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At least 559 records · Page 31

Quantum Information for Fusion Energy Sciences (Final Technical Report)

The simulation of plasma dynamics is a critical area of Fusion Energy Sciences (FES) due to it’s usefulness in predicting, controlling, and confining plasmas in the context of potential fusion reactors. The simulation of plasmas is a computationally difficult problem in both classical and quantum physics, motivating investigation into the potential of quantum computers to simulate these systems. This project took several concrete steps towards this goal by developing tools for improving the control, characterization, and calibration of quantum gates on a superconducting quantum computer, developing error suppression and mitigation tools to reduce errors on the quantum computer, and utilizing these advancements to simulate reduced models of plasma dynamics on the quantum computer. In order to efficiently simulate plasma physics, an optimal control method which synthesizes, directly at the pulse level, any quantum gate on qubit and qutrit systems was developed. Using four superconducting transmon quantum processors at Rigetti and LLNL, it was demonstrated that any arbitrary quantum gate on qubits and qutrits could be implemented with high fidelity, leading to a significantly reduced length of a gate sequence. A problem of interest in FES is the nonlinear optical process of laser pulse compression within a plasma. Since quantum physics is linear, simulating nonlinear operations is not naturally feasible on a quantum computer, however it is possible to simulated a quantized version of the nonlinear process. A quantization approach to convert nonlinear wave-wave interaction problems to Hamiltonian simulation problems was developed and demonstrated using two qubits on a Rigetti device. In this experiment, a number of error suppression and mitigation techniques were investigated to determine how best to utilize the finite quantum resources. This study provides an example of how plasma problems may be solved on near-term, noisy quantum computing platforms and identified a promising set of techniques. Building on the insights of these experiments, the investigation turned to linear electron-plasma wave physics. A connection was identified between a local one-dimensional lattice spin model and linear wave phenomena, allowing a plasma physics problem to be efficiently mapped to the quantum computer. In this framework, reflection and transmission of plasma waves at a sharp boundary was studied, as well as the propagation of waves through an inhomogeneous plasma medium. In addition to the suite of error suppression and mitigation techniques developed, this experiment introduced the use of a digital-analog gate scheme designed to efficiently simulate the plasma Hamiltonian. With hardware available at the conclusion of the project, simulation at the scale of 9 qubits and 15 timesteps (60 entangling layers) was achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Open-source simulation platform for air source heat pump integrated with thermal energy storage

Here, this article introduces a modular simulation platform for assessing thermal energy storage (TES) integrated with air source heat pumps (ASHP). The Python platform is an open-source library that includes classes for modeling air-air and air-water heat pumps, TES devices, and the heating load of residential buildings. To validate the ASHP model, the study utilized experimental data obtained from a commercial heat pump evaluated at the National Renewable Energy Laboratory (NREL). The results indicate a mean deviation of 0.7% for COP across the operating range, with a maximum relative deviation of 12.6%. In terms of system heating capacity, the model had an average deviation of 4.3% compared to experimental results, with a maximum deviation of 8.2%. Three classes were implemented for modeling distinct types of TES devices: a generic TES based on energy balances, a sensible isothermal water tank, and a stratified water tank. Details of the mathematical models are provided, along with their respective strengths and limitations. An example is provided showcasing the integration of a residential 10 kWh thermal storage unit with an ASHP operating in Denver, CO. The comparison of two different discharge criteria for the TES unit highlights the importance of control strategies in the system performance.

25 ENERGY STORAGE↗

The Road to Useful Quantum Computers

Building a useful quantum computer is a grand science and engineering challenge, currently pursued intensely by teams around the world. In the 1980s, Richard Feynman and Yuri Manin observed independently that computers based on quantum mechanics might enable better simulations of quantum phenomena. Their vision remained an intellectual curiosity until Peter Shor published his famous quantum algorithm for integer factoring, and shortly thereafter a proof that errors in quantum computations can be corrected. Since then, quantum computing R&D has progressed rapidly, from small-scale experiments in university physics laboratories to well-funded industrial efforts and prototypes. Hype notwithstanding, quantum computers have yet to solve scientifically or practically important problems -- a target often called quantum utility. In this article, we describe the capabilities of contemporary quantum computers, compare them to the requirements of quantum utility, and illustrate how to track progress from today to utility. We highlight key science and engineering challenges on the road to quantum utility, touching on relevant aspects of our own research.

