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Abstract and Figures

While equation-based object-oriented modeling language Modelica can evaluate practical energy improvements for district cooling systems, few have adopted Modelica for this type of large-scale thermo-fluid system. Further, to our best knowledge, district cooling modeling studies have yet to include hydraulics in piping networks alongside plant models featuring realistic mechanical systems and controls. These are critical details to include when looking to make energy and control improvements in many physical system installations. To fill these gaps, this study released new open-source district cooling models at the Modelica Buildings Library and leveraged these models for a real-world case study at the University of Colorado Boulder. The site includes six buildings connected to a central chiller plant featuring a waterside economizer. Several energy saving strategies are pursued based on the validated model, including control setpoint optimization, equipment modification, and pump setpoint adjustments. Results indicate that a combination of the studied measures can save the campus annually 84.6 MWh of energy, 8.9% of electricity costs, 58.0 metric tons of carbon dioxide emissions, while the waterside economizer cuts down chillers’ run times by 201 days/year, reducing maintenance costs and extending chiller life.
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Graphical Abstract
New open-source models at the Modelica Buildings library enable detailed energy analysis of
complete district cooling systems including network hydraulics and realistic plant designs to
achieve energy, cost, and carbon emission reductions.
Energy Cost
Reference: K. Hinkelman, J. Wang, W. Zuo, A. Gautier, M. Wetter, C. Fan, N Long. 2022. “Modelica-based modeling and simulation of district cooling systems: A case study.” Applied Energy.
Case Study
Findings:
Energy
Efficiency
Measures:
Carbon Emissions
Results
Combining measures from the optimized Fixed and operating 2 CWP each at 50 kg/s ( bar above) can save annually:
15.3% of energy, 8.9% on the cost of electricity, and reduce carbon emissions by 15.0% without any additional financial investments.
Pre-Process
Measured Data
Validate the
Baseline Model
Identify System
Improvements
Collect Physical System
Information & Data
Develop the
Models
T
M
M
M
M
Run Numerical
Simulations
.\dymosim.exe
>_
Evaluate
Impacts
$$
Baseline Model
No Waterside Economizer
Fixed + 2 CWP at 50 kg/s
Fixed condenser water supply temperature setpoint ( ) Optimization
Fixed approach temperature ( ) Optimization
Adjusted Optimization
1 Condenser Water Pump (CWP) at 126 kg/s
1 CWP at 100 kg/s
2 CWP at 50 kg/s
Understand the
Problem
Tapp
Tapp
TCW,set
Tapp
Tapp
K. Hinkelman, J. Wang, W. Zuo, A. Gautier, M. Wetter, C. Fan, N. Long. 2022.
"Modelica-Based Modeling and Simulation of District Cooling Systems: A Case
Study." Applied Energy, 311, pp.118654, doi.org/10.1016/j.apenergy.2022.118654.
Highlights
One of the first district cooling case studies to consider plant mechanical and control system details and pipe hydraulics
Presents a systematic methodology for Modelica modeling and simulation of existing district cooling systems
Identified investment-free annual savings of 15% energy, 9% electricity cost, and 15% carbon emissions
Models used in the case study are open-source released at the Modelica Buildings Library
Modelica-Based Modeling and Simulation of District Cooling Systems: A Case Study
Kathryn Hinkelmana, Jing Wanga,b, Wangda Zuoa,b,, Antoine Gautierc, Michael Wetterc, Chengliang Fana,d, Nicholas Longb
aCivil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO, USA
bNational Renewable Energy Laboratory, Golden, CO, USA
cLawrence Berkeley National Laboratory, Berkeley, CA, USA
dSchool of Civil Engineering, Guangzhou University, Guangzhou, 510006, China
Abstract
While equation-based object-oriented modeling language Modelica can evaluate practical energy improvements for district cooling
systems, few have adopted Modelica for this type of large-scale thermo-fluid system. Further, to our best knowledge, district cooling
modeling studies have yet to include hydraulics in piping networks alongside plant models featuring realistic mechanical systems
and controls. These are critical details to include when looking to make energy and control improvements in many physical system
installations. To fill these gaps, this study released new open-source district cooling models at the Modelica Buildings Library and
leveraged these models for a real-world case study at the University of Colorado Boulder. The site includes six buildings connected
to a central chiller plant featuring a waterside economizer. Several energy saving strategies are pursued based on the validated
model, including control setpoint optimization, equipment modification, and pump setpoint adjustments. Results indicate that a
combination of the studied measures can save the campus annually 84.6 MWh of energy, 8.9% of electricity costs, 58.0 metric tons
of carbon dioxide emissions, while the waterside economizer cuts down chillers’ run times by 201 days/year, reducing maintenance
costs and extending chiller life.
Keywords: District Cooling, Modelica, Modeling and Simulation, Waterside Economizer, Optimization, Case Study
1. Introduction
Aggregating cooling equipment at the district scale provides
important opportunities for cities and organizations to serve the
cooling needs of their communities through financially viable
means. Space cooling continues to grow faster than any other
building end use [1], largely due to the improving standards
of living and warming climate conditions across the globe. To
meet climate action targets and reduce fossil fuel consumption,
many experts recommend a shift from treating buildings as iso-
lated entities to operating communities of buildings as intercon-
nected systems. District cooling (DC) is one such community-
scale technology that provides benefits both financially (e.g.,
economy of scale, centralized maintenance) and environmen-
tally (e.g., more ecient equipment, higher renewable energy
integration).
Computer modeling and simulation is an eective means to
further improve the energy utilization of DC systems. Several
tools have been adopted throughout literature for DC applica-
tions. Using TRNSYS, Anderson et al. [2] adjusted the operat-
ing time of chillers (compressor and absorption), cooling tow-
ers, and thermal storages with a lumped campus thermal load
to minimize exergy destruction. Chow et al. [3] evaluated sev-
eral water-cooled chiller plant configurations (including ther-
mal storage, several heat rejection methods, and various pump-
ing configurations) with TRNSYS for the plant/district simu-
Corresponding author.
lation and HEVACOMP/DOE2 for the building thermal load
models. Using MATLAB, Oppelt [4] implemented dynamic
thermo-hydraulic models tailored specifically for DC networks,
with buildings and the central plant modeled as single heat ex-
changers. Some works did not present their modeling frame-
work nor their simulation tools, yet still ought to be mentioned.
For example, Gang et al. [5] evaluated chiller plants (containing
electric chillers, double-eect chillers for ice production, and an
absorption chiller) with ice and hydro pumped storage systems
to reduce peak cooling loads. In addition, Matsouka and Hil [6]
optimized the number of cooling towers and condenser water
(CW) flow rate for a central plant containing turbo-chillers for
an online process simulation.
However, there are limitations among these modeling tools
and existing methodologies. First, many of these programs
use imperative programming languages that tightly intertwine
the model equations with the numerical solution method, such
as with C/C++ (e.g., EnergyPlus) or Fortran (e.g., TRNSYS).
Further, some traditional languages are causal (e.g., MAT-
LAB/Simulink) and do not support acausal modeling. While
these traditional languages can be characteristically slow for
development of heterogeneous cyber-physical models [7], in-
cluding DC systems, they also are less flexible to support
new use cases [8]. Further, most traditional tools have pre-
defined numerical solvers; however, dierent solvers may be
required to solve the dierential equation problem for dierent
use cases [9].
As a result, the past literature generally did not consider
Email address: wangda.zuo@colorado.edu (Wangda Zuo)
Applied Energy April 1, 2022
K.. Hinkelman, J. Wang, W. Zuo, A. Gautier, M. Wetter, C. Fan, N. Long. 2022.
"Modelica-Based Modeling and Simulation of District Cooling Systems: A Case
Study." Applied Energy, 311, pp.118654, doi.org/10.1016/j.apenergy.2022.118654.
both the hydraulics in the distribution network and realistic
plant configurations and controls, and had to make simplify-
ing assumptions in one of the two categories instead. Yet, hy-
draulics in the distribution network can significantly impact the
pump energy consumption [10], can cause controllability prob-
lems [11], and aect the eectiveness of the DC system. Mean-
while, as central plants improve their energy utilization through
free cooling economizers and more advanced controls, it be-
comes increasingly critical to model these plant details to iden-
tify realistic energy solutions [12]. The prevalence of econo-
mizers and their associated control will only increase too, as
the International Energy Conservation Code now requires air or
waterside economizers for chilled water systems above certain
capacities in most climate zones (all except extremely/very hot
and humid 0A and 1A) [13].
