ARTICLE IN PRESS
Building and Environment 41 (2006) 184–194
www.elsevier.com/locate/buildenv
Evaluation of simplified models for predicting CO2 concentrations
in small commercial buildings
Thomas M. Lawrencea,, James E. Braunb
a
Department of Biological and Agricultural Engineering, Driftmier Engineering Center, University of Georgia, Athens, GA 30602, USA
b
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Received 3 April 2004; accepted 4 January 2005
Abstract
Evaluation of a building for application of demand-controlled ventilation (DCV) typically involves the use of computer
simulations to predict energy use/costs for both fixed ventilation and ventilation adjusted to maintain fixed CO2 levels within the
space. The simulation tools incorporate models for predicting CO2 concentrations in response to internal sources (people),
infiltration/exfiltration, and ventilation. This paper presents a detailed evaluation of different modeling approaches for predicting
levels of CO2 in occupied spaces for small, single-zone commercial buildings employing packaged air-conditioning equipment. Twozone and three-zone transient models were compared with a quasi-static equilibrium model applied to three distinctly different
building types. Baseline data were derived from computational fluid dynamic models that were developed for field sites. A complete
building system simulation model was then used to compare the impact of the different modeling approaches on the predicted
energy cost savings associated with application of DCV in each building type. The use of a transient CO2 model did not have a
significant impact on model prediction accuracy and energy cost savings predictions as compared with the quasi-static model. The
difference in predicted annual energy costs between the various CO2 modeling types were small and less than might result from
errors introduced by factors such as CO2 sensor uncertainty. Therefore, the use of an equilibrium model is sufficient for use in
evaluating DCV for small commercial buildings.
r 2005 Elsevier Ltd. All rights reserved.
Keywords: Demand control ventilation; Energy simulation; Carbon dioxide; Modeling; CFD
1. Introduction
Demand-controlled ventilation (DCV) is a method
used to minimize the energy penalty associated with
providing appropriate ventilation for removing odors
and contaminants within a room. With DCV, the
amount of ventilation air is adjusted according to the
occupancy level. Typically, CO2 is used as a passive
tracer gas to determine human occupancy in the
space, as originally proposed by Kusuda [1]. The best
potential applications for DCV are rooms with highly
Corresponding author. Tel.: 1 706 5424322; fax: +1 706 5428806.
E-mail address: [email protected] (T.M. Lawrence).
0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.buildenv.2005.01.003
variable occupancy, such as restaurants, stores, or
auditoria [2].
Published studies going back to the 1970s (for
example, [3]) have indicated the potential for energy
savings with the application of ventilation control based
on occupancy or CO2 levels. Emmerich and Persily [4,5]
provided a thorough review of the published studies,
summarizing the application of DCV in approximately
20 field studies, plus other published papers and
standards on simulation studies and sensor locations.
Alalawi and Krarti [6] presented a laboratory study
comparing the effect of different feedback control
strategies on the CO2 levels and HVAC equipment
energy consumption. Schell and Smith [7] outlined
the various control system decisions needed to retrofit
ARTICLE IN PRESS
T.M. Lawrence, J.E. Braun / Building and Environment 41 (2006) 184–194
Nomenclature
mix
C
C_ p
Np
V
V_
Zv
oa
occ
ocst
r
s
st
v-st
vent
z
concentration (ppmv)
CO2 generation rate per person (l/min)
number of persons in building zone
volume (m3)
volumetric flow rate (m3/s)
ventilation effectiveness
Subscripts
inf
185
mixture flow between ventilation and occupied zone
outdoor air
occupied zone
flow between occupied and storage zones
return
supply
storage zone
flow between ventilation and storage zones
ventilation zone
zone (occupied zone)
infiltration
CO2-based DCV in larger scale buildings and presented
a case study that discussed the detailed modifications
needed for a retrofit at one office building. Their
discussion was based in part on earlier work [8] which
described the use of the upper level CO2 set point in a
proportional control strategy as an anchor point for
evaluating zone ventilation rates. This work also
outlined a method to estimate actual ventilation for an
occupied space based on CO2 levels and known
occupancy.
Most of the published studies and proposed analysis methods have assumed perfect mixing in the
room under consideration, for example [9–14]. The
perfect mixing assumption simplifies the modeling of
room CO2 concentrations, but at the expense of
accuracy. Knoespel et al. [15] developed a pollutant
transport model for analyzing the rate of change of
contaminant concentrations in a building with multiple
zones. O’Neill and Crawford [16] used the same model
format to develop an inverse model for determining
interzonal airflows and ventilation effectiveness from
experimental data. Federspiel [13,14] used a similar
model with the assumption of perfect room mixing and
developed a method for recursively estimating the
source strength when some of the transport parameters
are unknown.
Persily [17,18] noted that the assumption of equilibrium conditions for estimating ventilation rates using
mass balance equations may not be valid. For example,
one particular study was described where air ventilation
rates would be overestimated by a factor of two if
equilibrium conditions were assumed to exist when in
fact they did not. Under constant occupancy conditions,
the time needed for a building or room to reach
equilibrium is a function of the air exchange rate. A
time period with stable occupancy and ventilation rate
equal to three times the room time constant is required
for room CO2 levels to reach 95% of their steady-state
value [19]. Thus, in a room with a low air exchange rate,
it may take up to 12 h of constant occupancy
for equilibrium conditions to be reached [20]. Such
Building
Construction
Data
HVAC
Equip’t Data
Occupancy
Information
Weather Data
Building System Simulation using Component Models
DCV / Economizer
Controller
Building
Thermal
Load
HVAC
Equipment
Performance
Zone
CO2
Model
Output: Predicted Energy Use by
HVAC Equipment, CO2 Levels
Fig. 1. General information flow diagram for DCV analysis modeling.
a condition would exist for offices set to older
ventilation standards of around 170 l/min per person,
or 0.25 air changes per hour in the building measured.