Emerging Technologies (cs.ET)↗

Influence of simple terrain on the spatial variability of a low-level jet and wind farm performance in the AWAKEN field campaign

In wind energy research, scientific challenges are often associated with complex terrain sites, where orography, vegetation, and buildings disrupt flow uniformity. However, even sites characterized as simple terrain can exhibit significant spatial variability in wind speed, particularly during stable boundary layers (SBLs) and low-level jets (LLJs). This study investigates these terrain interactions using both simulations and observations from the American WAKe ExperimeNt (AWAKEN). We employ a multiscale Weather Research and Forecasting (WRF) model simulation, integrating mesoscale forcing in the coarse domains and representing three rows of turbines from the King Plains wind farm as generalized actuator disks (GAD) in the large-eddy simulation (LES) domains. During a nocturnal LLJ event on 3 April 2023, the downstream, wake-affected turbine rows outperformed the upstream, unwaked row by 25 %–51 %. This counterintuitive result arises from terrain-induced streamwise variations in hub-height wind speed of approximately 4 m s −1 over 5 km – equivalent to ∼50 % of the upstream reference speed. This enhancement outweighs the wake-induced reduction in mean wind speed (∼12 %) and global blockage effects reported in the literature (∼1 %–3.4 %). The multiscale simulations capture the intra-farm spatial variability in power performance observed in SCADA data. Terrain-induced vertical displacement of the LLJ, coupled with large wind shear below the jet maximum, drives the substantial streamwise acceleration within the wind farm. These findings underscore the importance of accounting for spatial variability related to terrain, even in simple landscapes, particularly during LLJ conditions. Incorporating such effects into reduced-order modeling frameworks for wind farm design and control could significantly enhance their effectiveness.

17 WIND ENERGY↗

End-Use Savings Shapes Measure Documentation: Dispatch Schedule Generation for Demand Flexibility Measures

This supplemental document describes the methodology used for determining the dispatch timing of various EUSS demand flexibility measures. Demand flexibility measures are designed to reduce/dispatch electricity demand in buildings during especially beneficial/critical times. The method used in this work utilizes predictions of building loads to generate a schedule that reflects the periods when the building's daily peak load occurs to support decision making in demand flexibility measures. The dispatch schedule generation method described in this document creates an hourly schedule that includes a load dispatch (peak) window for each day for a whole year based on load prediction, with options using different prediction methods: perfect prediction, bin-sampling method, fixed schedule, and outdoor air temperature (OAT)-based prediction method. The perfect prediction method performs a simulation to obtain the annual load profile as predicted load, representing the scenario of perfect load prediction. The bin-sampling method (1) categorizes days into representative bins by temperature characteristics, (2) performs simulations on sample days from each of those bins to create representative (or predicted) load, and (3) assigns representative loads for all days in a year based on the bin categorization. The fixed schedule method defines uniform start and end time of peak window with assumed fixed daily peak time, for all days in a season or a year. The OAT-based prediction method uses the statistics of OAT (minimum and maximum) as the indicators of peak load, with specified delay response time from building loads to temperature. Given the load prediction, daily peak periods are determined as a time window with specified length in each day that include the predicted daily peak load and with a secondary rule such as maximizing energy saving potential. The dispatch schedule generation method is not a standalone measure and is intended to be combined with other demand flexibility measures that could leverage the peak schedule and apply demand controls on specific systems or devices for demand response, such as measures described in "Measure Documentation - Thermostat Control for Load Shedding" and "Measure Documentation - Thermostat Control for Load Shifting".