Modelica [14] is a modeling language, governed by an open
standard, that can eectively address these limitations. First, as
an equation-based and object-oriented language that supports
both causal and acausal modeling, Modelica allows developers
to build up complex system models featuring both thermo-fluid
system models (typically acausal) and realistic controls (typ-
ically causal) using a graphical, hierarchical approach, from
individual equipment to subsystems and districts. These fea-
tures allow models to be constructed with standard-form phys-
ical equations (i.e., not constrained to only input/output formu-
lations) and may contain continuous, discrete, and hybrid dif-
ferential equations, aiding flexibility for use cases and signifi-
cantly reducing model development time [7]. Second, simula-
tion code is generated automatically, and in contrast to many
traditional tools, the model equations are separated from the
simulation code. This code separation and the availability of
several, selectable numerical solvers improves the developer’s
ability to successfully simulate complex system models, partic-
ularly “sti” models with both fast and slow dynamics, which
are common in DC applications. For applied energy projects,
the development time reductions are particularly blaring when
making small design modifications in an existing model to ex-
plore dierent energy eciency measures. Lastly, the Modelica
community has rich open-source libraries that span multiple do-
mains, which enable users to construct their case study models
from like systems and share resources among transdisciplinary,
external groups.
The case study by Zabala et al. [15] leveraged the benefits
of Modelica for DC applications, creating reduced-order mod-
els of a chiller plant based on high-fidelity Modelica models
for real-time, model predictive control (MPC) applications. As
part of this work, the District Cooling Open Source Library
was publicly released [16]. While Zabala et al. [15] developed
their chiller models from Modelica, they simulated the entire
DC system externally using Python. This approach was highly
eective for MPC, but numerous benefits of Modelica for DC
analysis remain unexplored. Beyond this work, there is surpris-
ingly very little Modelica-based research for DC analysis.
Leveraging the benefits of Modelica, this is one of the first
DC system modeling and simulation studies for detailed energy
analysis that considers hydraulics in the piping networks and
realistic plant system design and control. To support future sci-
entific endeavors, we developed and open-source released new
DC models at the Modelica Buildings Library [17] (version
8.1.0), documented a systematic methodology for case studies
of existing DC systems, and adopted the new models and pro-
posed methodology for a real-world case study at the University
of Colorado Boulder. The selected case study contains a chiller
plant with a waterside economizer (WSE), a popular and eec-
tive way to improve chiller service life and reduce plant energy
consumption [18, 19, 9] that is increasingly being required by
code. Despite their importance, to our best knowledge, oth-
ers have yet to model DC systems featuring a WSE. Further,
we also evaluate and present the numerical performance (i.e.,
the scalability) of a detailed plant model connected to complete
districts of several sizes, which is important to understand the
capabilities and limitations of large Modelica models for DC
analysis. Lastly, this paper’s case study extends our previous
work on the campus’s central plant [20] by presenting a sys-
tematic methodology in modeling and simulation of an existing
DC system, adding models for the distribution network with
individual building loads, improving the central plant models,
and extending the impact analysis to include financial and car-
bon savings.
It should be noted that there are many similarities be-
tween heating and cooling at district-scale [21]. In addition,
Modelica-based modeling of other DHC types such as com-
bined heat and power or ambient water networks [10, 22, 23]
and chiller plants in non-DC applications [24, 25, 26, 27, 28]
are also extensive. However, there is a general lack of publica-
tions on DC modeling and simulation [29], which we address
herein through the contribution of new open-source models, a
well-structured methodology, and an exemplifying case study.
For demonstration, we select several energy eciency mea-
sures that do not require capital investment, including control
setpoint optimization, assessing the eectiveness of the non-
integrated WSE, and adjusting pump setpoints, but the open-
source models and proposed methodology can be used for other
analysis as well. This includes the evaluation of energy and fi-
nancial impacts when replacing chillers or adding thermal stor-
age, or system flexibility analysis made possible by the inherent
thermal inertia of the distribution piping. Although out of the
scope for this case study, other approaches such as these may
require capital investment but can be highly lucrative.
The rest of this paper is organized as follows. To support
future Modelica-based DC system studies, we summarize our
systematic methodology in section 2. The case study’s DC sys-
tem is presented in section 3, followed by the corresponding
Modelica models (section 4). After verification and validation
of the DC baseline models in section 5, section 6 presents the
baseline performance, energy eciency improvements includ-
ing quantification of the financial and environmental impacts,
as well as the numerical performance and scalability analysis.
Finally, section 7 presents our conclusions.
2. Methodology
As shown in Figure 1, we followed a systematic methodology
for improving the energy performance of the DC system using
2
Modelica, from problem definition to simulation-based impact
evaluation. While the fundamental steps can be considered typ-
ical best practices when applying modeling and simulation for
energy and control analyses, the details within each step are
uniquely proposed for existing DC system case studies. In prin-
ciple, this methodology is suitable for any existing DC systems
with some degree of measured data available. The following
sections describe each of the eight steps in this methodology.
2.1. Step 1: Understand the Problem
Before collecting data or beginning modeling, it is critical to
first understand the problem. This includes defining the scien-
tific experiment and understanding what question the models
should be able to answer. The goal is not to have the models
represent all aspects of the real system, but only the features that
are necessary per the problem objective. For example, this work
aimed to study the thermo-fluid and control performance of the
DC system during normal operation. Emergency protocols and
atypical operating conditions were not included. Similarly, any
equipment pertaining to chemical treatment was excluded. Af-
ter formulating the problem, we then draw system schematics
and define control inputs and loops. These schematics are in-
valuable blueprints for successful model development.
2.2. Step 2: Collect Physical System Information and Opera-
tional Data
Physical system information and operational data can be used
to design the system models, provide input data for the mod-
els directly, and verify and validate model accuracy. With ex-
isting DC systems, it is best to gather information and data
from a variety of sources. District-scale systems often change
over time as new buildings are added or plant equipment is ex-
changed. Thus, collecting redundant information helps verify
sizing and performance specifications are up-to-date. The va-
riety of sources includes mechanical and control specification
documents, site visits (e.g., operator interviews, nameplates,
control panels), and other manufacturer performance files.
2.2.1. Electrical System
For electrical measurement data, logged energy and power
consumption of buildings and major equipment should be col-
lected if available. Collecting real power data at 15-minute
intervals is preferred for validation since it is also commonly
used by electric utility companies when determining peak de-
mand charges [30]. While equipment submetered data is the
best way to validate equipment electrical performance, this is
often unavailable. Thus, the electrical performance validation
with measured data might only be possible at the system level,
while equipment need to be validated by other means. If this
is the case, equipment electrical performance can be verified
with the available electrical specification documents to ensure
the power is always operating within the expected range.
2.2.2. Thermo-Fluid System
For thermo-fluid measurement data, the plant and buildings
contain sensors that log data at given intervals. We recommend
the interval should preferably be no bigger than 15-minutes to
capture transient dynamics of the cooling equipment as well as
pumps and valves. However, to identify potential control insta-
bilities, spot measurements may be done at shorter frequencies
such as 1 minute. For chiller-only plants, it is important that
the data collected span full and part load conditions at a mini-
mum. Further, data for chiller plants with WSEs also need to
include Free Cooling (FC), Mechanical Cooling (MC), and Par-
tial MC modes, if present. In general, we recommend collect-
ing at least two years of historical data if available to account
for inevitable gaps and errors in the data sets as well as the
variation of weather condition and cooling load profiles. Data
types can include supply and return temperatures, mass flow
rates, pump head pressure, and heat flow rates for major sys-
tems (e.g., plant, buildings) and equipment (e.g., chillers, WSE)
on both the chilled water (CHW) and CW sides.
