optimization of air-conditioning system operating strategies for hot and humid climates
TRANSCRIPT
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Energy and Buildings 40 (20Optimization of air-conditioning system operating strategies for hot
and humid climates
Jung-Ho Huh a, Michael J. Brandemuehl b,*a Architectural Engineering, University of Seoul, 90 Jeonnong-Dong Dongdaemoon-Gu, Seoul 130-743, Republic of Korea
b Civil, Environmental, and Architectural Engineering, University of Colorado, 428 UCB, Room ECOT 441, Boulder, CO 80309 USA
Received 16 August 2007; accepted 30 October 2007
Abstract
This paper describes research into the optimal operation of building heating, ventilation, and air-conditioning (HVAC) systems focusing on both
temperature and humidity control. While most previous work on HVAC optimization has been limited to evaluation of conventional temperature-
based control systems, this study emphasizes the humidity control issue in meeting both sensible and latent building loads. The analysis is based on
a combination of a realistic simulation of a direct expansion (DX) air-conditioning system and a direct-search numerical optimization technique.
The simulation models have been validated through comparisons with field data. Optimization was performed on five different system control
variables to minimize system power consumption while meeting building loads and maintaining comfort. Indoor temperature and humidity are also
optimized within standard comfort constraints. Building loads were modeled using an extended bin method that allows consideration of the
interactions between loads and indoor conditions. Results indicate that minimum energy use typically occurs at low airflow rates, with indoor
humidity levels below the upper comfort limit. Results also show that coil air bypass and evaporator circuiting control are typically not necessary
unless operation would otherwise result in overcooling. The optimization results also translate to relatively simple strategies for system control.
Significant savings are demonstrated over conventional control strategies used in packaged DX equipment.
# 2007 Elsevier B.V. All rights reserved.
Keywords: Dehumidification; Energy consumption; Air-conditioning system; Simulation; Optimization
1. Introduction
Humidity problems can be found in many applications
including office buildings, supermarkets, art galleries,
museums, libraries, electronics manufacturing facilities,
pharmaceutical clean rooms, indoor swimming pools and
other commercial facilities. In many HVAC applications, the
cooling and dehumidification coil is unable to properly meet the
dehumidification requirements of the building when the latent
load is high, either due to large internal moisture generation or
through communication with humid outdoor conditions.
Depending on the application, the mismatch between building
latent load and equipment latent capacity can degrade occupant
comfort and productivity, cause damage from mold and
condensate, and increase energy costs through reheating. These
* Corresponding author. Tel.: +1 303 492 8594; fax: +1 303 492 7317.
E-mail address: [email protected] (M.J. Brandemuehl).
0378-7788/$ – see front matter # 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.enbuild.2007.10.018
problems are exacerbated by the increased demand for outdoor
air in buildings to address indoor air quality.
In most commercial and residential applications, the
humidity in the space is not directly controlled. In the process
of meeting the sensible loads of the building, the air is forced
below the dew-point temperature, coincidentally providing
dehumidification as a result of the cooling process. The relative
humidity in the space is controlled only indirectly and it floats
up and down as a result of the changing match between the
sensible and latent capacities of the equipment compared to the
sensible and latent loads. In some commercial applications,
most notably supermarkets, both temperature and humidity of
the space are directly controlled. The most common method
employed today to meet the coincident loads of a supermarket
is to operate the constant-air-volume system at whatever
compressor capacity is required to maintain both space
temperature and humidity at or below the desired levels. If
the system operation is dictated by space temperature, the space
humidity is allowed to fall below the setpoint, causing
increased energy use to remove more moisture than necessary.
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–1213 1203
If the system operation is dictated by space humidity, the space
temperature is allowed to drop only so far, typically to the
heating setpoint, before reheating is required to maintain
comfort conditions. If waste heat is not available, there is a cost
penalty for both overcooling the air and then reheating it.
The first step in addressing dehumidification needs involves
comprehensive system design. Design and selection of an
appropriate HVAC and dehumidification system requires that
the system meet both sensible and latent loads. However, since
design conditions typically occur at times of high sensible load,
off-design conditions often present situations of low sensible
load but high latent load. It is necessary to operate the system to
match the equipment performance with the building loads over
a broad range of off-design operating conditions, while
constrained to maintain temperature and humidity within a
desired range.
The ‘‘match’’ between the sensible and latent components of
the equipment capacities and building loads is represented by
the sensible heat ratio, SHR. The equipment capacity SHR is
defined as the ratio of the sensible capacity to total capacity, and
the load SHR is defined as the ratio of sensible load to total load,
where the total is the sum of the sensible and latent.
SHRcap ¼CAPsen
CAPsen þ CAPlat
(1)
SHRload ¼Qsen
Qsen þ Qlat
(2)
Low SHR implies a greater latent fraction and better
dehumidification. Under steady-state conditions, energy and
mass balances dictate that SHRcap = SHRload.
Given a particular system design, the goal of this research is
to develop optimal operational strategies for a direct expansion
(DX) HVAC system with respect to both energy consumption
and thermal comfort. The objective will be achieved by
applying numerical optimization techniques with a validated
simulation model.
Optimization techniques have not been widely used in the
study of HVAC system operation, and relatively little research
on optimal HVAC system operation has been reported in the
literature. Several HVAC systems have been previously studied
for optimal control in meeting temperature-cooling require-
ments only. To date there has been no comprehensive study on
the optimal set of HVAC operating parameters for the complete
thermal environment. In most applications both temperature
and humidity must be maintained, presenting a tougher
optimization problem than simple temperature control. Since
providing greater comfort is one of main objectives in today’s
HVAC industry, the need for efficient active humidity control
becomes more important.
