Modeling and optimization of building mix and energy ...

Applied Energy 159 (2015) 161–177

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Modeling and optimization of building mix and energy supply technology for urban districts Robert E. Best ⇑, Forest Flager, Michael D. Lepech Stanford University, Department of Civil and Environmental Engineering, 473 Via Ortega, Stanford, CA 94305, United States

h i g h l i g h t s
Modeled variation of building mix and energy supply technology endogenously.
Optimized district-scale energy supply and demand simultaneously.
Case study with CHP engines, chillers, and 21 building types run for San Francisco.
Potential to achieve over 70% efficiency with low carbon emissions and low cost.
Ability to provide decision support for urban planners and infrastructure designers.

a r t i c l e

i n f o

Article history: Received 28 March 2015 Received in revised form 14 August 2015 Accepted 17 August 2015

Keywords: District energy systems Multiobjective optimization Genetic algorithm Combined heat and power Energy modeling

a b s t r a c t Reducing the energy consumption and associated greenhouse gas emissions of urban areas is paramount in research and practice, encompassing strategies to both reduce energy consumption and carbon intensity in both energy supply and demand. Most methods focus on one of these two approaches but few integrate decisions for supply and demand simultaneously. This paper presents a novel model that endogenously simulates energy supply and demand at a district scale on an hourly time scale. Demand is specified for a variety of building uses, and losses and municipal loads are calculated from the number of buildings in the district. Energy supply is modeled using technology-specific classes, allowing easy addition of specific equipment or types of energy generation. Standard interfaces allow expansion of the model to include new types of energy supply and demand. The model can be used for analysis of a single design alternative or optimization over a large design space, allowing exploration of various densities, mixes of uses, and energy supply technologies. An example optimization is provided for a community near San Francisco, California. This example uses 21 building types, 32 combined heat and power engines, and 16 chillers. The results demonstrate the ability to compare performance tradeoffs and optimize for three objectives: life cycle cost, annual carbon dioxide emissions, and overall system efficiency. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Motivation Cities occupy 3% of the earth’s land area, yet consume 75% of natural resources and produce 60–80% of global greenhouse gas emissions [1]. These impacts will grow as urbanization increases from 54% of world population today to 66% by 2050 [2]. In the

⇑ Corresponding author at: John A. Blume Earthquake Engineering Center, Stanford University, 439 Panama Street, Stanford, CA 94305, United States. Tel.: +1 (818) 456 6919. E-mail addresses: [email protected] (R.E. Best), [email protected] (F. Flager), [email protected] (M.D. Lepech). http://dx.doi.org/10.1016/j.apenergy.2015.08.076 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

United States, urban buildings and infrastructure consume 33% of energy and produce 40% of national greenhouse gas emissions [3]. This drives a need to reduce emissions, which comes at a cost; the Intergovernmental Panel on Climate Change Fourth Assessment Report projected that buildings and fuel switching can reduce greenhouse gas emissions 36–56% by 2020 at a cost ranging from $0 to $100/ton CO2 [4]. A common response is to address energy supply and demand independently through regulation and voluntary certification. In practice, a proliferation of voluntary and prescriptive green building codes (e.g., Leadership in Energy and Environmental Design (LEED) [5], Living Building Challenge [6], California Green Building Standard [7]) have attempted to improve the efficiency of new and retrofitted buildings through quantitative and

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qualitative standards. Reducing the carbon intensity of energy supply has involved a combination of renewable energy mandates and financial incentives [8]. However in both research and practice, few methods exist to help planners and policymakers trade off solutions for balancing energy supply and demand interventions simultaneously. Balancing energy supply and demand can also happen at a local district or community scale. Herein, ‘‘district or community scale” is defined as 102–103 neighboring buildings with peak power consumption generally on the order of 101–102 MW; this is similar to the scale of district networks examined by Rezaie and Rosen [9]. A recent proliferation of rating systems has attempted to incentivize sustainable community development through point-based certification (e.g., LEED for Neighborhood Development [10], Sustainability Tools for Assessing and Rating Communities [11]). However these systems lack a comprehensive method for valuing tradeoffs between demand and supply interventions. This is in part because of a lack of modeling ability; a survey of urban energy system models by Keirstead et al. [12], showed that only a small number of models consider energy supply and demand endogenously, with the majority using qualitative decision making techniques rather than quantitative evaluation of economic and environmental benefits. This paper describes one approach to balancing interventions in energy demand and supply and valuing the environmental and economic benefits. 1.2. Prior research A review of literature on urban and community energy system models revealed the following four criteria for a tool to be useful in balancing urban planning and energy infrastructure development. An ideal tool should: (1) Endogenously simulate and vary energy supply and demand: Keirstead et al. [12], following the definition laid out by Jaccard [13], emphasize that an urban energy model should capture both supply and demand within a local context considering energy production, storage, transportation, and conversion to end service. (2) Be capable of accurately assessing the dynamics of energy systems at a district or community scale: Jaccard [13] stressed that the scale for simulation must be community-based to capture the observed gaps in supply and demand modeling and to match the scale of planning and zoning. (3) Simulate on no greater than an hourly time scale: Evins et al. [14] and Hawkes and Leach [15] showed that networked systems require hourly analysis to capture spikes in demand and ramping effects of generators that can dramatically impact performance and efficiency. (4) Be easily adapted to new energy supply and building technologies: Van Dam and Keirstead [16] and Manfren et al. [17] argued that an urban energy model must be capable of incorporating a broad spectrum of technologies and should leverage existing methodologies through a common ontology. Existing tools and methods documented in literature generally address only a subset of these characteristics and can be characterized by their focus on community or district-scale energy supply optimization, building and urban energy demand modeling, and combined energy supply and demand models. 1.2.1. Energy supply literature Community energy supply modeling predominantly involves simulation and optimization of district heating and cooling systems. Liu et al. [18] provides an overview of combined cooling, heating and power (CCHP) technologies and systems that have