2.3. Step 3: Pre-Process Measured Data
Before using the data, it is necessary to pre-process the
datasets so that they are suitable for use as model inputs and
validation. While there are not data size restrictions on mea-
sured data for calibration purposes, data used as model inputs
needs further refinement to reduce file sizes and verify expected
performance. To pre-process the data, we first inspect the en-
tire dataset for each building, plant, and equipment to see if they
follow expected trends and fall within reasonable limits. Data
points containing errors can then be eliminated. For example,
the water in the building pipes stabilizes at the ambient room
temperature (20C) when no water is flowing, which at times
produces negative temperature drops due to variability across
the sensor locations and sensitivity levels. These data points
should be cleaned to correctly indicate zero cooling. If neces-
sary, the datasets can be smoothed by a moving average, making
it suitable for use as model inputs. For instance, CHW supply
and return temperature data at the buildings can be smoothed
to eliminate sensor noise from the measurements. Finally, we
can round the building measured data to an appropriate decimal
point to further reduce the file size for model inputs. For exam-
ple, temperature measurements can be rounded to the nearest
0.1C and heat flow rates to the nearest 1 W.
2.4. Step 4: Develop the Models
There are numerous Modelica modeling resources available
for DC system energy analysis that include hydraulic system
dynamics and typical chiller plants. Open-source libraries con-
tain packaged models from equipment through district-scale
systems that can be adapted directly or modified for case study
projects. We developed new models for DC applications that
we open-source released in the Modelica Buildings Library
version 8.1.0. These models include a DC plant with paral-
lel electric chillers, parallel cooling towers with a bypass, and
representative controls; a consumer connection model that can
interchange the pipe models; and a vector-based distribution
network model to allow various configurations. In addition to
these new models we developed, the Data Center package of
the Buildings Library [9] provides many equipment, subsystem,
3
Figure 1: Steps in the proposed systematic methodology for modeling and simulation of existing DC systems.
and control models for chiller plants with and without WSE.
Further, AixLib [31], IDEAS [32], and Building Systems [33]
are all open-source libraries that contain resources for DC sys-
tem model development, in addition to the District Cooling
Open Source Library [16] previously mentioned. While mod-
els from these open-source libraries can often be used directly,
it is common that custom system-level models need to be devel-
oped for the case study application. As such, we present in this
work the customized models we created for a real-world case
study based on the new models we open-source released in the
Buildings library.
For successful model development of large-scale thermal-
fluid systems, compartmentalizing the system into sub-
components is key. This allows the sub-components to be tested
in isolation and errors to be detected. Further, adding unit tests
helps to verify that the sub-components continue to perform as
expected as the model evolves. Once all sub-components have
been developed and tested, then the full system model can be
assembled hierarchically.
2.5. Step 5: Run Numerical Simulations
Modelica simulations can run in multiple environments. Dy-
mola [34] is a popular commercial tool that provides a user-
friendly graphic interface and several numerical solvers suit-
able for DC system analysis. The OPTIMICA Compiler
Toolkit [35], with its a graphical user interface IMPACT, is
also available commercially. OpenModelica [36] and JModel-
ica [37] provide open-source environments for Modelica-based
modeling and simulation. While there are many suitable numer-
ical solvers for solving DC system models, we frequently adopt
CVODE [38] for its suitability for solving stiproblems. In our
experience of adopting CVODE in Dymola, it typically simu-
lates thermo-fluid systems quickly and robustly. For this case
study, all models were simulated in Dymola using CVODE as
the numerical solver with a tolerance of 106.
When simulating complex thermo-system models, debug-
ging models is often required to improve numerical perfor-
mance. From our experiences, applying second-order filters to
step functions (e.g., for valve opening or pump signals) often
helps to improve numerical stability. Such a filter is built-in to
HVAC models of many Modelica libraries. Furthermore, much
attention should be paid towards PI controller gains to avoid
control instability. While out of the scope of this paper, there
are many resources available to help first design numerically-
ecient models [39], and then simulate them eectively [40].
2.6. Step 6: Validate the Baseline Model
District-scale heating and cooling systems can have larger
uncertainties in measured data than for individual building sys-
tems, particularly due to the lack of sucient quantitative data
at such scale [41]. While the uncertainty can have an averaging
eect at district-scales for some features, it is potentially com-
pounding for others [42]. Thus, it is important for modelers
to recognize the impacts of uncertainly in measured data when
validating complete DC systems. To address this challenge, we
suggest verifying modeling assumptions and validating simula-
tion results for DHC energy-based studies across two primary
dimensions: (1) electrical and thermo-fluid systems; and (2)
equipment and system levels.
2.6.1. Electrical System
For electrical validation, it is common that electrical data is
available at the plant and buildings’ main meters, but subme-
tering is not available for individual equipment. Further, build-
ings’ main meters typically have equipment beyond the cool-
ing system. For example, central plants frequently contain both
heating and cooling equipment that serve the district, as well
as heating, ventilation, and air conditioning (HVAC) equipment
serving the plant building itself and other electrical loads (e.g.,
interior and site lighting, plug loads). To address this uncer-
tainty, we suggest to validate system level DC power consump-
tion from simulations with respect to the range of expected DC
real power from measured data at the building’s main electrical
meter. An upper limit to DC plant power range PPla is given as
PPla =PMea ,(1)
where PMea is the measured real power data from the electrical
meter. To represent the lower limit PPla, we adjust PMea by
scaling factor σusing
PPla =σPMea where (2)
σ=fPDPla,i
PDPla,i+PDOth,j
(3)
In this formulation, σrepresents the ratio of the peak demands
from all individual cooling plant equipment DPla,ito the total
peak demand of the main meter, including other loads DOth,j,
which are not apart of the DC system. An additional safety fac-
tor fof 1.25 is included to account for the likelihood of equip-
ment operating at dierent part load ratios. In this case study,
σwas 0.42. An example of such analysis is shown in Figure 9.
For equipment-level validation, submetered data should be
used if available. If not available, modelers can verify that the
power consumption of each equipment is always at or under the
stated nominal value during the annual simulation. An example
of this alternate approach is shown in Figure 10, where box
plots depict the annual distribution of power required for major
equipment, normalized by their rated nominal powers.
4
2.6.2. Thermo-Fluid System
For thermo-fluid validation, on-site sensors provide temper-
ature and flow rate data from various points throughout the sys-
tem. Following ASHRAE Guideline 14 [43], we evaluate both
the Coecient of Variation of the Root Mean Square Error
CV RMS E =qP(yiˆyi)2
N1
¯y,(4)
and the Normalized Mean Bias Error
NMBE =P(yiˆyi)
(N1)¯y,(5)
where yiis the individual measured data, ˆyiis the corresponding
simulation data, ¯yis the mean of the measured dataset, and Nis
the total number of data points. With hourly data, the CVRMSE
and NMBE need to be within 30% and 10% respectively for the
model to be considered validated [43].
It is important to note that ASHRAE Guideline 14 is in-
tended for measurement of energy and demand savings. Thus,
they do not provide specific guidance on temperature and mass
flow measurements. However, the same standard was accepted
herein across all thermo-fluid data types. For temperature, units
of Kelvin were adopted, while mass flow was represented in
kg/s. Furthermore, it is possible that after pre-processing and
removing sensor errors, a full year of clean measured data may
not be available. In this case, both system and equipment level
thermo-fluid conditions can be validated using representative
time periods. For instance, this study selected two representa-
tive weeks in both summer and winter to validate the system
models.
2.7. Step 7: Identify System Improvements
With the validated baseline model, several energy eciency
improvements for the DC system can be simulated to quantify
their potential benefits. While providing guidance on which en-
ergy eciency measures to select is out of the scope of this
work, other literature provide comprehensive methodologies
for identifying optimal energy eciency measures for build-
ings [44] and control strategies for central plants [45]. For
demonstration, we selected three measures that require little to
no financial investment. This includes optimizing the CW sup-
ply temperature setpoint (TCW,set), assessing the eectiveness
of the WSE, and adjusting CW pump flow rate settings. These
were selected after analyzing the baseline energy results and
identifying high potential areas for improvement that can read-
ily be adopted by the system operators.
As an example for the TCW,set optimization, we can formulate
a single objective optimization problem to minimize the plant’s
annual energy consumption as
min
x[x,x]EPla,i(TCW,set(x)),(6)
with x= x1
x2!,and (7)
EPla(TC W,set(x)) =Zt2
t1
(PCH (TCW,set(x),s)+PC W (TCW,set(x),s)+
(8)
PCHW (TC W,set(x),s)+PCT (TCW,set(x),s))d s,
where xrepresents the free parameters to be tuned during the
optimization process, EPla is the total plant energy during the
optimization period t[t1,t2), PCH is the power of the chillers,
PCW is the power of the CW pumps, PCH W is the power of the
CHW pumps, PCT is the power of the cooling towers, xcon-
tains the tuner parameter lower limits, and xcontains the tuner
parameter upper limits.
