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At least 253 records · Page 14

Wide-field microwave magnetic field imaging with nitrogen-vacancy centers in diamond

Non-invasive imaging of microwave (MW) magnetic fields with microscale lateral resolution is pivotal for various applications, such as MW technologies and integrated circuit failure analysis. Diamond nitrogen-vacancy (NV) center magnetometry has emerged as an ideal tool, offering micrometer-scale resolution, millimeter-scale field of view, high sensitivity, and non-invasive imaging compatible with diverse samples. However, up until now, it has been predominantly used for imaging of static or low-frequency magnetic fields or, concerning MW field imaging, to directly characterize the same microwave device used to drive the NV spin transitions. In this work, we leverage an NV center ensemble in diamond for wide-field imaging of MW magnetic fields generated by a test device employing a differential measurement protocol. The microscope is equipped with a MW loop to induce Rabi oscillations between NV spin states, and the MW field from the device-under-test is measured through local deviations in the Rabi frequency. This differential protocol yields magnetic field maps of a 2.57 GHz MW field with a sensitivity of ∼9 μT Hz −1/2 for a total measurement duration of T=357 s, covering a 340 × 340 μm 2 field of view with a micrometer-scale spatial resolution and a device-under-test input power dynamic range of 30 dB. This work demonstrates a novel NV magnetometry protocol, based on differential Rabi frequency measurement, that extends NV wide-field imaging capabilities to imaging of weak MW magnetic fields that would be difficult to measure directly through standard NV Rabi magnetometry.

crystallographic defects↗

Offline Power Systems Applications Enabled by Phasor Measurement Units: Technical Assistance to the Power Sectors of Southeast Asia

This report provides a brief overview of several offline (non-real-time) applications facilitated by high-resolution time-synchronized measurements recorded by phasor measurement units (PMUs). The high reporting rate and time-synchronization of PMU records provide a detailed view of power system dynamics, enabling electric utilities to obtain a better understanding of their systems. In this report, the following applications have been reviewed: Power plant model validation, System model validation, Ringdown oscillation analysis, Frequency response analysis, Postmortem analysis of disturbance events Along with a brief technical background of the applications above, applicable North American Electric Reliability Corporation (NERC) standards have been discussed, and examples of implementation in North American organizations have been provided. Implementing several of the discussed applications may need a preliminary stage of data gathering from multiple entities, and several frameworks and process flows have been formulated by organizations around the world for this purpose. However, the data-gathering stage has not been considered in the scope of the present report.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Beam dynamics corrections to the Run-1 measurement of the muon anomaly $a_{\mu}$ at Fermilab

The Fermi National Accelerator Laboratory (FNAL) Muon $g\!-\!2$ Experiment has measured the positive muon magnetic anomaly $a_{\mu} \equiv (g_{\mu}-2)/2$ with a precision of 0.46 parts per million, with data collected during its first physics run in 2018. The experimental result combined with the measurement from the former experiment at Brookhaven National Laboratory increases the tension with the Standard Model expectation to $4.2\sigma$, thus strengthening evidence for new physics.The magnetic anomaly is determined from the precision measurements of the muon spin precession frequency, relative to the muon momentum, and the average magnetic field seen by the beam. In an ideal case with muons orbiting in a horizontal plane with a uniform vertical magnetic field, the anomalous precession frequency $\omega_a$ is given by the difference between the spin ($s$) and cyclotron ($c$) frequencies, $\omega_a = \omega_s - \omega_c$. The observable $\omega_a$ is proportional to $a_{\mu}$.This proceeding presents the beam dynamics systematic corrections that are required to adjust the measured muon precession frequency $\omega^{m}_{a}$ to its true physical value $\omega_{a}$.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Nominal and adversarial synthetic PMU data for standard IEEE test systems