Persily also specified a criterion for a building to be
considered in equilibrium [18].
The evaluation of a site for DCV retrofit should
ideally involve the use of a simulation model that
estimates energy savings as compared with fixed
ventilation rates. Fig. 1 depicts the simulation process,
inputs, and models needed to perform this evaluation.
The goal of the work described in this paper was to
identify an appropriate model for predicting space CO2
concentrations to be used in analyzing DCV retrofits for
small commercial buildings having packaged HVAC
equipment. The existing approaches typically use quasistatic models and no previous study has evaluated the
effect of modeling approach on energy cost savings
predictions.
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T.M. Lawrence, J.E. Braun / Building and Environment 41 (2006) 184–194
2. Methodology
The process of identifying appropriate modeling
approaches was carried out in several steps. Different
field sites were identified that have a range of different
occupancy patterns. Computational fluid dynamics
(CFD) models were prepared for the sites in order to
provide detailed benchmark data for evaluating the
ability of simplified models to predict transient variations in space CO2 levels under realistic operating
conditions. Transient and quasi-static models of the
CO2 distribution were developed from the CFD results
for each site. These models were then incorporated into
a system simulation that allowed comparison of the
impact of the different CO2 model types on predicted
cost savings for DCV.
Fig. 2. School site CFD physical model and layout.
2.1. Test sites
Three field test sites were selected for study. These
sites were instrumented and monitored as part of a
larger research project investigating potential energy
conservation technologies in commercial buildings, and
are described in more detail in Braun et al. [21]. The sites
selected include modular schoolrooms, children’s play
areas located in fast food restaurants and retail stores.
The buildings are all single rooms (i.e., no internal walls
partition the rooms) and are conditioned by packaged
HVAC equipment located on the rooftop or building
sidewall. They range in size from fairly small, approximately 75 m2 (800 ft2) up to 835 m2 (9000 ft2) of floor
area.
The modular school site is a portable trailer type
building with floor dimensions of 12.2 m 6.1 m
(40 20 ft) and a ceiling height of 2.75 m (9 ft).
The room is normally occupied by 32 students plus the
teacher. The room layout provides desk spaces for
the students lined up in several rows within the room,
but can vary depending on the teacher’s personal
preferences. Space conditioning is provided by a
sidewall-mounted unit that delivers 0.52 m3/s
(1100 cfm) of supply air. Conditioned air is ducted
to two 0.6 m (2400 ) supply air diffusers located in the
drop ceiling in line with the heat pump. A 0.6 m 0.8 m
(2400 3000 ) grill opening in the wall aligned with the
back of the HVAC unit allows return air back to
the system for reconditioning. Additional items such
as storage shelves and a file cabinet are included.
Fig. 2 shows a cutaway view of the physical model
used in creating the CFD model for the modular
schoolroom site.
The restaurant play area site consists of a more
complicated room layout containing fixed seating
areas and large play equipment located in the center
of the room. The site has the basic room dimensions of
15.2 m 7.6 m (50 ft 25 ft) with a ceiling height of
Fig. 3. Restaurant site CFD physical model and layout.
5.5 m (18 ft). The play structure contains two levels
with a floor footprint of 4.6 m 7.6 m (15ft 25 ft).
The specific site modeled contains a 1.2 m 2.4 m 3 m
(4ft 8 ft with a height of 10 ft) entrance foyer
section from the main dining room area, as shown
in the physical model layout in Fig. 3. A maximum design occupancy of 80 people is assumed.
Conditioned supply air (2.265 m3/s or 4800 cfm) is
provided by three directional diffusers in the upper
sidewall and a single return air grill in the upper
corner. The room also has ceiling fans installed
which are occasionally run. Provisions for the
ceiling fans are included in the CFD model, but
they are assumed not running in this study for
simplicity.
The retail store site is a rectangular floor plan with
basic dimensions of 30.5 m 27.5 m (100 90 ft) and a
ceiling height of 4.25 m (14 ft). The major room features
are the product display shelves located on a regular
pattern throughout the room. Four separate packaged
rooftop units, each providing 1.7 m3/s (3600 cfm), are at
regularly spaced locations. Each unit supplies air via
four diffusers with a central return air grill, as seen in
Fig. 4. For this study, a normal full occupancy of 90
people was assumed.
ARTICLE IN PRESS
T.M. Lawrence, J.E. Braun / Building and Environment 41 (2006) 184–194
III.
IV.
Fig. 4. Retail store site CFD physical model and layout.
V.
2.2. CFD models
CFD models were built representing the three field
test site types to generate benchmark data for evaluating
the CO2 modeling approaches. The goal was not to have
models that provided exact predictions for the specific
field sites, but rather to have models that gave
representative predictions and allowed investigation of
the primary factors that affect internal CO2 concentrations. Each site has specific configuration issues that can
affect the overall airflow and/or occupancy distribution.