Earlier optimization studies of HVAC systems mainly
focused on control of water-side equipment in a chilled water
plant, not air-side, and room air humidity was not controlled
directly. Even recent studies [1–3] investigated optimal control
of supply air temperature and/or airflow in air-handling unit
systems without considering humidity as a controlled variable.
Over the years, there have been many studies focusing on the
dehumidification performance of the air conditioners, including
issues of simulation, design, and operations. For example,
studies have been performed by Shirey [4], Brandemuehl and
Khattar [5], Kosar et al. [6], Mumma [7], Murphy [8], Khattar
[9], and Harriman and Judge [10]. There have also been many
studies of thermal comfort control involving optimal energy
use. Whitmer [11] minimized the energy requirements for a
simple system by determining the optimal combination of
environmental variables (air temperature, humidity, and air
velocity) with the thermal comfort constraint. Henderson et al.
[12] investigated the impact of controlling an HVAC system to
maintain constant comfort rather than fixed setpoint tempera-
ture under humid climate. More recently, Mazzei et al. [13]
conducted a critical review regarding the thermal comfort-
based HVAC dehumidification systems.
While there is a rich literature on all of the various aspects of
the problem, there has been no systematic effort to address
optimal off-design operation of an air-conditioning system to
satisfy both temperature and humidity constraints imposed by
the needs of occupant comfort and health. This evaluation will
be performed using validated simulation models of DX HVAC
equipment, simplified load models that include the effects of
changing indoor conditions on sensible and latent loads, and
constrained, direct-search optimization techniques.
2. Description of the analysis
2.1. System model
Fig. 1 shows a schematic diagram of a typical direct
expansion air-conditioning system focusing on air-side system
configuration considered in this study. Return air from the
building zone is mixed with outdoor air to provide mixed air to
the air handler. A reheat coil is included to provide reheat as
necessary to maintain a humidity setpoint.
A combined theoretical/empirical modeling strategy has been
adopted, which allows confidence in predicting performance over
a very wide range of operating conditions. The DX system model
is based on a set of physically based models for the components of
a DX system [14]. The components include compressors, dry-
surface heat exchangers (e.g., air-cooled condenser), wet-surface
heat exchangers (e.g., cooling coil), heat pipes, fans, and outdoor
air mixing chambers. The individual component models are then
combined into a complete system.
The compressor model is an empirically and statistically
based correlation for positive displacement compressors. The
model has polynomial fits for the cooling capacity, CAP, and
the power draw of the compressor, Pcomp. There are two
independent variables in each ten-term equation—the saturated
suction temperature, SST, and the saturated discharge
temperature, SDT.
CAP ¼ C1 þ C2SSTþ C3SDT þ C4SST2 þ C5ðSSTÞðSDTÞþ C6SDT2 þ C7SST3 þ C8ðSDTÞðSST2Þþ C9ðSSTÞðSDT2Þ þ C10SDT3 (3)
of air-conditioning system.
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–12131204
2
Pcomp ¼ P1 þ P2SSTþ P3SDTþ P4SST þ P5ðSSTÞðSDTÞþ P6SDT2 þ P7SST3 þ P8ðSDTÞðSST2Þþ P9ðSSTÞðSDT2Þ þ P10SDT3 (4)The rating procedure and the form of the equations are
specified by ARI Standard 540 [15]. While the results can be
corrected for different superheat and subcooling levels, our
analysis assumes fixed superheat of 11.1 8C and fixed
subcooling of 8.3 8C. The coefficients, Ci and Pi, are typically
available directly from the manufacturers.
The condenser is simulated using an air-to-liquid coil model
that accounts for heat transfer between air and a liquid through a
dry finned coil surface. The model is based on simple
effectiveness–NTU heat exchanger relationships, described in
most introductory heat transfer textbooks, and assumes that the
temperature of the refrigerant throughout the coil is fixed at the
SDT.
The evaporator is also modeled using effectiveness–NTU
relationships, modified to account for both the heat and mass
transfer of the cooling and dehumidifying coil [16,17]. In
particular, the cooling coil models accounts for both heat and
moisture transfer effects assuming a Lewis number of unity and
using a locally linear saturation curve. The model accounts for
both fully wet and partially wet coils by calculating coil surface
temperatures throughout the coil and comparing with local air
dew-point temperatures. The model also assumes that the
refrigerant temperature is constant at the SST through the coil.
The overall system is modeled by combining the compo-
nents. Computationally, the system performance is determined
by solving for the SST and SDT under a given set of operating
conditions. The required operating conditions are the airflow
Fig. 1. Schematic diagram
rate, air temperature, and humidity ratio entering each of the
coils.
The results of the model include the power consumption of
the compressor, indoor fan, and outdoor fan, as well as the
temperature and humidity of the air delivered to the building
and the average run-time fraction of the system.
The specific models of the individual components can be
calibrated with a combination of manufacturer’s data or
measured field performance. The compressor coefficients of
Eqs. (3) and (4) are generally available from the compressor
manufacturer. The air-cooled condenser model requires an
overall heat transfer coefficient to describe the physical size and
heat transfer performance of the condenser. The evaporator
model requires an overall heat transfer coefficient and the
fraction of this overall coefficient that is associated with the
external fin surfaces. These parameters can be back-calculated
knowing the condenser and evaporator heat transfer at a given
set of rating conditions.
Alternatively, the model parameters can be identified by
correlation to measured performance data. For this study, the
model has been calibrated to match the performance of a 30-
tonnes (105.6 kW) unit installed in a supermarket in Florida [5].