GridSTAGE (Spatio-Temporal Adversarial scenario GEneration) is a framework for the simulation of adversarial scenarios and the generation of multivariate spatio-temporal data in cyber-physical systems. GridSTAGE is developed based on Matlab and leverages Power System Toolbox (PST) where the evolution of the power network is governed by nonlinear differential equations. Using GridSTAGE, one can create several event scenarios that correspond to several operating states of the power network by enabling or disabling any of the following: faults, AGC control, PSS control, exciter control, load changes, generation changes, and different types of cyber-attacks. Standard IEEE bus system data is used to define the power system environment. GridSTAGE emulates the data from PMU and SCADA sensors. The rate of frequency and location of the sensors can be adjusted as well. Detailed instructions on generating data scenarios with different system topologies, attack characteristics, load characteristics, sensor configuration, control parameters are available in the Github repository - https://github.com/pnnl/GridSTAGE. There is no existing adversarial data-generation framework that can incorporate several attack characteristics and yield adversarial PMU data. The GridSTAGE framework currently supports simulation of False Data Injection attacks (such as a ramp, step, random, trapezoidal, multiplicative, replay, freezing) and Denial of Service attacks (such as time-delay, packet-loss) on PMU data. Furthermore, it supports generating spatio-temporal time-series data corresponding to several random load changes across the network or corresponding to several generation changes. A Koopman mode decomposition (KMD) based algorithm to detect and identify the false data attacks in real-time is proposed in https://ieeexplore.ieee.org/document/9303022. Machine learning-based predictive models are developed to capture the dynamics of the underlying power system with a high level of accuracy under various operating conditions for IEEE 68 bus system. The corresponding machine learning models are available at https://github.com/pnnl/grid_prediction.

99 GENERAL AND MISCELLANEOUS↗

The precession frequency measurement in the Muon $g - 2$ experiment at Fermilab

The Muon g-2 (E989) experiment aims to reduce the uncertainty on the muon magnetic anomaly value (aμ = g-22 ) by a factor four (0.14 ppm) compared to the previous experiment at Brookhaven National Laboratory (BNL) in order to clarify the difference (now greater than 3 σ) between the experimental value and the Standard Model (SM) prediction. E989 collected a dataset with the same statistical power of the BNL experiment during the Run 1 data taking (2018). The analysis of data is approaching the final stage and the first result should become available in2021. In this paper, I will briefly describe the experimental setup and discuss the measure of the muon’s spin anomalous precession frequency.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Methodology to Evaluate the Grid Reliability Impact of Oscillations Induced by Large Loads

The rapid growth of hyperscale AI data centers is bringing renewed attention to the reliability risk that sustained forced oscillations pose to bulk power systems, with cyclic computational workloads emerging as a new forcing source. Unlike the broadband, stochastic disturbances from traditional industrial loads such as arc furnaces, AI training and inference facilities can inject large active power swings concentrated at specific frequencies over extended durations - characteristics that existing grid planning practices do not account for. While the North American Electric Reliability Corporation (NERC) has recognized this gap and called for system-level studies of large load interconnections, no standardized methodology exists to screen, simulate, and quantify these risks at the planning stage. This report presents the Risk Assessment Tool for Large Load-induced Events (RATLLE), a Python-based, publicly available script suite developed at the Pacific Northwest National Laboratory to evaluate bulk power system reliability risks from data center-induced oscillations. RATLLE implements a three-module workflow: a screening module that identifies vulnerable interconnection locations and excitable system modes; a simulation module that models cyclic data center load behavior using a commercial positive sequence simulation platform; and an analysis module that computes risk metrics and generates interactive visualization dashboards. The risk metrics, formulated around simulation observables, map oscillation impacts to a three-stage severity scale spanning latent equipment fatigue through imminent cascading failure. The methodology is demonstrated on two Western Electricity Coordinating Council (WECC) system models: a publicly available 240-bus reduced representation and a detailed 2031 Heavy Winter planning case. Case studies illustrate that even modest 50 MW forced oscillations at resonant frequencies can produce wide-area power swings, N-1 security constraint violations, and cascading generator trips through protection actions - outcomes that would not occur under normal operating conditions without oscillations present. The results underscore the need for standardized oscillation impact assessment in large load interconnection studies and provide a reproducible, extensible framework for utilities to adopt or customize within their existing planning workflows.

