While equation-based object-oriented modeling language Modelica can evaluate practical energy improvements for district cooling systems, few have adapted 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 network nor waterside economizers. 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 applies newly developed open-source models from the Modelica Buildings library. For a real-world case study, we modeled and simulated a district cooling system at a college campus in Colorado, United States, with 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 optimizing the condenser water supply temperature setpoint can save 2.5% to 4.4% energy; the nonintegrated waterside economizer saves 6.4% energy while cutting down the chillers’ run times by 201 days /year, reducing maintenance costs, and extending chiller life; and adjusting the condenser water pump flow settings can save 10.2% energy. Through a combination of the studied measures, the campus can annually save 84.6 MWh of energy, 8.9% of electricity costs, and 58.0 metric tons of carbon dioxide emissions. Further, the numerical results of simulating districts from tens to hundreds of buildings are presented. Keywords: District Cooling, Modelica, Modeling and Simulation, Waterside Economizer, Optimization, Numerical Performance 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 e fficient equipment, higher renewable energy integration). Computer modeling and simulation is an e ffective 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- ∗Corresponding author. Email address: wangda.zuo@colorado.edu (Wangda Zuo)mal storage, several heat rejection methods, and various pump- ing configurations) with TRNSYS for the plant /district simu- lation and HEV ACOMP /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-e ffect 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. First, current tools generally do not consider the hydraulics in the distribution network. However, in some systems hydraulics in the distribution network has shown to have significant im- pact on the pump energy consumption [7], can cause controlla- bility problems [8], and a ffect the e ffectiveness of the DC sys- tem. Second, current tools struggle to surmount the numerical hurdles of simulating large-scale models with fully-integrated plant, district, and controls. Thus, modeling simplifications had to be made by decoupling plant and district simulations or re- ducing the level of detail. Through these simplifications, many Preprint submitted to Applied Energy July 28, 2021 energy implications of real system features cannot be captured, such as the impact of system- and subsystem-level plant con- trol on the DC system’s transient power conditions. Lastly, many platforms, such as EnergyPlus or TRNSYS, require pro- grammers to manually write simulation code. Those programs are based on procedural languages (e.g., FORTRAN or C ++), which are characteristically slow for development of heteroge- neous cyber-physical models [9], including DC systems. This added task makes modeling and simulation of large, complex system models such as DC systems particularly burdensome. Modelica [10] is a modeling language, governed by an open standard, that can e ffectively address these limitations. As an equation-based, object-oriented, and acausal modeling lan- guage, Modelica allows engineers to build up complex system models using a graphical, hierarchical approach, from individ- ual equipment to subsystems and districts. From this represen- tation, simulation code is generated automatically. Equation- based acausal modeling has proven to significantly reduce model development time [9]. For applied energy projects, the development time reductions are particularly blaring when making small design modifications in an existing model to ex- plore di fferent energy e fficiency measures. Further, the Mod- elica community has rich open-source libraries, and the wide- variety of solvers available in Modelica simulation environ- ments allows the above-mentioned numerical challenges to be addressed. The case study by Zabala et al. [11] leveraged the benefits of Modelica for DC applications, creating reduced- order models of a chiller plant based on high-fidelity Modelica models for real-time, model predictive control (MPC) applica- tions. As part of this work, the District Cooling Open Source Library was publicly released [12]. While Zabala et al. [11] developed their chiller models from Modelica, they simulated the entire DC system externally using Python. This approach was highly e ffective for MPC, but numerous benefits of Mod- elica for DC analysis remain unexplored. Beyond this work, there is surprisingly very little Modelica-based research for DC analysis. Three principal contributions to DC modeling and simula- tion are made through this work. First, this is one of the first Modelica-based DC system modeling studies for detailed en- ergy analysis that considers hydraulics in the piping networks. As such, we documented our methodology on how to model and simulate complex DC systems including a detailed plant model, the network topology, and individual building thermal models. Through