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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Direct Radiative Forcing by Anthropogenic Airborne Mineral Aerosols

Although airborne mineral aerosols are traditionally considered a natural component of the earth-atmosphere climate system, an examination of dust production mechanisms and dust source regions reveals that a significant fraction of the dust loading could be due to human activities. We find that the global mean direct solar radiative forcing by anthropogenically generated mineral aerosols may be comparable to the direct solar radiative forcing by other anthropogenic aerosols. The net regional forcing by mineral aerosols can greatly exceed the regional forcing by sulfate aerosol and can even be comparable to the net forcing by clouds. An improved understanding of the radiative forcing due to mineral aerosols requires better knowledge of the regional patterns of dust production rates and dust optical depths, more comprehensive measurements of dust microphysical and optical characteristics, as well as a comprehensive assessment of the role of dust aerosols on infrared radiative forcing.

Sokolik, Irina N.↗
NASA NTRS1993

Present-day secular variations in the zonal harmonics of earth's geopotential

The mathematical formulation required for predicting secular variation in the geopotential is developed for the case of a spherically symmetric, self-gravitating, viscoelastic earth model and an arbitrary surface load which can include a gravitational self-consistent ocean loading component. The theory is specifically applied to predict the present-day secular variation in the zonal harmonics of the geopotenial arising from the surface mass loading associated with the late Pleistocene glacial cycles. A procedure is outlined in which predictions of the present-day geopotential signal due to the late Pleistocene glacial cycles may be used to derive bounds on the net present-day mass flux from the Antarctic and Greenland ice sheets to the local oceans.

Mitrovica, J. X.↗
DOE OSTI2023

Techno-Economic Analysis and Optimization of a Compressed-Air Energy Storage System Integrated with a Natural Gas Combined-Cycle Plant

To address the rising electricity demand and greenhouse gas concentration in the environment, considerable effort is being carried out across the globe on installing and operating renewable energy sources. However, the renewable energy production is affected by diurnal and seasonal variability. To ensure that the electric grid remains reliable and resilient even for the high penetration of renewables into the grid, various types of energy storage systems are being investigated. In this paper, a compressed-air energy storage (CAES) system integrated with a natural gas combined-cycle (NGCC) power plant is investigated where air is extracted from the gas turbine compressor or injected back into the gas turbine combustor when it is optimal to do so. First-principles dynamic models of the NGCC plant and CAES are developed along with the development of an economic model. The dynamic optimization of the integrated system is undertaken in the Python/Pyomo platform for maximizing the net present value (NPV). NPV optimization is undertaken for 14 regions/cases considering year-long locational marginal price (LMP) data with a 1 h interval. Design variables such as the storage capacity and storage pressure, as well as the operating variables such as the power plant load, air injection rate, and air extraction rate, are optimized. Results show that the integrated CAES system has a higher NPV than the NGCC-only system for all 14 regions, thus indicating the potential deployment of the integrated system under the assumption of the availability of caverns in close proximity to the NGCC plant. The levelized cost of storage is found to be in the range of 136–145 $/MWh. Roundtrip efficiency is found to be between 74.6–82.5%. A sensitivity study with respect to LMP shows that the LMP profile has a significant impact on the extent of air injection/extraction while capital expenditure reduction has a negligible effect.

25 ENERGY STORAGE↗
DOE OSTI2021

Formation and surface melting of nanoparticle superlattices in a solution

The wisdom in the saying of “There are no two snowflakes alike” lies in the importance of history or kinetic pathways in the phase transitions of solids. Likewise, “artificial solids,” namely superlattices consisting of functional nanoparticles, have lattice size, surface morphology, crystallinity, symmetry, and structural reconfiguration (for example, transition into a disordered state) highly dependent on the kinetic pathways as the nanoparticles interact with each other in solution [1]. Great progresses have been made in understanding the formation pathways of superlattices using liquid-phase transmission electron microscopy (TEM) [2-4]. For example, by tracking single nanoparticle’s trajectories, especially aided by U-net neural network-based machine learning, previous studies mapped the fundamental nanoparticle interactions at nanometer resolution [5]. Nonclassical, two-step nucleation pathway has also been elucidated in the system of nanoprisms, by optimizing protocols such as loading nanoparticle suspensions over the supersaturation threshold and minimizing particle‒substrate interaction [2]. Surface morphologies or exposed facets of superlattices have been shown to follow the principles of Wulff construction rule, where the facet-dependent surface energy can be measured based on the capillary wave theory [4]. However, the reverse process of crystallization of superlattices, the conversion from crystalline to disordered state, has been much less explored. On one hand, the melting of nanoparticle superlattices can provide a preferred pathway to induce structural reorganization or shuffling of building blocks for them to transform into different types of crystal structures. On the other hand, understanding nanoscale superlattice melting and comparing such behaviors with the prevailing surface melting theories developed for atomic/molecular solids can provide a potent way to engineer phase transitions of supra- and hierarchical structures constructed from nanoscale entities (e.g., DNA-coated nanoparticles, proteins), for their applications in reprogrammable and switchable materials with multifunctional properties [6, 7]. The experimental challenges to observe melting of superlattices are twofold. Practically it is difficult to load the initial superlattice form, in an intact manner, into the highly confined liquid-phase TEM chamber for in-situ observation. Here, the triggering of melting also needs meticulous manipulation of nanoparticle concentration, interparticle interaction, and solution environment.