Three separate optimization problems are solved with TCW,set
prescribed as
TCW,set(x1)=x1,(9)
TCW,set(x1)=Twb +x1,(10)
TCW,set(x1,x2)=Twb +x1+x2PLR,(11)
where in Equation 9, TC W,set is a fixed temperature (Fixed
TCW,set) equal to constant x1; in Equation 10, TC W,set is a fixed
approach temperature (Fixed Tapp) equal to x1oset from
the measured ambient wetbulb temperature Twb; and in Equa-
tion 11, TCW,set is an adjusted approach temperature (Adjusted
Tapp) oset x1from Twb and scaled by x2based on the cen-
tral plant’s part load ratio (PLR). In this case study, optimiza-
tion problems are solved for t[0,365) days with the Op-
timization library version 2.2.4 [46], a Modelica library that
is released alongside Dymola that can solve nonlinear multi-
criteria parameter and trajectory optimization problems involv-
ing Modelica model simulations. There are numerous numeri-
cal optimization algorithms available in this library, and more
information is available in [47]. For this case study, we adopt
the local simplex method, and solve the optimization problems
with optimization and simulation tolerances of 105and 106,
respectively.
2.8. Step 8: Evaluate Impacts
Beyond energy consumption alone, evaluating the impacts
that cooling infrastructure has on humans and the environment
require higher-level evaluation metrics. Our approaches are as
follows.
2.8.1. Energy Impacts
There are several metrics available to evaluate energy im-
pacts for DC systems. Annual site and source energy consump-
tion are two common metrics. In addition, peak power is a help-
ful indicator to understand the instantaneous rate of energy re-
quired at a given time. For cooling plants, the plant eciency
is often represented by kW/ton. This is defined as the ratio of
5
total cooling plant power (including chillers, pumps, and cool-
ing tower fans) to the total cooling load served by the plant. For
chillers, the kW/ton is also a common metric to represent the
equipment energy eciency ratio. Similarly, the coecient of
performance is used as an equipment or system eciency indi-
cator. This is a unitless value representing the ratio of the cool-
ing load to the electrical power. For buildings, common energy
metrics also include the energy use intensity (ratio of cooling
energy to total floor area served). In this study, we adopt the
annual site energy consumption as the primary energy impact
metric but also assess the kW/ton and peak power.
2.8.2. Economic Impacts
We evaluate the annual cost of electricity for operating the
DC system based on the electric rate schedule from the local
utility. While many electric utilities employ static pricing pro-
grams, there are increasing trends towards dynamic pricing pro-
grams (e.g., critical peak pricing, time of use pricing). Because
the return on investment of dierent energy eciency measures
is often sensitive to the pricing program [48], it is important to
represent the pricing scheme accurately. As an example for this
case study, we adopt the static pricing program assigned to the
central plant. In this case, electricity is charged on a monthly
basis $0.00458 per kWh of energy used and $3.86 per kW of
billing demand.
2.8.3. Environmental Impacts
Representative environmental indicators can be selected
based on previous knowledge of the life cycle impacts of build-
ing systems. Operational phase energy consumption dominates
typical building life cycle impacts and its greenhouse gas emis-
sions represent the largest impact category [49]. This is par-
ticularly true for cooling plants where their primary function is
to produce CHW for the district. Although calculating green-
house gas emissions would be more comprehensive for assess-
ing climate impacts, carbon dioxide (CO2) is the dominating
byproduct of fossil fuel-based electricity generation. Thus, it is
reasonable to use CO2as a proxy indicator. To calculate CO2,
Cambium’s datasets provide hourly cost and operational data
for the U.S. electricity sector [50]. For this case study, we adopt
Cambium’s 2018 Midcase Scenario data for the average CO2
emission rate (kg/MWh) of generation induced by Colorado’s
regional load. This dataset provides hourly carbon emissions
based on the dynamic electricity mix for the state, including
intermittent renewable generation, while also including the ef-
fects of imported and exported power as well as distribution
losses.
3. System Description
A case study of DC system modeling and optimization is
conducted using the methodology mentioned in section 2. The
case study site is a satellite campus of the University of Col-
orado Boulder with DC services provided to six buildings. This
section describes the analyzed system, including the distribu-
tion network, the central plant, and the connected buildings.
3.1. Distribution Network
The distribution network is a radial layout (Figure 2) con-
necting six buildings with a central plant. The total length of
supply and return pipes is around 1.5 km. The pipes can be
divided into 11 segments. Some segments are insulated pipes
located in underground tunnels while others are direct buried.
Additional information for the district pipes can be found in the
Appendix (Table A.1).
CHW Supply
CHW Return
Central Plant
Building 1
Building 5
Building 6
Building 4
Building 2
Building 3
1
10
2
3
4
5
6
7
8
9
11
Figure 2: Network topology for the DC system. Details about the numbered
pipe segments are given in the Appendix (Table A.1).
3.2. Central Plant
As shown in Figure 3, the primary-only central plant includes
two water-cooled chillers with a parallel WSE on both the CHW
and CW legs. This WSE configuration is commonly referred as
nonintegrated, and the WSE can only run when it is capable
of meeting the entire cooling load. In contrast, an integrated
WSE is in series with the chillers on the CW or CHW legs,
such that the WSE can share the cooling load with the chillers
when it cannot meet the entire demand. At this plant, CW is
cooled by two open-circuit cooling towers before returning to
the chillers/WSE. The nominal power for each chiller compres-
sor (2 chillers total, 1 compressor per chiller), CW pump (2
total), CHW pump (3 total), and cooling tower fan (4 total) is
366 kW, 56 kW, 30 kW, and 22 kW, respectively. The plant’s
hierarchical control is implemented through a Supervisory Con-
trol and Data Acquisition system; at top Master Control level,
the plant operates in either MC mode (running the chillers only)
or FC mode (running the WSE only). Further details about the
mechanical and control system configurations, including sys-
tem schematics and nominal information for the plant equip-
ment, can be found in [20].
6
Figure 3: Schematic diagram for the central plant.
3.3. Connected Buildings
The serviced buildings are primarily student dormitories with
some academic and dining functions (Table 1). Each building
is connected to the district via an energy transfer station (ETS)
with a direct piping connection (no heat exchanger). A bypass
loop at the ETS maintains minimum CHW return temperatures
to the district. The six buildings account for a total of 93,990 m2
gross floor area, while the cumulative peak load across all build-
ings is 1,772 kW. Like many district energy projects, the cam-
pus originally anticipated more buildings being added to the site
than exists currently. As such, the sizing of the central plant ac-
counted for an additional twelve buildings which have not been
constructed yet.
Table 1: Buildings connected to the district network.
Building No. Area (m2) Primary Function
1 13,126 Dormitory/Classrooms
2 23,170 High-rise Dormitory
3 11,420 High-rise Dormitory
4 10,680 Dining and Recreation
5 17,730 Mid-rise Apartments
6 17,730 Mid-rise Apartments
The measured load duration curves from this site (Figure 4)
show how the cooling needs vary from building to building in
2018. The CHW heat flow rate is calculated using the sup-
ply and return temperature and mass flow rate sensors at each
building’s ETS. For example, the peak cooling demands range
from 248 kW (building 1) to 653 kW (building 2). During
2018, buildings 2 and 4 had cooling demand year-round, while
building 3 had cooling needs for only 40% of the year. The to-
tal cooling load varies from 1,263 MWh/year for building 4 to
246 MWh/year for building 1.
Figure 4: Cooling load duration curves from 2018 measured data.
4. Modelica Implementation
As part of this work, we developed and open-source released
subsystem- and system-level models needed for DC applica-
tions in the Buildings library. The version 8.1.0 release includes
a detailed central plant featuring both mechanical and control
systems as well as several distribution piping networks. In ad-
dition, we are continuing to improve and expand the DHC pack-
age of the Buildings library with more system types and config-
urations, control implementations, and interconnected building
features, to be included in future releases. Leveraging the new
models to date, we developed the case study at the University
of Colorado Boulder. In this section, we present the customized
models pertinent to the case study in a top-down approach.