been implemented at the community scale as well as the management, control and optimization of these systems. Vasebi et al. [19] and Merkel et al. [20] examine dispatch of an interconnected, community-scale grid powered by multiple combined heat and power (CHP) plants; Evins, Pointer, and Vaidyanathan devised a similar approach using a logic tree and a harmony search algorithm (2011). Casisi et al. [21] extend from purely dispatch to include optimization of location of CHP microturbines and a central power plant in Italy. Chinese and Meneghetti [22] use a mixed integer linear program to optimize deployment and operation of boilers in an Italian district heating system. Nuytten et al. [23] presents a method to determine the theoretical maximum of flexibility of district CHP systems and discusses the implications for various energy storage concepts for a reference district. Many studies have also examined planning and economics of district energy systems. Gustafsson and Karlsson [24], Fu et al. [25], and Sugihara et al. [26] simulated district heating systems using CHP plants in Sweden, China, and Japan, respectively. All three showed that cost and energy could be reduced by approximately 20%. CourchesneTardif et al. [27] used the TRNSYS software to simulate community-scale district heating and solar thermal under various policy scenarios. Keirstead et al. [28] examined the effect on system cost and energy efficiency of different policy restrictions on CHP plant location using a mixed integer linear program. Orehounig et al. [29] describes a method of decentralized energy systems at neighborhood scale using the energy hub concept, which is used to study a variety of energy supply configurations for a village in Switzerland considering energy autonomy and CO2 emissions. In addition to these studies, Connolly et al. [30] identified 37 software tools currently available for planning or evaluating distributed energy resources, CHP installations, and district energy systems. They noted large diversity among these tools in scale of analysis, technologies considered, and objectives evaluated. Yet a common thread in these tools and the aforementioned studies is the focus on supply without the ability to modify or examine the impact of energy demand on cost, efficiency, and environmental impact. 1.2.2. Energy demand literature Energy demand modeling often has taken the form of simulating individual buildings using available software packages (e.g. EnergyPlus, eQuest, TRACE) [31]. In some cases this has been extended to parametric evaluation of building performance [32] or to optimize building form to minimize cost and environmental impact [33]. Nguyen et al. [34] provides a comprehensive review of simulation-based methods the have been applied to optimize energy performance at the building scale. Yao [35] studied how to optimize the building design for different housing units to minimize both the total demand of the development as well as the differences in consumption between individual housing units. Salat [36] used building energy modeling to demonstrate the role of massing and neighborhood morphology on individual building energy consumption. However, in general, Markovic et al. [37] found that no existing energy modeling tools assess community energy demand and the impact of policy scenarios. Jennings et al. [38] created a model to examine the deployment and impact of policies governing thermal and electrical energy retrofits for houses in London using a mixed integer linear program. From an urban planning and energy system perspective, Chow et al. [39] examined the mix of five building types that optimally diversified cooling load to maximize the efficiency of a district cooling system in Hong Kong. Fonseca and Schlueter [40] characterized electricity, heat, and cooling consumption patterns of buildings over a year to understand the role of location and building type in consumption. They used this to suggest energy efficiency upgrades and participation in district heating loops to reduce energy consumption and