Kim, Ahyoung↗
DOE OSTI2024

Dataset For: A Guide to Residential Energy Storage and Rooftop Solar: State Net Metering Policies and Utility Rate Tariff Structures

Federal and state decarbonization goals have led to numerous financial incentives and policies designed to increase access and adoption of renewable energy systems. In combination with the declining cost of both solar photovoltaic and battery energy storage systems and rising electric utility rates, residential renewable adoption has become more favorable than ever. However, not all states provide the same opportunity for cost recovery, and the complicated and changing policy and utility landscape can make it difficult for households to make an informed decision on whether to install a renewable system. This paper is intended to provide a guide to households considering renewable adoption by introducing relevant factors that influence renewable system performance and payback, summarized in a state lookup table for quick reference. Five states are chosen as case studies to perform economic optimizations based on net metering policy, utility rate structure, and average electric utility price; these states are selected to be representative of the possible combinations of factors to aid in the decision-making process for customers in all states. The results of this analysis highlight the dual importance of both state support for renewables and price signals, as the benefits of residential renewable systems are best realized in states with net metering policies facing the challenge of above-average electric utility rates. This dataset is intended to allow readers to reproduce and customize the analysis performed in this work to their benefit. Suggested modifications include: location, household load profile, rate tariff structure, and renewable energy system design.

14 SOLAR ENERGY↗
DOE OSTI2024

Nuclear Energy Cost Estimates for Net Zero World Initiative

This report provides recommended parameters for incorporating nuclear energy systems into decarbonization modeling scenarios. The values are primarily intended for the Net Zero World (NZW) Initiative but are expected to prove useful to other related efforts. Both costs and operational metrics are provided in the study. Several cost factors, namely overnight capital costs (OCC) and operational costs are taken to be country specific. OCC is defined as the value of building the reactor in one night considering all costs prior to the start of operations including fuel for the initial core load. The value assumes the build is neither a first nor a ‘Nth’ of a kind, but somewhere in between. All costs are escalated to 2022 USD values.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Deep Analysis Net with Causal Embedding for Coal-fired Power Plant Fault Detection and Diagnosis (DANCE4CFDD)

Fault detection and diagnosis is critical to power plant operation to ensure attaining high reliability while reducing operation cost. As more renewable power is introduced to the power grid, traditional fossil power plants take on the extra burden of excessive load cycling to compensate the generation variability from renewable power. Such load cycling will pose more reliability challenges to power plant operation. There are a number of challenges faced by today’s asset health management system in coal- fired (or gas) power plants: 1) high-dimensional nonlinear interaction among multiple time series measurements; 2) high measurement variance induced by operational conditions/modes; 3) variation among asset types and plant configurations; and 4) a small number of faulty events to learn from. To cope with these challenges, today’s fielded asset health management systems rely heavily on manual efforts from domain experts and hand-crafted features or rules based on domain knowledge. Despite its role in plant reliability, such a practice is costly and hinders its scalability and sustainability, particularly when a plant undergoes modifications. The objective of this project is to develop a novel end-to-end AI learning system that is trainable (i.e., the AI representation of a complex system behavior can be directly learned from properly labeled data) for accurate fault detection and root cause analysis. The ability to create a fault detection model directly from time series could alleviate the efforts associated with today’s asset management solution development. In the course of this project, we have achieved the following: Created an AI model development environment incorporating state-of-the-art neural network architectures for rapid model development and evaluation; Developed novel learning strategies for training of fault detection model; Developed special-purpose neural network architecture embedded with variable association graph aiming for better interpretability; Developed a learning strategy to leverage a small number of faulty events for enhanced fault detection capability; Conducted detailed experimental study based on public benchmark datasets and demonstrated the effectiveness of the proposed solution; and Validated the developed system with data from both a coal-fired plant boiler dynamic simulation model and real-world coal-fired power plant covering multiple asset and fault types. Overall, the project attained a technology readiness level of TRL 5 from TRL 2 at the beginning of the project.