Biswas, Shuchismita↗

Field evaluation of semi‐automated moisture estimation from geophysics using machine learning

Geophysical methods can provide three-dimensional (3D), spatially continuous estimates of soil moisture. However, point-to-point comparisons of geophysical properties to measure soil moisture data are frequently unsatisfactory, resulting in geophysics being used for qualitative purposes only. This is because (1) geophysics requires models that relate geophysical signals to soil moisture, (2) geophysical methods have potential uncertainties resulting from smoothing and artifacts introduced from processing and inversion, and (3) results from multiple geophysical methods are not easily combined within a single soil moisture estimation framework. To investigate these potential limitations, an irrigation experiment was performed wherein soil moisture was monitored through time, and several surface geophysical datasets indirectly sensitive to soil moisture were collected before and after irrigation: ground penetrating radar, electrical resistivity tomography (ERT), and frequency domain electromagnetics (FDEM). Data were exported in both raw and processed form, and then snapped to a common 3D grid to facilitate moisture prediction by standard calibration techniques, multivariate regression, and machine learning. A combination of inverted ERT data, raw FDEM, and inverted FDEM data was most informative for predicting soil moisture using a random regression forest model (one-thousand 60/40 training/test cross-validation folds produced root mean squared errors ranging from 0.025–0.046 cm 3 /cm 3 ). This cross-validated model was further supported by a separate evaluation using a test set from a physically separate portion of the study area. Machine learning was conducive to a semi-automated model-selection process that could be used for other sites and datasets to locally improve accuracy.

54 ENVIRONMENTAL SCIENCES↗

Correlation polarimeter-interferometer in the DIII-D tokamak

A correlation polarimeter-interferometer system has been developed for the DIII-D tokamak to detect small amplitude magnetic and density fluctuations. Two collinear, frequency-offset (5–15 MHz), orthogonally polarized (right- and left-handed, circularly polarized) electromagnetic waves at 650 GHz probing the plasma are used to detect the Faraday effect. A third, linearly polarized, electromagnetic wave serves as the local-oscillator to provide a measure of the line-averaged density. Correlation polarimetric measurement is accomplished by correlating the Faraday effect measured along the same line of sight using two independent detectors, whereas simultaneous correlation interferometric measurement is realized by correlating the line-averaged density measured at two different intermediate frequencies. The noise floor of the correlation polarimeter-interferometer has been demonstrated to be more than one order of magnitude lower than that of a standard polarimeter-interferometer measurement. Line-averaged correlation polarimetric-interferometric measurements in DIII-D H-mode plasmas show broadband (up to 750 kHz) magnetic and density fluctuations with amplitudes as low as 0.03 $Gauss$/$\sqrt{kHz}$ and 4 × 10 13 m –3 /$\sqrt{kHz}$, respectively.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Search for Baryon-Number-Violating Processes in B − Decays to the Ξ ¯ c 0 Λ ¯ c − Final State

We report the results of the first search for B − decays to the Ξ ¯ c 0 Λ ¯ c − final state using 711 fb − 1 of data collected at the ϒ ( 4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The results are interpreted in terms of both direct baryon-number-violating B − decay and Ξ c 0 − Ξ ¯ c 0 oscillations which follow the standard model decay B − → Ξ c 0 Λ ¯ c − . We observe no evidence for baryon number violation and set the 95% confidence-level upper limits on the ratio of baryon-number-violating and standard model branching fractions B ( B − → Ξ ¯ c 0 Λ ¯ c − ) / B ( B − → Ξ c 0 Λ ¯ c − ) to be < 2.7 % and on the effective angular frequency of mixing ω in Ξ c 0 − Ξ ¯ c 0 oscillations to be < 0.76 ps − 1 (equivalent to τ mix > 1.3 ps ). Published by the American Physical Society 2024