this study, we added newly developed models for district heating and cooling (DHC) analysis to the the Mod- elica Buildings library [13], an open-source library for build- ing energy and control systems. It should be noted that there are many similarities between heating and cooling at district- scale [14]. In addition, Modelica-based modeling of other DHC types such as combined heat and power or ambient wa- ter networks [7, 15, 16] and chiller plants in non-DC applica- tions [17, 18, 19, 20, 21] are also extensive. However, there is a general lack of publications on DC modeling and simula- tion [22]. Thus, applications of DC system analysis with Mod- elica is an important gap addressed by this paper. Second, we evaluate the control and energy performance of a chiller plantwith a waterside economizer (WSE) connected to a district net- work. The WSE is a “free cooling” heat exchanger that is a popular and e ffective way to improve chiller service life and re- duce plant energy consumption [23, 24, 25]. From a modeling standpoint, Modelica is particularly suited to capture the non- linearities present in chiller plants with WSE [26], which is not always possible with other tools. Despite their importance, to our best knowledge, others have yet to model DC systems fea- turing a WSE. This is another critical gap. Lastly, we evaluate the numerical performance (i.e., the scalability) of a detailed plant model connected to complete districts of several sizes. This is important to understand the capabilities and limitations of large Modelica models for DC analysis. These contributions are presented using a validated model of an actual DC system at a satellite campus of the Univer- sity of Colorado Boulder. Based on our previous work on this campus’s central plant [27], this study presents a system- atic methodology in modeling the DC system, adds models for the distribution network with individual building loads, and im- proves the central plant models. In addition, several energy efficiency measures that do not require capital investment are explored, including control setpoint optimization, assessing the effectiveness of the nonintegrated WSE, and adjusting pump setpoints. Furthermore, to quantify impacts beyond energy con- sumption alone, we also evaluate the financial and carbon emis- sion savings. While these measures were explored herein, it is important to note that the model can be used for other analysis as well, such as replacing the chillers or adding thermal storage, to name a few. Although out of the scope for this case study, other approaches such as these 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 workflow in section 2. The case study’s DC system is presented in section 3, followed by the corresponding Mod- elica models (section 4). After verification and validation of the DC baseline models in section 5, section 6 presents the baseline performance, energy e fficiency improvements including quan- tification 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 workflow for improving the energy performance of the DC system using Modelica, from problem definition to simulation-based impact evaluation. In principle, this workflow is suitable for any exist- ing DC systems with some degree of measured data available. The following sections describe each of the eight steps in this workflow. 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 2 Figure 1: Workflow of the proposed methodology for Modelica-based DC system impact analysis. 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 [28]. 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 thatthe 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 (20◦C) 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 0.1◦C 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 includes hydraulic sys- tem dynamics. Open-source libraries contain packaged mod- els from equipment through district-scale systems that can be adapted directly or modified for case study projects. We used models from the Buildings library version 7.0.0 [13] and the Modelica Standard library version 3.2.3 [29]. For DC sys- tems in particular, the Data Center package of the Buildings library [25] provides many equipment and subsystem models for chiller plants with and without WSE. Further, AixLib [30], IDEAS [31], and Building Systems [32] are all open-source li- braries suitable for DC system model development, in addition 3 to the District Cooling Open Source Library [12] previously mentioned. While models from these open-source libraries can often be used directly, it is common that custom system-level models need to be developed for the case study application. As such, we developed several new models for DHC analysis, which will be open source released in a future version of the Buildings library. This includes distribution network models from first through fifth generation DHC, standardized plant and building interconnections with interchangeable designs, and ex- amples of complete DHC systems. 