For example, the restaurant play area has seating
located just under the play equipment. This region is
both likely to be occupied, and hence have CO2
generated within, and is blocked from much of the
direct interaction with the HVAC supply airflow.
Careful attention was given to developing reasonable
physical representations for each site.
Several key features were common to the CFD
models and are described below.
I. CO2 sources were located in areas expected to be
occupied: for example, the seating areas in both the
restaurant play areas and the modular schoolrooms.
The retail store represents a different situation
where the occupants are more mobile and the CO2
sources were evenly distributed.
II. CO2 source generation was represented by a low
velocity, low volumetric air–CO2 mixture flow from
the top or side surface of solid blocks. For the
school and restaurant sites, the blocks are
0.2 m 0.2 m square and 1 m high. The retail store
site model used an air–CO2 mixture flow from the
sides of several of the product display shelves. The
solid blocks represent occupied seating areas, for
the restaurant and school sites, or the product
shelves for the retail store configuration. These
blocks also develop a more representative flow field
in the zones since these represent areas of generally
VI.
187
no or very low airflow due to blockage. The
volumetric flow from the blocks introduces only a
minor error to the overall flow field and air balance
in the CFD simulation results, with the mixture flow
being between 1.4% and 3% of the total HVAC
supply flow for all building types modeled.
The CO2 source generation rate was varied by
adjusting the relative concentration of CO2 in the
air–CO2 mixture flowing from the source blocks. A
source generation rate of 0.31 l/min per person was
assumed.
The directional character of the HVAC supply
airflow introduced into the zone was modeled as
close as possible based on the outlet diffuser design
at each site.
The total supply airflow to the zone was taken from
the manufacturer’s rating information for the
HVAC equipment and from field site evaluations.
Infiltration flow for each site was assumed to enter
the occupied zone via the door openings at the
specified volumetric flow rate.
The basic room physical descriptions were transformed into models using a commercially available mesh
generation package and a commercial CFD simulation
program. Cutaway views of the physical models created
for each site are given in Figs. 2–4 for the school,
restaurant and retail store sites, respectively. Features to
note in the school physical model shown in Fig. 2 are the
circular diffusers in the ceiling, the student desk
locations and the return air grill in the right-hand
sidewall. The restaurant play area model shown in Fig. 3
contains the table seating areas, two directional supply
air diffusers in the upper center region, a single return
grill in the upper left corner and the play equipment
floor surface located approximately 2.5 m above the
floor in the room center. In Fig. 4, the 13 product
display shelves make up the bulk of the retail store floor
space. Also shown are the locations of the four supply
outlets and central return grill for the four HVAC
rooftop units.
The schoolroom CFD model was meshed with the
edge nodes, representing the room volume, the student
desks, file cabinet and storage desk, on a spacing of
0.2 m. This mesh size criterion matched the size of the
CO2 mixture flow blocks. The inlet and outlet airflow
areas were meshed to a finer spacing to get better
resolution of the flow. The doors and return grill had
edges meshed to 0.15 m spacing. The supply air openings
were meshed with a total of 12 nodes around the
circumference of the circles, for a node spacing of
approximately 0.15 m also. The supply air registers are
designed with louvers to provide air in a mostly radial
direction so as not to direct airflow down on the
students below. Although no hard data were available to
indicate the resulting flow angle from the supply vent,
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T.M. Lawrence, J.E. Braun / Building and Environment 41 (2006) 184–194
based on the louver construction the air was assumed to
be leaving the vent at a 301 angle from the horizontal.
The room volume was meshed using a hybrid tetrahedron scheme, as was done for all the site models. The
final meshed room had a total of 159,477 mesh volumes.
The impact of mesh size was studied and finer mesh
volumes had minimal impact on the results. A comparison of the effect of using a courser grid based on 0.4 m
spacing indicated minimal impact (o3% difference) on
the predicted return CO2 levels when tested during the
first occupancy transient of the school base case.
Although the majority of the room airflow for each site
was expected to be nearly laminar flow, in the regions
near the supply air vents and the return grill turbulent
flow would be expected. Therefore, the flow field was
determined using a viscous flow solver with the k-epsilon
two-equation model.
For the restaurant play area model, a total of 20
blocks for low volumetric air–CO2 mixture flow were
located in the seating areas and within the play
equipment space. The supply air flow was modeled to
include the directional characteristic that matched the
vane pattern on each diffuser outlet. A similar mesh size
philosophy was followed as with the modular schoolroom in that a standard mesh node spacing of 0.2 m was
applied to all surface, and a finer grid of 0.15 m applied
to the air inlet and outlet points. The final meshed room
had a total of 214,315 volume cells.
The retail store model is a simpler layout and
therefore a somewhat courser grid spacing could be
employed. This included a standard node spacing of
0.5 m applied on all wall and block surfaces and a finer
node spacing of 0.25 m was used for all flow (supply and
return) surfaces. The final meshed room had a total of
192,926 volume cells.
The three field sites have very different occupancy,
ventilation requirements and air flow patterns. Compared to the other sites the school site has a relatively
small ventilation time constant with respect to the length
of time for each different occupancy period. The
restaurant and retail store sites are larger in volume
and take longer to reach steady-state conditions. The
restaurant site in particular has a complicated internal
air flow pattern, with some seating areas located under
the children’s play areas which are effectively blocked
from good airflow distribution.