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utilize waste heat. All of these studies allow better understanding of energy demand characteristics but do not balance demand measures with tradeoffs in energy supply. 1.2.3. Integrated energy supply and demand literature Relatively few studies have attempted to create a comprehensive model for energy supply and demand at a community-scale. Manfren et al. [17] reviewed existing models and found none capable of handling the full range of community scale energy supply and demand options. Keirstead et al. [12] mention only a small number capable of endogenously handling urban energy supply and demand models. Robinson et al. [41] created CitySim to simulate energy supply and demand using simplified models of thermal loads, radiation, and occupant behavior coupled with models for distributed solar power and district heating. The model was demonstrated on a case study in Switzerland but not used to evaluate or choose between multiple scenarios despite its documented optimization ability. Gang et al. [42] modeled both the buildings and the cooling systems for a new district in Hong Kong in order to compare central cooling system options with that of individual buildings; although it included detailed building energy models, the current building plan was assumed and scope of the study did not include any decisions which affected energy demand. Keirstead et al. [43] presented the SynCity model which can optimize the layout of zoning blocks simultaneously with the choice of energy supply technology and district thermal piping layout. For an eco-town plan in the United Kingdom, they documented a 39% reduction in transportation and energy services costs with the optimized layout. This approach, however, only samples representative periods in the year and does not allow analysis of individual buildings, limiting its resolution and applicability to smaller geographic scales. 1.3. Objective This paper documents a novel model for endogenously simulating supply and demand of heating, cooling, and electricity within any district, community, or sub-city geographic area on the order of 102–103 buildings and 101–102 MW peak electrical demand. The approach is comprised of modules that are easy to adapt to any climate, building typologies, and energy supply technologies that may exist or be proposed for study in the location desired. An iterative solver is used to calculate hourly energy demand and supply conditions based on internally calculated energy load profiles and control schema that leverage native energy supply modules. The method can be used to directly compare scenarios in the same or different geographic locations and is scalable to larger and smaller development sizes within the aforementioned range. Furthermore, it provides decision support by employing an evolutionary algorithm to rapidly search thousands of solutions and find improved solutions along multiple objectives. 2. Model development A model was developed in the Python programming language to simulate energy supply and demand of a community for any combination of building uses and energy supply technologies. The model uses a modular, dynamic framework to allow easy addition, deletion, or modification of building types and energy supply technologies. This flexibility is important as the model is intended for use as an early stage planning tool to facilitate understanding of tradeoffs in selection of a wide range of building types, energy demand characteristics, and energy supply equipment. Simulation is performed over 8760 h to capture seasonal and intra-day effects of energy ramping and spikes in energy demand. This construction

allows the model to meet the four criteria laid out previously for an effective urban energy model. The model is constructed using three modules: (1) energy demand simulation, (2) energy supply characterization and dispatch, and (3) analysis and optimization. Standardization of the module interfaces creates a flexible framework that simplifies addition or modification of any proposed supply and demand equipment or additional building types. Fig. 1 provides a graphical overview of the model architecture. Inputs are noted by boxes with solid shading, and outputs are noted by the diagonal striped boxes. Decision variables (half shaded and half white) can be either user-controlled inputs for single analysis runs or controlled by the optimization module. The supply and demand modules provide the interface with the user and aggregate inputs into a community energy profile and energy supply resource stack based on the decision variables. Inputs to the demand module include hourly column vectors of heating, cooling, and electricity loads for every building type to be considered. These vectors are aggregated into a single look-up table for analysis and optimization. The size of this look-up table is flexible to accommodate larger and smaller numbers of buildings to accommodate the requirements of a particular study. The demand module also calculates distribution losses in the energy system and municipal electrical demand for street lighting. Inputs to the supply module include operating and design parameters based on performance data for each supply technology. Class objects per technology type specify required inputs and allow easy addition of new pieces of equipment. Unit dispatch is controlled in the supply module. Classes and additional dispatch requirements can be added using a common input/output framework to accommodate any technology desired for a particular study. The analysis and optimization module uses the lookup tables and supply class objects to determine annual cost, emissions, and Total Fuel Cycle Efficiency (TFCE). Optimization is performed through an evolutionary algorithm that improves performance according to one or more objectives specified in the analysis. The optimization parameters can be adjusted by the user, and constraints can be added to represent accurately the location being studied. When optimization studies are being performed, the optimization module controls the decision variables. The following sections describe in detail each of the three modules, their components, inputs, and outputs. Each section also describes the specification of the modules for an illustrative test case based loosely on a proposed mixed-use residential, commercial, and light industrial development in San Francisco, California, US. Further description of the test case, results, and analysis are presented in Section 3. 2.1. Demand module The demand module is used to create a load profile for the community. A profile is created for every configuration of building decision variables selected by the user or the optimization module. The demand module operates by taking as input hourly load profiles of electricity, heating, and cooling for all building typologies specified by the user. These can either be simulated profiles from an energy modeling software (i.e., EnergyPlus, eQuest, or TRACE), or direct measurement of building energy consumption. Heating, cooling, and electricity consumption are required. Individual building energy consumption data is then stored as a look-up table. Each entry denotes a specific building type and *

*

contains three vectors, one each for heating, Hi , cooling, C i , and *

electricity, E i . Note that the index i denotes each individual building. In addition to energy data, metadata including building size, dimensions, number of stories, and use type are required inputs.

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Fig. 1. Block diagram of the community energy systems model. Each block represents a major process or decision in the model. Gray blocks indicate user inputs as part of model setup, diagonally striped blocks indicate outputs. Decision variables are shown in both gray and white indicating that they are inputs when a single analysis is run and controlled by the program in optimization runs. The three main modules (supply, demand, and analysis and optimization) are noted with dashed boxes.

The demand decision variables, bi, represent the number of each building type (denoted by the subscript i) in the community. These values are used to construct the overall electricity, heating, and *

*

*

cooling load profile vectors for the community, E C , HC , and C C through summation over i of the decision variables and the building demand profiles for all B buildings in the study as shown in Eqs. (1)–(3). *

EC ¼

B X * bi E i

ð1Þ

i¼1

*

HC ¼

B X * bi H i

ð2Þ

i¼1

*

CC ¼

B X * bi C i

pipe [45]. Following the breakdown of losses provided by Mungkung et al. [46] and the assumption that 6% of electricity is lost in transmission and distribution in the United States [47], electrical loss is assumed to be 5% of total electrical demand. Losses are added to the community energy demand profiles, and the output *

*

*

of the demand module is the set of E C , HC , and C C vectors representing the final community energy demand inclusive of municipal demand and distribution losses. It should be noted that pumping loads for distribution of hot and chilled water from the central power plant are included as internal loads for the energy supply infrastructure and not accounted for separately. Furthermore, it should be noted that assumptions about loss are encoded as parameters that can be altered for different contexts (e.g., different locations with different ground temperatures, added pipe insulation, different electrical grid topology).