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 [33] 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 [34], with its a graphical user interface IMPACT, is also available commercially. OpenModelica [35] and JModel- ica [36] provide open-source environments for Modelica-based modeling and simulation. While there are many suitable nu- merical solvers for solving DC system models, we frequently adopt CVODE [37] for its suitability for solving sti ffproblems. In our experience of adopting CVODE in Dymola, it typically simulates thermo-fluid systems quickly and robustly. We run all simulations using a tolerance of 10−6. 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 HV AC 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- efficient models [38], and then simulate them e ffectively [39]. 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 su fficient quantitative data at such scale [40]. While the uncertainty can have an averaging effect at district-scales for some features, it is potentially com- pounding for others [41]. 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 (HV AC) 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 PPlais given as PPla=PMea, (1) where PMeais the measured real power data from the electrical meter. To represent the lower limit PPla, we adjust PMeaby scaling factor σusing PPla=σPMea where (2) σ=fPDPla,iPDPla,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- torfof 1.25 is included to account for the likelihood of equip- ment operating at di fferent part load ratios. In this case study, σwas 0.42. An example of such analysis is shown in Figure 9. Forequipment-level validation, submetered data should be used if available. If not, 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 de- pict the annual distribution of power required for major equip- ment, normalized by their rated nominal powers. 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 [42], we evaluate both the Coe fficient of Variation of the Root Mean Square Error CVRMS E =qP(yi−ˆyi)2 N−1 ¯y, (4) and the Normalized Mean Bias Error NMBE =P(yi−ˆyi) (N−1)¯y, (5) where yiis the individual measured data, ˆ yiis the corresponding simulation data, ¯ yis the mean of the measured dataset, and Nis the total number of data points. With hourly data, the CVRMSE 4 and NMBE need to be within 30% and 10% respectively for the model to be considered validated [42]. 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 andequipment 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 e fficiency improvements for the DC system can be simulated to quantify their potential benefits. While providing guidance on which en- ergy e fficiency measures to select is out of the scope of this work, other literature provide comprehensive methodologies for identifying optimal energy e fficiency measures for build- ings [43] and control strategies for central plants [44]. 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 e ffectiveness 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,setoptimization, 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(TCW,set(x))=Zt2 t1(PCH(TCW,set(x),s)+ (8) PCW(TCW,set(x),s)+PCHW(TCW,set(x),s)+ PCT(TCW,set(x),s))ds, where xrepresents the free parameters to be tuned during the optimization process, EPlais the total plant energy during the optimization period t∈[t1,t2),PCHis the power of the chillers, PCWis the power of the CW pumps, PCHW is the power of the CHW pumps, PCTis 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, TCW,setis a fixed temperature (Fixed TCW,set) equal to constant x1; in Equation 10, TCW,setis a fixed approach temperature (Fixed Tapp) equal to x1offset from the measured ambient wetbulb temperature Twb; and in Equa- tion 11, TCW,setis an adjusted approach temperature (Adjusted Tapp) offsetx1from Twband scaled by x2based on the cen- tral plant’s part load ratio PLR. In this case study, optimization problems are solved for t∈[0,365) days with the Optimiza- tion library version 2.2.4 [45] using the local simplex method. Optimization and simulation tolerances of 10−5and 10−6re- spectively are used. 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 e fficiency is often represented by kW /ton. This is defined as the ratio of 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 e fficiency ratio. Similarly, the coe fficient of performance is used as an equipment or system e fficiency 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 di fferent energy e fficiency measures is often sensitive to the pricing program [46], 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 5 typical building life cycle impacts and its greenhouse gas emis- sions represent the largest impact category [47]. 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 (CO 2) is the dominating byproduct of fossil fuel-based electricity generation. Thus, it is reasonable to use CO 2as a proxy indicator. To calculate CO 2, Cambium’s datasets provide hourly cost and operational data for the U.S. electricity sector [48]. For this case study, we adopt Cambium’s 2018 Midcase Scenario data for the average CO 2 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). 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 [27]. CHW Supply CHW Return Central Plant Building 1 Building 5 Building 6 Building 4 Building 2 Building 3 1 102 34 56 7 89 11Figure 2: Network topology for the DC system. Details about the numbered pipe segments are given in the Appendix (Table A.1). 