At the top level, the Modelica DC system model (Figure 5)
includes a central plant, a distribution network, and intercon-
nected buildings. With a vector of fluid connectors in the Dis-
tribution Network model, a district with any number of build-
ings can quickly be represented, given that the computer has
sucient resources to solve the problem. Through packaged hi-
erarchical modeling, each major DC component can seamlessly
be replaced; for example, high-order or reduced-order building
models can be integrated into the flexible modeling framework.
4.1. Boundary Conditions
Modeled weather and ground conditions are consistent with
the local environment. Historical 2018 weather data from on-
site sensors were collected and averaged on an hourly basis. We
then overwrote the ambient drybulb temperature, dew point, rel-
ative humidity, and barometric pressure data from a typical me-
teorological year 3 (TMY3) data set corresponding to a regional
weather station with the on-site data. The TMY3 file was then
imported via the Weather Data block from the Buildings library,
in which Twb is calculated. We assumed the tunnel temperature
7
TCWS,Set
K
preTem
freqHz=1/31536000
TWetBul
weaBus
Buildings [:]
Central Plant
Weather Data
Ground
Temperature Distribution Network
Measured dp
Figure 5: Top level diagram of Modelica model for the DC system.
is the same as the ground three meters below the surface, rep-
resented by a sinusoid ranging from 4.6C (March) to 15.9C
(September). This is consistent with average regional ground
temperatures. Since we used measured data for the building
loads, the model is not using solar irradiation data. Hence,
overriding only the temperature data still provides consistent
boundary conditions.
4.2. Distribution Network
A vector-style distribution network model was developed to
allow interconnection with any number of buildings. Shown
in Figure 6, the Distribution Network model consists of a
series of Connection models. These distribution and con-
nection models can adopt several dierent pipe models and
are included in the new open-source release of the Build-
ings library. Supply and return pipes between each connec-
tion are modeled as plug flow pipes (using the model Build-
ings.Fluid.FixedResistances.PlugFlowPipe). Developed with
DHC in mind, this pipe model eciently and accurately eval-
uates pipe pressure drop, heat losses through the distribution
network, and fluid transport delay. It also produced the small-
est errors in comprehensive DHC experiments compared to
other available models. While more information about this pipe
model can be found in [51], the fundamental equations are as
follows. The transfer of energy along the pipe and heat lost
to the external environment can be expressed with a combined
energy and continuity equation as
(ρcvT A)
t+
ρνAcvT+p
ρ
x=(12)
νAp
x+1
2ρν2|ν|fDS+
x kA T
x!˙qe
where positive ˙qeis the heat loss from the pipe to the surround-
ings, xis the axial position with time t,ρis the density, cvis the
specific heat at constant volume, Tis temperature, pis pressure,
νis the flow velocity, Ais the pipe’s cross sectional area, Sis
the pipe circumference, and fDis the Darcy friction coecient,
and kis the thermal conductivity. Eliminating negligible terms
(e.g., diusive heat transfer, heat loss due to pressure drops and
wall friction), taking a Lagrangian approach, and integrating
the simplified energy balance equation with respect to dT and
m_flow
p_rel
T
T
+
-1
+1
k=cp_default
Supply to
Supply
Plant
Supply to
Downstream
Connections
Lossless Pipe
Mass Flow
Heat
dT
Supply Pipe
Rate
...
Connection [1]
...
Connection [2] Connection [6]
Buildings
Return from
Buildings
Port
Heat Flow
Rate
Pressure
Difference
Return from
Downstream
Connections
from
Return
Plant
to
Return Pipe
Figure 6: Hierarchical diagram of vector-style network interconnection model.
dt yields
Tout =Tb+(Tin Tb) exp tout tin
RC (13)
where subscripts in,out, and bsignify the pipe inlet, pipe out-
let, and surroundings, respectively; Ris the fluid thermal resis-
tance; and Cis the thermal capacitance. The thermal capacity
of the pipe wall is also added to the model to account for its
thermal inertia, represented by a single capacitance at the out-
let of each pipe segment. This thermal model is comparable
to other works [52, 53, 54], reinforcing its suitability for DHC
applications.
In addition to the heat transport and losses, the fluid delay
time is described in the PlugFlowPipe model using the one-
dimensional wave equation
z(x,t)
t+ν(t)z(x,t)
x=0 (14)
where z(x,t) is the transported fluid quantity. This equation is
used to describe the delay time of fluid parcels through the pipe
and their associated properties (i.e., enthalpy), and produces
similar results to that by Velut and Tummescheit [54].
4.3. Central Plant
The detailed central plant model represents the physics of
the real mechanical and control systems, following the system
schematics and control specifications of the plant. Even though
this exact plant model cannot be publicly released for confiden-
tially reasons, the DC plant model available in the Buildings li-
brary represents a typical configuration in both equipment and
control. Following the proposed systematic methodology in this
8
research, others can tailor this generic model for their own case
studies, as done herein. While Modelica diagrams and model
details about the case study’s central plant can be found in [20],
the mathematical models for key equipment (chiller, cooling
tower, and pump) are as follows.
Chillers are modeled with the ElectricEIR model in the
Buildings library, which is based on the DOE-2 electric
chiller [55]. This model consists of three curves for the avail-
able capacity (CAPFT), full-load eciency (EIRFT), and e-
ciency as a function of chiller PLR (EIRFPLR), defined as
CAPFT =a1+b1TCH W +c1T2
CH W (15)
+d1TCW +e1T2
CW +f1TC HW TCW ,
EIRFT =a2+b2TCH W +c2T2
CH W +d2TCW +(16)
e2T2
CW +f2TC HW TCW ,and
EIRFPLR =a3+b3PLR +c3PLR2,(17)
where TCH W is the chilled water supply temperature, TCW is
the condenser water supply temperature, ai,bi,ci,ei,and fiare
regression coecients, and the PLR of the chiller is defined as
PLR ˙
Q
˙
Qre f CAPFT(TC HW ,TC W ),(18)
where ˙
Qis the chiller capacity and ˙
Qre f is the capacity at
the reference evaporator and condenser temperatures where the
curves come to unity.
Cooling towers are modeled based on the variable speed
Merkel model in EnergyPlus version 8.9.0 [56], which deter-
mines the total heat transfer between air and water entering
the tower based on Merkel’s theory. The fundamental basis
for Merkel’s theory is that the steady-state total heat transfer
d˙
Qtot is proportional to the dierence between the enthalpy of
air in the free stream haand the enthalpy of saturated air at the
wetted-surface temperature hs, represented by
d˙
Qtot =UdA
cp
(hsha),(19)
where cpis the specific heat of moist air at constant pressure, U
is the cooling tower overall heat transfer coecient, and Ais the
heat transfer surface area. For o-design conditions, Sheier’s
adjustment factors are included to modify the current UA value
with respect to the current wetbulb temperature, air flow rate,
and water flow rate. With these bases, the cooling tower per-
formance is modeled using the eectiveness-NTU relationships
for a counter-flow regime.
Contrary to many past DC modeling projects, this work in-
cluded pump models at the central plant that reflect the perfor-
mance curves of the installed equipment. For example, the case
study by Zabala et al. [15] assumed the pumping power was
negligible, since their energy consumption was much smaller
than the chillers. In contrast, the pumping power in this central
plant is far from negligible, as is shown in Section 6.1 below.
Indeed, pumping energy for large DC systems is often a major
contributor to the overall energy consumption, and others have
focused solely on dierent pumping configurations in order to
save energy [57].
Because pump models that use anity laws – change in pres-
sure pr(t)2, with r(t) being the rotational speed, and vol-
umetric flow rate ˙
V(t)r(t) – can lead to singular sets of
equations, we implement a composite pump model from the
Modelica Buildings Library that is consistent with anity laws.
