Energy performance comparison of a chiller plant using the conventional staging and the co-design approach in the early design phase of hotel buildings

energies
Article
Energy Performance Comparison of a Chiller Plant Using the
Conventional Staging and the Co-Design Approach in the Early
Design Phase of Hotel Buildings
Yamile Díaz Torres 1 , Paride Gullo 2, * , Hernán Hernández Herrera 3 , Migdalia Torres del Toro 4 ,
Roy Reyes Calvo 5 , Jorge Iván Silva Ortega 6 and Julio Gómez Sarduy 5
1
2
3
4
5
6
*
Citation: Díaz Torres, Y.; Gullo, P.;
Hernández Herrera, H.; Torres del
Toro, M.; Reyes Calvo, R.; Silva
Ortega, J.I.; Gómez Sarduy, J. Energy
Performance Comparison of a Chiller
Plant Using the Conventional Staging
and the Co-Design Approach in the
Early Design Phase of Hotel
Instituto Superior Politécnico de Tecnologías e Ciências (ISPTEC), Departamento de Engenharias e
Tecnologias, Ave Luanda Sul, Luanda P.O. Box 583, Angola
Department of Mechanical and Electrical Engineering, University of Southern Denmark (SDU),
6400 Sønderborg, Denmark
Faculty of Engineering, Universidad Simón Bolivar, Barranquilla 080005, Colombia
Instituto Superior Politécnico Alvorecer da Juventude (ISPAJ), Departamento de Engenharias e Ciências
Exactas, Urbanição Nova Vida, Rua 45. Kilamba Kiaxi, Luanda P.O. Box 583, Angola
Studies Center for Energy and Environment, Universidad Carlos Rafael Rodríguez, Cienfuegos 55100, Cuba
Department of Energy, Universidad de la Costa, Barranquilla 080005, Colombia
Correspondence: parigul@sdu.dk; Tel.: +45-65507314
Abstract: As part of the design process of a chiller plant, one of the final stages is the energy testing
of the system in relation to future operating conditions. Recent studies have suggested establishing
robust solutions, but a conservative approach still prevails at this stage. However, the results of
some recent studies suggest the application of a new co-design (control–design) approach. The
present research involves a comparative analysis between the use of conventional staging and the codesign approach in the design phase of a chiller plant. This paper analyzes the energy consumption
estimations of six different chiller plant combinations for a Cuban hotel. For the conservative
approach using on/off traditional staging, the results suggest that the best option would be the
adoption of a chiller plant featuring a symmetrical configuration. However, the outcomes related to
the co-design approach suggest that the best option would be an asymmetrical configuration. The
energy savings results were equal to 24.8% and the resulting coefficient of performance (COP) was
59.7% greater than that of the symmetrical configuration. This research lays firm foundations for the
correct choice and design of a suitable chiller plant configuration for a selected hotel, allowing for
significant energy savings in the tourism sector.
Buildings. Energies 2023, 16, 3782.
https://doi.org/10.3390/
en16093782
Keywords: chiller plant; co-design; traditional staging; optimal chiller loading; optimal chiller sequencing
Academic Editor: Rafik Belarbi
Received: 28 February 2023
Revised: 13 April 2023
Accepted: 26 April 2023
Published: 28 April 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
1. Introduction
Selecting all of a chiller plant’s parameters involves considering the system’s cooling
capacity and its configuration. Fang et al. [1] demonstrated that poor design of a plant
causes a significant deviation in the efficiency of each element in the system from its
optimum point of operation. According to ASHRAE [2], the sequential procedure suggests
that a chiller plant design should involve the evaluation of the total cooling load demand
of a building, which needs to be increased by an extra load for safety reasons, and, finally,
the selection of the other features, i.e., the type of chiller, the number of chillers, the cooling
load distribution, and the hydraulic arrangement. Several studies and recommendations
related to these steps were summarized by Diaz et al. [3], and the overall procedure is
shown in Figure 1.
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4.0/).
Energies 2023, 16, 3782. https://doi.org/10.3390/en16093782
https://www.mdpi.com/journal/energies
Energies 2023, 16, x FOR PEER REVIEW
Energies 2023, 16, 3782
2 of 24
2 of 23
recommendations related to these steps were summarized by Diaz et al. [3], and the
overall procedure is shown in Figure 1.
Cooling load demand analysis
under deterministic approach
Cooling Peak load demand value
Safety Factor, Unmet hours
According international and /or
local standars
Total cooling capacity
Redundancy
Depend of type facility
requirements
CHILLER PLANT CONFIGURATION
Type of chiller
According technical advantanges,
building requirements, budged,
space, among others technical and
economic criteria
Number of units
(N+1)
According engineering
recommendation ,
budged
Cooling distribution
among chillers
Symetrical, Assimetrical, mixed
According standards or
engineering recommendation
Hidraulic arragement
Pararell,Serie,Mixed
According standards or
engineering recommendation
Figure 1. A traditional methodology for designing the primary circuit of centralized chiller/heat
Figure 1. A traditional methodology for designing the primary circuit of centralized chiller/heat
pump plants [3].
pump plants [3].
Over time,
time, the
traditional chiller
Over
the traditional
chiller plant
plant design
design methodology
methodology has
has been
been improved.
improved.
Taylor
[4]
recommended
adding
the
estimation
of
the
energy
consumption
according
to
Taylor [4] recommended adding the estimation of the energy consumption according
to the
the
critical
operating
conditions
of
the
building
to
the
traditional
methodologies
for
critical operating conditions of the building to the traditional methodologies for selecting
selecting
lowest
lifeAncycle
cost. An
importantinimprovement
this traditional
the
lowestthe
life cycle
cost.
important
improvement
this traditionalinmethodology
was
methodology
was
its
conversion
into
an
iterative
process,
where
the
uncertainty
analysis
its conversion into an iterative process, where the uncertainty analysis of cooling loads
of cooling
loads was
with energy
performance,
considering
an and/or
energy,
was
incorporated
withincorporated
energy performance,
considering
an energy,
economic,
economic,
and/or
life
cycle
cost
approach
called
robust
design.
This
methodology
allows
life cycle cost approach called robust design. This methodology allows for selecting
the
for
selecting
the
chiller
that
meets
the
technical
requirements
of
the
facility
chiller that meets the technical requirements of the facility and simultaneously offersand
the
simultaneously
offers
best empirically
performancedetermined
from several
empirically
determined where
chiller
best
performance
fromthe
several
chiller
plant combinations,
plant combinations,
whereare
certain
design
(e.g.,
number of
certain
design parameters
modified
(e.g.,parameters
the numberare
of modified
chillers and
the the
distribution
chillers and
the distribution of cooling capacity).
cooling
capacity).
etal.
al.[5][5]determined
determined
capacity
number
of cooling
units using
an
Cheng et
thethe
capacity
andand
number
of cooling
units using
an unceruncertainty
procedure
to
determine
the
cooling
load
demand
profile
and
the
Markov
tainty procedure to determine the cooling load demand profile and the Markov method to
method an
to energy
perform
an energy
the different
proposedThis
configurations.
This
perform
analysis
of theanalysis
differentof
proposed
configurations.
analysis involved
analysis involved
preventive
maintenance
reliability.
Using a similar
preventive
maintenance
and reliability.
Usingand
a similar
methodology,
Yang etmethodology,
al. [6] defined
the
optimal
chiller
plant
byplant
modifying
the chiller
type and the
and
Yang
et al. [6]
defined
theconfiguration
optimal chiller
configuration
by modifying
thenumber
chiller type
size
of the
chillers.
compares
results
with thethe
application
of the
the application
traditional
and the
number
andFigure
size of1the
chillers. the
Figure
1 compares
results with
design
methodology.
Themethodology.
chiller plant savings
wereplant
equal
to 26%were
of theequal
life cycle.
of the traditional
design
The chiller
savings
to 26% of the
Despite
the
undeniable
improvements
presented
in
the
previous
studies,
there are still
life cycle.
aspects
that need
to be addressed
to obtain a more
decisive
result
in the selection
of chiller
Despite
the undeniable
improvements
presented
in the
previous
studies, there
are
plants.
This is
especially
case due totothe
fact that
these
coolingresult
systems,
once
installed
still aspects
that
need to the
be addressed
obtain
a more
decisive
in the
selection
of
in
buildings,
automatic
control
systems,
which
for systems,
increasingonce
the
chiller
plants.usually
This isincorporate
especially the
case due
to the
fact that
theseallow
cooling
overall
efficiency
by synchronizing
the coolingautomatic
load of thecontrol
chillerssystems,
with the which
coolingallow
demand.
installed
in buildings,
usually incorporate
for
In
this
case,
it
is
possible
that
this
system
would
incorporate
another
design
scenario,
very
increasing the overall efficiency by synchronizing the cooling load of the chillers with the
different
from the In
onethis
considered
both traditional
robust
design
methodologies.
cooling demand.
case, it isinpossible
that thisand
system
would
incorporate
another
As
the
most
suitable
configuration
for
a
certain
building
is
being
evaluated,
the
design scenario, very different from the one considered in both traditional
and robust
premise
is that chiller plants usually comprise N + 1 units. As the energy performance
design methodologies.
analysis
is carried
out fromconfiguration
the design stage,
rules
are used
in different
As the
most suitable
for asimple
certainstaging
building
is being
evaluated,
the
simulation
software
and
research
analyses.