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 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. 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. 6 CHW Return from District Waterside EconomizerChillersCondenser Water PumpsCW Bypass Chilled Water Pumps CHW Supply to DistrictCHW BypassCooling Towers Check ValveTwo-Way ValveSump CWR CWSCHWSCHWRFigure 3: Schematic diagram for the central plant. 01000 2000 3000 4000 5000 6000 7000 8000 Number of Hours0100200300400500600700Cooling Load (kW)Building 1 Building 2 Building 3Building 4 Building 5 Building 6 Figure 4: Cooling load duration curves from 2018 measured data. 4. Modelica Implementation The DC system is modeled using the Modelica language and open-source components from the Buildings and Model- ica Standard libraries. New system and equipment-level mod- els were developed as part of this project, which will be open- source released in the Buildings library. The system models are presented in a top-down approach in the following sections. 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 sufficient resources to solve the problem. Through packaged hi- erarchical modeling, each major DC component can seamlessly TCWS,Set KpreTem freqHz=1/31536000TWetBulweaBusBuildings [:] Central Plant Weather Data Ground TemperatureDistribution NetworkMeasured dpFigure 5: Top level diagram of Modelica model for the DC system. 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 Twbis calculated. We assumed the tunnel temperature is the same as the ground three meters below the surface, rep- resented by a sinusoid ranging from 4 .6◦C (March) to 15 .9◦C (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 ofConnection models. Supply and return pipes between each connection are modeled as plug flow pipes (using the model Buildings.Fluid.FixedResistances.PlugFlowPipe ). Developed with DHC in mind, this pipe model e fficiently and accurately evaluates pipe pressure drop, heat losses through the distribu- tion network, and fluid transport delay. It also produced the smallest errors in comprehensive DHC experiments compared to other available models. More information about this pipe model can be found in [49]. 4.3. Central Plant The detailed central plant model represents the physics of the real mechanical and control systems. Modelica diagrams and model details about the central plant can be found in [27]. 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 7 m_flow p_relTT +-1 +1k=cp_defaultSupply to Supply PlantSupply to Downstream ConnectionsLossless PipeMass FlowHeat dT Supply PipeRate...Connection [1] ...Connection [2] Connection [6] BuildingsReturn from Buildings PortHeat Flow Rate Pressure Difference Return from Downstream Connectionsfrom Return Plantto Return PipeFigure 6: Hierarchical diagram of vector-style network interconnection model. study by Zabala et al. [11] 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 di fferent pumping configurations in order to save energy [50]. In Figure 7, the CW pump curves are shown as an example. When looking to revise flow setpoints during MC and /or FC modes, it is important to ensure that the minimum flow does not surpass the minimum continuous 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 con- denser flow required by the chillers, and the minimum pump speed required to meet the cooling towers’ static lift [51]. 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 di fference. The control valve modulates the flow to match the tabulated mass flow rate for each building. 40506070Power (kW)(a)Power FC Operating Point MC Operating Point 0 50 100 150 200 250 Mass Flow Rate (kg/s)200250300350400Head (kPa)(b) Head Pressure 0.00.20.40.60.8 Efficiency (%)EfficiencyMCSFFigure 7: Condenser water pump performance curves for (a) electrical power and (b) head pressure and e fficiency, adapted from manufacturer documents. IntEHea I k=1 TheaFloRat TRet ++1 +1k=-cp_defaultgai k=1/ssca MPI m_flow +T Q_flowCooling Heat Flow Rate Cooling EnergyTabulated Energy Transfer StationInlet Port Outlet PortControl ValvePI ControllerInput Figure 8: Diagram of the time series building model. As seen in Figure 8, the building-side HV AC 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 e fficient 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. 