To ensure that solutions to the dierential algebraic system of
equations posed by the thermo-fluid model can be computed
robustly and eciently by Newton-based solvers, the pump is
formulated in such a way that the resulting equations of the
fluid flow network has a unique solution in each operable re-
gion, and is dierentiable in all inputs. While complete details
for the pump formulation are available in [58], the fundamen-
tal formulation when the pump operates far from the origin is
as follows. Let δ=0.05 be a small number that is below the
typical normalized pump speed and S0
n={(˙
Vi,pi)}n
i=1be the
user-supplied performance data at full speed r=1, with ˙
Vi0
and pi0 for all i∈ {1,...,n}. Here, nrepresents the to-
tal number of operating points. For conditions r> δ (i.e., far
from the origin), the anity laws are satisfied while the maxi-
mum volumetric flow rate ˙
Vmax and maximum pressure change
pmax are linearly extrapolated as
˙
Vmax =˙
Vn˙
Vn˙
Vn1
pnpn1
pnand (20)
pmax = ∆ p1p2p1
˙
V2˙
V1
˙
V1.(21)
The fan performance curve for r(t)> δ is defined as
p+(r(t),˙
V(t)) =ˆp(˙
V(t)) +r(t)2h ˙
V(t)
r(t),S0
n!,(22)
with the curve end points represented by p+(1,˙
Vmax )=0 and
p+(1,0) = ∆pma x , while h(·,S0
n) is a cubic hermite spline that
maps ˙
Vto p, and ˆp(˙
V(t)) represents the model of flow resis-
tance approximated by a linear function as
ˆp(˙
V(t)) =˙
V(t)pmax
˙
Vmax
δ2
10 .(23)
In addition to conditions r> δ, Wetter [58] also defines formu-
lations for near origin (r< δ/2) and composite (r[δ/2, δ])
conditions to complete the pump model. Lastly, a set of
data points is defined for electrical power consumption P0
n=
{(˙
Vi,Pi)}n
i=1per the pump’s performance documentation. Total
eciency ηis then computed as
η=Wf lo
P,(24)
from the flow work Wflo and electrical power input P, with Wf lo
defined per the first law as
Wf lo =|˙
Vp|.(25)
In Figure 7, the CW pump curves used to define S0
nand P0
n
are shown as an example. When looking to revise flow set-
points during MC and/or FC modes, it is important to ensure
9
that the minimum flow does not surpass the minimum continu-
ous stable flow (MCSF) point. As an upper limit, the pump is
restricted by the maximum power of the motor. Further, there
are system-level limitations on the flow rate as well, including
the minimum flow required by the cooling towers to keep the
surfaces wetted, the minimum condenser flow required by the
chillers, and the minimum pump speed required to meet the
cooling towers’ static lift [59].
Figure 7: Condenser water pump performance curves for (a) electrical power
and (b) head pressure and eciency, adapted from manufacturer documents.
4.4. Connected Buildings
Because the CHW supply and return temperatures and the
mass flow rate are metered at the ETS, building models were
created to accept these tabulated data files directly. The build-
ing model (Figure 8) includes the district-side CHW piping and
equipment. The rejected heat from the building’s cooling equip-
ment is transferred to the district’s CHW at the ETS (using the
model Buildings.Fluid.HeatExchangers.Heater T). This model
measures the CHW supply temperature, and returns the CHW
based on the tabulated temperature dierence. The control
valve modulates the flow to match the tabulated mass flow rate
for each building.
As seen in Figure 8, the building-side HVAC systems (in-
cluding the primary CHW pumps), piping, and thermal zones
are not modeled. Therefore, the heat transferred at each build-
ing represents the metered heat flow rather than the cooling
loads at the thermal zones. Some limitations of this approach
are that (1) some design optimization between building and dis-
trict operation cannot be tested and (2) the thermal comfort at
the rooms cannot be verified. However, the simplification does
provide an accurate and numerically ecient implementation
for time series loads metered at the ETS, which is commonly
available among existing DC systems. Models to be added to
the library will include lumped thermal zone load models to
increase the flexibility of the modeling platform.
IntEHea
I
k=1
T
heaFloRat
TRet
+
+1
+1
k=-cp_default
gai
k=1/s
sca
M
PI
m_flow
+
TQ_flow
Cooling Heat
Flow Rate
Cooling
Energy
Tabulated
Energy Transfer Station
Inlet Port
Outlet Port
Control
Valve
PI Controller
Input
Figure 8: Diagram of the time series building model.
5. Verification and Validation
5.1. Electrical System
The central plant’s electric power was validated with histori-
cal metered data from the plant’s main electrical meter (see Fig-
ure 9) since there was no submetering for the central plant. The
extra power in the measurement includes HVAC for the plant,
the district heating plant, and other site loads. Within the limits
of expected uncertainty, the simulated DC power matched the
expected range of real central plant power from measured data.
The upper and lower limits of this expected power range were
determined using the methodology described in section 2.6.1.
While this approach was necessary in this case study based on
the available measured data, the validation could be improved
by installing submeters on major cooling equipment.
Figure 9: Validation results of the electrical system.
For equipment-level validation, the electrical power of each
equipment operated at or below their nominal rated power
throughout the entire annual simulation (Figure 10). The box
plot eectively depicts the distribution characteristics of each
equipment’s power consumption, normalized by the nominal
rated power of each equipment. In Figure 10, the thick middle
line represents the median, the upper and lower ends of the box
10
represent the upper and lower quartiles, the whiskers represent
power rates outside of the middle 50%, and the circles depict
the outliers. In this simulation, while the chillers, CW pumps,
and CHW pumps tended to run at low part load ratios (with me-
dian normalized powers less than 0.4), the cooling tower fans
frequently ran at full power, as exemplified by the median nor-
malized power near 1. When on, the cooling towers ran at full
power for 50% of the time, while they ran at part loads between
0.1 and 1 for 25% of the time.
Figure 10: Validation results of major central plant equipment.
5.2. Thermo-Fluid System
Two typical periods from summer (Aug. 1–14, 2018) and
winter (Jan. 28 – Feb. 11, 2018) seasons were selected for
thermo-fluid validation. The results are summarized in Table 2
for the summer period and Table 3 for the winter period. On an
hourly basis, the simulations fell within the acceptable ranges of
modeling uncertainty for all locations. Please note that the ac-
ceptable ranges per ASHRAE Guideline 14 [43] depend on the
measurement frequency (e.g., hourly, monthly) and other fac-
tors. The acceptable ranges quoted are specifically for hourly
calibration with whole building simulation. During the summer
period, the plant operated in MC mode with the chiller meeting
the entire cooling demand. The buildings were well controlled
across all data types, and temperature errors were small across
all locations.
During the winter period, the plant operated in FC mode,
with the WSE meeting the entire cooling demand. Two build-
ings (1 and 3) did not have a cooling load during this period,
and thus were excluded from winter validation. Similar to the
summer period, all simulation test locations fell within the ac-
ceptable ranges of modeling uncertainty, as seen in Table 3.
By validating the DC model across multiple layers and system
types, we can gain confidence in the model’s representation of
the real system for further energy analyses.
6. Results and Discussion
6.1. Baseline Energy Performance
In the annual simulation, the central plant consumed
552 MWh. As seen in Figure 11, the CW pumps repre-
sented the major energy consumer in the cold months, while
Figure 11: Baseline energy consumption results of the central plant by equip-
ment type.
the chillers were the major consumer in the hot months. Pro-
ducing 3,878 MWh of cooling energy for the year, the cooling
plant operated with an average COP of 7.03. The chillers, CW
pumps, CHW pumps, and cooling tower fans were responsible
for 41.4%, 37.1%, 10.8%, and 10.8% of the plant’s annual en-
ergy consumption, respectively. As expected, the plant’s energy
consumption was the highest in the summer, but a minimum
monthly load of 21.3 MWh was maintained (February 2018).
In colder seasons, the CW pumps dominated the plant’s energy
consumption for three main reasons: (1) two pumps run dur-
ing FC mode while only one pump runs during MC mode when
one chiller is on; (2) the CW pumps operate at a lower e-
ciency during FC than MC (as shown in Figure 7); and (3) the
CW side of the WSE has higher-pressure resistance compared
to the chiller’s condenser.
Figure 12 shows the detailed analysis of the central plant op-
eration for two sample windows during FC (Feb. 13–18, 2018)
and MC (Aug. 19–24, 2018) modes. During FC mode, the
plant’s overall kW/ton was higher than that during MC mode.