A
common
practice
in
chiller
plant
design is
premise is that chiller plants usually comprise N+1 units. As the energy performance
to
consider
the progressive
according
to the cooling
the size
analysis
is carried
out from startup
the design
stage, simple
staging load
rulesdemand
are usedand
in different
of the chillers. Huang et al. [7] and Li et al. [8] recommended the startup of the chiller
involving the highest cooling capacity first. Figure 2 illustrates the cooling load-based
chiller sequencings of chiller on/off staging suggested by Sun et al. [9] and Huang et al. [7].
simulation software and research analyses. A common practice in chiller plant design is
to consider the progressive startup according to the cooling load demand and the size of
Energies 2023, 16,the
3782chillers. Huang et al. [7] and Li et al. [8] recommended the startup of the chiller
3 of 23
involving the highest cooling capacity first. Figure 2 illustrates the cooling load-based
chiller sequencings of chiller on/off staging suggested by Sun et al. [9] and Huang et al.
[7]. Figure 2 shows
the2 energy
consumption
forecasting
of the i-th
chiller
the j-th
hour
Figure
shows the
energy consumption
forecasting
of the
i-th in
chiller
in the
j-th hour using
the PLR-COP
curve of chiller
generalmodels
chiller models
according
to acapacity.
fixed capacity.
using the PLR-COP
curve of general
according
to a fixed
Figure 2. CoolingFigure
load-based
chiller
sequencing
representation
of the traditional
principle
of principle of chiller
2. Cooling
load-based
chiller
sequencing representation
of the
traditional
chiller on/off staging.
Reprinted/adapted
with
permission
from
Ref
[9].
on/off staging. Reprinted/adapted with permission from Ref. [9].
Energyprediction
consumption
prediction
is an
important
phase
in chiller
design, which
Energy consumption
is an
important
phase
in chiller
plant
design,plant
which
involves
the technical characteristics
of the
chiller and
operating
involves considering
theconsidering
technical characteristics
of the chiller and
operating
factors
suchfactors such
as theof
characteristics
of the
and
thevariation
thermal load
variation
predict the interaction
as the characteristics
the facility and
thefacility
thermal
load
to predict
thetointeraction
of
the
chiller
plant.
Designers
must
adapt
the
chilled-water
system
to the
of the chiller plant. Designers must adapt the chilled-water system to the cooling
loadcooling load
variations
over
time.
However,
this
is
when
the
following
questions
arise:
variations over time. However, this is when the following questions arise: Would it beWould it be
possible for a chiller plant which was designed under the traditional staging principle to
possible for a chiller plant which was designed under the traditional staging principle to
be able to operate efficiently when incorporating an automatic control system? Should its
be able to operate efficiently when incorporating an automatic control system? Should its
staging involve considering another principle?
staging involve considering
another principle?
Despite the major improvements in design methodologies presented by [5–8,10–13],
Despite thewhere
majordifferent
improvements
in design
methodologies
presented
[5–8,10–13],
parameters
were optimized
and these
optimalby
chiller
plant configurations
where different were
parameters
were
optimized
and
these
optimal
chiller
plant
configurations
then finally tested under traditional staging, it is likely that in the exploitation phase,
were then finally
tested
under traditional
staging,
it isforecasts
likely that
in thein
exploitation
phase,This is why
these
configurations
cannot
meet the
defined
the initial study.
these configurations
cannotdesign
meet of
thethe
forecasts
defined
in be
theguaranteed,
initial study.
This is why
an optimal
chiller plant
must
considering
thean
impact of the
optimal design automatic
of the chiller
plant
must tobebeguaranteed,
considering the impact of the
control
methods
used in the future.
In this research
area,
a gap
that persists is that there is not enough research in the
automatic control methods
to be used
in the
future.
literature
to identifying
the impact
theenough
initial design
stage
chiller plants
In this research
area,dedicated
a gap that
persists is that
there isofnot
research
inof
the
on the
[14,15].stage
Recent
studiesplants
call foron
extending the
literature dedicated
tosubsequent
identifyingexploration
the impactof
ofthe
thesystems
initial design
of chiller
concept
centralized
and air
(HVAC)
the subsequent design
exploration
ofofthe
systems heating,
[14,15]. ventilation,
Recent studies
callconditioning
for extending
the systems to
include
possible
interaction
with
the
automatic
control
system,
which
usually
design concept of centralized heating, ventilation, and air conditioning (HVAC) systems increases
efficiency
in later
phases.
Garcia [16]control
defined
this novelty
named co-design, as
to include possible
interaction
with
the automatic
system,
whichapproach,
usually increases
a conceptual design process that uses dynamic systems as a variable to achieve optimal
efficiency in later phases. Garcia [16] defined this novelty approach, named co-design, as
results. Rampazzo [17] described the optimized operation of a chiller plant as a nonlinear
a conceptual design process that uses dynamic systems as a variable to achieve optimal
combinatorial mathematical problem, restricted to continuous and discrete variables, being
results. Rampazzo
[17] described
the optimized
operation
of aHowever,
chiller plant
as a nonlinear
a challenge
for standard
optimization
methods.
few researchers
have presented
combinatorial mathematical
problem,
restricted
to
continuous
and
discrete
variables, et al. [15]
studies using the co-design concept in the design of HVAC systems. Bhattacharya
being a challenge
for standard
optimization
methods.
However,
few ofresearchers
carried
out Bayesian
optimization
using black
box models
the chillers.have
They optimized
presented studies
using
thesystem
co-design
concept
in and
the the
design
of load
HVAC
systems.
the size
of the
(cooling
capacity)
cooling
chiller
sequencing. They
Bhattacharya etalso
al. [15]
carriedanout
Bayesian
optimization
usingetblack
boxused
models
of the
included
economic
analysis.
Masburah
al. [18]
a deep
reinforcement
chillers. They optimized
the sizetoofprovide
the system
(cooling
capacity)
and the
cooling
learning language
different
control
architectures
to the
HVACload
systems during
the simulation
process inan
the
design phase.
Here,
this study
cooling
storage
chiller sequencing.
They also included
economic
analysis.
Masburah
et focuses
al. [18] on
used
a
system
capacitylanguage
and charging
and discharging
deep reinforcement
learning
to provide
differentstrategies.
control architectures to the
In previous
research,
Diaz in
et the
al. [19,20]
a new
methodology
for the design
HVAC systems during
the simulation
process
designproposed
phase. Here,
this
study focuses
of
chiller
plants
for
hotel
facilities.
This
methodology
integrated
different
procedures
that
on cooling storage system capacity and charging and discharging strategies.
consisted
of
multiple
statistical
analyses
of
cooling
demands
[20]
to
obtain
load
patterns
In previous research, Diaz et al. [19,20] proposed a new methodology for the design
allowed obtaining individual chiller cooling capacities and then a mathematical proof chiller plantsthat
for hotel
facilities. This methodology integrated different procedures that
cedure to create multiple chiller plant combinations, modifying several design variables
and also considering compliance with technical standards. Subsequently, they presented
an energy simulation procedure [19] carried out using the solution of a mathematical opti-
Energies 2023, 16, 3782
4 of 23
mization problem of optimal chiller loading (OCL) and optimal chiller sequencing (OCS)
analyses to establish an effective operating strategy. The final selection allowed designers
to choose the system that best adapted to the variations in the thermal demands of the
installation, working under an optimized mode, which would imply the implementation
of an automatic control system for the HVAC system. However, the comparison of the
effectiveness of this methodology was only based on the comparison of its results and
the plant configuration selected according to the technical standard (a symmetrical chiller
plant), and no comparative analysis was presented to validate its contribution with respect
to the traditional methodologies currently used.
Thangavelu et al. [21] showed that chiller plants can reduce their energy consumption
by up to 40% in medium-capacity plants and by up to 20% in small-capacity plants by
employing these techniques. This means a significant reduction in the environmental
impact associated with electricity generation and considerable economic benefits. OCL is a
method that optimizes the total distribution of cooling loads in regulated time intervals
through several periods subjected to optimization constraints. OCS defines the conditions
in which the chillers should operate or not, according to the cooling demand. Therefore, it
adjusts the number of chillers in operation to the fluctuation of the cooling load, maximizing
the plant’s efficiency.
An efficient chiller plant must be designed based on the theoretical operating conditions that largely coincide with the future exploitation conditions in a building. However,
there are still design standards and methodologies that include traditional sequencing
staging in the energy assessment of chiller plants. Automatic control systems usually fit
these systems; however, the savings achieved would likely be limited by errors during the
initial design.
This research contributes to chiller plant design in buildings. Considering that this
process is carried out according to the technical standards and procedures outlined in
Figure 1, the use of optimization techniques contributes to a better design of the plant
and ensures that it operates under an efficient operating regime. The main objective is to
demonstrate, through the energy comparison of two design trends, the impact that both
have on the selection of the most suitable configuration for future operating conditions.
This paper aims to verify the impact on the design of a chiller plant configuration of the use
of a traditional sequencing staging approach or the use of co-design methodology, using
the OCL and OCS in the energy performance forecasts study. These outcomes can serve as
an inflexion point in the design philosophy of chiller plants.