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 HV AC for the plant, 8 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. Aug 25 Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Aug 31 Date050100150200250300Power (kW)Upper Limit: PMea Lower Limit: PMea Total DC Plant Power (Simulated) Expected Range of Real DC Plant Power Figure 9: Validation results of the electrical system. Forequipment-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 e ffectively depicts the distribution characteristics of each equipment’s power consumption, normalized by the nominal rated power of each equipment. In Figure 10, the thick mid- dle line represents the median, the upper and lower ends of the box represent the upper and lower quartiles, the whiskers rep- resent 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, the cooling tower fans frequently ran at full power. Chillers CW Pumps CHW Pumps Cooling Towers0.00.20.40.60.81.0Normalized Power 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 forthermo-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 [42] 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 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 ffi- 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-e fficiency, variable speed, variable flow chillers during MC mode allow the chillers to operate at higher e fficiency while serving larger cooling loads. During FC 9 Table 2: Validation results for a typical summer period. LocationCVRMSE (%) NMBE (%) Acceptable Range: [0,30%] Acceptable Range: [-10,10%] ˙QCHW ˙mCHW TCHWS TCHWR˙QCHW ˙mCHW TCHWS TCHWR 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. LocationCVRMSE (%) NMBE (%) Acceptable Range: [0,30%] Acceptable Range: [-10,10%] ˙QCHW ˙mCHW TCHWS TCHWR˙QCHW ˙mCHW TCHWS TCHWR 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 JanFebMarAprMay JunJulAugSepOctNovDec Month020406080Monthly Site Energy (MWh)Chillers CW PumpsCHW Pumps Cooling T owers Figure 11: Baseline energy consumption results of the central plant by equip- ment type. 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,setis 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 FCand 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). 6.2. Energy E fficiency Improvements Several energy e fficiency 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 TCW,setduring MC mode, (2) as- sessing the e ffectiveness 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,setoptimizations reduced the plant’s annual energy consumption by 2.5% to 4.4%. Both the Baseline and the Fixed TCW,setoptimization case (Equation 9) have fixed temperature setpoints. Simply changing the fixed TCW,setfrom 15.6◦C to 18.7◦C can save 2.5% energy. While some engineers reduce TCW,setas low as possible (around 15◦C) to allow the chillers to operate at a higher COP [52], there is often a trade-o ffbetween chiller energy and cooling tower fan energy [53]. This trade-o ffwas present in this DC simu- lation. Raising TCW,setto a higher level caused chiller energy to increase 5.5%, but saved 42.8% in cooling tower fan energy. 10 0.00.51.0kW/ton(a) Total Efficiency 0100200kg/s(b) WSE Mass Flow Rates Feb 13 Feb 14 Feb 15 Feb 16 Feb 17 Feb 18 FC Mode5 0510C (c) WSE Temperatures0.00.51.0kW/ton(d) Total Efficiency Plant 0100200kg/s(e) Chiller Mass Flow Rates CHW CW Aug 19 Aug 20 Aug 21 Aug 22 Aug 23 Aug 24 MC Mode5101520C (f) Chiller Temperatures Ambient Wetbulb Entering CW Setpoint Entering CW Leaving CW Leaving CHW Setpoint Entering CHW Leaving CHWFigure 12: Detailed performance of central plant during FC (left) and MC (right) modes. 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 Tappbased on wetbulb and part load ratios; for example, Liu and Chuah [54] 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 Tappwere 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 inTwband part load ratios were reduced to the warm MC sea- sons only. Based on these results, it is recommended that the plant control TCW,setbased on a fixed Tappof 1.9 K above Twb. Table 4: Condenser water supply temperature optimization results. CaseOptimized x Energy Savings Variable Value (MWh) (%) Baseline (no optimization)x1 15.6◦C 551.8 – Fixed TCW,set x1 18.7◦C 537.9 2.5 Fixed Tapp x1 1.9◦C 527.5 4.4 Adjusted Tappx1 2.1◦C527.5 4.4x2−0.44A few limitations of the TCW,setoptimization 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 Twbsensors can be inac- curate and prone to drift [55]. Thus, the energy savings from the Fixed and Adjusted Tappcases may be overstated. Despite this, TCW,setbased on wetbulb approach temperatures are adapted in industry [23, 56, 18]. 6.2.2. The E ffectiveness 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,setis required to meet the TCHWS 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 e fficiency improvements are likely possible by reconfiguring the WSE to be connected in 11 200 250 300 350 400 450 500 550 600 Equipment On Time (days)50100150200250300350Annual Energy (MWh)2 Chillers 2 CW Pumps3 CHW Pumps 2 Cooling Towers Baseline No WSEFigure 13: Energy consumption and total running times of equipment for DC system models with (baseline) and without the WSE. Table 5: Energy results when revising the condenser water flow rate setpoint during FC mode. Flow rates given are per pump. CaseCW 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 series with the chillers on the CHW side (e.g., integrated). An integrated WSE is often the most energy e fficient solution be- cause it allows the WSE and chillers to share the cooling load even when the WSE cannot handle the entire load [24, 26, 57]. 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 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 e fficiency during FC mode, around 34% on average. However, the pumps are also operating at a lower power and with higher temperature di fferences 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 di fference to save operating costs [51]. Pump flow rate adjustments such as these present practical cost-free retrofit measures that the cen- tral plant can readily implement. 