For each site, a base case was defined to represent a
‘‘typical’’ operating day. Changes in occupancy and
infiltration flow conditions were made hourly or as
necessary for the two commercial sites, while the basic
class schedule for the school site was used to define its
occupancy. Table 1 summarizes the occupancy levels
and infiltration flow rates used in the base case
simulation runs. The occupancy loading listed under
the ‘‘% Occupied’’ column represents the occupancy
expressed as percentage of the listed design occupancy
Table 1
CFD simulation base case test plan
Building: school
Design occupancy ¼ 32
Start time
End time
% Occupied
Infiltration (l/min)
Status
8:30
10:50
11:05
12:30
13:15
14:20
14:30
10:50
11:05
12:30
13:15
14:20
14:30
15:00
100%
10%
100%
0%
100%
10%
100%
1416
8496
1416
2832
1416
8496
1416
Class
Recess
Class
Lunch
Class
Recess
Class
Building: restaurant
9:00
11:00
12:00
13:00
14:00
15:00
17:00
19:00
20:00
21:00
11:00
12:00
13:00
14:00
15:00
17:00
19:00
20:00
21:00
22:00
5%
25%
75%
100%
75%
50%
60%
70%
50%
15%
2832
2832
4248
4248
4248
4248
4248
4248
4248
2832
Design occupancy ¼ 80
Morning
Initial
Lunch
Lunch
Lunch
Intermittent
Dinner
Dinner
Intermittent
Cleanup
Building: retail
8:00
12:00
13:00
17:00
19:00
12:00
13:00
17:00
19:00
22:00
10%
20%
10%
25%
10%
5664
5664
5664
5664
5664
Design occupancy ¼ 90
Morning
Noon shoppers
Afternoon
Evening rush
Evening
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for each site. Changes in occupancy were implemented
as a step function at the times noted in Table 1.
Variations on the base case model conditions were also
run and evaluated. These included variations in the
infiltration flow rates and patterns, changing the
occupancy patterns on a more frequent basis than
hourly (such as every 15 min), and changing the source
locations at the restaurant play area site by turning off
the sources located in the play area. Although several
different variations to the base case conditions were run,
these were found to have no impact on the overall
conclusions discussed in this paper. Therefore, only the
results from CO2 modeling investigations for the base
case are presented here, since they provide sufficient
information to evaluate the modeling types.
The use of hourly step changes in occupancy is
conservative in terms of evaluation of the simplified
models and should exaggerate the importance of considering transient effects. Only the school site experiences large
step changes in occupancy similar to those given in Table
1. The occupancies within the restaurant and retail store
sites change more continuously.
All models were run to simulate a complete daily
occupancy period. Before beginning the simulated day,
the CFD models were first run to obtain a steady-state
flow field solution using the flow and turbulence models.
The transient simulations used an implicit first-order
solver and the species transport solution used a full
multi-component diffusion model. The occupancy and
flow schedules listed in Table 1 were then implemented
using a time step of 1 min. The impact of time step on
model predictions was considered and a smaller step had
a relatively minor effect on results. The solution
convergence criterion was when the residual in the
overall mass balance being less than 5 108.
189
on the stratification model originally defined by Janssen
et al. [22] and included in Appendix F of the ASHRAE
Standard 62-2001 [23], with the addition of a term for
infiltration. The ventilation effectiveness is a measure of
how well the supply airflow mixes with the occupied
zone for removal of CO or other pollutants and is
2
defined as
Zv ¼
Cr Cs
,
Cz Cs
(2)
where Cr is the CO2 concentration in the return air.
A two-zone transient model which relies on interzonal airflow is shown in Fig. 5. This model is similar to
the quasi-static stratification model, with the difference
being that two distinct volumes for the occupied and
ventilation zones and an interzonal airflow term are
used instead of the ventilation effectiveness term. An
alternative three-zone model, which assumes that a
portion of the room is partially isolated from the main
breathing and ventilation zones, is illustrated in Fig. 6.
The three-zone model may be better suited to situations
like the restaurant play area or modular school room
sites in that there are regions within the rooms at these
sites that will have limited interaction with the ventilation air paths (such as under and between the desks or
under the play area equipment) or are not normally
occupied.
The corresponding coupled equations for each model
are given in Eqs. (3)–(7).
where
Return
Supply
Both ventilation zone and
occupied zone are
considered fully mixed.
Ventilation Zone
2.3. Simplified CO2 models
The following model formats and variations were
evaluated as compared with transient CO2 predictions
from CFD models:
Occupied Zone
Fig. 5. Two-zone room model with interzonal airflow.
(a) a quasi-static (equilibrium) model;
(b) a two-zone transient model with interzonal airflow;
(c) a three-zone transient model with interzonal airflow.
where
Supply
Return
A generalized quasi-static model for predicting zone
CO2 concentrations can be represented as follows:
(1)
Zv V_ s ðC z C s Þ ¼ N p C_ p þ V_ inf ðC oa C z Þ,
where V_ is volumetric flow rate, C is CO2 concentration,
C_ p is CO2 generation rate per person, Np is number of
people in the zone, ZV is ventilation effectiveness, while
the subscripts inf, oa, s, and z refer to conditions
associated with air from the infiltration stream, outdoor
ambient, supply to zone, and zone. The model is based
Both ventilation
zone and occupied
zone are
considered fully
mixed.