This paper is structured as follows: The methodology is described in Section 2, while
the results are presented and discussed in Section 3. Finally, the conclusions are summarized
in Section 4.
2. Materials and Methods
2.1. Methodology
To meet the thermal demand of a chiller plant, regardless of the selected approach, the
following steps need to be taken:
1.
2.
3.
Calculation of the cooling load demand of the building.
Implementation of accurate energy models of the HVAC systems for simulation
purposes.
Implementation of chiller plant sequencing algorithm and energy performance evaluation.
2.2. Cooling Load Demand of Building
In this work, the thermal load of the investigated facility, i.e., a Cuban hotel, was
calculated using the deterministic method suggested by [22]. The time base for the input
data and thermal properties of the building was established by using the interface TRNBuild
of TRaNsient SYstems Simulation software (TRNSYS 16) [23].
Energies 2023, 16, 3782
5 of 23
Using TRNSYS 16, heat load profiles (ki) representing a 24 h scenario were obtained.
In addition, the different implemented thermal demand profiles, which represented 24 h
heat load scenarios (ki), suggested the use of the following steps:
1.
2.
3.
4.
Consideration in the simulation of activity levels in public areas and the activity
patterns of hotels near the case study, which have in common the type of hotel, total
capacity, and type of tourism.
Consideration of the variation in the occupancy levels in each thermal zone with the
aid of the historical occupancy levels in similar hotels.
Establishment of energy efficiency measures in the thermal zones related to the rooms’
areas according to the suggestions of Yang et al. [6].
Establishment of the concept of a partially loaded room for thermal zones belonging to the rooms. This measure included comfort conditions in unoccupied rooms,
considering a set point of 25 ◦ C, which ensured high indoor air quality levels in
tropical-climate hotels.
The sensible and latent heat portions were considered following the ASHRAE 55 recommendations [24]. The heat gained from the electrical equipment rated was calculated by
considering its electrical power, duty factor, load factor, and efficiency. The heat fractions by
convection and radiation were set at 0.7 and 0.3, respectively, and at 0.6 and 0.4 for artificial
lighting [23]. Finally, a database was built, in which, for each ki, the thermal demand values
(CLi) for each time interval (i) were reflected.
2.3. Implementation of Accurate Simulation Models of Air-Cooled Chiller Unit
The mathematical models were based on the generalized least-squares method and the
use of black box methodology for the implementation and selection presented by [25]. In
this study, a multiple linear regression model was carefully chosen for enhanced simulation.
.
The cooling capacity (Qchi ) (Equation (1)) is a function of the subsequent independent
variables. Tcair,in , Tchw,s , and Tcair are defined in Annex 1. x0 , x1 , and x2 represent the
regression coefficient of the mathematical model.
Qchi (kW) = xo + x1 Tcair,in + x2 Tch w,s
xj ∈ Q,j = [0, 1, 2], Tcair,in f(Tamb)
(1)
To calculate the power input of the i-th chiller (Pch,i), it was decided that the independent variables were those that could be operationally modified, leading to Equation (2).
aj ∈ Q,i = [0, 1, 2], Tcair,in , Tch w,r ∈ Q
Pchi (kW) = ao + a1 Tch w,r + a2 Tcair
(2)
in which Tch w,o represents the chilled-water return temperature, which is given by Equation (3):
Tchw,r (o C) =
Cli
+ Tchw,s
mi Cp
(3)
The statistical indices used for evaluating the error calculation of the model were
the correlation coefficient (R2 ) (Equation (4)) and the mean of the absolute error (MAE)
(Equation (5)). R2 is equal to the ratio of SCE (i.e., measure of the variability of the regression
model) and SCT (corresponding to the measure of the variability of Y without considering
the effect of the explanatory variables X).
R2 =
SCE
,
SCT
0 ≤ R2 ≤ 1
(4)
The mean of the absolute error is the average absolute value of the residuals and
shows the average error in the response prediction using the fitted model.
_
N
MAE =
∑
i=1
xi − x
N
i
(5)
The mean of the absolute error is the average absolute value of the residuals and
shows the average error in the response prediction using the fitted model.
N
MAE = 
Energies 2023, 16, 3782

xi − xi
i =1
6 (5)
of 23
N
The development of the regression model was based on White’s test for homoscedasThe development
of the regression
was
on White’s
test forautocorrelahomoscedasticity [26].
The Breusch–Godfrey
test [27]model
allowed
forbased
checking
the residual
ticity
[26].
The
Breusch–Godfrey
test
[27]
allowed
for
checking
the
residual
autocorrelation
tion nonappearance in the selected mathematical model. In addition, the Jarque–Bera test
nonappearance
in to
theanalyze
selected
mathematical
model. In
addition,
the Jarque–Bera
testof[28]
[28]
was employed
normality.
Compliance
with
the classical
assumptions
a
was
employed
to
analyze
normality.
Compliance
with
the
classical
assumptions
of a reregression model guaranteed that the estimators obtained by the least-squares method
gression
modelconsistent,
guaranteed
that
the estimators obtained by the least-squares method were
were
unbiased,
and
efficient.
unbiased,
consistent,
and
efficient.
As an initial state in the analysis, the chiller plant was assumed to be a decoupled
Asi.e.,
ancomposed
initial stateofinn the
analysis,
the chiller
plant
assumed
to 3).
be The
a decoupled
system,
air-cooled
chillers
arranged
inwas
parallel
(Figure
energy
system,
i.e.,
composed
of
n
air-cooled
chillers
arranged
in
parallel
(Figure
3).
The energy
analysis was only applied to the primary circuit (section of chillers).
analysis was only applied to the primary circuit (section of chillers).
Tchw,s
Tchw,s
Tcair,in
Chiller (n)
Cooling capacity
black box model
(Qchi)
Tchw,r
ṁn
Tchw,s
Tchw,s
Tcair,in
Chiller (2)
Cooling capacity
black box model
(Qchi)
Tcair,in
Chiller (1)
Cooling capacity
black box model
(Qchi)
Tchw,r
ṁ2
Building
cooling load
(Cli)
Tchw,r
ṁ1
Tchw,r
Figure3.3.The
Thegeneral
generalframework
frameworkofofthe
thedecoupled
decoupledchiller
chillerplant.
plant.
Figure
Thewater
waterchiller
chillerplant
plantshould
should be
be composed
composed of
The
of(n
(n++1)
1)chillers.
chillers.Many
Manyauthors
authors[6,9,29–31]
[6,9,29–
have
recommended
that
in
the
case
of
a
plant
with
different
chiller
capacities,
the
oneone
with
31] have recommended that in the case of a plant with different chiller capacities, the
the
highest
cooling
capacity
should
be
switched
on
first.
Therefore,
in
the
scenario
involvwith the highest cooling capacity should be switched on first. Therefore, in the scenario
ing the traditional
principle
of chiller
on/off
staging,
the chillers
werewere
activated
in order
involving
the traditional
principle
of chiller
on/off
staging,
the chillers
activated
in
from the highest to the lowest capacity (Equation (6)):
order from the highest to the lowest capacity (Equation (6)):
Qch22 ((kW
)
) ≥) ≥Qch
) ≥· ·· Qch
Qch Qch
kW) ≥
Qch
1 (kW
n (kW
1 (kW
n (kW
)
(6)
(6)
2.3.1. Approach Using the Traditional Principle of Chiller On/Off Staging
2.3.1. Approach
the Traditional
Principle
of in
Chiller
On/Off
To answerUsing
how many
chillers were
working
a certain
timeStaging
interval (i) depended on
answer
how many
were(CL
working
in
a
certain
time
interval
depended
the To
thermal
demand
of thechillers
installation
)
and
the
cooling
capacity
of each(i)chiller
Qchn,i
i
oninthe
thermal
demand
of
the
installation
(CL
i
)
and
the
cooling
capacity
of
each
chiller
each time interval (i). Therefore, Equation (7) gives the total operating chillers.
Qchn,i in each time interval (i). Therefore, Equation (7) gives the total operating chillers.
Nc= f(CLi ; Qchi )
(7)
Nc =
f (CL i ; Qch i )
(7)
The cooling load capacity of the water chiller plant as well as the electrical power
The cooling load capacity of the water chiller plant as well as the electrical power
required are in function of the variables shown in Equations (8) and (9), respectively.
required are in function of the variables shown in Equations (8) and (9), respectively.
Qch
Qch
Tcair,in
; Tch Tch)
= n,i = f f((Tc
air, in ; w,s
n, i
w, s
Pch Pch
; Qch
Tcair,in
Qch
n,i = ff(Tc
n,i
n, i =
air,;in
n, i )
)
(8)
(8)
(9)
(9)
The total cooling load supplied by the chiller plant, composed of n chillers, as well as
the total electrical energy consumption are given by Equations (10) and (11), respectively.
QchN,i ≤
PchN,i ≤
n
∑ Qchn,i
n ∈ N∀, n ≥ 2
(10)
∑ (Pchn,i )
n ∈ N∀, n ≥ 2
(11)
k=1
n
k=1
Energies 2023, 16, 3782
7 of 23
Equation (12) describes the cooling load that the plant delivers to the building as
constrained according to the thermal demand of the building. This also influences the total
number of chillers in operation, whose constraint is shown in Equation (13).