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Customer enrollment and participation in building demand management programs: A review of key factors

Increasing the efficiency and flexibility of electricity demand is necessary for ensuring a cost-effective and reliable transition to zero-carbon electricity systems. Such demand-side management (DSM) resources have been procured by utilities for decades via energy efficiency and demand response programs; however, the key drivers of program enrollment and customer participation levels remain poorly understood — even as governments and grid planners seek to scale up the deployment of DSM assets to meet climate targets. Here we systematically review the evidence on multiple factors that may influence customer enrollment and participation in building DSM programs, focusing primarily on residential and commercial buildings. We examine the contexts in which relationships between DSM factors and outcomes are most often explored and with which methods; we also score the strength, direction, and internal consistency of each factor's reported impact on the enrollment and participation outcomes. We find that studies most commonly assess the effects of economic incentives for load flexibility on program participation levels, often using simulation-based methods in lieu of measured data. Few studies focus on program enrollment outcomes or regulatory drivers of either enrollment or participation, and gaps are also evident in the coverage of emerging DSM opportunities like load electrification. Removal of structural barriers (e.g., the lack of controls infrastructure) and the use of third party services (e.g., load aggregators) are the factors with the largest positive impacts on DSM outcomes, but no single factor emerges as clearly most impactful. For a given factor, the range of reported impacts typically varies widely across the relevant studies reviewed. Our findings provide a snapshot of the state of knowledge about building DSM and customer decision-making, and they expose key gaps in understanding that must be filled if building DSM is to expand as a critical resource for operating clean power grids.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Non-close-packed plasmonic Bravais lattices through a fluid interface-assisted colloidal assembly and transfer process

Abstract The assembly of colloids at fluid interfaces followed by their transfer to solid substrates represents a robust bottom-up strategy for creating colloidal monolayers over large, macroscopic areas. In this study, we showcase how subtle adjustments in the transfer process, such as varying the contact angle of the substrate and controlling deposition speed and direction, enable the realization of all five two-dimensional Bravais lattices. Leveraging plasmonic core–shell microgels as the building blocks, we successfully engineered non-close-packed plasmonic lattices exhibiting hexagonal, square, rectangular, centered rectangular, and oblique symmetries. Beyond characterizing the monolayer structures and their long-range order, we employed extinction spectroscopy alongside finite difference time domain simulations to comprehensively investigate and interpret the plasmonic response of these monolayers. Additionally, we probed the influence of the refractive index environment on the plasmonic properties by two methods: first, by plasma treatment to remove the microgel shells, and second, by overcoating the resulting gold nanoparticle lattices with a homogeneous refractive index polymer film. Graphical Abstract

Chemistry↗

Covariance operator estimation via adaptive thresholding

This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the sample covariance function using an estimate of the variance component. Building on recent results from empirical process theory, we derive an operator norm bound on the estimation error in terms of the sparsity level of the covariance and the expected supremum of a normalized process. Furthermore, our theory and numerical simulations demonstrate the advantage of adaptive threshold estimators over universal threshold and sample covariance estimators in nonstationary settings.

Al-Ghattas, Omar [University of Chicago, IL (Unite↗

State Dependent Optimization with Quantum Circuit Cutting

Quantum circuits can be reduced through optimization to better fit the constraints of quantum hardware. One such method, initial-state dependent optimization (ISDO), reduces gate count by leveraging knowledge of the input quantum states. Surprisingly, we found that ISDO is broadly applicable to the downstream circuits produced by circuit cutting. Circuit cutting also requires measuring upstream qubits and has some flexibility of selection observables to do reconstruction. Therefore, we propose a state-dependent optimization (SDO) framework that incorporates ISDO, our newly proposed measure-state dependent optimization (MSDO), and a biased observable selection strategy. Building on the strengths of the SDO framework and recognizing the scalability challenges of circuit cutting, we propose nonseparate circuit cutting-a more flexible approach that enables optimizing gates without fully separating them. We validate our methods on noisy simulations of QAOA, QFT, and BV circuits. Results show that our approach consistently mitigates noise and improves overall circuit performance, demonstrating its promise for enhancing quantum algorithm execution on near-term hardware.