ð3Þ

i¼1

An adjustment is added to the community electricity load profile to account for municipal demand for street lighting. The length and width of each building are upsized by 5% to account for site area outside the building perimeter. A weighted average site length and width is then calculated based on the ratio of the bi variables and used to calculate street frontage per block. Blocks are assumed to be comprised of 8 buildings, meaning that street frontage for each block is 16 lengths and 4 widths. Lighting demand is constructed following a schedule based on the City of San Jose, California, Public Streetlight Design Guide [44]. It is assumed that all roadways fall into the classification of collector roads requiring 9450 lumens which mandates 190 W low pressure sodium lights on both sides of the roadway spaced 48.8 m apart. An adaptive street lighting schedule is assumed whereby lighting power is reduced to 50% between 2 am and 7 am. Calculation of community energy demand vectors and municipal lighting loads are repeated for each analysis or optimization run using the same look-up tables. Distribution losses are calculated based on the total number of buildings in each analysis. An average distance between buildings was calculated to be 35 m given the sizes of the buildings used for the case study. In general, the average distance can be calculated from the length and width of the building lots. A loss factor of 3 W/m of pipe was assumed for heating distribution, and a loss factor of 17 W/m of pipe was assumed for cooling distribution; these assume an insulated hot water pipe and an uninsulated cold water

2.1.1. Demand module construction for the test case For the test case, 21 building types were used that varied use type, density, and building form. Fifteen of these were taken from the DOE Commercial Prototype Buildings dataset, which is based on the results of the Commercial Building Energy Consumption Survey [48]. A single-family house model generated by the DOE from the results of the Residential End-Use Consumption Survey was also used [49]. To construct three high-density, mixed-use buildings, parameters from three of the DOE prototypes were combined and zoned by floor such that retail occupied the ground story and commercial or residential occupied the upper stories. Table 1 provides a summary of the building types used in the test case and the metadata for each. Each building was constructed from the parameters provided by DOE and simulated in EnergyPlus v. 8.0.0 [50]. EnergyPlus was chosen as it has been shown to simulate a variety of buildings with greater accuracy than other commercial energy modeling programs [51]. 2.2. Supply Module The supply module utilizes a set of classes to define objects representing different types of energy supply equipment (heating, cooling, and electricity supply). These objects calculate the hourly performance and cost of satisfying energy loads. The user is required to specify, add, or modify objects to include all energy supply technologies desired for a given analysis or optimization.

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R.E. Best et al. / Applied Energy 159 (2015) 161–177 Table 1 Types of buildings and their massing parameters used in model for the test case. Building

Footprint (m2)

Number of stories

Building length (m)

Building width (m)

Residential High Rise Condo Residential Midrise Apartment Residential Townhouse Residential Single Family House Large Office Medium Office Small Office Retail Strip Mall Stand Alone Retail Full Service Restaurant Quick Service Restaurant Supermarket Warehouse Large Hotel Small Hotel Hospital Outpatient Building Primary School Secondary School Mixed Use Condo and Retail Mixed Use Large Office and Retail

9405 3135 392 223 46,320 4982 511 2090 2294 511 232 4181 4835 11,345 4013 22,422 3804 19,592 6871 9405 46,320

12 4 2 1 12 3 1 1 1 1 1 1 1 6 4 5 3 1 2 12 12

56.0 56.0 28.0 14.9 76.1 49.9 27.7 91.4 54.6 22.6 15.2 79.2 103.1 84.8 54.9 76.4 42.1 171.4 71.8 56.0 76.1

14.0 14.0 7.0 14.9 50.7 33.3 18.5 22.9 42.0 22.6 15.2 52.8 46.9 22.3 18.3 58.7 30.1 114.3 47.9 14.0 50.7

Each class represents a single type of energy supply technology (e. g., CHP engines, chillers, photovoltaic panels, ground-source heat pumps, etc.). All objects within a class use a common analysis methodology which standardizes inputs and outputs. Required inputs consist of equipment characteristics, and outputs include heating, cooling, and electricity generated, parasitic losses in the equipment, cost, and emissions. Analysis methodologies differ between classes, meaning that addition of a new technology requires formulating an analytical approach that satisfies the standard inputs and outputs. Adding objects within an existing class only requires specification of a standard set of parameters for the new object. Decision variables used in the analytical framework specify which object from each class (if any) are used in a given analysis. It is assumed that only one technology from each class is used for any given run. It would be possible in future work to allow a variety of technologies to be used from a single class. A control methodology in the supply module determines what portion of the community demand is allocated to each supply object, similar to a dispatch model for an electrical grid. For objects requiring further control on operating parameters, such as those that provide heating and electrical service, additional control methods are used to accurately simulate generation. The output of the supply module is a set of vectors over all hours, t, representing the generated *