20 FOSSIL-FUELED POWER PLANTS↗
NASA NTRS2007

Neural Net Safety Monitor Design

The National Aeronautics and Space Administration (NASA) at the Dryden Flight Research Center (DFRC) has been conducting flight-test research using an F-15 aircraft (figure 1). This aircraft has been specially modified to interface a neural net (NN) controller as part of a single-string Airborne Research Test System (ARTS) computer with the existing quad-redundant flight control system (FCC) shown in figure 2. The NN commands are passed to FCC channels 2 and 4 and are cross channel data linked (CCDL) to the other computers as shown. Numerous types of fault-detection monitors exist in the FCC when the NN mode is engaged; these monitors would cause an automatic disengagement of the NN in the event of a triggering fault. Unfortunately, these monitors still may not prevent a possible NN hard-over command from coming through to the control laws. Therefore, an additional and unique safety monitor was designed for a single-string source that allows authority at maximum actuator rates but protects the pilot and structural loads against excessive g-limits in the case of a NN hard-over command input. This additional monitor resides in the FCCs and is executed before the control laws are computed. This presentation describes a floating limiter (FL) concept1 that was developed and successfully test-flown for this program (figure 3). The FL computes the rate of change of the NN commands that are input to the FCC from the ARTS. A window is created with upper and lower boundaries, which is constantly floating and trying to stay centered as the NN command rates are changing. The limiter works by only allowing the window to move at a much slower rate than those of the NN commands. Anywhere within the window, however, full rates are allowed. If a rate persists in one direction, it will eventually hit the boundary and be rate-limited to the floating limiter rate. When this happens, a persistent counter begins and after a limit is reached, a NN disengage command is generated. The tunable metrics for the FL are (1) window size, (2) drift rate, and (3) persistence counter. Ultimate range limits are also included in case the NN command should drift slowly to a limit value that would cause the FL to be defeated. The FL has proven to work as intended. Both high-g transients and excessive structural loads are controlled with NN hard-over commands. This presentation discusses the FL design features and presents test cases. Simulation runs are included to illustrate the dramatic improvement made to the control of NN hard-over effects. A mission control room display from a flight playback is presented to illustrate the neural net fault display representation. The FL is very adaptable to various requirements and is independent of flight condition. It should be considered as a cost-effective safety monitor to control single-string inputs in general.

Larson, Richard R.↗
NASA NTRS2009

Implementation of an Adaptive Controller System from Concept to Flight Test

The National Aeronautics and Space Administration (NASA) at the Dryden Flight Research Center (DFRC) has been conducting flight-test research using an F-15 aircraft (figure 1). This aircraft has been specially modified to interface a neural net (NN) controller as part of a single-string Airborne Research Test System (ARTS) computer with the existing quad-redundant flight control system (FCC) shown in figure 2. The NN commands are passed to FCC channels 2 and 4 and are cross channel data linked (CCDL) to the other computers as shown. Numerous types of fault-detection monitors exist in the FCC when the NN mode is engaged; these monitors would cause an automatic disengagement of the NN in the event of a triggering fault. Unfortunately, these monitors still may not prevent a possible NN hard-over command from coming through to the control laws. Therefore, an additional and unique safety monitor was designed for a single-string source that allows authority at maximum actuator rates but protects the pilot and structural loads against excessive g-limits in the case of a NN hard-over command input. This additional monitor resides in the FCCs and is executed before the control laws are computed. This presentation describes a "floating limiter" (FL) concept that was developed and successfully test-flown for this program (figure 3). The FL computes the rate of change of the NN commands that are input to the FCC from the ARTS. A window is created with upper and lower boundaries, which is constantly "floating" and trying to stay centered as the NN command rates are changing. The limiter works by only allowing the window to move at a much slower rate than those of the NN commands. Anywhere within the window, however, full rates are allowed. If a rate persists in one direction, it will eventually "hit" the boundary and be rate-limited to the floating limiter rate. When this happens, a persistent counter begins and after a limit is reached, a NN disengage command is generated. The tunable metrics for the FL are (1) window size, (2) drift rate, and (3) persistence counter. Ultimate range limits are also included in case the NN command should drift slowly to a limit value that would cause the FL to be defeated. The FL has proven to work as intended. Both high-g transients and excessive structural loads are controlled with NN hard-over commands. This presentation discusses the FL design features and presents test cases. Simulation runs are included to illustrate the dramatic improvement made to the control of NN hard-over effects. A mission control room display from a flight playback is presented to illustrate the neural net fault display representation. The FL is very adaptable to various requirements and is independent of flight condition. It should be considered as a cost-effective safety monitor to control single-string inputs in general.