Compressor coefficients were obtained from the manufacturer
and overall heat transfer coefficients for the evaporator and
condenser were obtained through parameter identification
using measured data.
The DX system model has been validated through
comparisons with manufacturers’ published performance data
and field data at several sites in the southeastern U.S. Fig. 2
shows a comparison of measured and predicted compressor
power of the system for operation during a 2-month period in
summer. Similar comparisons are obtained for sensible and
Fig. 2. Comparison of measured and simulated compressor power.
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–1213 1205
latent capacities, as well as suction and discharge pressures. In
each case, the comparisons have an R2 value of greater than
0.88.
2.2. System control strategies
Five different system control variables are considered in the
optimization process. Each control variable has an independent
effect on the efficiency of the refrigeration system and/or the
sensible versus latent capacity of the equipment as described by
the SHRcap. The first two control variables discussed here focus
on the compressor and condenser subsystem.
� C
ompressor capacity control. There are a variety of methodsto control compressor capacity, including variable speed
operation, on–off cycling, inlet guide vanes for centrifugal
compressors, slide valves for screw compressors, and
compressor unloading for reciprocating compressors. In
each case, the level of capacity control can be represented as a
fraction of full load capacity under the given operating
conditions. In this analysis, it is assumed that the compressor
capacity is continuously modulated.
� C
ondenser fan control. Air-cooled condensers typically havemultiple fans with provision for varying the number of
operating fans. Several manufacturers offer variable speed
operation on one fan to provide continuous airflow control.
Condenser airflow is typically controlled based on com-
pressor capacity, outdoor air temperature, and discharge
pressure. However, the airflow is actually an optimization
variable. At high airflow, condenser fan power increases
while the compressor power is reduced due to lower
discharge pressures. The optimal values also depend on
evaporator conditions and control. In this analysis, it is
assumed that the condenser fans and effective condenser area
are continuously staged. That is, as the condenser airflow is
reduced, it is assumed that the condenser area for heat transfer
is also proportionally reduced.
The following control variables have a direct effect on
the split between sensible and latent capacity of the system,
the SHRcap, by affecting the evaporator temperature and the
interactions of the evaporator with the moist air stream. In
general, a lower coil temperature dictates improved
dehumidification performance through reductions in the
SHRcap.
� S
upply airflow rate. Changes in the evaporator airflow ratehave a significant effect on system dehumidification
performance. Like the condenser, changes in evaporator
airflow cause trade-offs between compressor power and fan
power. Lower airflow yields lower fan power, but increased
compressor power because of lower suction pressure.
However, more importantly, changes in airflow rate have a
strong influence over the dehumidification performance of
the cooling coil. For DX systems, reduction in airflow lowers
the coil temperature and gives a closer approach of the
leaving air temperature to the coil temperature, both of which
reduce SHRcap. For this analysis, constraints are placed on the
control variables to ensure that the saturated suction
temperature is greater than �2.2 8C for freeze protection.
� B
ypass air around cooling coil. Practical considerations limitthe minimum supply airflow rate. In many cases, a minimum
flow or supply duct pressure is required to assure adequate air
circulation in the building. One common method to reduce
coil airflow without affecting the supply airflow is to bypass
part of the air stream around the coil through the use of a coil
face-bypass damper. While there are no additional savings
due to fan power reductions, the reduced coil airflow can save
energy by providing a better match between SHRcap and
SHRload.
� C
ooling coil face-split circuit control. It is common,especially in multiple compressor systems, to disable part
of the evaporator surface at part-load conditions. For
example, a rooftop unit might have two equal compressors,
each with 50% cylinder unloading, for effective capacity
staging. It is common to provide two separate evaporator
coils, one for each compressor, stacked on top of each other in
the air stream. More generally, it is possible to design the
system with variable evaporator area available for refrigerant
flow. For the purposes of this analysis, it is assumed that the
evaporator refrigerant flow is controlled in a ‘‘face-split’’
arrangement, using the full depth of the coil. With this
circuiting arrangement, reducing the evaporator area lowers
the suction temperature and lowers the SHRcap.
It should be noted that the mixed air conditions entering the
air handler have a significant effect of DX system performance.
Since the mixed air is comprised of outdoor and return air, the
outdoor air fraction is an important control variable. For this
analysis, it is assumed that the outdoor airflow rate is fixed at
15% of the design airflow rate to meet indoor air quality
concerns. In particular, as the supply airflow rate is decreased,
the outdoor air fraction increases.
2.3. Building load models
In evaluating optimal control strategies for temperature and
humidity control, one major constraint on system operation is
that the sensible and latent loads be met. Alternatively, the
indoor temperature and humidity must be maintained within
Fig. 3. Simplified load model from detailed computer simulation.
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–12131206
desired ranges. As discussed in the next section, the analysis
includes evaluation of optimization to maintain a desired
comfort level in which indoor temperature and humidity can
vary as long as overall comfort is maintained. Unfortunately,
since a portion of the building load derives from the difference
between indoor and outdoor conditions, changes in indoor
temperature and humidity cause changes in the loads. Since
changes in the loads have a dramatic effect on energy
consumption, evaluation of optimal control strategies requires
consideration of the interactions between loads and indoor
conditions.
A detailed dynamic hourly analysis of these interactions
would require dynamic optimization to account for heat and
moisture storage in the building, which would involve daunting
computational difficulties. Instead, the interactions between
loads and indoor conditions are estimated using an extension of
the modified bin method [18]. The building loads have been
simplified to represent the sensible cooling load as a function of
the difference between outdoor air temperature and indoor air
temperature. Latent cooling loads are represented as a function
of the difference between outdoor and indoor humidity ratios.