CLi ≤
Nc =






Nc = n − 1










Nc = n



n
∑ Qchn,i
n ∈ N∀, n ≥ 2
(12)
k=1
if(Cli − Qchi ) ≤ 0
if(Cli − Qchi ) > 0
then


 Ch1,i
sj = 1(on)
..
.


 Chn,i sj = 0(off)

 Ch1,i sj = 1(on)
..
then
.


Chn,i sj = 0(off)
Sj ∈ {0; 1}
(13)
The chilled-water supply temperature range is set according to Equation (14):
Tchw,s (o C) ∈ N, Tchw,s = 7 . . . 13
(14)
The “on” and “off” interval status to be analyzed is defined with the variable sj.
Equation (15) defines the constraint denoted to the minimum range between the activation
and deactivation time of a chiller to avoid too many on/off cycles. Chang et al. [32]
recommended that the minimum time between the activation and deactivation of a chiller
needs to be between 30 min and 1 h. In [33], Witkowski gives a similar range.
n
h
i
o
Sj = f CL(i) (kW)= mx CL(t−1) : CL(t)
(15)
t ∈ N, t = 1 . . . .24
The constraints of the typical sequencing chiller strategy can be summarized as follows:
1.
2.
3.
Step 1: If cooling load CLi ≤ Qch1 , then chiller 1 satisfied the system load (with
Qch1 > Qch2 );
Step 2: If Cli > Qch1 , then chiller 1 provided the full cooling load and the remaining
thermal demand was provided by chiller 2;
Step 3: If Cli ≥ Qch1 + Qch2 + . . . Qchn +, then chillers Ch1 , Ch2 , . . . , Chn were turned
on (in which Qch1 > Qch2 > . . . > Qchn ).
2.3.2. Optimal Chiller Loading and Optimal Chiller Sequence Staging Approach:
Co-Design of Chiller Plant Approach
The chiller energy performance simulation is considered an optimal chiller sequence
staging approach [18]. This study combined the four OCS strategies defined, the total
cooling load-based sequencing control, and the direct power-based sequencing control. To
ensure optimal results and to avoid an incorrect designation of the partial load ratio (PLR)
value, as only one chiller can satisfy the thermal needs of the system without the use of
two or more units, a strategic baseline was built, as is shown in Figure 4. The chillers were
arranged from lowest to highest according to their individual cooling capacity, defined by
the variable (Qchi).
The sequencing chiller strategy shown in Figure 4 can be summarized as follows:
1.
2.
3.
Step 1: If CLi ≤ Qch1,i, then chiller 1 satisfied the system load;
Step 2: If Qch1,i < CLi ≤ Qch2,i , then chiller 2 met system load;
Step 3: If (Qch1,i + Qch2,i ) ≤ CLi ≤ Qchn−1,i, the OF of chillers 1 and 2 was optimized
and derived from the optimal load problem, and the results were quantified. The
results were compared with the electrical power consumption of the chiller (n − 1).
If (Pch1,i + Pch2,i ) < Pchn−1 , chillers 1 and 2 were turned on. If not, chiller n − 1
turned on;
2.3.2. Optimal Chiller Loading and Optimal Chiller Sequence Staging Approach: CoDesign of Chiller Plant Approach
The chiller energy performance simulation is considered an optimal chiller sequence
staging approach [18]. This study combined the four OCS strategies defined, the total cooling load-based sequencing control, and the direct power-based sequencing control.
8 ofTo
23
ensure optimal results and to avoid an incorrect designation of the partial load ratio (PLR)
value, as only one chiller can satisfy the thermal needs of the system without the use of
two or more units, a strategic baseline was built, as is shown in Figure 4. The chillers were
4.
Step 4: If CLi ≥ Qch1,i + Qch2,i + . . . Qchn,i, then chillers 1, 2, . . . , n were turned on.
arranged from lowest
to highest according to their individual cooling capacity, defined by
OF was optimized for chillers 1,2, . . . , n.
the variable (Qchi).
Energies 2023, 16, 3782
Start
Building cooling load (CLi)
Chillers Black models (Qch); (Pch)
Meteorological data typical day (Tamb)
Chilled water set point temperature (Tchw,s)
N chiller plant
composed of n chillers
Set Objetive Fuction
(OF) and constrains
Set baseline for OCS analysis
CLi≤ Qch(1)
No
No
Qch(1)< CLi≤ Qch(2)
(Qch(1)+Qch(2)) ≥ CLi ≥ Qch(N-1)
Yes
Yes
On Qch(1)
On Qch(2)
Genetic algorithm fuction
Solve OF(Qch(1)+Qch(2))
Quantify:
PLRi,
∫(Pchi)dt
COPi
Quantify:
PLRi,
∫(Pchi)dt
COPi
∑Pchi[(1)i+(2)i] <∑Pch(n-1)i
Yes
Yes
No
On Qch(1)+Qch(2)
On Ch(n-1)
Quantify
PLRi,
∫(Pchi)dt
COPi
Quantify
PLRi,
∫(Pchi)dt
COPi
Order from min→max [∫(Pchi)dt ]
Order from max→min [COPi ]
End
Figure
Figure 4.
4. Baseline
Baseline schedule
schedule of
of OCS
OCS strategy
strategy [18].
[18].
The sequencing
chiller
strategy
shown
in Figurewere
4 can
be summarized
ason
follows:
conditions in
which
the chillers
operated
defined
depending
the cooling
demand.
Therefore,
the
number
of
chillers
in
operation
was
adjusted
according
to
1. Step 1: If CLi ≤ Qch1,i, then chiller 1 satisfied the system load;
the
fluctuation
of
the
thermal
demand
using
an
optimization
algorithm,
which
allowed
2. Step 2: If Qch1,i < CLi ≤ Qch2,i, then chiller 2 met system load;
minimizing
required
cooling
capacity
and
energy
goal ofand
the
3.
Step 3: Ifthe
(Qch
1,i + Qch
2,i) ≤ CLi
≤ Qchn−1,i,
the
OF of consumption.
chillers 1 and 2The
wasmain
optimized
optimization
procedure
is to maintain
the comfort
ofwere
the facility
with The
the results
lowest
derived from
the optimal
load problem,
and thelevels
results
quantified.
energy
consumption
of the
chiller
plant.
As an
initial stage,ofthe
were
compared with
the
electrical
power
consumption
thesystem
chiller (chiller
(n − 1). plant)
If (Pchis
1,i
decoupled,
in
order
to
analyze
only
the
direct
interaction
between
the
chiller
plant
and
the
+ Pch2,i) < Pchn−1, chillers 1 and 2 were turned on. If not, chiller n − 1 turned on;
thermal
the 1,i
building.
The Qch
OCLn,i,problem
to be1,solved
classified
as on.
a nonlinear
4.
Stepdemand
4: If CLiof
≥ Qch
+ Qch2,i +…
then chillers
2,…, niswere
turned
OF was
optimization
problem
with
constraints
and
a
combinatorial
optimization
problem
with
optimized for chillers 1,2,…, n.
continuous, discrete, and binary variables.
The conditions in which the chillers operated were defined depending on the cooling
Each analyzed period was solved simultaneously and determined the on/off status,
demand. Therefore, the number of chillers in operation was adjusted according to the flucPLRi ; Pchi , and COPi for each chiller. OCS complemented the OCL expressed in the objectuation
of the(OF)
thermal
demand
using
optimization
algorithm, which
allowed
minimiztive function
(Equation
(16)),
andan
the
constraints (Equations
(17)–(20))
complemented
the variable decision PLR (Equation (21)), shown below.
Objective function (OF) is as follows:
(
minPLR
n
∑
j=1
a0 + a1
CLi PLRi
+ Tchw,s
mi Cp
!
+ a2 Tcair
n
+
Qch,mx − ∑ Qchi,n PLRi
j=1
!
+
n
∑nj=1 COP
!)
sj
(16)
Energies 2023, 16, 3782
9 of 23
OF is subject to the following:
CLi (kW) ≤
n
∑ (Qchi ∗PLRi )(kW)
n ∈ N∀, n ≥ 2
(17)
k=1
Tchw,in (o C) ∈ N, Tchw,in = 7 . . . 13
h
i
CL(i) (kW)= mx CL(t−1) : CL(t)
t ∈ N, t = 1 . . . .24
(18)
(19)
The value of the PLR variable in Equation (20) determines the on/off status, which is
a difference between the individual chiller staging and the strategy shown in Section 2.2.
Sj =
if
if PLR = 0 then Sj = 0(off)
Sj ∈ {0; 1}
0 < PLR ≤ 1 then Sj = 1 (on)
(20)
In OCL and OCS problems, the literature commonly uses the PLR as a decision
variable, as can be seen in different papers [34–37]. The theoretical (PLRn,i ) of each chiller
is as shown in Equation (21).
CLi
(21)
PLRn,i =
Qchi
For the OCL solution, a genetic algorithm (GA) was used. GA is a metaheuristic
method offering an optimal solution to an optimal combinatorial problem, which has many
possibilities for a solution. The variables to be processed were the decision variable (PLRn,i )
of the chiller unit and the arrangement of the chiller working in parallel.