Storage Zone
Occupied Zone
Fig. 6. Three-zone room model with interzonal airflow.
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190
Two-zone model:
V vent
dC r
¼ V_ mix ðC z C r Þ þ V_ s ðC s C r Þ þ V_ inf ðC z C r Þ,
dt
(3)
V occ
dC z
¼ V_ mix ðC r C z Þ þ N p C_ p þ V_ inf ðC oa C z Þ.
dt
(4)
Three-zone model:
V vent
V occ
V st
dC r
¼ V_ mix ðC z C r Þ þ V_ s ðC s C r Þ þ V_ inf ðC z C r Þ
dt
ð5Þ
þ V_ v-st ðC st C r Þ,
dC z
¼ V_ mix ðC r C z Þ þ N p C_ p þ V_ inf ðC oa C z Þ
dt
þ V_ oc-st ðC st C z Þ,
ð6Þ
dC st
¼ V_ oc-st ðC z C st Þ þ V_ v-st ðC r C st Þ.
dt
on the overall average room concentration. The cost
function was the root-mean-square error (RMSE) of the
predicted versus actual CFD model results of the bulk
room average CO2 concentration. During the model
training process, the room concentration was computed
based on a volume-weighted average of the two or three
zones. The RMSE cost function was computed using
simulation results from the entire occupied day as a
training data set.
The parameter estimation process used a commercially available optimization routine to obtain estimates
of the learned parameters. The optimization procedure
is based on the gradient of change in the cost function
with respect to the parameters of interest. A Nelder–Mead simplex (direct search) method determines the
step taken along the steepest gradient. The only
constraints placed on the flow and volume parameters
during the estimation process were that they remain
positive values.
(7)
In these equations, the volume subscripts vent, occ
and st refer to the ventilation, occupied and storage
zones, respectively. For the flow rates, the subscripts
mix, vst, and ocst refer to flows between the
ventilation and mixing zones or between the occupied
and storage or ventilation and storage volumes. Note
that in all models considered, the infiltration rate could
be negative and represent exfiltration.
In the application of the different CO2 models, the
supply concentration is solved for based on a mass
balance in the mixing of room and outdoor air. The
room, zone and storage (in the three-zone model)
concentration are obtained through numerical integration of Eqs. (3)–(7).
The quasi-static model in Eq. (1) is based on an
empirical room ventilation effectiveness. Separate CFD
test cases were run with constant CO2 source and flow
rates until steady-state conditions were reached. The
steady-state return and bulk room CO2 concentrations
were then computed and the ventilation effectiveness
determined using Eq. (2).
A parameter estimation process was applied to learn
unknown values in the two-zone and three-zone models.
In the two-zone model, the two zone volumes (V vent and
V occ ) and the inter-zonal flow (V_ mix ) are unknown, with
the other values either known from the CFD model or
calculated as part of the equation solution and parameter estimation process. For the three-zone model, the
additional storage zone volume (V st ) and inter-zonal
airflows associated with the storage zone (V_ ocst and
V_ vst ) are also learned parameters.
The building system simulation program used for
DCV evaluations bases the amount of outdoor ventilation air required on the bulk room CO2 concentration.
Therefore, training of the zone CO2 models was based
3. CO2 model training results
Tables 2–4 summarize model training results for the
various formats studied and applied to the base case at
each site. Based on the RMSE, the trained models all
performed well. This conclusion is also supported by the
plots of Figs. 7–9 for the school, restaurant and retail
store sites, respectively. These plots show the ability of
each model form to predict CO2 concentration transients for the base case simulated day as compared with
the CFD predictions. For simplicity, the CFD runs were
set up assuming 100% outdoor air for the supply flow
ðC s ¼ C oa Þ and the values given in Figs. 7–9 are
differences between the average room and supply
concentrations.
Table 2
CO2 model evaluation for school site base case
SCHOOL
Volume: 206 m3
Model format
Values
Quasi-static
Room CO2 RMSE (ppmv)
48.3
Two-zone
V v ðm3 Þ
V occ ðm3 Þ
V_ mix ðm3 =sÞ
75.7
35.7
0.571
Three-zone
V v ðm3 Þ
V occ ðm3 Þ
V st ðm3 Þ
V_ mix ðm3 =sÞ
V_ oc-st ðm3 =sÞ
V_ v-st ðm3 =sÞ
75.8
24.7
10.8
0.374
0.248
0.072
8.2
8.1
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Table 3
CO2 model evaluation for restaurant site base case
Restaurant
Volume: 608 m
Model format
Values
3
Quasi-static
Room CO2 RMSE (ppmv)
7.8
Two-zone
V v ðm3 Þ
V occ ðm3 Þ
V_ mix ðm3 =sÞ
111.6
353.5
1.498
Three-zone
V v ðm3 Þ
V occ ðm3 Þ
V st ðm3 Þ
V_ mix ðm3 =sÞ
V_ oc-st ðm3 =sÞ
V_ v-st ðm3 =sÞ
124.4
264.3
7.5
0.485
0.104
0.039
4.1
Bulk Room Concentration Above Supply
(ppmv)
T.M. Lawrence, J.E. Braun / Building and Environment 41 (2006) 184–194
450
400
350
Quasi-static
250
Values
Two-Zone and
Three-Zone
Models Give
Nearly Identical
Results
150
100
50
0
60
120
180
240
300
360
Minutes from start of day
Fig. 7. Predicted room CO2 levels compared to CFD: school base case.