Li, Xinpeng↗

Predictions of Cell-to-Cell Propagation and Vent Gas Production in the Thermal Runaway of Lithium-Ion Battery Stacks

This work presents the thermal runaway propagation model LIM1TR (Lithium-ion Modeling with 1-D Thermal Runaway) as an efficient tool to predict different cell-to-cell thermal runaway propagation scenarios. Here, we explored the vent gas volume production and reaction duration highlighting the relationship between these parameters and thermal runaway propagation due to convection by the vented gases. Two metrics based on gas production rate and heating rate are utilized as good indicators of the start and end of thermal runaway. LIM1TR results are compared with and validated by experiments from the literature for single-cell and multicell array experiments of 5 Ah and 10 Ah cells. By accounting for intraparticle diffusion of reacting species in the electrodes, we were able to capture the general dynamics of thermal runaway propagation and estimate acceptable reaction durations compared with the experimental values. Simulation results further demonstrated that varying heating modes lead to distinct reaction durations, consistent with experimental observations. Vent gas volume predictions indicate the need to consider both full and partial oxidation of the electrolyte. The outcomes of this work are building blocks for further investigations of module-to-module propagation by vented gases through convective heat transfer.

25 ENERGY STORAGE↗

NEAMS Burnup Extension Accomplishments and Remaining Modeling Gaps

The economic viability of light-water reactors (LWRs) in the United States is declining in heavily subsidized markets, and as a result, the nuclear industry is looking for opportunities to enhance the economic competitiveness of nuclear power. This is not a foreign concept to the nuclear industry: in the mid-2000s, the nuclear industry set out to achieve zero fuel failures by 2010. The goal in this effort was to drive down the cost of reactor shut down by replacing a pin or bundle in response to fuel rod failure. 2010 brought about the initiative to deliver the nuclear promise to reduce operating cost by 30% to improve nuclear energy’s economic competitiveness before 2020. The emergence of accident-tolerant fuel also offers the nuclear industry an opportunity to build on these past successes and deliver affordable, clean energy. Accident-tolerant fuel has been shown to provide superior performance compared to traditional Zircaloy/UO2 fuel concepts, offering the unique ability to remove operational limitations that inhibit the economic viability of nuclear power. This has led the industry to begin building a technical case to extend the peak rod average burnup beyond 62 GWd/tU to extend pressurized water reactor cycle lengths to 24 months and to develop more efficient boiling water reactor core designs. The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program mission is to develop advanced modeling and simulation tools and capabilities to accelerate the deployment of advanced nuclear energy technologies. The primary safety concern inhibiting the nuclear industry from extending burnup is related to high-burnup fuel fragmentation, relocation, and dispersal. Therefore, the NEAMS program developed a targeted 5-year plan to support the industry’s efforts to extend burnup. This milestone report summarizes the 5-year plan that was enacted in FY20, followed by a discussion of the ongoing activates required to fulfill the 5-year plan, as well as the approach to address the current modeling gaps. Additionally, an LWR stakeholder meeting was held to communicate work performed in the NEAMS program over the past three years, to assess the LWR community’s perspective on the impact of the program, and to identify remaining significant gaps in the NEAMS suite of capabilities. This engagement will be documented by the Electric Power Research Institute and used by NEAMS to redirect current LWR scope as needed and to develop the next phase for LWR research and development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗

Thermal performance and energy consumption validation of an occupied local government office building outfitted with ceiling tile phase change materials