After the variables were encoded into chromosomes, the information built 10
into
Energies 2023, 16, x FOR PEER REVIEW
of the
24
chromosomes was the total PLRs of the units running in parallel. A GA flowchart for OCL
problems is presented in Figure 5.
Figure5.5.General
GeneralGA
GAflowchart
flowchartfor
forOCL
OCLproblems.
problems.
Figure
CaseStudy
Study
3.3.Case
Themethods
methodsdescribed
describedininthe
theprevious
previoussubsections
subsectionsapplied
appliedtotoaahotel
hotelbeing
beingbuilt
builtinin
The
Cienfuegos (Cuba) and involving three functional areas: rooms, public areas, and service
Cienfuegos (Cuba) and involving three functional areas: rooms, public areas, and service
areas. The room area has 87 rooms, 45 of which are part of the main building and 42 of
areas. The room area has 87 rooms, 45 of which are part of the main building and 42 of
which are individual modules and cabins. One of the functional areas includes public areas, such as a lobby designed with natural air ventilation, a gift store, a specialized restaurant, a kitchen, and a nightclub. Finally, the service area, including different office modules, was also considered in the total cooling chiller plant capacity. The main characteris-
Energies 2023, 16, 3782
10 of 23
which are individual modules and cabins. One of the functional areas includes public areas,
such as a lobby designed with natural air ventilation, a gift store, a specialized restaurant, a
kitchen, and a nightclub. Finally, the service area, including different office modules, was
also considered in the total cooling chiller plant capacity. The main characteristics of the
functional areas are summarized in Table 1.
Table 1. Main characteristics of the functional areas of the hotel.
Functional
Areas
Type of Thermal Zone
Top floor (East)
Top floor (West)
Top floor (Intermediate rooms)
Low levels (Intermediate rooms)
Low levels (Intermediate
rooms–east–west corner)
Cabins (West corner)
Cabins (East corner)
Cabins (Intermediate rooms)
Thermal
Zone ID
Type of Thermal
Zone
1
2
3
4
Restaurant
Cabaret
Shops
Double office
5
North office
6
7
8
South office
Intermediate office
Rooms
Functional Areas
Thermal Zone ID
9
10
11
12
Public areas
13
Service areas
14
15
For the cooling demand analysis of the facility, the thermal properties of the hotel
walls were obtained from TRNSYS 16 library [22] and are listed in Table 2.
Table 2. Thermal properties of the hotel’s walls.
Wall Type
Nomenclature
Thermal Conductivity
(W·m−2 ·K−1 )
Overall Transmittance
(W·m−2 ·K−1 )
Outwall
O
2.05954
11.40879
Inwall
I
2.09029
11.67302
Ground
G
3.40909
29.18919
Roof
Window
R
W
3.25960
5.8
26.31854
5400
Material (Thickness (m))
Concrete block (0.15); Cement+clay (0.02);
Cement+clay (0.01)
Brick (0.15); Cement+clay (0.01);
Cement+clay (0.01)
Concrete (0.24); Ceramics (0.01);
Cement+clay (0.01)
Concrete (0.24); Rasilla (0.02)
Single crystal (0.008)
The detailed composition of each functional area, the thermal properties of their
construction materials, the heat gains deriving from occupation, and the use of equipment
were considered (Tables 3 and 4).
Table 3. Thermal comfort features of main building rooms and cabins (room area).
Thermal Zone ID
Number of Rooms
Dimensions (m3 )
Wall Type
Heat Gains
1
2
3
4
5
6
7
8
3
3
9
18
12
3
3
36
108
108
108
108
108
111.38
111.38
111.38
W(1); O (1); I (2); R(1);
W(1); O (1); I (2); R(1);
W(1); I (4);
W(1); I (3); G (1)
W(1); O (1); I (2); G(1);
W(1); O (1); I (1); R(1); G(1);
W(1); O (1); I (1); R(1); G(1);
W(1); I (2); R(1); G(1);
Electronic appliances: 1643 W
Lighting: 13 W·m−2
People: Max 3 guests
(sensible/latent: 65/55 W)
Energies 2023, 16, 3782
11 of 23
Table 4. Thermal comfort features of public areas and service area.
Thermal Zone ID
Number of Rooms
Dimensions (m3 )
Wall Type
Heat Gains
9
1
951.34
W(2); O (2); R(1); G(1);
Electronic appliances: 21,080 W
Lighting: 16 W·m−2
Max 58 guests (sensible/latent: 65/55 W)
Max 9 employees (sensible/latent: 75/55 W)
10
1
1463
O (2); R(1); G(1)
Electronic appliances: 7317.61 W
Lighting: 10 W·m−2
Max 500 guests (sensible/latent: 90/160 W)
Max 9 employees (sensible/latent: 65/55 W)
11
2
111.38
W(2); O (2); R(1); G(1);
Electronic appliances: 700 W
Lighting: 13 W·m−2
Max 12 guests (sensible/latent: 65/55 W)
Max 3 employees (sensible/latent: 75/55 W)
12
13
14
15
3
1
1
4
47.73
23.4
23.4
23.4
W(1); O (1); I(1); R(1); G(1);
W(1); O (1); I(1); R(1); G(1);
W(1); O (1); I(1); R(1); G(1);
W(1); R(1); G(1); I(2);
Electronic appliances: 413 W
Lighting: 13 W·m−2
Max 2 employees (sensible/latent: 63/52 W)
The hotel design criteria were establishing according to thermal inside comfort Cuban
standard NC 217:2002 [38].
Using TRNSYS 16, the standard procedure for thermal demand analysis recommended
in ASHRAE Fundamentals [2] was applied, taking into consideration the worst operating
conditions scenario at the hotel and other future operating scenarios that reflected the great
variation in the nature of activities in the facility.
Different cooling profiles suggest the need for energy efficiency measures to mitigate
the different occupancy levels of the hotel. In addition, this analysis considered the occupancy and employment patterns of a hotel in operation (from the same hotel chain) based
on a previous study [19,22,39,40]. Furthermore, the hotel featuring these partners was
characterized by a service disruption between 10:00 am and 4:00 pm (defined as transit
hotel classification). The occupied room indicator (Hdo) fluctuated according to the tourist
season from low occupancy (Hdo ≤ 10%) to medium occupancy (45% ≤ Hdo ≤ 50%) to
high occupancy (75% ≤ Hdo ≤ 90%) to full hotel occupancy (Hdo = 100%). Therefore,
several cooling load profiles (ki) in the functional areas, i.e., the rooms, public areas, and
service areas, were implemented.
In addition, for the ki calculation:
(1)
(2)
(3)
The concept of a “partially loaded” room (unoccupied rooms which were kept at
26 ◦ C by an air conditioner) was applied [32].
Different occupancy rates between 10%, 50%, 75%, and 100% for the hotel in the rooms
and public areas were considered.
The load diversity through occupancy strategies was eliminated using the lowestthermal-demand rooms for occupancy rates of 75% and 50%.
Six chiller plants with an arrangement of two air-cooled screw-type water chillers were
proposed to be installed in the hotel; see Table 5. The primary circuit was characterized
by a constant chilled-water mass flow rate. The installed cooling capacity varied between
538 kW and 589 kW, representing the common practice of a load safety factor between 10%
and 20% of the total installed capacity (as recommended in [2]). The plant configurations
are presented in Table 5.
Energies 2023, 16, 3782
12 of 23
Table 5. Chiller plant configurations.
Chiller Plant
Configuration
*
(kW)
*
(kW)
Chiller Cooling Capacity
Distribution (%)
Total Cooling Capacity (kW)
Safety Factor
1
2
3
4
5
6
180.1
198.7
201.6
228.9
271.2
271.2
357.8
357.8
357.8
310.6
271.2
310.6
33/67
36/64
36/64
42/58
50/50
47/53
537.92
556.59
559.82
539.53
542.46
581.85
10.2
14.1
14.7
10.6
11.7
19.2
* Chiller cooling capacity in standard conditions (STD): chilled-water supply/return of 7/12 ◦ C, air temperature
at the condenser inlet of 32 ◦ C.
Using the manufacturer’s data set of the chillers selected, the mathematical models
that represent the Qch and Pch, using Equations (1) and (2), were determined through the
least-squares method. The regression coefficients and the quality of the black box models
were defined using the software Eviews 12 [41]. The results of the adjustability as well as
the quality of the models are shown in Table 6.
Table 6. Quality measurement of the selected chiller black box models [41].
t Student
Diagnostic Test
10−14
−7.822 ×
0.990
Stadígraph
p-value
White
Breusch–Godfrey
Jarque–Bera
10.947
0.952
29,046
4.929 × 10−7
4.152
0.125
In the performed tests, the p-value for compliance with the null hypothesis was ≥0.05.
It was observed that the selected models fulfilled the established statistical assumptions.
The selected models did not fulfil the assumption of the nonexistence of autocorrelation.
This is a consequence of the cyclical nature of the data used for their construction. Finally,
the fourth assumption, i.e., the null hypothesis that dictated normality in the data, was
fulfilled as well. It is emphasized that this is an inviolable requirement of regression.