Room CO2 RMSE (ppmv)
Quasi-static
5.0
Two-zone
V v ðm3 Þ
V occ ðm3 Þ
V_ mix ðm3 =sÞ
2.5
408.7
1952.7
6.516
Three-zone
V v ðm3 Þ
V occ ðm3 Þ
V st ðm3 Þ
V_ mix ðm3 =sÞ
V_ oc-st ðm3 =sÞ
V_ v-st ðm3 =sÞ
279.0
470.7
1008.7
2.035
0.692
0.011
Bulk Room Concentration Above Supply
(ppmv)
Model format
Two-Zone
200
0
Table 4
CO2 Model evaluation for retail site base case
Volume: 3360 m3
CFD
300
3.9
Retail store
191
200
150
100
CFD
Quasi-Steady State
50
Two-Zone
Three-Zone
0
0
60 120 180 240 300 360 420 480 540 600 660 720 780
Minutes from start of day
Fig. 8. Predicted room CO2 levels compared to CFD: restaurant base
case.
Certain anomalies appear in the model training results
shown in Figs. 8 and 9 for the restaurant and retail store
sites. For some of the periods, the trained CO2 models
did not match as well as the others, for example, during
the middle of the day when the occupancy decreased
after the noon-time rush. This is because there was not
sufficient time for the CO2 levels to stabilize between the
occupancy step changes.
Only minor differences were seen between the twozone and three-zone transient models, and they both
resulted in good predictions of the transient room
concentration. Even with the quasi-static model, the
maximum RMSE computed using 1-min time step data,
48 ppmv at the school site, was less than the manufacturer’s rated accuracy of 50 ppm for the sensors used at
the field test sites. The RMSE values listed in Tables 2–4
Bulk Room Concentration AboveSupply
(ppmv)
1.7
70
60
CFD Room
Quasi-Static
Two-Zone
Three-Zone
50
40
30
20
10
0
0
60 120 180 240 300 360 420 480 540 600 660 720 780 840
Minutes from start of day
Fig. 9. Predicted room CO2 levels compared to CFD: retail store base
case.
are based on the 1-min time scales. If the errors in the
quasi-static predictions are based on 5-min and 1-h
averages of the data, then the maximum RMSE values
for the school site decrease to 41 and 15 ppmv,
respectively. The CFD simulations used step changes
in the occupancy, while actual field sites generally would
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T.M. Lawrence, J.E. Braun / Building and Environment 41 (2006) 184–194
have more gradual changes. Therefore, although the
transient simulations do provide somewhat better model
predictions, the differences are exaggerated by the
assumption of large step changes in occupancy and the
quasi-static model may be adequate. This was evaluated
formally by comparing predictions of DCV cost savings
using a building system simulation model.
4. Evaluation of CO2 model formats using a building
system simulation
Even though different CO2 modeling approaches may
give different CO2 levels, especially during periods of
rapid or significant changes in occupancy, the impact of
these differences on the overall cost savings estimates
when evaluating DCV control may be relatively small. If
this were the case, then the simplest modeling approach
would be the most appropriate choice. The practical
significance of using a transient CO2 model or the more
simple quasi-equilibrium approach was studied by
comparing results of yearly simulations. The program
chosen for this analysis was based on the model
developed by Brandemuehl and Braun [2] for evaluation
of DCV cost savings. The program was modified to use
the quasi-equilibrium and transient CO2 model formats.
The simulation model performs calculations with an
hourly timestep and incorporates separate models for
transient heat gains from the building envelop, mass and
energy balances on the air within the zone and
distribution system, and HVAC equipment energy
requirements. The overall input and output information
flow is outlined in Fig. 1, using hourly input of the local
weather and building occupancy. Heat gains/losses from
external walls, roofs and floors are modeled using onedimensional transfer functions. The cooling and heating
equipment are modeled using routines from the ASHRAE toolkit [24]. The program compares DCV with a
base case for fixed ventilation associated with satisfying
ASHRAE Standard 62-2001. Energy costs are computed using a three-tiered utility rate structure consisting
of on-peak, mid-peak and off-peak pricing. For each
site, the local utility rate structure information in place
in late 2002 was obtained and used for the analyses in
this study. The simulation program was validated
against other commercial and public domain building
simulation models, as documented in Mercer [25].
The original simulation program employed a quasistatic model for room CO2 concentrations and mass and
energy balance calculations were performed on an
hourly basis. For the transient CO2 models, a smaller
internal timestep was used. Calculations of room and
return CO2 concentrations and ventilation adjustments for DCV were performed using 1-min timesteps.