Physics↗

Modeling and Characterization of Surface Discharges in Insulating Material for Spacers: Electrode Shape, Discharge Mode, and Revision of the Creepage Concept

In the design of MV AC and DC spacers, the predominant factors are surface and interface conditions. Design is generally carried out on specifications and standards which are based on long-term experience and lab testing. However, the diffusion of power electronics with a trend to increase electric field, switching frequency, and rise time to achieve higher power density calls for an innovative, global approach to optimized insulation system design. A new methodology, based on field simulation, discharge modeling, and partial discharge inception measurements, called the three-leg approach, can form the basis to optimize insulation design for any type of supply voltage waveform. This paper focuses on the influence of the type of electrode on the inception and phenomenology of surface discharges and, as a consequence, on the interpretation of the results used for application of the three-leg approach. It is demonstrated that a typical electrode system used for insulating material testing can generate both gas and surface discharges at the triple point, when the electrodes have a smooth profile that is used to avoid corona or flashover. Hence, testing partial discharge may not provide a straightforward indication of the surface discharge inception and, thus, be partially misleading for insulation design. Another takeover is that such analysis must benefit from PD testing tools endowed with analytics able to provide automatic identification of the type of defect generating PD, i.e., internal, surface, and corona, since design and remedy actions can be taken, and adequate insulating materials developed, only knowing the type of source generating PD. Hence, testing partial discharge may not provide a straightforward indication of surface discharge inception and, thus, be partially misleading for insulation design. In addition to the importance of the three-leg approach to favor reliable and optimized design of insulation systems, there is a clear need to have a PD testing tool endowed with analytics. It should preferably be able to provide automatic identification of the type of defect generating PD, i.e., internal, surface, and corona.

36 MATERIALS SCIENCE↗

In-Home Mobility Frequency and Stability in Older Adults Living Alone With or Without MCI: Introduction of New Metrics

Background: Older adults spend a considerable amount of time inside their residences; however, most research investigates out-of-home mobility and its health correlates. We measured indoor mobility using room-to-room transitions, tested their psychometric properties, and correlated indoor mobility with cognitive and functional status. Materials and Methods: Community-dwelling older adults living alone ( n = 139; age = 78.1 ± 8.6 years) from the Oregon Center for Aging & Technology (ORCATECH) and Minority Aging Research Study (MARS) were included in the study. Two indoor mobility features were developed using non-parametric parameters (frequency; stability): Indoor mobility frequency (room-to-room transitions/day) was detected using passive infrared (PIR) motion sensors fixed on the walls in four geographic locations (bathroom; bedroom; kitchen; living room) and using door contact sensors attached to the egress door in the entrance. Indoor mobility stability was estimated by variances of number of room-to-room transitions over a week. Test-retest reliability (Intra-class coefficient, ICC) and the minimal clinically important difference (MCID) defined as the standard error of measurement (SEM) were generated. Generalized estimating equations models related mobility features with mild cognitive impairment (MCI) and functional status (gait speed). Results: An average of 206 days (±127) of sensor data were analyzed per individual. Indoor mobility frequency and stability showed good to excellent test-retest reliability (ICCs = 0.91[0.88–0.94]; 0.59[0.48–0.70]). The MCIDs of mobility frequency and mobility stability were 18 and 0.09, respectively. On average, a higher indoor mobility frequency was associated with faster gait speed (β = 0.53, p = 0.04), suggesting an increase of 5.3 room-to-room transitions per day was associated with an increase of 10 cm/s gait speed. A decrease in mobility stability was associated with MCI (β = −0.04, p = 0.03). Discussion: Mobility frequency and stability in the home are clinically meaningful and reliable features. Pervasive-sensing systems deployed in homes can objectively reveal cognitive and functional status in older adults who live alone.