Separate load relationships can be used at night and during the
day to account for the difference in solar effects, lighting levels
and occupancy.
The following relationships describe the loads as functions
of indoor and outdoor conditions.
Qsen ¼ KsenðToa � Tz þ DTgainÞ (5)
Qlat ¼ K latðwoa � wz þ DwgainÞ (6)
DTgain ¼Gsen
Ksen
(7)
Dwgain ¼Glat
K lat
(8)
where
Qsen = zone sensible load (W),
Ksen = linear load coefficient for sensible loads (W/8C),
Gsen = effective sensible internal gain (W),
Toa = outdoor temperature (8C),
Tz = building zone temperature (8C),
DTgain = temperature difference associated with internal
heat gains (8C),
Qlat = zone latent load (W),
Klat = linear load coefficient for latent loads (W),
Glat = effective latent internal gain (W),
woa = outdoor humidity ratio,
wz = building zone humidity ratio,
Dwgain = humidity ratio difference associated with internal
moisture gains.
Fig. 3 shows a comparison of the simplified sensible loads
for the retail store as obtained from hourly simulation [14]. The
fluctuations are largely due to the simplified accounting of
solar gains and to fluctuations in occupancy and infiltration.
Notice that there is a net positive cooling load at very low
outdoor temperatures, indicating that the internal heat gains
dominate the envelope heat gains in determining the cooling
requirements.
The simplified relationships were developed using the
results of hourly load simulations of a retail store in Miami [14].
Ksen ¼ 986:4 W=�C Gsen ¼ 32; 192:5 W
K lat ¼ 1:172� 106 W Glat ¼ 1; 490:5 W
The load models used here appear very simple. However, it
can be argued that they are also very appropriate to the task of
comparing dehumidification alternatives. While the simple bin
models do not explicitly account for solar effects or dynamic
variations in load due to thermal storage in the building, the
regressions for sensible load have been developed from a model
that does explicitly handle these effects. While the results of the
detailed model show variations in sensible load at a given
outdoor temperature, the averaging of these variations can be
appropriate for comparisons of annual energy consumption.
Most significantly, the moisture transport and latent load model
of the most common hourly building simulation programs are
identical to the latent load model employed here. That is, the
latent load is a function only of the scheduled internal moisture
gains and the difference between indoor and outdoor humidity
ratio. In an effort to account for the effects of indoor humidity
on latent load and equipment performance, the simplified
model used here represents less of a compromise than typically
required in other bin analyses.
3. Optimization method
3.1. Objective function and constraints
The objective function and constraints for this HVAC system
optimization problem derive directly from the desire to
minimize energy use while satisfying building loads and
maintaining indoor conditions within desired ranges. There
could be two approaches to devise the objective function
depending on whether the comfort constraints are handled as
part of the objective function or constraint functions. While
both techniques have been evaluated, the discussions here will
focus on the simpler objective function. The objective function
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–1213 1207
will then be confined to the power consumption of the
compressor, condenser fans, and air handler fans. Since the
analysis will be performed assuming quasi-steady-state
operation, minimizing power is synonymous with minimizing
energy use.
Jðu; fÞ ¼ Pcomp þ Pcond þ Pahu (9)
where
J = the objective function and the,
u = vector of controlled variables,
f = vector of uncontrolled variables,
Pi = power consumption of component i.
As noted above, the power use of the HVAC system is a
function of the sensible and latent loads, the outdoor
environmental conditions, the indoor environmental condi-
tions, and the system control variables. The vector of
uncontrolled variables, f, includes the sensible and latent
loads and the outdoor temperature and humidity. In this case,
with the loads a function of outdoor and indoor conditions, the
outdoor conditions are effectively the only uncontrolled
variables.
The vector of controlled variables, u, includes the five
equipment variables described above in the section on system
control variables. Specifically, the vector includes the following
variables:
ucomp = fraction of compressor capacity at given operating
conditions,
ucond = fraction of design condenser airflow,
uahu = fraction of design air handler airflow rate,
ubyp = coil air bypass fraction,
uevap = fraction of evaporator coil with refrigerant flow, face
split.
For this analysis, the indoor conditions are also considered to
be controlled variables. That is, we desire to identify the
optimal values of the indoor temperature and humidity that
minimize energy use while maintaining comfort. Since comfort
is subjective and a function of both temperature and humidity, it
is possible to find alternative pairs of temperature and humidity
that provide the same comfort, but that require different energy
consumption from the HVAC system. Constraints are subse-
quently required to ensure that the indoor environment is
comfortable.
In this study, there are two groups of the constraints:
building sensible and latent loads, and thermal comfort. The
building loads represent inequality constraint functions,
specifying that (1) the sensible capacity of the equipment is
greater than or equal to the sensible load of the building and (2)
the latent capacity of the equipment is greater than or equal to
the latent load of the building. If overcooling of the building is
required to meet the latent loads, reheat is required to maintain
comfort.
Constraints on the indoor conditions are applied in three
different forms:
1. C
onstant setpoint for indoor temperature and maximumsetpoint for humidity. That is, the temperature is maintained
precisely, using reheat if necessary, but the humidity is
allowed to float down below the setpoint.
2. S
et minimum and maximum values for the temperature andhumidity ratio. That is, comfort is defined in terms of a
rectangular section of the psychrometric chart.
3. S
et minimum and maximum values for the predicted meanvote (PMV).
The PMV is a single index of comfort that includes the
effects of air temperature, air humidity, radiant temperature, air
velocity, clothing level, and activity level [19]. Numerical
values have been assigned to the responses according to the 7-
point thermal sensation scale that runs from cold (�3) to hot
(+3). It has further been determined that 90% of people will be
express satisfactory thermal comfort within the range
�0.5 � PMV � +0.5.