The regression coefficients of each of the investigated chiller plant configurations, as
well as the results of the adjustment measurement, are shown in Table 7. It was found
that they have a high explanatory percentage with an R2 above 99% and lower values of
MAE and AIC. Considering these results and considering that the violation of the third
assumption did not invalidate the estimators obtained by the least-squares method, this
can establish that the regression coefficients (x0 , x1 , x2 ; a0 , a1 , a2 ) and the chillers’ black box
models obtained are unbiased, consistent, and efficient.
Table 7. Regression coefficients and fitting measurements of the models.
Cooling Capacity Model
Chiller Cooling
Capacity at STD
180.1
198.7
201.6
228.9
271.2
310.6
357.8
ṁ (kg·s−1 )
8.67
9.56
9.72
11
13
14.9
17.2
Regression Coefficients
Electrical Power Model
Fitting Measurements of
the Models
Regression Coefficients
Fitting Measurements of
the Models
x0
x1
x2
R2
MAE
AIC
a0
a1
a2
R2
MAE
AIC
203.1
221.0
226.0
257.0
302.7
345.3
403.5
−2.30
−2.42
−2.51
−2.87
−3.37
−3.80
−4.55
7.21
7.91
8.07
9.12
10.9
12.4
14.2
99.6
99.7
99.7
99.8
99.6
99.7
99.6
1.08
0.97
1.04
0.93
1.64
1.51
2.15
0.32
0.28
0.29
0.27
0.32
0.27
0.32
19.55
22.93
22.69
24.57
30.15
34.96
39.07
0.84
0.92
0.93
1.18
1.29
1.39
1.68
0.24
0.33
0.37
0.26
0.37
0.53
0.47
99.0
98.8
98.9
98.8
99.0
98.8
99.1
0.60
0.74
0.71
0.96
0.93
1.10
1.18
0.40
0.40
0.39
0.40
0.40
0.41
0.40
4. Results and Discussion
The cooling thermal demand of each feasible scenario was calculated according to
the elements and design criteria exposed in Section 3. The thermal profiles k1 and k2
are the critical scenarios of the hotel, i.e., the maximum demand and minimum demand,
respectively. The other thermal profiles simulate different occupation scenarios and activity
Energies 2023, 16, 3782
13 of 23
levels which could occur in the hotel. The eight load profiles of the hotel were generated
using TRYNSYS 16 [22]. The time interval for the analysis was 24 h in a typical summer
day profile, obtained using METEONORM data [42]. For each thermal zone, a graphical
interface was built into the program. For the infiltration gains, a factor of 0.8 was assumed.
The convection/radiation fraction of the heat gain due to the use of electronic equipment
was 0.3/0.7.
The simulation in TRNBuild [22] was carried out using the power level control, while
the cooling loads of the building were calculated considering the information above. The
results of the demand load values are shown in Table 8.
Table 8. Cooling load demand values of the 8 analyzed profile schedules.
Time (h)
01:00
02:00
03:00
04:00
05:00
06:00
07:00
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
00:00
Cooling Load Demand Values Cli (kW)
k1
k2
k3
k4
k5
k6
k7
k8
387.74
387.38
347.84
342.10
340.69
339.16
338.36
337.45
383.76
388.71
415.22
436.97
456.91
473.62
483.59
488.26
487.54
476.32
439.19
424.56
418.87
411.23
399.14
401.53
96.04
90.41
84.47
79.59
76.32
73.67
85.59
94.15
105.42
115.99
120.71
147.52
166.02
179.50
187.89
192.69
182.40
171.97
165.65
168.73
158.23
129.84
115.54
105.80
345.74
345.50
308.20
300.86
299.47
299.01
321.25
324.88
339.18
337.89
347.08
388.49
410.54
427.18
425.09
429.24
417.64
402.85
402.86
410.88
406.21
384.29
358.72
360.86
289.30
293.56
255.96
248.02
245.88
245.12
259.69
261.63
273.98
270.96
290.72
325.39
344.90
361.45
357.58
362.48
362.43
349.18
356.05
345.47
340.41
333.80
306.89
309.27
241.30
240.44
203.32
195.66
194.00
193.56
208.61
211.11
223.42
220.60
239.84
274.35
293.54
309.25
304.90
309.00
307.99
293.42
299.13
288.27
283.37
277.40
251.49
254.51
154.79
154.19
117.04
109.07
107.80
105.96
196.54
156.40
150.03
148.47
150.19
239.18
207.44
223.27
220.91
225.00
315.73
224.23
278.36
232.83
227.59
206.63
181.54
183.68
146.45
150.38
112.93
104.52
102.50
100.58
180.10
137.89
132.46
129.14
141.46
227.26
193.01
208.75
204.77
209.61
264.88
215.08
276.51
212.25
206.81
200.85
174.26
176.64
142.45
141.26
104.29
96.36
94.82
93.42
170.42
128.37
125.50
122.38
134.18
223.02
188.45
203.35
199.09
203.13
214.84
200.12
260.79
196.05
190.97
185.45
159.66
162.68
For the comparison of the energy performance of the chiller plants presented in Table 5
with the eight thermal demand profiles calculated in Section 3, Equations (1)–(3) were used
by substituting the correlation coefficients listed in Table 7 and setting a fixed temperature
setpoint value equal to 7 ◦ C. In addition, the ambient temperature profile corresponding
to the same day when the thermal demand was calculated was extracted. Subsequently,
the mathematical algorithm described by Equations (12)–(15) was implemented using
MATLAB 2018 [43]. The on/off schedule of each chiller plant and the PLRi values of each
chiller are shown in Figures 6 and 7, respectively. As shown in Figure 6, this operating
staging forced the first chiller to always be running, regardless of the thermal demand. The
second chiller covered the remaining demand if requested, regardless of the load regime to
which it was subjected. Figure 7 describes this type of operation causing at least one of the
chillers to work in a critical partial regime.
The total energy consumption as well as the average COP of each investigated chiller
plant are listed in Table 9. According to the results, there were no significant differences in
energy performance between the proposed chiller plant configurations. The highest energy
consumption was given by the chiller plant configuration #6, which consumes 5.3% greater
than the one offering the minimum consumption of electricity (chiller plant #5).
Energies 2023, 16, x FOR PEER REVIEW
Energies 2023, 16, 3782
07:00
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
00:00
14 of 24
14 of 23
338.36 Table 9.85.59
321.25 and average
259.69COP values
208.61
196.54 chiller180.10
Energy consumption
of the investigated
plant options.170.42
337.45
94.15
324.88
261.63
211.11
156.40
137.89
128.37
Chiller
Plant
Configuration
Energy
Consumption
(kWh)
Average
COP
383.76
105.42
339.18
273.98
223.42
150.03
132.46
125.50
2.43
388.71
115.99 1
337.89
270.96 14,088.54
220.60
148.47
129.14
122.38
2.35
415.22
120.71 2
347.08
290.72 14,187.96
239.84
150.19
141.46
134.18
3
14,162.84
2.22
436.97
147.52 4
388.49
325.39 14,186.33
274.35
239.18
227.26
223.02
2.68
456.91
166.02 5
410.54
344.90 13,882.52
293.54
207.44
193.01
188.45
2.78
6
14,619.42
2.53
473.62
179.50
427.18
361.45
309.25
223.27
208.75
203.35
483.59
187.89
425.09
357.58
304.90
220.91
204.77
199.09
488.26
192.69
429.24
362.48
309.00
225.00
209.61
203.13
Using the traditional load-based sequencing methodology and without the application
487.54 of optimization
182.40 procedures,
417.64 chiller
362.43
307.99 #5 was
315.73
214.84
plant configuration
selected for264.88
the hotel facility,
476.32 being the
171.97
402.85
349.18
293.42
224.23
215.08
200.12
highest-performing.
For
the energy 402.86
performance 356.05
of the chiller 299.13
plants using the
mathematical
optimization
439.19
165.65
278.36
276.51
260.79
shown
in
Equations
(16)–(20),
the
same
operating
conditions
used
in
the
investigated
hotel
424.56
168.73
410.88
345.47
288.27
232.83
212.25
196.05
The406.21
principle of 340.41
simultaneously
reaching the
optimum operating
of
418.87 were employed.
158.23
283.37
227.59
206.81 point
190.97
each
chiller
and
the
chiller
plant
was
defined
using
the
methodology
depicted
in
Figure
4.
411.23
129.84
384.29
333.80
277.40
206.63
200.85
185.45
For
the
evaluation
of
the
objective
function
and
the
constraints,
a
genetic
algorithm
was
399.14
115.54
358.72
306.89
251.49
181.54
174.26
159.66
adjust the control
(Table 10).
MATLAB Simulink
[43] was used162.68
for
401.53 used to105.80
360.86parameters
309.27
254.51
183.68 2018 176.64
carrying out the evaluation.