*

*

electricity, E S , heat generated HS , cooling generated C S , operating cost OE, capital cost CE, fuel required, F, and carbon dioxide emitted CO2. The test case for the model used only two classes of technologies: CHP engines and chillers. To illustrate the creation and validation of class objects, the modeling approach taken for these components is provided in detail, as is the control methodology for dispatching the units. 2.2.1. Combined heat and power equipment models As described in Section 2.3, the initial model contains only a single class of CHP engines that services electricity and heat loads. 32 CHP engines of 7 different engine types and fuel sources were modeled as a single class. Engines were grouped by prime mover type and fuel source, and within a given engine type, individual engine options differed primarily by capacity and power-to-heat ratio. This differentiation is designed to reflect the market availability of different CHP engines as well as allow for suitability to a wider range of district development sizes. Characteristics for

these engines were taken from the Environmental Protection Agency (EPA) ‘‘Catalog of CHP Technologies” [52] and ‘‘Catalog of Biomass CHP Technologies” [53]. Table 2 provides a breakdown of these 32 engines. The selected engines provided a sample of common types of CHP engines, as well as emerging low carbon technologies. The engine model was created as a six step process for each class of engine. Equations for each step including all required inputs are presented in Appendix A: (1) Manufacturer provided capacity is adjusted based on the altitude of the site and hourly ambient temperature. This adjustment is calculated using a linear regression based on manufacturer data. Fig. 2a shows an altitude regression plot, and Fig. 2b shows an air temperature regression plot for a gas turbine. (2) Based on the engine class, internal electrical consumption from gas compression is calculated. Incoming gas line pressure is assumed to be 480 kPa unless otherwise provided. Internal electrical consumption for pressurizing gas is treated as a parasitic load and added to the electrical demand for the given time period; it must be satisfied along with the external load for the simulation to be valid. (3) Operating point is calculated based on the number of CHP engines required in the current time period and the part load ratio (PLR). The engines are assumed to operate in parallel, so that load is equally shared. A class-specific cubic

Table 2 Types of CHP engines, fuel sources, and the number of each specific technology used in the model for the test case. Different options within an engine type are differentiated by capacity and power-to-heat ratio. Engine type

Fuel source

Number included

Gas Turbine Microturbine Reciprocating Engine Steam Turbine Fuel Cell Stoker Boiler/Turbine Fluidized Bed/Turbine Gasifier/Turbine

Natural Gas Natural Gas Natural Gas Natural Gas Hydrogen Biomass Biomass Biomass

5 3 5 3 6 3 3 4

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Fig. 2. Regression plots for the gas turbine class of CHP engines used as inputs to the model for the test case. (a) shows the relationship of unit efficiency as a function of engine part load. (b) and (c) show the effect of ambient temperature on maximum capacity and efficiency. (d) and (e) show the effect of altitude on the maximum power and maximum efficiency.

regression equation based on manufacturer data is used to relate hourly efficiency to PLR. A regression plot for a gas turbine is shown in Fig. 2c. (4) Hourly efficiency is adjusted based on altitude and hourly outdoor dry-bulb temperature using a linear regression equation calculated from manufacturer data. A regression plot for a gas turbine engine is provided in Fig. 2d, and a temperature-based regression is provided in Fig. 2e. (5) The usable heat generated by the engine, fuel consumption, and efficiency are calculated for the hour. (6) The capital cost, CostCap,CHP,t, variable cost, CostVar,CHP,t, and carbon emissions, CO2,t, are calculated from the required fuel in the hour. Capital cost is a function of the number of engines, capacity, and installed cost per kilowatt. Variable cost is calculated from operations and maintenance cost per kilowatt-hour of electricity produced, and the fuel cost, CostFuel. Carbon emissions are calculated based on kilowatthours of electricity generated. It is important to note that this does not capture changes in emissions rates or variable cost from changing efficiency of the unit; it assumes a constant rate of cost and emissions per unit of electricity produced. 2.2.2. Validation of heat and power engine models To ensure that the regression-based approach accurately characterizes the performance of the modeled CHP engines, each of the 32 engines was simulated in the HOMER software, a leading commercial power plant and microgrid simulation tool originally developed at the National Renewable Energy Laboratory and commercialized by HOMER Energy [54]. For each engine, both the model and the HOMER representation were given an identical sawtooth electrical demand curve which ramped from the minimum allowable PLR to the maximum capacity. Ideal conditions (temperature and altitude) were assumed. A second demand curve representing thermal demand was also provided. Thermal demand was fixed for each cycle of electrical demand, and then increased for the next cycle, resulting in a sawtooth curve with a longer period. Since HOMER will not allow an engine to operate to produce heat but not electricity, auxiliary boilers to satisfy excess heat demand were added in both simulations and set to have identical efficiencies of 80.0%. Electrical production, heat production from