Wu, Chao-Yi↗

A Synoptic System for Capturing Ecosystem Control Points Across Terrestrial‐Aquatic Interfaces

Interconnected landscape features such as terrestrial‐aquatic interfaces play an outsized role in biogeochemical cycles as ecosystem control points, but it is notoriously challenging to characterize these. Here, we document a synoptic sensor network design that is (a) flexible to accommodate diverse ecosystem interfaces and gradients, (b) adaptable to monitoring and modeling needs of small and large projects alike, (c) standardized for intercomparability across sites and field experiments, and (d) adequately replicated to capture heterogeneity of each parameter monitored. This real‐time monitoring of surface water, groundwater, soil, and vegetation supports configuration and evaluation of models that span upland, wetland, open water strata, and transitions between them. We established the network at seven sites along the Chesapeake Bay and Lake Erie coastlines, including large‐scale flood manipulation experiments in both regions. A central design element is “one data logger program to rule them all”—a collection of sensor‐specific modules deployed on 40 loggers controlling ∼2,000 sensors, with the goal of streamlining maintenance, debugging, and reproducible data processing. The network generates ∼6 M observations per month, capturing system dynamics at the broad spatial and fine temporal scales needed to initialize and benchmark models; measurement frequency can be modified remotely to capture events. This network design has also revealed behaviors not represented in Earth system models, such as transient groundwater oxygen pulses. Completely documented and open source, this standardized, flexible, and efficient sensor network design can reduce barriers to understanding environmental changes and ecosystem responses across systems and scales.

Ward, Nicholas D. [Pacific Northwest National Labo↗

High-bandwidth image-based predictive laser stabilization via optimized Fourier filters

Controlling the delivery of kHz-class pulsed lasers is of interest in a variety of industrial and scientific applications, from next-generation laser-plasma acceleration to laser-based x-ray emission and high-precision manufacturing. The transverse position of the laser pulse train on the application target is often subject to fluctuations by external drivers (e.g., room cooling and heating systems, motorized optics stages and mounts, vacuum systems, chillers, and/or ground vibrations). For typical situations where the disturbance spectrum exhibits discrete peaks on top of a broad-bandwidth lower-frequency background, traditional PID (proportional-integral-derivative) controllers may struggle, since as a general rule PID controllers can be used to suppress vibrations up to only about 5%–10% of the sampling frequency. Here, a predictive feed-forward algorithm is presented that significantly enhances the stabilization bandwidth in such laser systems (up to the Nyquist limit at half the sampling frequency) by online identification and filtering of one or a few discrete frequencies using optimized Fourier filters. Furthermore, the system architecture demonstrated here uses off-the-shelf CMOS cameras and piezo-electric actuated mirrors connected to a standard PC to process the alignment images and implement the algorithm. To avoid high-end, high-cost components, a machine-learning-based model of the piezo mirror’s dynamics was integrated into the system, which enables high-precision positioning by compensating for hysteresis and other hardware-induced effects. A successful demonstration of the method was performed on a 1 kHz laser pulse train, where externally-induced vibrations of up to 400 Hz were attenuated by a factor of five, far exceeding what could be done with a standard PID scheme.

Natal, Joseph↗

Double exponential approximation and inverse double exponential fit for Bell Labs and International-Military Standard EMP waveforms

We summarize here the double exponential and inverse double exponential approximations for two common EMP waveforms, the Bell Laboratories (Bell Labs) and the International- military standard (IEC-MIL-STD). Both models have been used frequently due to their relatively easy analytical expressions for both the time domain waveforms and their associated frequency domain spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Clock Precision beyond the Standard Quantum Limit at 10 −18 Level