For the comparison of the energy performance of the chiller plants presented in Table
5 with the eight thermal demand profiles calculated in Section 3, Equations (1)–(3) were
used by substituting
the correlation coefficients listed in Table
Population size
150.007 and setting a fixed temperatureSelection
setpointoperator
value equal to 7 °C. In addition, the
ambient
temperature profile correuniform
stochastic
Reproduction:
elitism
2.00
sponding to the same day when the thermal demand was calculated was extracted. SubCrossover
factor
0.80
sequently,
the mathematical
algorithm described by Equations
(12)–(15) was impleMutation uniform
0.01
mented using MATLAB 2018 [43]. The on/off schedule of each chiller plant and the PLRi
Crossover heuristic
1.50
values of each chiller are shown in Figures 6 and 7, respectively.
Table 10. GA control parameters.
Chiller plant #1
Chiller plant #2
Figure 6. Cont.
Energies 2023, 16, x FOR PEER REVIEW
Energies 2023, 16, 3782
15 of 24
15 of 23
Chiller plant #3
Chiller plant #4
Chiller plant #5
On
Off
Chiller plant #6
6. On/off
schedule
chiller
plant
options
using theon/off
traditional
on/off
approach
of chiller
FigureFigure
6. On/off
schedule
of chillerof
plant
options
using
the traditional
approach
of chiller
staging.
staging.
As shown in Figure 6, this operating staging forced the first chiller to always be running, regardless of the thermal demand. The second chiller covered the remaining de-
Energies 2023, 16, x FOR PEER REVIEW
mand if requested, regardless of the load regime to which it was subjected. Figure 7 de16 of 23
scribes this type of operation causing at least one of the chillers to work in a critical partial
regime.
Energies 2023, 16, 3782
6
6
5
5
5
4
4
4
3
2
POT
6
POT
COP
16 of 24
3
2
2
Ch 357.8 kW
1
0
0.0
0.2
0.4
0.6
0.8
Ch 357.8 kW
1
Ch 180.1 kW
1.0
Chiller plant #1
0.4
0.6
PLR
0.8
0.0
1.0
Chiller plant #2
4
4
4
POT
5
3
Ch 310.6 kW
1
Ch 228.9 kW
0.2
0.4
0.6
PLR
Chiller plant #4
0.8
1.0
1.0
3
Ch 310.6 kW
1
Ch 271.2 kW
Ch 271.2 kW
Ch 271.2 kW
0
0
0.8
2
2
2
0.4
0.6
PLR
Chiller plant #3
5
3
0.2
6
5
POT
POT
0.2
6
0.0
Ch 201.6 kW
0
0.0
6
1
Ch 357.8 kW
1
Ch 198.7 kW
0
PLR
3
0.0
0.2
0.4
0.6
PLR
0.8
1.0
0
0.0
Chiller plant #5
0.2
0.4
0.6
PLR
0.8
1.0
Chiller plant #6
Figure
curvesofofchiller
chiller
plant
configuration
Figure 7.
7. COP-PLR
COP-PLR curves
plant
configuration
ns. ns.
The total
proposed
procedure
allowed
identification
of the
optimal
PLRi
of each chiller
at
The
energy
consumption
as well
as the average
COP
of each
investigated
chiller
each demand
through
the established
optimalthere
sequence,
on/off status,
and the
plant
are listedpoint,
in Table
9. According
to the results,
were the
no significant
differences
number
chillers in operation.
The
on/off schedule
andconfigurations.
PLI-COP curve
diagrams
are
in
energyofperformance
between the
proposed
chiller plant
The
highest enshown
in
Figures
8
and
9,
respectively.
ergy consumption was given by the chiller plant configuration #6, which consumes 5.3%
Figure
shows
markedthe
difference
between
the operation
of the chiller
greater
than8the
one aoffering
minimum
consumption
of electricity
(chillerplant
plantand
#5).the
cooling demand profile obtained in Table 9, concerning the mode of operation shown in
Table
Energy
consumption
average
COP
of the
investigated
plant options.
Figure9. 6.
In this
case, it canand
be seen
how
thevalues
staging
sequencing
of chiller
the chillers
is adjusted
to the individual cooling capacity and in correspondence to the specific cooling demand.
Chiller Plant Configuration
Energy Consumption (kWh)
Average COP
This mode of operation has a positive influence on the individual efficiency of each chiller
1
14,088.54
and in turn on the overall efficiency of the chiller plant, as shown in Figure 2.43
9.
2
2.35 for a more
Figure 9 demonstrates
that the strategy14,187.96
designed for the chiller plant allows
3
2.22the largest
efficient operating
regime (range of the PLR14,162.84
greater than 0.5) for the chiller with
4
14,186.33
2.68 capacity.
cooling capacity by sacrificing the efficiency of the chiller with the smallest cooling
5 the energy consumption and
13,882.52
2.78
Table 11 shows
average COP values of all the
chiller plant
options. The results
reveal that the best configuration
was chiller plant configuration
#1
6
14,619.42
2.53
(i.e., an asymmetric chiller plant with a cooling distribution of 33/67% and safety factor of
10.2%).
Using the traditional load-based sequencing methodology and without the application of optimization procedures, chiller plant configuration #5 was selected for the hotel
facility, being the highest-performing.
For the energy performance of the chiller plants using the mathematical optimization
shown in Equations (16)–(20), the same operating conditions used in the investigated hotel
were employed. The principle of simultaneously reaching the optimum operating point
4. For the evaluation of the objective function and the constraints, a genetic algorithm was
used to adjust the control parameters (Table 10). MATLAB Simulink 2018 [43] was used
for carrying out the evaluation.
Table 10. GA control parameters.
Energies 2023, 16, 3782
17 of 23
Population size
150.00
Selection operator
uniform stochastic
elitism
2.00
Table 11. Reproduction:
Energy consumption
and average COP values of chiller plant
options.
Crossover factor
0.80
Chiller Plant
Configuration
Mutation
uniform Energy Consumption (kWh)
0.01 Average COP
Chiller
plant #1
10,446.251
4.491
Crossover
heuristic
1.50
Chiller plant #2
10,681.532
4.312
Chiller plant #3
10,696.964
4.304
The proposed procedure allowed identification of the optimal PLRi of each
chiller at
Chiller plant #4
10,596.201
4.481
each demand Chiller
point, through
the
established
optimal
sequence,
the
on/off
status,
and the
plant #5
11,953.838
3.872
number of chillers
operation.
The on/off schedule
are
Chillerinplant
#6
11,707.874and PLI-COP curve diagrams
3.991
shown in Figures 8 and 9, respectively.
Chiller plant #1
Chiller plant #2
Chiller plant #3
Figure 8. Cont.
Energies 2023, 16, x FOR PEER REVIEW
Energies 2023, 16, 3782
18 of 24
18 of 23
Chiller plant #4
Chiller plant #5
Chiller plant #6
Figure Figure
8. On/off
schedule
of chiller
plantplant
options
using
thethe
optimized
chillerstaging.
8. On/off
schedule
of chiller
options
using
optimizedon/off
on/offprinciple
principle of
of chiller
staging.
Considering that the GA tool provided an approximated result, three runs of the
Figure
8 shows
a marked
between
thethe
operation
theoptimization
chiller plantprocedures.
and
program
were carried
out difference
to verify the
results of
OCL andof
OCS
the cooling
demand
profilewere
obtained
in Tableusing
9, concerning
thestandard
mode ofdeviation
operation(RSD).
shown
The results
obtained
corroborated
the relative
Table 12
reveals
ofitless
1%,how
proving
the existence
of a great
fit chillers
in the control
parameters
in Figure
6. In an
thisRSD
case,
canthan
be seen
the staging
sequencing
of the
is adjusted
of the GA. cooling capacity and in correspondence to the specific cooling demand.
to the individual
This mode of operation has a positive influence on the individual efficiency of each chiller
12. the
Results
obtained
with the
and inTable
turn on
overall
efficiency
of GA
the tool.
chiller plant, as shown in Figure 9.
Chiller Plant
Configuration
Test 1
Test 2
Test 3
RSD (%)
1
2
3
4
5
6
10,446.25
10,681.53
10,696.96
10,596.20
11,953.83
11,707.87
10,446.29
10,681.51
10,696.82
10,595.67
11,953.83
11,708.70
10,446.25
10,681.55
10,696.90
10,594.91
11,953.83
11,709.26
0.02
0.02
0.07
0.61
0.00
0.60
of 23
19 of1924
7
7
6
6
6
5
5
5
4
4
4
3
3
3
2
Ch 180.1 kW
1
0
0.0
0.4
0.6
0.8
2
0
0.0
1.0
PLR
Chiller plant #1
0.4 0.6
PLR
0.8
Chiller plant #2
6
6
5
5
5
4
4
4
3
3
3
1
0
0.0
0.4 0.6 0.8
PLR
Chiller plant #4
Ch 271.2 kW
1
Ch 310.6 kW
0.2
COP
6
2
1.0
0
0.0
0.4 0.6 0.8
PLR
Chiller plant #5
0.4 0.6
PLR
2
0.8
1.0
Ch 271.2 kW
1
Ch 271.2 kW
0.2
0.2
Chiller plant #3
7
Ch 228.9 kW
Ch 357.8 kW
0
0.0
1.0
7
2
Ch 201.6 kW
1
Ch 357.8 kW
0.2
2
7
COP
COP
Ch 198.7 kW
1
Ch 357.8 kW
0.2
COP
7
COP
COP
Energies
2023,
3782PEER REVIEW
Energies
2023,
16, 16,
x FOR
1.0
0
0.0
Ch 310.6 kW
0.2
0.4 0.6
PLR
0.8
1.0
Chiller plant #6
Figure 9. COP-PLR performance curves of chiller plant options.