For this analysis, only temperature and humidity have
been varied in the comfort calculations. Metabolic rate was
1.2 mets and no external work are assumed, corresponding to
standing, but relaxed, activity. Light summer clothing is fixed
as 0.5 clo. Relative air velocity is fixed at 0.2 m/s. Room air
temperature and mean radiant temperature are assumed to be
identical.
3.2. The complex search method
Essentially, the simplex method is a rudimentary steep
ascent procedure, in which a sequence of experimental designs,
each in the form of a regular simplex, is used. (The convex hull
of n + 1 points is called an n-dimensional simplex.) The
direction of steepest ascent is estimated from observations at
the vertices of a regular simplex and proceeds from the center of
the simplex out through that face which is opposite to (does not
contain) the point corresponding to the lowest observation.
Thus, the optimization procedure is to continually move into
the adjacent regular simplex obtained by discarding the point of
the current simplex corresponding to the lowest observation and
replacing it by its mirror image in the plane (hyperplane) of the
remaining points.
The original complex method has the advantage of easy
handling capability for implicit inequality constraints, and of
not requiring computation of any derivative such as in the
gradient method. It has, however, the disadvantage of
relatively slow convergence to an optimum point and requires
many iterative computations. Therefore, improvement of the
convergence rate of the method has been attempted by
modifying it without introducing many complexities. The
improved algorithm, the golden complex search method, is
based on the Box’s Complex Method [20] and was developed
by Hughes [21] and extended by Malik [22] in the form of the
general-purpose subroutine. This algorithm has subtle
improvements for handling infeasible points, for avoiding
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–12131208
local minima, and for accelerating convergence by weighted
centroid calculations.
4. Results and discussion
An optimization analysis has been performed for a retail
building using a direct expansion air-conditioning system, as
described previously. The building has a design-cooling load
of 105.6 kW. The air-conditioning system has a rated COP of
3.0 and SHR of 0.7. The air handler delivers a design airflow
rate of 5663 or 53.6 L/s kW with a fan power at design flow of
8.5 kW.
The analysis uses the extended bin analysis, which
characterizes sensible and latent cooling loads as functions
of indoor and outdoor temperatures and humidities. The
analysis has been performed with the building located in
Miami, which exhibits humid weather conditions during the
summer. Weather data for Miami were obtained from typical
meteorological year (TMY) data.
The analysis is based on coincident sensible and latent loads,
which requires bin weather data for coincident temperature and
humidity. Fig. 4 shows coincident temperature and humidity
data for Miami, FL. For the purpose of this analysis, the hourly
dry-bulb temperature is organized in bins of 2.0 8C and
humidity ratio in bins of 0.002. The analysis is performed for
the months of May through September. Bins with less than 15 h
were excluded from the analysis, giving a total of 3335 h with
temperatures between 23 8C and 33 8C.
The analysis is performed at each outdoor temperature and
humidity bin, corresponding to a specific set of uncontrolled
variables, f. The optimization has been performed under several
different sets of operating conditions and constraints on indoor
Fig. 4. Coincident outdoor temperature
conditions. The following sections describe results of these
scenarios.
4.1. Base case
The base case represents typical operations in retail
buildings using rooftop air-conditioning systems. The indoor
temperature is set to 25.6 8C and the indoor relative humidity is
limited to a maximum of 55% (0.0113 humidity ratio). Supply
airflow is constant at design flow with no coil bypass. The air-
conditioning equipment operates with modulated capacity
control using 100% of the evaporator coil. As with typical
system operation, the compressor capacity fraction, ucomp, is
determined to meet the loads and the condenser fan fraction,
ucond, tracks the compressor capacity fraction. As such, there is
no optimization involved in the base case.
The results of the base case analysis are given in Fig. 5. Total
cooling energy consumption was calculated to be 122,132 kWh
for the 3335 h of the analysis. The figure also displays results
for the individual outdoor temperature and humidity bins,
showing the power and compressor fraction at each bin. As
shown in the figure, compressor power to meet the loads in each
bin increases with increasing temperature and humidity. The
figure of compressor fraction shows similar trends, ranging
between values of 0.44 and 1.0.
4.2. Variable indoor conditions within specified bounds
A zone thermostat is the most common device that controls
the operation of a commercial rooftop DX system. If humidity
is directly controlled, as in a supermarket, the control signal is
typically a dew-point sensor in the zone. If setpoints are to be
and humidity data for Miami, FL.
Fig. 5. Base case results (conventional operation).