the engine, heat production from the boiler, fuel consumption by the engine, and fuel consumption by the boiler were calculated by both programs and compared. Fig. 3 shows the result of this validation. In all cases, the HOMER representation and the modeled representation were found to provide very similar hourly and annual values for consumption of fuel and heat production. As expected with identical electricity demand curves, in all cases electricity production was equal between HOMER, the model, and the demand curve since both models were set to produce to the electricity demand. The largest deviations observed for any class were for microturbines, presumably due to the smaller size of these units. Another interesting observation was the existence of an aberration in HOMER whereby the fuel cells always put out a minimum amount of thermal energy above the lowest value of heat demand. Therefore an average deviation of nearly 10% existed between the two programs. 2.2.3. Chiller equipment models Two types of central cooling equipment were used in the test case; absorption (heat-driven) chillers and centrifugal (electrically-driven) chillers. Seventeen total chillers were simulated; 8 absorption and 9 centrifugal. Chiller options were differentiated by total cooling capacity and Coefficient of Performance to provide a range of possible options suitable to various sizes of developments. Table 3 provides a summary of the equipment modeled. 2.2.3.1. Centrifugal chiller models. The methodology for modeling centrifugal chillers followed the HVAC Simulation Guidebook prepared through the California Energy Design Resources program [55]. This methodology uses three regression equations per chiller with coefficients defined by manufacturer data. To account for variability in condenser and chilled water temperatures, an iterative step was added looping over condenser and chilled water temperatures until convergence. Nine water-cooled electric centrifugal chillers with various sizes and COPs were modeled using data from the Lawrence Berkeley Laboratory Modelica Buildings Library [56]. Modeling the centrifugal chillers requires inputs of Chilled Water Supply Temperature (CWST), wet bulb temperature, dry bulb temperature, and cooling load. CWST is assumed to be constant, and there is no tolerance for not meeting this criteria. Future

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167

Fig. 3. Summary of validation study comparing the proposed model to HOMER. Black bars indicate the deviation in fuel consumption between the model and HOMER for the same electrical load input. White bars indicate the difference in total electrical output between the model and HOMER. Gray bars indicate the difference in total thermal deviation between the model and HOMER.

Table 3 Classes of chillers, driving energy source, and Coefficient of Performance (COP) range used in the model for the test case. Chiller options within each type are differentiated by COP and cooling capacity. Chiller type

Energy input source

COP range

Centrifugal Absorption

Electricity Heat

5.58–9.16 0.71–0.83

work could test the effect of allowing CWST to vary within an acceptable range. With this assumption, the energy requirement of the chiller is fully specified by the heat rejected by the condenser, and Entering Condenser Water Temperature (ECFT). However, solving for chiller electricity consumption is dependent on hourly cooling load, COP, chiller capacity, and Leaving Condenser Water Temperature, the latter three of which are updated during calculation of heat rejection. A full description of chiller performance modeling is provided in Appendix B. An iterative procedure was chosen similar to that employed in EnergyPlus, though with different initial conditions and updating of values between iterations [57]. To reduce simulation time, an informed guess of starting conditions was used. It was assumed that the design condition of the cooling tower is a function of the hourly wet bulb temperature, WBt, and the cooling tower design approach, DTCT. Cooling towers were not explicitly modeled, except to approximate electrical consumption, but it is assumed that the cooling tower bank would be sized to accommodate complete heat rejection from the condenser down to the design condition. Thus in each hour, the starting assumption for ECFTt was given by Eq. (4).

ECFT t ¼ WBt þ DT CT

ð4Þ

Using this starting guess, rapid convergence to a stable solution was found for all nine chillers. The performance was checked against EnergyPlus using a standard test building to check for deviation in performance and the impact of multiple iterations on average and maximum hourly difference between the programs. Fig. 4 shows these average and maximum differences for a single chiller. Average is taken over all 8760 h, while maximum is the highest maximum deviation in a single hour. Deviation is measured as a percent of the load and run time is given in seconds. It can be seen that after two iterations, very little change in average chiller power consumption occurred, and additional iterations did not improve the maximum deviation. After the final iteration, the electricity consumption to meet the cooling load in the given hour was known. Cooling tower electricity consumption was calculated and added to the chiller electrical demand using the methodology and data presented by Benton et al. [58]. The final step in modeling the centrifugal chillers was to model the capital cost of the units operating in the given hour. The hourly capital cost, CostCap,CC,t, is based on the manufacturerprovided capital cost per ton of cooling capacity and the number of chillers required in the given hour.

2.2.3.2. Absorption chiller modeling. Absorption chillers were modeled following the methodology of the EnergyPlus building simulation software module for ‘‘Indirect Absorption Chillers” assuming water to water heat rejection. Unlike with the centrifugal chillers, no sets of parameters describing chiller operating conditions were

Fig. 4. Results of a test of the chiller simulation over multiple iterations to check convergence rates. The run time, maximum power difference, and average power difference between the proposed model and EnergyPlus as a base case is shown. It is evident that convergence happens rapidly, and after two iterations, no further improvement is seen.