Larson, Richard R.↗
NASA NTRS1993

Propulsion Systems Panel

Topics addressed are: (1) cryogenic tankage; (2) launch vehicle TPS/insulation; (3) durable passive thermal control devices and/or coatings; (4) development and characterization of processing methods to reduce anisotropy of material properties in Al-Li; (5) durable thermal protection system (TPS); (6) unpressurized Al-Li structures (interstages, thrust structures); (7) near net shape sections; (8) pressurized structures; (9) welding and joining; (10) micrometeoroid and debris hypervelocity shields; (11) state-of-the-art shell buckling structure optimizer program to serve as a rapid design tool; (12) test philosophy; (13) reduced load cycle time; (14) structural analysis methods; (15) optimization of structural criteria; and (16) develop an engineering approach to properly trade material and structural concepts selection, fabrication, facilities, and cost.

Bianca, Carmelo J.↗
NASA NTRS2009

Device, system and method for a sensing electrical circuit

The invention relates to a driven ground electrical circuit. A driven ground is a current-measuring ground termination to an electrical circuit with the current measured as a vector with amplification. The driven ground module may include an electric potential source V.sub.S driving an electric current through an impedance (load Z) to a driven ground. Voltage from the source V.sub.S excites the minus terminal of an operational amplifier inside the driven ground which, in turn, may react by generating an equal and opposite voltage to drive the net potential to approximately zero (effectively ground). A driven ground may also be a means of passing information via the current passing through one grounded circuit to another electronic circuit as input. It may ground one circuit, amplify the information carried in its current and pass this information on as input to the next circuit.

Vranish, John M.↗
NASA NTRS2010

Interference-Fit Life Factors for Ball Bearings

The effect of hoop stresses on the rolling-element fatigue life of angular-contact and deep-groove ball bearings was determined for common inner-ring interference fits at the ABEC-5 tolerance level. The analysis was applied to over 1150 bearing configurations and load cases. Hoop stresses were superimposed on the Hertzian principal stresses created by the applied bearing load to calculate the inner-race maximum shearing stress. The resulting fatigue life of the bearing was recalculated through a series of equations. The reduction in the fatigue life is presented as life factors that are applied to the unfactored bearing life. The life factors found in this study ranged from 1.00 (no life reduction)--where there was no net interface pressure--to a worst case of 0.38 (a 62-percent life reduction). For a given interference fit, the reduction in life is different for angular-contact and deep-groove ball bearings. Interference fits also affect the maximum Hertz stress-life relation. Experimental data of Czyzewski, showing the effect of interference fit on rolling-element fatigue life, were reanalyzed to determine the shear stress-life exponent. The Czyzewski data shear stress-life exponent c equals 8.77, compared with the assumed value of 9. Results are presented as tables and charts of life factors for angular-contact and deep-groove ball bearings with light, normal, and heavy loads and interference fits ranging from extremely light to extremely heavy.