Optical atomic clocks with unrivaled precision and accuracy have advanced the frontier of precision measurement science and opened new avenues for exploring fundamental physics. A fundamental limitation on clock precision is the standard quantum limit (SQL), which stems from the uncorrelated projection noise of each atom. State-of-the-art optical lattice clocks interrogate large ensembles to minimize the SQL, but density-dependent frequency shifts pose challenges to scaling the atom number. The SQL can be surpassed, however, by leveraging entanglement, though it remains an open problem to achieve quantum advantage from spin squeezing at state-of-the-art stability levels. Here, we demonstrate clock performance beyond the SQL, achieving a fractional frequency precision of 1.1 × 10 −18 for a single spin-squeezed clock. With cavity-based quantum nondemolition measurements, we prepare two spin-squeezed ensembles of ∼30 000 strontium atoms confined in a two-dimensional optical lattice. A synchronous clock comparison with an interrogation time of 61 ms achieves a metrological improvement of 2.0(2) dB beyond the SQL, after correcting for state preparation and measurement errors. These results establish the most precise entanglement-enhanced clock to date and offer a powerful platform for exploring the interplay of gravity and quantum entanglement.

cavity quantum electrodynamics↗

Stochastic Simulation of Daily Suspended Sediment Concentration Using Multivariate Copulas

Estimation of daily suspended sediment concentration (SSC) is required for water resources and environment management. In this paper, a copula-based stochastic method was proposed for daily SSC simulation. Here, the multivariate copula function, constructed based on a bivariate copula and two bivariate conditional probability distributions, was used to model the temporal and cross dependence structures in daily SSCs. Then, the daily SSCs were generated by sampling from the multivariate conditional distribution. As a result, synthetic long-term SSCs data beyond the limited observation period can be provided for water resources managers, which plays a critical role in accurately estimating frequency and magnitude of extreme SSCs events. The proposed method was under rigorous examination by applying to a case study at Pingshan station in the Jinsha River Basin, China. Results showed that the generated daily SSC sequences not only had a high degree of accuracy in preserving the statistical characteristics of the daily SSC observations, but also captured both the temporal correlation and the cross-correlation between the daily streamflow and daily SSC. Specifically, the average daily relative error values corresponding to mean, standard deviation, skewness, lag-1 temporal correlation, and cross correlation were 0.87%, 4.24%, 7.52%, 0.51% and 2.02%, respectively. The multivariate copula framework proposed here can accurately and efficiently generate long-term daily SSC data for water resources management such as frequency analysis and risk assessment of extreme SSC events.

54 ENVIRONMENTAL SCIENCES↗

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators

Here, we conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C 2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C 2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C 2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ComStock Measure Documentation: Heat Pump Rooftop Units with Standard Performance

This documentation focuses on a single end-use savings shape measure - heat pump rooftop units (HP-RTUs) with standard efficiencies that are prevalent in the current market. Today, these products are claimed as standard efficiency by the manufacturers and are most commonly installed. This document will primarily discuss the additional changes of performance and configuration of the standard efficiency HP-RTUs while a comprehensive overview of the fundamental modeling methodology and background of the HP-RTU measure, including applicability, sizing scheme, and other key assumptions can be found in the original documentation: Heat Pump RTU. The definition of "standard efficiency" can be a bit vague when considering detailed specifics other than efficiency metrics of a heat pump. Thus, we have focused on reflecting products where manufacturers claim as standard efficiency and products that are not top-of-the-line in their model lineup. Based on gathering information from eight products from four major manufacturers, there are some common (or relatively prevalent) characteristics and we have defined standard efficiency product as follows: direct drive outdoor unit fan, two stages of heat pump cooling, single stage heat pump heating (i.e., all compressors running at the same time), heat pump minimum lockout temperature of 0°F (-17.8°C), backup electric resistance heating, backup heating runs at the same time as heat pump heating , heat pump heating locking out below minimum operating temperature, IEER in between 11-13, and HSPF in between 8-8.9. There are cases where some of these products have other variations: a variable frequency drive fan, dual fuel (i.e., gas backup heating) option, three or more cooling stages, two stages of heat pump heating, no backup heating as default , etc. However, this work tried to reflect the most common and prevalent options for a standard efficiency product.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