This surprising result is primarily due to (1) the lower cool-
ing load during FC (260 kW average during the mid-February
week compared to 2,700 kW during the late August week) and
(2) the higher power required for the CW pumps during FC
mode. Even though the cooling load is small during FC mode,
the plant still needs to run equipment at their minimum lim-
its. Conversely, the high-eciency, variable speed, variable
flow chillers during MC mode allow the chillers to operate at
higher eciency while serving larger cooling loads. During FC
mode, the cooling tower fans run periodically, but the plant of-
ten bypasses the cooling towers to maintain TCW,set. The cool-
ing tower bypass is used more consistently during MC mode,
largely because TCW,set is higher in MC than in FC mode. Fur-
ther, the CW mass flow rate through the WSE is consistently
and significantly greater than the CHW mass flow for both FC
and MC modes. This results in a very small Ton the CW
side compared to the CHW side for the WSE (Figure 12c) and
chillers (Figure 12f).
11
Table 2: Validation results for a typical summer period.
Location
CVRMSE (%) NMBE (%)
Acceptable Range: [0,30%] Acceptable Range: [-10,10%]
˙
QCHW ˙mCHW TCH WS TC HW R ˙
QCHW ˙mCHW TCH WS TC HW R
Plant 18.8 12.9 0.3 0.2 9.7 7.4 -0.1 -0.1
Chiller 22.2 15.5 0.2 0.3 8.7 7.4 -0.1 -0.1
Building 1 2.2 0.7 0.2 0.2 0.04 1.1 0.1 0.2
Building 2 2.4 0.1 0.2 0.2 0.02 0.6 -0.01 -0.02
Building 3 3.6 0.4 0.3 0.3 0.02 0.8 0.2 0.2
Building 4 1.3 0.7 0.2 0.2 -0.02 -0.1 0.04 0.04
Building 5 1.6 0.4 0.2 0.2 0.04 0.4 0.08 0.07
Building 6 2.2 0.5 0.2 0.2 -0.05 0.5 0.01 0.01
Table 3: Validation results for a typical winter period. Buildings with a ?had zero cooling demand during the winter period.
Location
CVRMSE (%) NMBE (%)
Acceptable Range: [0,30%] Acceptable Range: [-10,10%]
˙
QCHW ˙mCHW TCH WS TC HW R ˙
QCHW ˙mCHW TCH WS TC HW R
Plant 14.6 3.1 0.2 0.3 -0.2 2.5 0.1 0.1
WSE 15.6 3.1 0.3 0.2 7.3 2.5 0.1 0.1
Building 1?– – – –
Building 2 3.9 0.1 0.3 0.3 -0.02 0.3 -0.1 -0.1
Building 3?– – – –
Building 4 2.3 0.8 0.3 0.3 0.1 0.6 0.03 0.02
Building 5 10.0 1.4 0.3 0.3 0.2 6.3 0.1 0.1
Building 6 6.9 1.3 0.2 0.2 0.4 5.6 0.1 0.1
6.2. Energy Eciency Improvements
Several energy eciency measures were simulated based on
the validated baseline results. As demonstration cases, three
measures that do not require additional financial investments
were pursued: (1) optimizing TC W,set during MC mode, (2) as-
sessing the eectiveness of the WSE, and (3) revising the CW
pump flow rate setpoints during FC mode. The results and dis-
cussion from these cases are as follows.
6.2.1. Condenser Water Supply Temperature Optimization
As seen in Table 4, all three TCW,set optimizations reduced the
plant’s annual energy consumption by 2.5% to 4.4%. Both the
Baseline and the Fixed TCW,set optimization case (Equation 9)
have fixed temperature setpoints. Simply changing the fixed
TCW,set from 15.6C to 18.7C can save 2.5% energy. While
some engineers reduce TCW,set as low as possible (around 15C)
to allow the chillers to operate at a higher COP [60], there
is often a trade-obetween chiller energy and cooling tower
fan energy [61]. This trade-owas present in this DC simu-
lation. Raising TC W,set to a higher level caused chiller energy
to increase 5.5%, but saved 42.8% in cooling tower fan energy.
These results reinforce the need to consider the entire plant’s
operation when optimizing control setpoints.
Interestingly, the Fixed Tapp (Equation 10) and Adjusted Tapp
(Equation 11) optimizations produced equivalent energy sav-
ings, reducing the annual energy consumption by 4.4%. Other
researchers similarly studied Fixed and Adjusted Tapp based on
wetbulb and part load ratios; for example, Liu and Chuah [62]
found that optimizing the Adjusted Tapp (based on wetbulb,
chiller load ratio, and chiller and cooling tower fan performance
characteristics) saved more than 4% annual energy for chiller
plants without WSE, with the greatest savings occurring in cli-
mates with high seasonal variation of Twb. However, additional
savings from Fixed to Adjusted Tapp were not seen in this case
study, primarily due to the presence of the WSE and the central
plant’s control logics. In this DC system, the optimized TCW,set
is only applicable during MC mode; thus, the seasonal variation
in Twb and part load ratios were reduced to the warm MC sea-
sons only. Based on these results, it is recommended that the
plant control TCW,set based on a fixed Tapp of 1.9 K above Twb.
Table 4: Condenser water supply temperature optimization results.
Case
Optimized x Energy Savings
Variable Value (MWh) (%)
Baseline (no
optimization)
x115.6C551.8 –
Fixed TCW,set x118.7C537.9 2.5
Fixed Tapp x11.9C527.5 4.4
Adjusted Tapp
x12.1C527.5 4.4
x20.44
12
Figure 12: Detailed performance of central plant during FC (left) and MC (right) modes.
A few limitations of the TCW,set optimization should be noted.
First, we used a local optimization method, and it is possible
that only a local rather than the global optimum was found.
Future cases can use a hybrid approach to reduce the search
space with a global optimization method, before selecting a lo-
cal optimum. Second, the energy savings listed assume that the
measurements are ideal, but physical Twb sensors can be inac-
curate and prone to drift [63]. Thus, the energy savings from the
Fixed and Adjusted Tapp cases may be overstated. Despite this,
TCW,set based on wetbulb approach temperatures are adapted in
industry [18, 64, 25].
6.2.2. The Eectiveness of the Waterside Economizer
To evaluate the savings that the WSE can bring, we simu-
lated the same plant model but without the WSE. The results
are shown in Figure 13. Through this experiment, we deter-
mined that the nonintegrated WSE saves 6.9% of the plant’s
annual energy consumption. While these savings are notable,
the largest benefit of the WSE is the reduction in chiller run
time. With the nonintegrated WSE, the total run time of the
two chillers decreases from 373 to 172 days per year, which is
a 54% reduction. These large changes in run time extend the
service life of the chillers and reduce maintenance costs. Con-
versely, the total run times of the CW pumps and cooling towers
are higher by approximately 202 days each when the WSE is
added. This is because of the control specification that two CW
pumps run during FC mode, and a lower TCW,set is required to
meet the TCH WS setpoint with the WSE than with the chillers,
causing the cooling tower fans to run more often. While out of
the scope for this study, further energy eciency improvements
are likely possible by reconfiguring the WSE to be connected in
series with the chillers on the CHW side (e.g., integrated). An
integrated WSE is often the most energy ecient solution be-
cause it allows the WSE and chillers to share the cooling load
even when the WSE cannot handle the entire load [19, 12, 65].
Figure 13: Energy consumption and total running times of equipment for DC
system models with (baseline) and without the WSE.
6.2.3. Condenser Water Flow Rate Adjustments
With high CW pumping energy from the baseline model, we
tested various pump flow rates and staging configuration to re-
duce the annual pumping energy during FC mode. The tested
cases include operating one CW pump near its maximum flow
rate (1-CWP-126), one CW pump at 100 kg/s (1-CWP-100),
and two CW pumps at 50 kg/s each (2-CWP-50). As seen in Ta-
ble 5, the 1-CWP-126 case saved 5.2% energy, while the other
13
Table 5: Energy results when revising the condenser water flow rate setpoint
during FC mode. Flow rates given are per pump.
Case
CW Pump Settings Energy Savings
Qty. On Flow (kg/s) (MWh) (%)
Baseline 2 76 551.8
1-CWP-126 1 126 522.8 5.2
1-CWP-100 1 100 495.3 10.2
2-CWP-50 2 50 495.3 10.2
two cases saved 10.2%. In addition to energy savings, it is ben-
eficial to operate one pump instead of two when possible to
improve the pump service life and reduce maintenance costs.