0.00.51.01.52.02.5Temperature Difference (C) (a)Baseline 1-CWP-1261-CWP-100 2-CWP-50 30405060Efficiency (%)(b) Feb 10 Feb 11 Feb 12 Feb 13 Feb 14 Feb 15 Feb 16101520253035Electric Power (kW)(c)Figure 14: Detailed results of CW flow rate adjustments, including (a) the CW temperature di fference, (b) the pump operating e fficiency, and (c) the total CW pump electrical power. 6.3. Impact Evaluation By improving the energy e fficiency 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 en- ergy, operating costs, and carbon emissions. From individual measures, the greatest cost savings came from the Fixed and Adjusted Tappoptimizations, primarily due to the larger de- crease in monthly peak powers. Meanwhile, the largest car- bon savings from individual measures came from changing the CW pump flow settings during FC mode to 1-CWP-100 and 2-CWP-50. With combined measures of the Fixed Tappopti- mization and operating two CW pumps at 50 kg /s, the best sav- ings were achieved, reducing annual energy consumption by 84.6 MWh (15.3%), costs by $930 (8.9%), and carbon emis- sions by 58.0 metric tons (15.0%). While the cost dollar sav- ings appear low, this is because of the relatively cheap cost of energy per the pricing structure stated in section 2.8.2. While this work evaluated economic and climate impacts as byprod- ucts of energy e fficiency strategies, future work can optimize these impact factors directly. 6.4. Numerical Performance For this case study, all simulations ran using Dymola 2021 on a Linux operating system. The computer contained 32 GB 12 450500550600Energy (MWh)(a) 250260270280Peak Power (kW)(b) Simulation Cases925095009750100001025010500Cost ($)(c) Baseline No WSE Fixed-Tapp + 2-CWP-50Fixed Tcw,set Fixed Tapp Adjusted Tapp1-CWP-126 1-CWP-100 2-CWP-50Simulation Cases320340360380400420CO2 (metric tons)(d)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. of RAM and a 3.60 GHz Intel®Xeon®CPU. With CVODE solver and an integration tolerance of 10−6, 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 ton(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) andO(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. [58] found that simulation CPU time scaled linearly with the number of buildings; how- ever, that study only evaluated small district sizes with two toTable 6: Number quantities of di fferent 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 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ln of Number of Buildings681012ln of Computing Time (s) (a) Power Relationship of 2.1 Simulations 4.5 5.0 5.5 6.0 6.5 7.0 7.5 ln of Number of Continuous Time States681012ln of Computing Time (s) (b) Power Relationship of 2.5 Simulations 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. 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. [59] simu- lated districts from 1 to 20 buildings and found computing time scales quadratically with DASSL solver, while Euler integra- tion scaled linearly. 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. The primary intention of this work was to fill this gap while comprehensively including underrepresented plant configurations in DC modeling (e.g., the 13 free cooling WSE) and addressing concerns for the suitability of large physics-based Modelica models for large-scale district analysis (e.g., the scalability tests). A systematic methodology is presented from understanding the problem through evaluat- ing system improvements when using Modelica for advanced energy and control analysis of DC systems. In this case study, we included detailed models of the central plant’s mechanical and control systems, a complete network topology, and simpli- fied building models to reflect the thermo-fluid dynamics of the real-world system. This enabled us to quantify practical energy efficiency improvements that the system operators can readily implement. All the while, the object-oriented nature of Mod- elica allows the models to be quickly reconfigured for future studies, such as integrating the WSE, adding thermal storage, or testing novel control schemes featuring deeper building-to- thermal-grid interaction. Beyond energy consumption alone, it is important to identify the impact of our engineering systems on humans and the envi- ronment. To this end, we evaluated the electricity costs and car- bon emissions as byproducts of the existing system configura- tion and energy improvement strategies. The best savings were achieved through combined measures of the optimized Fixed Tappand operating two CW pumps at 50 kg /s, reducing an- nual energy consumption by 84.6 MWh (15.3%), costs by $930 (8.9%), and carbon emissions by 58.0 metric tons (15.0%). Fu- ture 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 O ffice of Energy E fficiency and Renew- able Energy (EERE) under the Advanced Manufacturing O ffice, Award Number DE-EE0009139. This work was also supported by the Building Technologies O ffice 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.