
where
\(Cap_{T_H}\) is capacity at high temperature, W
TH is high temperature, °C
Distribution of Radiant Gains[LINK]
It is useful to consider the distribution of short wavelength (including visible) radiant energy separate from long wavelength (thermal) radiant energy because many materials have different optical properties at different wavelengths. An extreme example is glass that is opaque to the long wavelengths and transparent to the short. Properties of materials vary across the entire spectrum of wavelengths. In EnergyPlus, all radiant interactions are represented in terms of only two wavelengths: “short” and “long”. Short wavelength refers to the distribution given by a ~6000K black body source such as the sun. Long wavelengths refer to radiation from ~300K sources such as walls or people. There is negligible overlap between these two distributions. Some sources, such as lights, must be considered as emitting both long and short wavelength radiation in proportions that approximate their actual effects on room surfaces.
Long wavelength radiation from all internal sources, such as people, lights and equipment, is combined and then distributed over surfaces. (see Internal Long-Wave Radiation Exchange).
Some fraction of the beam solar radiation transmitted into the zone is directly absorbed by the interior surfaces according to the solar distribution algorithm (see Solar Distribution) selected by the user. The beam radiation not directly absorbed, plus the diffuse sky and ground-reflected radiation, plus the short wavelength radiation from lights are combined and distributed over the surfaces of the zone according to:
\[QS{I_i} = Q{S_n}{\alpha _i}/\sum\limits_{i = 1}^{NS} {{S_i}(1 - {\rho _i})}\]
If all surfaces in the room are opaque, the radiation is distributed in proportion to the area*absorptance product of each surface. For surfaces which are transparent,
\[{\rho _i} = 1 - {\alpha _i} - {\tau _i}\]
That fraction of radiation represented by \({\tau _i}\) is lost from the zone.
The transmittance and absorptance of transparent surfaces (windows or glass doors) are calculated as in section Window Calculation Module based on the optical properties of the window material layers. The total absorptance of the window is computed for the interior shading device, the inside surface, and the outside surface for diffuse solar radiation incident from outside the zone. Those absorptances are used for short wavelength radiation incident from inside the zone. In most cases, this should not cause significant error. When movable insulation covers the window, the radiation that would have been transmitted is absorbed at the outer surface of the window (thermally equal to the inside surface of the insulation).
References[LINK]
ASHRAE. 2001. Handbook of Fundamentals, pp 29.8-29.13, Atlanta: ASHRAE.
Carrier Air Conditioning Company. 1965a. Handbook of Air Conditioning System Design, pp 1-99 to 1-100. New York: McGraw Hill.
Carrier Air Conditioning Company. 1965b. Handbook of Air Conditioning System Design, pp 1-100, Table 48. New York: McGraw Hill.
Documentation content copyright © 1996-2026 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.