Buildings present an opportunity for energy conservation and the modulation of peak energy demand through controlled Heating, Ventilation, and Air Conditioning (HVAC) energy use. The administrative and office building stock in the United States holds potential to achieve energy and demand savings through retrofits such as insulation, weatherization, and thermal energy storage. Specifically, there is a need to validate passive phase change material (PCM) applications in full scale in aging administrative buildings in the US to evaluate the energy benefits. Aim of this study was to conduct a whole building level thermal and energy validation of an operational building and explore an alternative method for evaluating energy efficiency. To accomplish this, the study employed PCMs in the drop ceiling and carry out an energy audit and on-site measurement of HVAC systems' energy demand and consumption. A full-scale EnergyPlus energy model, modeled by the authors, served as a baseline for evaluation. The results show that calibrated model's envelope temperature measures fall within the accepted errors. HVAC energy simulation results also fall within the accepted errors for monthly and hourly pre- and post- PCM retrofit electricity and natural gas data. The novelty of this study is that it employees energy scales per Heating Degree Hour and Cooling Degree Hour, in contrast to the commonly used Heating Degree Days and Cooling Degree Days as reported in the literature to analyze energy savings. These findings underscore the pivotal role of a calibrated model in assessing the efficacy of a singular energy measure, like a PCM-retrofitted ceiling, in an occupied office building.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

MLSPICE: Machine Learning based SPICE Modeling Platform for Power Magnetics

Electrical power converters are critical to a wide range of applications ranging from renewable integration to transportation electrification, and can be a key factor determining the size, weight, and efficiency of energy conversion systems. Magnetic components are typically the largest and least efficient components in power electronics. While there have been major strides in the modeling and analysis of power semiconductor devices and circuit simulations, the necessary advances in the design of power magnetics have lagged. In this project, we have transformed the modeling and design of power magnetics with machine learning enabled methods and catalyze simultaneous disruptive improvements for ML-based power electronics design tools. A fully automated open-source machine learning based magnetics modeling platform – the MagNet project - with innovations in full stack have been developed to greatly accelerate the design process and provide new insights to magnetic material and geometry design. The ARPA-E funded MagNet platform contains three major building blocks: 1) a ML-Integrated Data Acquisition System (MIDAS): a highly automated data acquisition testbed which is capable of measuring a large number of magnetic cores with a wide range of electrical circuit excitations; 2) a ML-integrated Core Loss Model (MICLM): a machine-learning trained modeling method for modeling the core loss and saturation effects of magnetic materials for arbitrary excitation waveforms; 3) ML-guided Magnetics SPICE Simulation Tool (PMSPICE): a fully integrated CAD tool which can simulate the magnetics in SPICE. It can help the designers to quickly model the linear and non-linear characteristics of magnetic components and evaluate their behavior in SPICE simulations. The developed MagNet system has fully demonstrated the proposed performance target and has been open sourced to the entire power electronics community to advance the modeling and design of power magnetics from many different angles.

36 MATERIALS SCIENCE↗

Developing a Control Strategy for Minimum Airflow Setting Considering CO2 Level and Energy Consumption in a Variable Air Volume System

In an office building equipped with a Variable Air Volume (VAV) system, this paper introduces a novel method for controlling the minimum supply airflow fraction in each zone’s VAV box, having a capability to consider indoor CO2 level and energy consumption. The EnergyPlus simulation using the medium office prototype model was employed, which evaluated the performance of the energy and CO2 concentration for five VAV box airflow control strategies. The paper focuses on CO2 concentration-based airflow control method and compares it with other four methods including conventional single-max, reduced minimum single-max, demand-controlled ventilation(DCV), and dualmax control methods according to guidelines and common practices. The newly proposed control strategy directly correlates the minimum airflow fraction to CO2 concentration. A general trend emerged when comparing CO2 concentrations—lower minimum airflow fractions were associated with higher concentrations. The proposed control method effectively maintained low CO2 concentrations and enabled a lower airflow fraction contributing to energy consumption reduction. It was confirmed that heating energy consumption in climate zone 4A, 5B, and 6A showed a maximum saving of approximately 30% compared to the conventional single-max and dual max control strategies. It was found that cooling energy consumption in climate zone 4A and 6A can achieve a maximum saving of approximately 10% compared to the conventional control strategies. The proposed CO2 concentration-based control logic is promising as it not only improves the indoor air quality lowering the CO2 concentration in the occupied spaces, but also contributes to HVAC energy savings.