Figure 14 provides further insight into the CW flow rate ad-
justments. Interestingly, the 2-CWP-50 case operates at the
lowest eciency during FC mode, around 34% on average.
However, the pumps are also operating at a lower power and
with higher temperature dierences across the CW-side of the
WSE, which results in higher energy savings. These results
fall in line with modern industry recommendations to decrease
CW flow rate while increasing the temperature dierence to
save operating costs [59]. Pump flow rate adjustments such as
these present practical cost-free retrofit measures that the cen-
tral plant can readily implement.
Figure 14: Detailed results of CW flow rate adjustments, including (a) the CW
temperature dierence, (b) the pump operating eciency, and (c) the total CW
pump electrical power.
6.3. Impact Evaluation
By improving the energy eciency of the DC system, addi-
tional cost savings and greenhouse gas reduction are achieved.
Figure 15 summarizes the results across all simulation cases.
All cases except for the case without the WSE reduced energy,
operating costs, and carbon emissions. From individual mea-
sures, the greatest cost savings came from the Fixed and Ad-
justed Tapp optimizations, primarily due to the larger decrease
in monthly peak powers. Meanwhile, the largest carbon savings
from individual measures came from changing the CW pump
flow settings during FC mode to 1-CWP-100 and 2-CWP-50.
It is important to note that the magnitude of the energy sav-
ings from individual measures (2-7%) can be considered insuf-
ficient with respect to the model accuracy. Thus, these results
do not suggest that the DC system operators should employ in-
dividual measures alone. However, the magnitude of energy
savings from combined measures is greater than the 10% min-
imum threshold recommended in international standards [66],
and thus were recommended to the system operators, who agree
with the findings. With combined measures of the Fixed Tapp
optimization and operating two CW pumps at 50 kg/s, the best
savings were achieved, reducing annual energy consumption by
84.6 MWh (15.3%), costs by $930 (8.9%), and carbon emis-
sions by 58.0 metric tons (15.0%). While the cost dollar sav-
ings appear low, this is because of the relatively cheap cost of
energy per the pricing structure stated in section 2.8.2. While
this work evaluated economic and climate impacts as byprod-
ucts of energy eciency strategies, future work can optimize
these impact factors directly.
Figure 15: Impact summary of studied energy measures including (a) total site
energy consumption, (b) peak power, (c) energy cost, and (d) carbon emissions,
all on an annual basis.
6.4. Numerical Performance
For this case study, all simulations ran using Dymola 2021
on a Linux operating system. The computer contained 32 GB
of RAM and a 3.60 GHz Intel®Xeon®CPU. With CVODE
14
Table 6: Number quantities of dierent features in the translated model with
respect to the number of buildings in the DC system model. Sizes of nonlinear
SOE are given after Dymola’s built-in model manipulation.
Number Number Continuous Dimension of
of of Time the Largest
Buildings Equations States Nonlinear SOE
6 7,291 123 11
12 11,283 195 17
18 15,275 267 23
24 19,267 339 29
30 23,259 411 35
60 43,219 771 65
90 63,179 1,131 95
120 83,139 1,491 125
solver and an integration tolerance of 106, the annual simula-
tion took just under 20 minutes. There were 13 nonlinear sys-
tems of equations (SOE) in the baseline model, and the largest
nonlinear system contained 11 iteration variables. The iteration
variables appearing in this largest nonlinear SOE consisted of
the CHW mass flow rates through the plant, major equipment
(CHW pumps, WSE, chiller), and each building connection, as
well as the pressure drop at the CHW bypass check valve.
As a scaling test, the simulation was repeated with the same
plant model connected to multiples of the six-building district
network (Table 6 and Figure 16). Across all simulation cases,
the total cooling demand at the plant was held constant to sat-
isfy system sizing requirements. The numerical problem con-
tained 13 nonlinear SOE, regardless of the number of buildings
(n). While the total number of nonlinear SOE was constant with
respect to n, the dimension of the largest nonlinear system in-
creased in size proportional to (n+5), i.e., linear. The number of
continuous time states also increased near linearly with respect
to n(more specifically, O(n0.85)). These two factors typically
have the greatest impact on computing time.
Shown in Figure 16, the computing time scaled by O(n2.1)
and O(s2.5), where srepresents the number of continuous time
states. Over the range of district sizes, the computing time
scaled closer to linearly when nwas less than 20, while the
quadratic to cubic scaling was present for districts larger than
20. With the given computer configuration (primarily limited
by RAM capacity of 32 GB), the maximum number of build-
ings possible was about 300.
While scalability studies are limited for DHC, a few previ-
ous studies involving small to medium sized districts present
similar results. Schweiger et al. [67] found that simulation
CPU time scaled linearly with the number of buildings; how-
ever, that study only evaluated small district sizes with two to
nine end users. Our results indicated similar trends, where dis-
tricts with one to 20 customers had linear scaling, and it was
not until medium sized districts were included that the results
scaled at higher orders. Similarly, Jorissen et al. [68] simu-
lated districts from 1 to 20 buildings and found computing time
scales quadratically with DASSL solver, while Euler integra-
tion scaled linearly.
Figure 16: Computing time, presented on a natural log-log (ln) scale, with
respect to (a) the total number of interconnected buildings and (b) the number
of continuous time states.
7. Conclusion
There is a growing interest and need to include district-scale
cooling in advanced modeling platforms. While Modelica has
been successful in chiller plants and district heating applica-
tions, DC applications remain scarce. This case study is one
of the first modeling and simulation studies to include detailed
plant thermo-fluid and control system models as well as repre-
sentational network piping hydraulics, both of which are critical
for detailed energy analysis. This contribution was enabled by
the Modelica language, which is often more adept than tradi-
tional tools to model and simulate complex, stithermo-fluid
system models with realistic controls, particularly when con-
sidering small system modifications through energy retrofit ac-
tions. We developed and open-source released new models
at the Buildings library to support DC analysis of this vari-
ety, which provided a foundation for the real-world case study
exemplified in this paper. Further, we aimed to include plant
configurations (e.g., the free cooling WSE) that are underrepre-
sented in modeling studies but common in practice, while also
addressing concerns for the suitability of large physics-based
Modelica models for large-scale district analysis (e.g., the scal-
ability tests).
The case study included detailed models of the central plant’s
mechanical and control systems, a complete network topology,
and simplified building models to reflect the thermo-fluid dy-
namics of the real-world system. This enabled us to quantify
practical energy eciency improvements that the system opera-
tors can readily implement. However in addition, it is important
to identify the impact of our engineering systems on humans
and the environment beyond energy consumption alone. To
this end, we evaluated the electricity costs, carbon emissions,
15
and equipment run time reductions as byproducts of the existing
system configuration and energy improvement strategies. The
best savings were achieved through combined measures of the
optimized Fixed Tapp and operating two CW pumps at 50 kg/s,
reducing annual energy consumption by 84.6 MWh (15.3%),
costs by $930 (8.9%), and carbon emissions by 58.0 metric tons
(15.0%), while the waterside economizer reduced the total run
time of chillers by 201 days/year. Future studies will expand on
this preliminary work to optimize both costs and environmental
impacts directly.
8. Acknowledgements
This material is based upon work supported by the U.S. De-
partment of Energy’s Oce of Energy Eciency and Renew-
able Energy (EERE) under the Advanced Manufacturing Oce,
Award Number DE-EE0009139. This work was also supported
by the Building Technologies Oce of the U.S. Department
of Energy, under contract numbers DE-AC36-08GO28308 and
DE-AC02-05CH11231. Further, this work emerged from the
IBPSA Project 1, an international project conducted under the
umbrella of the International Building Performance Simulation
Association (IBPSA). Project 1 will develop and demonstrate a
BIM/GIS and Modelica Framework for building and commu-
nity energy system design and operation. The authors would
also like to thank the campus facilities team for their assistance
with data collection, expert advice, and overall support of this
project.
Appendix A. Distribution Network Parameters
See Table A.1.
Table A.1: Distribution network sizing for each single pipe. The same sizing
applies to both supply and return pipes.
Segment No. Length (m) Nominal Diameter (cm)
1 31 45.7
2 31 20.3
3 27 45.7
4 26 20.3
5 31 45.7
6 104 25.4
7 18 15.2
8 85 15.2
9 77 45.7
10 109 20.3
11 225 20.4
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