For each hour, average outdoor ventilation air requirements were computed and used along with building
envelope heat gains determined with 1-h time steps in
order to estimate total hourly equipment loads and
energy requirements. For the comparisons of the
different modeling approaches, a bulk room CO2
concentration of 950 ppmv was used as the setpoint for
DCV. This value resulted in a return air concentration
Table 5
Key building simulation model parameters for DCV analysis
Parameter
Building thermal
Window net transmissivity
Window resistance
Floor overall resistance
Floor overall capacitance
Wall overall resistance
Wall overall capacitance
Ceiling overall resistance
Ceiling overall capacitance
a; exterior wall
a; roof
Interior mass
Equipment and ventilation
Ventilation effectiveness
Supply fan power
Make up air
Infiltration air
Sensible gain lights & equip’t
Energy efficiency ratio—air conditioning (EERAC)
Furnace efficiency or heat pump COP
Supply air flow
Units
M2 K/W
M2 K/W
KJ/m2 K
m2 K/W
KJ/m2 K
m2 K/W
KJ/m2 K
kg/m2
W/(m3/min)
(l/min)/m2
(l/min)/m2
W/m2
M3/min
School
Restaurant
Retail store
0.52
0.27
2.65
39.4
1.25
4.4
2.84
12.1
0.7
0.6
122
0.63
0.27
0.19
238.3
1.26
7.5
3.19
12.1
0.7
0.7
73
0.39
0.27
0.41
24.8
1.84
83.2
3.80
19.8
0.7
0.7
366
0.79
12.4
15
30
27
9.5
3
31.2
0.57
10.6
30
60
9.7
9.5
75%
136
0.6
10.6
15
10
27
8.9
3
408
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of approximately 800 ppmv, which was the setpoint for
DCV studies at the field test sites.
The evaluation of a site for potential application of
DCV requires the determination of the ventilation flow
rate with both DCV control active and with the existing
control strategy. For CO2 modeling evaluations in this
study, the reference baseline assumed a fixed outdoor
ventilation level as prescribed in ASHRAE Standard 622001 for each specific site. The reference baseline for
each site also assumed enthalpy economizer cooling
control. Site-specific values for the building construction, plus the window area, shading and orientation,
were used for each building type studied, and these are
summarized in Table 5. Table 5 also includes sitespecific HVAC equipment parameters.
The system simulation tool was used to study the
sensitivity of DCV energy cost savings predictions to the
three different CO2 modeling approaches. The simulations evaluated the difference in HVAC heating and
cooling energy costs for DCV plus economizer control
(DCV On) compared to economizer cooling only (DCV
Off). These comparisons were done using estimates of
CO2 Generation Rate (liters/min)
10
School (Weekdays Only)
Retail Store (Weekday& Weekend)
9
8
7
6
5
4
3
2
1
0
8
9
10 11 12 13 14 15 16 17 18 19 20 21
Hour of Day
Fig. 10. Assumed CO2 source generation rate pattern for school and
retail store sites.
193
building occupancy (and hence the CO2 source generation rate) that were derived from preliminary investigations at the field sites. Separate average hourly CO2
source generation rates were used during the weekday or
weekend periods for the restaurant site. The school site
was assumed occupied only during weekdays. For the
retail store site, the same occupancy pattern was
assumed for both weekday and weekend periods. Fig.
10 shows the variation in assumed occupancy (CO2
generation rate) for the school and retail store sites,
while Fig. 11 provides this information for the weekend
and weekday periods at the restaurant site.
The annual energy cost savings for including DCV
plus economizer cooling control compared to the
baseline economizer cooling alone ranged from $260
(US) for the school site to over $3100 for the retail store
site. Fig. 12 shows a comparison of the annual energy
cost savings percentage associated with adding DCV.
The resulting differences in predicted energy cost savings
between the three different CO2 model types were very
small, ranging from 0.3% for the school and retail store
to around 1% for the restaurant site. In terms of
absolute costs, the net annual energy cost difference
between the equilibrium and transient models ranged
from a low of $8 for the school site to a high of $70 at
the restaurant site. Compared to the total energy cost
savings, the differences are only about 3% of the total
predicted savings. The difference in total energy cost
savings between the equilibrium and transient CO2
models for the retail store site, expressed as percentage
of the total savings, is only about 1.5%.
The differences in cost savings for DCV due to the
choice of CO2 model are less than any differences that
would be expected due to other uncertainties, such as
the occupancy schedule or errors in the CO2 sensor
readings. For example, Fig. 13 shows the estimated
energy cost savings for the restaurant site when the bulk
room CO2 setpoint was adjusted750 ppmv from the
baseline 950 ppmv setpoint. For this site, the difference
30%
Restaurant Weekday
Restaurant Weekend
20
Restaurant, Sacramento Area
Retail Store, RiversideArea
% Energy Cost Savings with DCV
Source Generation Rate (Liters/min)
25
15
10
5
0
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Hour of Day
Fig. 11. Assumed CO2 source generation rate pattern for restaurant
site.
25%
ModularSchool, Sacramento Area
20%
15%
10%
5%
0%
Equilibrium Model
Two-zone with control to
bulk room
Three-zone with control to
bulk room
Fig. 12. Comparison of energy cost savings for different CO2 model
types.
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194
30%
Restaurant building type
% Savings with DCV
25%
20%
15%
10%
5%
0%
Equilibrium Model, 900 ppm Equilibrium Model, 950 ppm Equilibrium Model, 1000 ppm
bulk room setpoint
bulk room setpoint
bulk room setpoint
Fig. 13. Variation in energy cost savings for different CO2 setpoints.
in annual energy costs estimated between a 900 ppmv
and a 1000 ppmv setpoint was nearly $300, or four times
the difference between using the equilibrium and
transient CO2 models.