Lee, Jong Man↗

The CHIMERAS project: design framework for the Collisionless HIgh-beta Magnetized Experiment Researching Astrophysical Systems

From the near-Earth solar wind to the intracluster medium of galaxy clusters, collisionless, high-beta, magnetized plasmas pervade our universe. Energy and momentum transport from large-scale fields and flows to small-scale motions of plasma particles is ubiquitous in these systems, but a full picture of the underlying physical mechanisms remains elusive. The transfer is often mediated by a turbulent cascade of Alfvénic fluctuations as well as a variety of kinetic instabilities; these processes tend to be multi-scale and/or multi-dimensional, which makes them difficult to study using spacecraft missions and numerical simulations alone. Meanwhile, existing laboratory devices struggle to produce the collisionless, high ion beta (β i ≳ 1), magnetized plasmas across the range of scales necessary to address these problems. As envisioned in recent community planning documents, it is therefore important to build a next generation laboratory facility to create a β i ≳ 1, collisionless, magnetized plasma in the laboratory for the first time. A working group has been formed and is actively defining the necessary technical requirements to move the facility towards a construction-ready state. Recent progress includes the development of target parameters and diagnostic requirements as well as the identification of a need for source-target device geometry. As the working group is already leading to new synergies across the community, we anticipate a broad community of users funded by a variety of federal agencies (including National Aeronautics and Space Administration, Department of Energy and National Science Foundation) to make copious use of the future facility.

astrophysical plasmas↗

The ATLAS experiment software on ARM

With an increased dataset obtained during the Run 3 of the LHC at CERN and the even larger expected increase of the dataset by more than one order of magnitude for the HL-LHC, the ATLAS experiment is reaching the limits of the current data processing model in terms of traditional CPU resources based on x86_64 architectures and an extensive program for software upgrades towards the HL-LHC has been set up. The ARM architecture is becoming a competitive and energy efficient alternative. Some surveys indicate its increased presence in HPCs and commercial clouds, and some WLCG sites have expressed their interest. Chip makers are also developing their next generation solutions on ARM architectures, sometimes combining ARM and GPU processors in the same chip. Consequently it is important that the ATLAS software embraces the change and is able to successfully exploit this architecture. We report on the successful porting to ARM of the Athena software framework, which is used by ATLAS for both online and offline computing operations. Furthermore we report on the successful validation of simulation workflows running on ARM resources. For this we have set up an ATLAS Grid site using ARM compatible middleware and containers on Amazon Web Services (AWS) ARM resources. The ARM version of Athena is fully integrated in the regular software build system and distributed in the same way as other software releases. In addition, the workflows have been integrated into the HEPscore benchmark suite which is the planned WLCG wide replacement of the HepSpec06 benchmark used for Grid site pledges. In the overall porting process we have used resources on AWS, Google Cloud Platform (GCP) and CERN. A performance comparison of different architectures and resources will be discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modeled Retrofit Package Performance for Schools

This report details modeled energy performance and savings from retrofit packages in prototypical school buildings in climate zones throughout the U.S. The information herein serves as a reference for elementary and secondary schools interested in implementing retrofit packages in their facilities for energy savings as well as health and safety benefits. School models developed for simulating package performance differentiated between rural and urban environments. Simulations were run for 10 distinct climate zones covering a range of climate conditions throughout the U.S. Results include savings estimates for electricity, natural gas, CO 2 emissions, and annual utility costs for nine different retrofit packages that combine energy conservation measures, including HVAC controls and equipment upgrades, lighting efficiency upgrades, and electrification technologies such as heat pumps for space conditioning and domestic hot water. Nine additional retrofit packages were also developed for elementary schools and modeled in two climate zones. Appendix B describes the additional retrofit packages and presents savings estimates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