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available through open datasets. Therefore, a set of five regression equations was obtained from data on York absorption chillers [59]. The York Engineering Guide provides data for 21 absorption chillers, of which parameters for 8 were chosen spanning the full range of sizes and operating conditions. Regression equations were chosen to be cubic both based on the number of data points and the requirements of the selected modeling approach. The five regression equations and the associated regression plots are provided in Fig. 5 below. Modeling the absorption chillers required as inputs the desired chilled water temperature (constant as with the centrifugal chillers), hourly wet bulb and dry bulb temperatures, hourly cooling load, and heat source temperature, which was assumed to be constant. As with the centrifugal chiller, the first step is to calculate ECFT based on the design conditions of the cooling tower. This step is identical to that shown in Eq. (4). From this value, and manufacturer provided parameters, the heat required to supply cooling can be fully determined. Unlike with the centrifugal chillers, this does not require an iterative loop given the performance curves provided in the York Engineering Guide. A full description of the equations used for this calculation is provided in Appendix C. As with the centrifugal chillers, hourly capital cost requirement, CostCap,AC,t, was calculated from the number of chillers required and the cost per ton of chiller capacity. 2.2.4. Chiller modeling validation The chiller models were validated by testing against results of a single modeled building in EnergyPlus. The validation model followed ANSI/ASHRAE Standard 140-2011 Test Case CE 100 [60]. The building was a rectangular building with 100 cm thick walls of insulation with no thermal mass. A single air conditioning zone was used, and a constant outdoor air temperature of 46.1 °C was maintained. Internal loads and insolation were varied hourly. Each chiller was tested as the sole air conditioning system for the space. The input file was used to generate an hourly record of cooling demand. This was used both by EnergyPlus and the model described above as the input for testing and comparing the chillers. In addition to this test, a second test of a multizone office building was performed following the same strategy.

The results of both of these validation exercises show that on an annual basis, the iterative model approach described above agrees well with the EnergyPlus solution. Furthermore, the average deviation per hour in energy required for cooling is small (less than 5%) though in some cases for the absorption chiller, a single hour may deviate by up to 30% in energy requirement. Fig. 6 below documents the results of the validation. 2.2.5. Unit dispatch and control The control algorithm iterates through the community energy demand vectors by hour to solve for the fuel resource required to meet the given demand. To do this, the heating, cooling, and energy demands are passed into the appropriate heat, power, and cooling supply equipment models. For any individual run, the supply equipment to be used is dictated by two variables, one identifying the heat and power engine and one identifying the chiller type. For the test case, the analysis module first sends the cooling energy requirement to the appropriate chiller model to determine the additional heat or power to meet the cooling requirement. The additional heat and power are then added to the community heat and power requirements. These are sent to the appropriate heat and power module per a control scheme dictated by the analysis module. It has been shown that the method of controlling CHP units makes a substantial difference in the fuel requirement and efficiency of the operating units [61]. In an attempt to maximize efficiency under the greatest possible range of conditions, the control scheme implemented was the Equivalent Electric Load Following method proposed by Kavvadias et al. [61]. Under this method, the units are operated to meet the greater of either heat or electricity demand. To implement this approach, the community electricity and heat demands (modified to include impacts from cooling) are first simulated assuming that electricity is the greatest resource required in the particular hour. The heat generated from production of this amount of electricity is then compared to the heat requirement for the community. If the generated heat is less than the requirement, the heat to power ratio of the equipment is used to find the electric equivalent to supply the required heat. This is

Fig. 5. Regression equations for the absorption chillers used in the model for the test case. These were taken from the York absorption chiller engineering guide. (a) and (b) relate capacity to condenser and evaporator water temperature, respectively. (c), (d), and (e) relate steam consumption to part load ratio, condenser water temperature, and evaporator water temperature.

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Fig. 6. Results of validation of the centrifugal and absorption chiller models used for the test case against EnergyPlus. Black bars indicate average deviation in hourly energy consumption for cooling over 8760 h. The gray bars is the total energy deviation for the year. All 11 chillers validated are within 5% deviation in an hour and over the entire year.

treated as the electrical demand, and sent with the heat demand to the appropriate engine. The heat and electricity output are again recorded and checked against the heat and electricity requirements to ensure that both have been satisfied. For every unit of time, hourly fuel requirement, Ft, carbon dioxide emissions, CO2,t, and variable cost CostVar,CHP,t are calculated and reported.

HCHP,T, of the CHP by the total fuel. Note that this includes the heating and electricity required for satisfying the cooling load via the centrifugal or absorption chillers. The equation for TFCE is shown in Eq. (9).

2.3. Analysis and optimization module

The analysis module also calculates urban planning indicators regarding the structure of the community. While no constraints restrict certain types of development (i.e., all residential or all industrial), the building metadata provided in the demand module is used to calculate the percentage of total gross floor area (GFA) and percentage of buildings of each use type (residential, commercial, retail, etc.). The total Floor Area Ratio (FAR) is also calculated. The percentages of each use type by GFA and number of buildings and the FAR are output from the analysis module alongside the summary metrics of environmental, cost, and thermodynamic performance.

2.3.1. Single run analysis The analysis function aggregates the output from the supply module into summary metrics of performance, cost, and community structure. This is based on the output of the supply module and the building metadata collected in the demand module. After analysis has been completed for all time increments, final calculations of annual fuel requirement, FT, carbon dioxide emissions, CO2,T, and operating cost, CostVar,CHP,T, are determined by summing over all hours, t as shown in Eqs. (5)–(7).