Table 1 (Continued )
Humidity Temperature (8C)
24 26 28 30 32
0.0160 1.00 1.00 1.00 1.00 1.00
0.0180 1.00 1.00 1.00 1.00 1.00
Optimal setpoint temperature
0.0100 78.00 78.00 78.00 78.00 78.00
0.0120 78.00 78.00 78.00 78.00 78.00
0.0140 78.00 78.00 78.00 78.00 78.00
0.0160 78.00 78.00 78.00 78.00 78.00
0.0180 78.00 78.00 78.00 78.00 78.00
PMV
0.0100 �0.03 �0.05 �0.06 �0.07 �0.08
0.0120 �0.02 �0.03 �0.04 �0.06 �0.07
0.0140 0.00 �0.02 �0.03 �0.04 �0.05
0.0160 0.01 0.0160 �0.01 �0.03 �0.03
0.0180 0.03 0.01 �0.01 �0.02 �0.02
Optimal compressor fraction
0.0100 0.31 0.37 0.45 0.54 0.60
0.0120 0.35 0.42 0.51 0.60 0.68
0.0140 0.48 0.48 0.57 0.66 0.77
0.0160 0.46 0.54 0.64 0.73 0.82
0.0180 0.50 0.60 0.71 0.82 0.93
Optimal bypass air fraction
0.0100 0.01 0.00 0.00 0.00 0.00
0.0120 0.00 0.00 0.00 0.00 0.00
0.0140 0.00 0.00 0.00 0.00 0.00
0.0160 0.00 0.00 0.00 0.00 0.00
0.0180 0.00 0.00 0.00 0.00 0.00
Optimal condenser fraction
0.0100 0.78 0.94 0.92 0.86 1.00
0.0120 1.00 1.00 0.94 0.90 1.00
0.0140 1.00 1.00 1.00 1.00 1.00
0.0160 1.00 1.00 1.00 1.00 1.00
0.0180 1.11 1.00 1.00 1.00 1.00
Optimal setpoint humidity ratio
0.0100 0.0092 0.0088 0.0085 0.0081 0.0077
0.0120 0.0097 0.0093 0.0090 0.0086 0.0082
0.0140 0.0101 0.0097 0.0094 0.0090 0.0086
0.0160 0.0105 0.0101 0.0098 0.0095 0.0093
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–1213 1209
changed, the most natural bounds for indoor conditions are dry-
bulb temperature and dew-point temperature, or humidity ratio.
The results of this section are generated by allowing the indoor
temperature to range between 22 and 26 8C and by allowing the
indoor humidity ratio to increase up to 0.012. The actual indoor
temperature and humidity are determined through optimiza-
tion, which seeks the optimal indoor conditions in conjunction
with optimal values of the five system control variables to
minimize system power consumption at each set of outdoor
temperature and humidity.
Table 1
Results for variable indoor conditions, bound temperature and humidity
Humidity Temperature (8C)
24 26 28 30 32
Relative power consumption ratio vs. Base case
0.0100 0.57 0.58 0.60 0.61 0.59
0.0120 0.60 0.61 0.63 0.65 0.65
0.0140 0.60 0.64 0.66 0.68 0.70
0.0160 0.60 0.66 0.69 0.72 0.75
0.0180 0.62 0.66 0.71 0.76 0.80
Optimal supply airflow fraction
0.0100 0.50 0.50 0.50 0.50 0.49
0.0120 0.50 0.50 0.50 0.50 0.50
0.0140 0.50 0.50 0.50 0.50 0.50
0.0160 0.50 0.50 0.50 0.51 0.55
0.0180 0.50 0.50 0.50 0.51 0.53
Optimal evaporator fraction
0.0100 1.00 1.00 1.00 1.00 1.00
0.0120 1.00 1.00 1.00 1.00 1.00
0.0140 1.00 1.00 1.00 1.00 1.00
0.0180 0.0109 0.0105 0.0102 0.0098 0.0096
Ventilation airflow: 850 L/s (15% OA design); minimum supply airflow rate:
50% of design airflow; location: Miami, FL; building type: retail store.
Total cooling energy consumption (kWh): 85,381. Saving: 30.1%.
Note: (1) 3335 h were analyzed during the cooling season (May through
September: total 3672 h)—OA conditions of low frequency occurrence (below
15 h) were excluded in this analysis.
(2) Bound of setpoint temperature: 22–26 8C.
(3) Bound of setpoint humidity ratio: 0.0044–0.0120.
Table 1 shows results for the analysis. As a seasonal
summary, total cooling energy consumption is 85,381 kWh.
This optimal operating strategy consumes 30% less energy
than the conventional operation. Comparing the power
consumption in each bin with the corresponding values in
Table 1, it can be seen the optimization reduces power
consumption at every set of outdoor conditions. The table also
shows a set of subtables that give the optimal values of each of
the seven optimized variables, which help to explain the causes
of the energy savings at each bin. Following trends are
observed:
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–12131210
compressor fraction: increases steadily with increases in
outdoor temperature and humidity, reflecting increases in
loads.
Supply airflow fraction: stays at minimum allowable value,
giving lowest fan power and improved dehumidification,
except at highest outdoor temperatures. Notice, though, that
the airflow fraction is greater than the compressor fraction
for the lower temperatures and humidities, indicating that
the airflow per unit compressor capacity is greater than at
design conditions.
Coil bypass fraction: stays closed for all bins. It is always
more cost effective to reduce air handler supply airflow than
to bypass coil. It is uneconomical to further lower indoor
humidity by opening the bypass damper without air handler
fan savings.
Evaporator surface fraction: uses full coil surface for all
bins. It is always more cost effective to reduce air handler
supply airflow than to eliminate coil surface area.
Condenser fan fraction: always greater than the compressor
fraction, indicating that, for this system, increases in
condenser fan power are compensated by improvements
in compressor efficiency.
Fig. 6. Results for bound indoor conditi
Indoor temperature: always at the maximum allowable
temperature, giving reduced sensible load.
Indoor humidity: not always at the maximum allowable
humidity. Optimal humidity level decreases as outdoor
temperature increases, and increases as outdoor humidity
increases.
Logically, it might be expected that the optimal indoor
conditions occur at the upper bounds of space temperature and
humidity ratio, which minimize the sensible and latent loads,
respectively. However, the optimization results indicate that the
performance of the HVAC equipment can dictate lower indoor
humidity levels. In this case, the optimal humidity setpoint is
largely determined by the airflow rate. Low airflow rate reduces
SHRcap, giving a lower indoor humidity. The lower humidity
also serves to reduce the compressor efficiency and to increase
the load on the compressor. However, since supply duct
pressure is not typically controlled in packaged rooftop
equipment, decreasing the airflow rate reduces the indoor
fan energy to the cubic power. The net effect of these competing
factors gives minimum energy at the reduced airflow, which in
turn, dictates the lower indoor humidity.
ons, reduced minimum airflow rate.