Figure 9. COP-PLR performance curves of chiller plant options.
Figure
9 demonstrates
the strategy
designed
forthe
thefollowing:
chiller plant allows for a
As mentioned
above,that
the results
obtained
revealed
more efficient operating regime (range of the PLR greater than 0.5) for the chiller with the
•
The application of the traditional load-based sequencing methodology suggested the
largest cooling capacity by sacrificing the efficiency of the chiller with the smallest cooling
adoption of chiller plant configuration #5, which showed an energy consumption of
capacity. Table 11 shows the energy consumption and average COP values of all the chiller
13,882.52 kWh and an average COP of 2.78.
plant options. The results reveal that the best configuration was chiller plant configuration
•
The implementation of the proposed optimization approaches suggested that the
#1 (i.e., an asymmetric chiller plant with a cooling distribution of 33/67% and safety factor
best option would be the adoption of chiller plant configuration #1 (asymmetric
of 10.2%).
configuration, chiller cooling capacity distribution of 33/67%, safety factor of 10.2%),
which showed an energy consumption of 10,446.25 kWh and an average COP of 4.44.
Table 11. Energy consumption and average COP values of chiller plant options.
The proposed optimization procedures led the chillers operating in the investigated
Chiller Plant Configuration
EnergyofConsumption
hotel to energy savings
about 24.8% (kWh)
and an increment in theAverage
averageCOP
COP by about
Chiller plant #1
10,446.251
4.491
59.7% compared with chiller
plant configuration #5 selected by the traditional
load-based
sequencing methodology. In10,681.532
addition, the results obtained supported the
adoption of asymChiller plant #2
4.312
metric configurations rather10,696.964
than symmetric arrangements. In particular,
Chiller plant #3
4.304it was observed
that
chiller
plant
configuration
#5,
which
featured
the
best-performing
arrangement in the
Chiller plant #4
10,596.201
4.481
energy
analysis
carried
out
under
traditional
staging
and
the
cooling
distribution
recomChiller plant #5
11,953.838
3.872
mended by the Cuban standard
NC 220-3:2009 [44] (a requirement 3.991
for building design
Chiller plant #6
11,707.874
companies), was actually the one with the worst energy performance after implementing
the optimization procedures (Figure 10). However, the main conclusion of this research
Considering that the GA tool provided an approximated result, three runs of the prois that the use of the proposed approaches prevents engineers from making an incorrect
gram were carried out to verify the results of the OCL and OCS optimization procedures.
decision regarding the chiller plant to be installed in a building. It is very important to
The results obtained were corroborated using the relative standard deviation (RSD). Table
keep in mind that in the design phase, it is not only enough to consider the installation of
12 reveals an RSD of less than 1%, proving the existence of a great fit in the control paramthe most advanced system supported by an efficient control system. It is also necessary to
eters of the GA.
Energies 2023, 16, 3782
Energy Consumption (kWh)
15,000
14,000
13,000
Conventional staging principle
Co-desing principle staging
12,000
11,000
1
2
3
4
5
6
Chillers plant configuration number (#)
(a)
Coeficient of Performance (COP)
bution recommended by the Cuban standard NC 220-3:2009 [44] (a requirement for building design companies), was actually the one with the worst energy performance after implementing the optimization procedures (Figure 10). However, the main conclusion of this
research is that the use of the proposed approaches prevents engineers from making an
20 of
23 imincorrect decision regarding the chiller plant to be installed in a building. It is
very
portant to keep in mind that in the design phase, it is not only enough to consider the
installation of the most advanced system supported by an efficient control system. It is
analyze
the future
conditions
as close to
reality as as
possible,
that the
also necessary
to operating
analyze the
future operating
conditions
close tosoreality
as design
possible, so
and
of the
are inofline
each
other.
thatthe
theoperation
design and
theproject
operation
thewith
project
are
in line with each other.
5.0
4.5
4.0
3.5
Conventional staging principle
Co-desing staging principle
3.0
2.5
2.0
1
2
3
4
5
6
Chiller plant configuration number(#)
(b)
Figure 10. Comparative analysis of the results obtained by different energy simulation approaches.
Figure 10. Comparative analysis of the results obtained by different energy simulation approaches.
(a) Energy consumption. (b) COP.
(a) Energy consumption. (b) COP.
Conclusions
5.5.Conclusions
Implementing energy-efficient chillers can significantly help in the fight against global
warming. To promote the adoption of highly performing chillers for hotel facilities, this
research studied the energy impact of the selection of the most appropriate chiller configuration for a Cuban hotel. Six different chiller plant combinations and two different approaches
to evaluating their energy performance have been considered. The first methodology was
based on the traditional staging approach that relies on the on/off principle, whereas the
second procedure used a co-design principle and involved the solution to a mathematical
optimization problem. The two selected optimization procedures were optimal chiller
loading (OCL) and optimal chiller sequencing (OCS).
The energy simulation using the two approaches in the earlier chiller plant design
stage for buildings demonstrated the following:
As regards the traditional principle of chiller on/off staging, the chiller plant with
the best energy performance was the solution, featuring a symmetric configuration, chiller
cooling capacity distribution of 50/50%, and a safety factor of 11.7%.
As regards the co-design approach with staging using OCL and OCS optimization
procedures, the best energy performance was provided by the solution involving an asymmetric configuration, chiller plant #1 (featuring an asymmetric configuration, chiller cooling
capacity distribution of 33/67%, and a safety factor of 10.2%), showing an energy consumption of 10,446.25 kWh and an average COP of 4.44. The approach based on mathematical
optimization offers a reduction in energy consumption by 24.8% and an increase in COP by
59.7%.
Therefore, it can be concluded that both analyzed approaches lead to different results
that imply selecting different configurations as optimal. However, in terms of practical
issues, it is known that for the case study analyzed, the implementation of an automatic
control system for the hotel air conditioning system was proposed. Therefore, the chiller
plant that is best adapted to the future operation of the system was chosen through the
co-design methodology. An erroneous selection of the chiller plant configuration can result
in significant energy consumption, environmental impact, and economic losses. It is also
highly recommended that different thermal load profiles are considered due to the diversity
of cooling load demand scenarios that hotels face during the exploitation phase, and the
energy performance analysis of the proposed chiller plant should be set under this premise.
Energies 2023, 16, 3782
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However, the present research still has limitations that will be addressed in the future,
such as the extension of the energy analysis to the rest of the secondary circuits of the
chiller plant. In this way, it will be possible to determine more accurately the impact of the
operating strategies on the whole chiller plant system. Another aspect that can enhance
the analysis is the establishment of the OCS analysis through other approaches such as
chilled-water return temperature-based (T-based) sequencing control or bypass flow-based
(F-based) sequencing control, in which, although the energy savings are lower, they do not
involve on/off chiller operating regimes, thus preserving the technology better.
Author Contributions: Conceptualization, Y.D.T. and P.G.; methodology, M.T.d.T.; software, Y.D.T.,
R.R.C. and J.G.S.; validation, Y.D.T., P.G. and R.R.C.; formal analysis, M.T.d.T. and H.H.H.; investigation, Y.D.T.; resources, Y.D.T., R.R.C. and J.G.S.; data curation, Y.D.T.; writing—original draft
preparation, Y.D.T.; writing—review and editing, P.G., H.H.H. and J.I.S.O.; visualization, P.G.; supervision, P.G., H.H.H. and J.I.S.O.; project administration, H.H.H.; funding acquisition, P.G. and H.H.H.
All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: The data presented in this study are available in: [19,20,25].
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclatures
Annex 1: Nomenclature
a0 , a1 , a2
Correlation coefficients of the black box model of electrical power
BLR
Building load ratio
CI
Specific consumption index
CLi
Building cooling load for each interval of time i (kW)
Comb
Combinations of chiller plant
COP
Coefficient of performance
cp
Specific heat at constant pressure of water at 7 ◦ C (kJ/(Kg·K))
GA
Genetic algorithm
Hdo
Occupied room indicator
ki
Simulation scenario
ṁ
Chilled-water mass flow (Kg/s)
nch
Total of chiller selected in each chiller plant
OCL
Optimal chiller loading
OCS
Optimal chiller sequencing
Pch
Power consumption of chiller (kW)
PLR
Partial load ratio
Qch
Cooling load for the chiller (kW)
Qcl
Total cooling load (kW)
Qchstd
Cooling capacity of the chiller at standard conditions according to manufacturer (kW)
Qcho
Cooling capacity of the reference chiller (kW)
Sj off
Stage off threshold
Sj on
Stage on threshold
Tc air,in
Condenser air inlet temperature (◦ C)
Tc hw,s
Chiller water supply temperature (◦ C)
Tc hw,r
Chiller water return temperature (◦ C)
x0 , x1 , x2
Correlation coefficients of the black box model of nominal cooling capacity
Subscripts
ch
Chiller water
i
ith
max
Maximum
min
Minimum
c
Condenser
in
Inlet
s
Supply
r
Return
Energies 2023, 16, 3782
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