FT ¼

8 760 X

ð5Þ

Ft

t¼1

CO2;T ¼

8 760 X

ð6Þ

CO2;t

t¼1

Cost Var;CHP;T ¼

8760 X

Cost Var;CHP;t

ð7Þ

t¼1

The capital cost, CostCap,T, is taken to be the greatest capital cost incurred in any hour to build the required chillers and heat and power engines as shown in Eq. (8).

Cost Cap;T ¼

X   max Cost Cap;k;t ; 8t ¼ ½1; 8760 ; k ¼ fCHP; CC; ACg k

ð8Þ It has been shown previously that supply equipment efficiency is often used as a metric of overall performance [62]. To calculate efficiency over the entire system and for all hours, a metric similar to well-to-wheel efficiency for vehicles was derived. This is referred to as Total Fuel Cycle Efficiency, and it represents the energy used to satisfy useful loads (i.e., building energy demand, municipal lighting) as a fraction of the overall energy content of the fuel. It is based on the first law of thermodynamics and calculated by dividing the total electrical output, ECHP,T, and heat output,

TFCE ¼

ET þ H T FT

ð9Þ

2.3.2. Multiobjective optimization Assessment of a single community structure that is supplied by a set of heat, power, and cooling equipment can be accomplished by running the model once. While multiple runs would allow analysis of several scenarios, the number analyzed is very small given the size of the design space, and potentially misses key insights for decision makers. For instance, a scenario where up to 50 structures of each individual building type can be constructed, powered by at most one type of heat and power engine and one type of chiller, has a total solution space of 8.74  1062. Computational optimization is used to more effectively explore this large solution space. To appropriately balance potentially conflicting objectives the multiobjective Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm was implemented using the Python package DEAP [63] due to its ability to effectively search large, nonconvex, nonlinear, constrained solution spaces and converge on the attributes that are likely to contribute to optimality [64]. Genetic algorithms have been applied to other problems in building design and urban planning as well, further documenting the usefulness of this class of algorithms for problems of this nature [65]. The objective function was specified to balance equally three objectives: (1) Maximize TFCE. (2) Minimize life cycle cost, defined as capital cost plus 30 years of undiscounted variable cost. (3) Minimize annual carbon dioxide emissions.

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Each of these was given equal weight in computation of the objective function. The decision variables were set as: (1) The 21 bi variables dictating the number of each building type to be constructed. (2) An integer variable describing the type of heat and power engine to be used, e. (3) An integer variable describing the type of chiller to be used, c. In the simplest formulation, the only constraints on the model are that none of the decision variables can be negative. In this scenario, it is assumed that an upper bound will be reached naturally

where thermal and electrical losses offset any additional gains in efficiency by building a larger central plant. Constraints can be added to satisfy other boundary conditions or real world scenarios where development may be constrained by geographic limits or zoning limits that encourage certain types of development. The algorithm first selects a population of 100 different community structures, termed ‘‘individuals.” Each is analyzed using the model described previously. With probability px, the best individuals are selected to ‘‘mate,” whereby attributes of these individuals are combined through simulated genetic crossover. This crossover cuts and splices the ‘‘genes” of the parent individuals at two points. With probability, pm any allele in the resulting individuals can

Fig. 7. Performance of the three objectives for the test case. (a) shows TFCE arranged from lowest to highest. Maximum observed efficiency is 71.39%. (b) shows life cycle cost arranged from lowest to highest. Minimum cost is $260,770. (c) shows annual carbon emissions arranged from lowest to highest. Minimum annual emissions is zero.

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mutate. The new individuals are then analyzed, and the results compared against the new generation and the individuals from the parent generation. Again, the best options are kept and the process repeats until a set number of iterations is reached. At the conclusion, the best option experienced in the entire process is preserved as the best solution. 3. Test case To demonstrate the capacity of the model and optimization approach as a means for rapidly testing early stage urban plans

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and infrastructure types, a simple example was formulated based on a 647,497 m2 (160 acre) proposed development site in San Francisco. This size provided an additional constraint on site GFA for the test case. Multiple mutation and crossover strategies are possible for any given optimization, as are various numbers of generations, Ngen, population sizes, Pop, and termination criteria. Following the work of Deb et al. [64], the mutation parameter selected was a polynomial bounded mutation strategy that uses a parameter, termed gm, to define how similar or different mutations are from parents. Prior research has shown that setting this parameter between 1 and 5 provides a reasonable level of variation [66]. The crossover strategy employed was a two-point crossover, which allows for any individual pair of solutions to exchange any section of ‘‘chromosomes,” as opposed to exchanging only one terminal half or another. Using these strategies, the optimization parameters were set as: Ngen = 1000. Pop = 100. pm = 0.05. gm = 2.5. px = 0.75.

Fig. 8. Normalized dispatch curve illustrating the hourly heat to power balance for the design configuration with the highest TFCE compared to the ideal ratio for the given supply technology. The difference between the demand curve and the ideal supply curves highlights the potential improvements to system TFCE.

In general, a high rate of crossover (>0.5) and a low rate of mutation are desirable (