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–1213 1211
4.3. Variable indoor conditions with PMV constraint
The results of Table 1 show that the optimal indoor
conditions result in excellent comfort, giving comfort in the
range of �0.09 � PMV � 0.03. It might be argued that such
conditions are ‘‘too comfortable’’ when additional cost
savings could be achieved by relaxing the comfort
requirements.
A similar analysis has been performed in which the PMV
was bound between �0.5 � PMV � 0.5. As expected, the
optimal indoor conditions at all bins of outdoor conditions were
found to be at the upper limit of PMV = 0.5. In all cases, the
resulting indoor temperatures were approximately 1.1 8Cwarmer than those in Table 1. Optimal indoor humidities were
also slightly higher, giving almost identical SHRload to those of
Table 1. Detailed results are not presented here, since all trends
in control variables were similar. However, it is noted that the
increases in indoor temperature and humidity resulted in total
energy savings of 40% compared to the base case.
Fig. 7. Results for supermarket lo
4.4. Low minimum supply airflow
The results of Table 1 suggest that the supply airflow is the
single most important variable in determining the SHRcap and
the resulting match between equipment performance and the
sensible and latent loads of the building. However, the
constraints of that analysis limit the supply airflow to 50%
of the design airflow. Fig. 6 shows results of the analysis if the
constraint is relaxed to allow lower values of supply airflow.
Depending on outdoor conditions, the results show that the
optimal airflow fraction could be as low as 36% of design
airflow. It is further noted that the supply airflow fraction is
always less than the compressor fraction, indicating that the
airflow per unit compressor capacity is lower than the design
values.
The lower airflow rates cause a lower SHRcap, which gives a
lower indoor humidity level and increased latent load. While
the lower airflow saves fan energy, it is offset by the additional
latent load, and the net energy savings are only slightly more
ads, bound indoor conditions.
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–12131212
than the case in which the supply airflow is constrained to be no
less than 50% of the design airflow. The minor increase in
savings indicates that the optimum is relatively ‘‘flat’’ with
respect to airflow rate in this region and suggests that a fixed
airflow rate of 50% design flow is nearly optimal.
4.5. Supermarket loads
The previous results are all based on a single load
relationship that represents sensible and latent loads for a
typical retail store. In general, retail store loads are
characterized as dominated by internal loads associated with
lights and occupancy. As shown in Fig. 4, there is a large
sensible load even when the outdoor temperature is below the
indoor temperature. As a result, the SHRload is relatively high
due to the large sensible component. By comparison, super-
market loads have much lower SHRload because of the cooling
effects of the refrigerated cases. It is not uncommon for a
supermarket to require dehumidification without a need for
cooling.
Fig. 7 shows the results of an optimization analysis for the
supermarket load characteristics. The analysis has been
performed with bounded indoor conditions having a slightly
tighter humidity control requirement. Like the retail store
analysis, the temperature is bound between 22 and 26 8C, but
the zone humidity ratio is limited to be lower than 0.0102.
(Zone humidity levels are often controlled to levels as low as
40% RH to save energy on the refrigeration system.) The
supply airflow rate has also been limited to no less than 50% of
the design airflow.
The most significant difference between the retail and
supermarket results is that, when the outdoor temperature is
below 29.4 8C, the HVAC equipment is unable to meet the latent
load without overcooling the zone air. The zone air temperature
drops to as low as 22.4 8C and the optimal humidity ratio is fixed
at the upper allowable value. Under these conditions, there is also
an incentive to exercise control over the coil bypass and the
evaporator coil area fraction. In the most extreme case of outdoor
conditions of 23.9 8C and 0.012 humidity ratio, the compressor is
operating at a part-load ratio of 14%, the supply fan airflow is
fixed at 50% of design airflow to ensure adequate circulation, and
74% of the supply air is bypassed around the cooling coil. Notice,
though, that the combination of the control actions results in
about 13% of the design airflow over the coil to accompany the
14% compressor part-load operation.
5. Summary and conclusions
This paper describes the methods and results of an
optimization of HVAC system controls to minimize energy
use while maintaining comfort, with a special emphasis on the
control of humidity in commercial buildings. The analysis has
been based on realistic modeling of a DX air-conditioning
system coupled with techniques for constrained direct-search
optimization. Loads have been linked to indoor and outdoor
conditions through an extended bin method. Results have been
presented for a range of outdoor conditions and load features,
and with a variety of constraints on comfort conditions and
system operation.
The results of the analysis indicate that significant energy
savings are available through optimization. The most sig-
nificant factors affecting operation are the interactions between
the compressor capacity control and the air handler fan control.
Coil bypass and evaporator circuiting control are only
appropriate to avoid overcooling. For the particular systems
considered, it was generally advantageous to operate with high
condenser fan fraction.
The results of the optimization also indicated that it is often
desirable to operate at indoor humidity levels that are below the
maximum allowed for comfort. While the lower indoor
humidity increases the load on the HVAC system, the design
of the equipment dictates that there would be a greater penalty
in fan power to operate the system at the higher SHRcap. In
contrast, the results indicate that it is almost always optimal to
operate at the highest allowable indoor temperature within
comfort constraints. The only exception is if the equipment
cannot meet the latent load without overcooling.
The results of the analysis suggest the following guidelines
for near-optimal operation of DX HVAC equipment to meet
both sensible and latent loads in hot and humid climates.