5. Conclusion
The use of a transient CO2 model is not necessary for
evaluating cost savings associated with DCV for small
commercial buildings. The errors are less than those that
would occur due to other uncertainties such as CO2
sensor errors. One of the most important factors
impacting DCV savings is the occupancy schedule. A
companion paper addresses the issue of identifying sitespecific occupancy schedules from field measurements
using a quasi-equilibrium model and parameter estimation [26].
Acknowledgments
This research was supported in part by the California
Energy Commission Pubic Interest Energy Research
(PIER) Building Energy Efficiency Program.
References
[1] Kusuda T. Control of ventilation to conserve energy while
maintaining acceptable indoor air quality. ASHRAE Transactions 1976;82(1).
[2] Brandemuehl MJ, Braun JE. Impact of demand-controlled and
economizer ventilation strategies on energy use in buildings.
ASHRAE Transactions 1999;105(2):39–44.
[3] Ogasawara S, Taniguchi H, Sukehira C. Effect of energy
conservation by controlled ventilation: case study in a department
store. Energy and Buildings 1979;2:3–8.
[4] Emmerich SJ, Persily AK. Literature review on CO2 based
demand controlled ventilation. ASHRAE Transactions
1997;103(2):229–43.
[5] Emmerich SJ, Persily AK. State-of-the-art review of CO2 demand
controlled ventilation technology and application. National
Institute of Standards Technical Report NISTIR 6729, July 2001.
[6] Alalawi MA, Krarti M. Experimental evaluation of CO2-based
demand-controlled ventilation strategies. ASHRAE Transactions
2002;108(2).
[7] Schell M, Smith D. Assessing CO2 control in retrofits. ASHRAE
Journal 2002;44(11):34–43.
[8] Schell MB, Turner SC, Shim RO. Application of CO2 based
demand controlled ventilation using ASHRAE Standard 62:
optimizing energy use and ventilation. ASHRAE Transactions
1998;104(2):1213–25.
[9] Drees KH, Wenger JD, Janu G. Ventilation air flow measurement
for ASHRAE Standard 62-1989. ASHRAE Journal 1992:40–5.
[10] Janu GJ, Wenger JD, Nesler CG. Strategies for outdoor airflow
control from a systems perspective. ASHRAE Transactions
1995;101:631–43.
[11] Sørensen B. Simulation of a small VAV plant. Proceedings of
Indoor Air ’96, vol. 2, 1996. p. 199–204.
[12] Ke Y, Mumma SA, Starke D. Simulation results and analysis of
eight ventilation control strategies in VAV systems. ASHRAE
Transactions 1997;103:381–91.
[13] Federspiel CC. Estimating the inputs of gas transport processes in
buildings. IEEE Transactions on Control Systems Technology
1997;5(5):480–9.
[14] Federspiel CC. Conditions for the input–output relation of
perfect mixing processes to be first order with application to
building ventilation systems. Transactions of ASME, Journal of
Dynamic Systems, Measurement and Control 1998;120:170–6.
[15] Knoespel PD, Mitchell JW, Beckman WA. Macroscopic model of
indoor air quality and automatic control of ventilation airflow.
ASHRAE Transactions 1991;97(2):1020–30.
[16] O’Neill PJ, Crawford RR. Identification of flow and volume
parameters in multi-zone systems using a single-gas tracer
technique. ASHRAE Transactions 1991;97(1):49–54.
[17] Persily AK. Ventilation, carbon dioxide and ASHRAE Standard
62-1989. ASHRAE Journal 1993;35(7):40–4.
[18] Persily AK. Evaluating building IAQ and ventilation with indoor
carbon dioxide. ASHRAE Transactions 1997;103(2):193–204.
[19] Seppänen OA, Fisk WJ, Mendell MJ. Associations of ventilation
rates and CO2 concentrations with health and other responses in
commercial and institutional buildings. Indoor Air 1999;9:226–52.
[20] Nabinger SJ, Persily AK, Dols WS. A study of ventilation and
carbon dioxide in an office building. ASHRAE Transactions
1994:1264–73.
[21] Braun JE, Lawrence TM, Mercer K, Li H. Description of Field
Test Sites. Report submitted to Architectural Energy Corporation
for the California Energy Commission Building Energy Efficiency
Program, Deliverables 2.1.1a, 2.1.1b, and 3.1.1a, December 2001.
[22] Janssen JE, Hill TJ, Woods JE, Maldonado EAB. Ventilation for
control of indoor air quality: a case study. Environment
International 1982;8:487–96.
[23] ASHRAE. ANSI/ASHRAE Standard 62-2001: Ventilation for
acceptable indoor air quality. Atlanta, GA: American Society of
Heating, Refrigerating and Air-Conditioning Engineers; 2001.
[24] Brandemuehl MJ, Gabel S, Andresen I. HVAC2 Toolkit:
Algorithms and Subroutines for Secondary HVAC System
Energy Calculations. ASHRAE, 1791 Tullie Circle, NE, Atlanta,
GA 30329, 2000.
[25] Mercer K. Modeling and testing strategies for evaluating
ventilation load reduction technologies. Master’s Thesis, Purdue
University, West Lafayette, IN, 2003.
[26] Lawrence TM, Braun JE. A methodology for estimating occupant
CO2 source generation rates from measurements in small
commercial buildings. Building and Environment, Submitted,
2004.