� C
ompressor capacity fraction is the primary control variablefor meeting loads over a wide range of outdoor conditions.
� F
or this system in which the condenser fan power isproportional to the airflow fraction, the condenser fan airflow
fraction is optimal at about twice the compressor capacity
fraction. Optimal condenser airflow increases with reductions
in air handler airflow.
� O
ptimal airflow rates are generally between 33.5 and 46.9 L/skW. However, the minimum is relatively flat.
� C
oil air bypass is only appropriate if overcooling wouldotherwise result because the HVAC system could not meet the
latent load at minimum air handler airflow. It is always more
economical to reduce airflow, if possible.
� T
here is no advantage to explicitly controlling indoorhumidity to a specific setpoint. Rather, allow humidity to
float below a maximum, dictated by the equipment
performance at the controlled air handler airflow.
As with most research, the results also ask additional
questions. The results were generated for two building types in a
single location with a single HVAC system, with a particular set
of compressor, condenser, and evaporator, and a particular set of
compressor and fan power characteristics. However, a packaged
rooftop DX system is commodity HVAC equipment and there is
considerable similarity in the performance among systems,
especially at typical efficiency levels. The relationship between
the building application, load details, and location climate will
clearly have an impact on the specific results. However, results at
selected additional locations in the hot and humid regions of the
southeastern US show similar trends in optimal operating
strategies. In locations with more temperate or dry climates, it is
not clear that the same strategies for supply airflow operation will
be optimal. Ideally, it would be possible to perform the
J.-H. Huh, M.J. Brandemuehl / Energy and Buildings 40 (2008) 1202–1213 1213
optimization on-line with a data-driven inverse model that
characterizes the installed performance of the specific system.
Perhaps the most significant restriction is that the work was
performed for a DX system. It is not clear that similar trends
will be observed with chilled water systems.
References
[1] Y.P. Ke, S.A. Mumma, Optimized supply-air temperature (SAT) in vari-
able-air-volume (VAV) systems, Energy 22 (6) (1997) 601–614.
[2] F. Engdahl, D. Johansson, Optimal supply air temperature with respect to
energy use in a variable air volume system, Energy and Buildings 36 (3)
(2004) 205–218.
[3] L. Song, M. Liu, Optimal outside airflow control of an integrated air-
handling unit system for large office buildings, Journal of Solar Energy
Engineering 126 (2004) 614–619.
[4] D.B. Shirey III, Demonstration of efficient humidity control techniques at
an art museum, ASHRAE Transactions 99 (1) (1993) 93–102.
[5] M.J. Brandemuehl, M. Khattar, Dehumidification performance of air-
conditioning systems in supermarkets, EPRI Report TR-106065, Palo
Alto, CA, Electric Power Research Institute, 1996.
[6] D.R. Kosar, et al., Dehumidification issues of standard 62-1989, ASHRAE
Journal 40 (3) (1998) 71–75.
[7] S.A. Mumma, Designing dedicated outdoor air systems, ASHRAE Journal
43 (5) (2001) 28–31.
[8] J. Murphy, Dehumidification performance of HVAC systems, ASHRAE
Journal 44 (3) (2002) 23–28.
[9] M.K. Khattar, Seperating the V in HVAC: a dual-path approach, ASHRAE
Journal 44 (5) (2002) 37–42.
[10] L.G. Harriman III, J. Judge, Dehumidification equipment advances,
ASHRAE Journal 44 (8) (2002) 22–29.
[11] L.R. Whitmer, Minimizing space energy requirements subject to
thermal comfort conditions, ASHRAE Journal 18 (6) (1976) 48–
51.
[12] H.I. Henderson Jr., K. Rengarajan, D.B. Shirey III, The impact of comfort
control on air conditoner energy use in humid climates, ASHRAE
Transactions 98 (2) (1992) 104–113.
[13] P. Mazzei, F. Minichiello, D. Palma, HVAC dehumidification systems for
thermal comfort: a critical review, Applied Thermal Engineering 25
(2005) 677–707.
[14] J.H. Huh, Optimal air-conditioning system operating strategies for com-
bined temperature and humidity control in buildings, Ph.D. Thesis,
University of Colorado at Boulder, 1995.
[15] ARI, ARI Standard 540-1999 Positive Displacement Refrigerant Com-
pressors and Compressor Equipment, Arlington, VA, Air-Conditioning &
Refrigeration Institute, 1999.
[16] T.H. Kuehn, J.W. Ramsey, J.L. Threlked, Thermal Environmental
Engineering, third ed., Prentice-Hall Inc., 1998.
[17] M.J. Brandemuehl, S. Gabel, I. Andresen, HVAC 2 Toolkit: Algorithms
and Subroutines for Secondary HVAC System Energy Calculations,
American Society of Heating, Refrigerating, and Air-Conditioning Engi-
neers, Inc., Atlanta, 1993.
[18] D. Knebel, Simplified Energy Analysis Using the Modified Bin Method,
American Society of Heating, Refrigerating, and Air-Conditioning Engi-
neers, Inc., Atlanta, 1985.
[19] ASHRAE, ASHRAE Handbook—Fundamentals, American Society of
Heating, Refrigerating, and Air-Conditioning Engineers, Inc., Atlanta,
2005.
[20] M.J. Box, A new method of constrained optimization and comparison with
other methods, Computer Journal 8 (1965) 42–52.
[21] R.R. Hughes, Mathematical models for process design optimization,
AIChE Today Series Notes (1972).
[22] R.K. Malik, Optimal design of flexible chemical processes, Ph.D. Thesis,
University of Wisconsin at Madison, 1979.