Oswald, Fred B.↗
DOE OSTI2021

Performance and flexibility improvements of Staged Pressurized Oxy-Combustion

Staged Pressurized Oxy-Combustion (SPOC) is a low-carbon coal combustion power technology being developed by Washington University in St. Louis (WUSTL). Oxy-combustion plants enable straightforward capture of carbon dioxide (CO 2 ) by removing most of the nitrogen in the combustion air prior to use, thereby burning fuel in near-pure oxygen instead of air, producing a flue gas containing primarily CO 2 and water. CO 2 capture at amounts > 90% is possible, often using cryogenic air separation. Oxy-combustion typically relies on flue gas recycle (FGR) to reduce the peak temperature and radiation that would otherwise occur in a fuel/oxygen only flame. SPOC reduces the peak temperatures of combustion by utilizing two or more pressurized boiler modules connected in series to produce fuel staging; hence, only a portion of the fuel is combusted in any given furnace module. This means that the thermal energy released at each stage can be captured and removed from the gases prior to subsequent stages, when more fuel is introduced. This allows the SPOC process to operate with minimal FGR, avoiding the associated efficiency losses and additional costs. Also, the process operates at an elevated gas-side pressure, reducing boiler size, enhancing heat transfer to achieve a compact boiler configuration as compared to an atmospheric-pressure boiler design, and allowing for recovery of the latent heat of the water from the flue gas at a temperature useful to the steam cycle. The resultant net efficiency of the system is over 3 percentage points greater than traditional atmospheric-pressure oxy-combustion, and 7 percentage points greater than the post combustion variant, representing a step-change improvement over first-generation capture technologies. To further develop the concept, WUSTL and the Electric Power Research Institute, Inc., organized a project with American Air Liquide, Inc., Doosan Babcock Limited, and the U.S. Department of Energy to investigate a practicable and workable boiler design. The team has identified the potential for enhanced process flexibility for controlling power generation over a wider load range than is normally available to conventional coal-fired power plants due to the staged nature of the heat release. With increasing intermittent renewable generator contribution, on-demand generators need to be highly flexible to participate in the future energy market, requiring extensive operation at reduced load. Conventional coal-fired steam generators typically face challenges in maintaining temperature control of the reheat steam and main steam at reduced loads. This results in inefficient operation, both in terms of the boiler efficiency and steam turbine heat rate. The results of this project show the SPOC process is capable of exceptional turndown, both on a stage basis and with the ability to bypass entire stages. Oxygen-supply flexibility was also investigated, as this is also a key consideration for the overall flexibility of the SPOC process given the operating constraints of conventional air separation units. A boiler design concept assessment was conducted and was focused on delivering compact and constructible design. The assessment checked appropriate tube operating metal temperatures at full load and at lower operating loads, balanced against the needs of efficient coal combustion, and the resultant slagging and ash environments. Combustion testing in the 100-kWth pressurized combustion test rig at WUSTL was carried out to validate the combustion, heat flux profiles and burnout at multiple loads. Combustion parameters investigated were flame stability, fuel burnout, ash composition, radiative heat flux, and temperature profiles. The results of these tests formed the basis of a full-scale boiler design that will encompass improvements in both efficiency and flexibility over conventional oxy-combustion processes. The air separation unit flexibility was investigated, and associated cost implications were addressed. Detailed economic assessment results for a 550 MWe net power block are also provided, allowing for a comparison against the baseline NETL oxy-combustion and post combustion capture cases.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2026

Overview of the ICRF heating system in SPARC

Ion Cyclotron Range of Frequencies (ICRF) heating is a critical system for the SPARC mission of demonstrating net positive fusion gain. In the first campaign, 20 MW of installed power at 120 MHz will be supplied to 10 four-strap antennas, arranged in poloidal pairs. The matching network is designed to accommodate for a range of loading conditions and a fast controller adjusts the matching during a pulse with frequency modulation of ±1 MHz. For the main L-mode scenario of the first experimental campaign, the power coupling and absorption is analysed in this work. Several feeding schemes are compared and limits on the amount of the total coupled power are evaluated. Coupling of the full 20 MW power is possible well within the limit of the peak electric field in the transmission line of 15 kV/cm. The 3 He minority and 2 nd harmonic T heating scheme is validated in full-wave modelling to be efficient for heating plasma in the SPARC L-mode Q>1 scenario, with dominant ion heating and efficient single-pass absorption. A range of ICRF wave parameters and minority concentration would be suitable for operation and allow tailoring the heating properties for plasma conditions and experimental objectives.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Why is My Zero Energy Home Not a Zero Carbon Home?

For years, carbon calculations were done very simply. The method of calculation was to take annual totals of energy consumption and multiply by an average emission factor, either for the grid serving a project or for a larger region (e.g. an EPA eGRID sub region). The level of accuracy of this approximation was reasonably good, although the issue of accuracy was not, to our knowledge, tested. And the data required were minimal – just a year’s worth of bills for each fuel and one lookup factor. But this method assures that a net zero energy home is automatically a net zero carbon home because zero times any possible emission factor is still zero. Starting in the early 2010s, things changed – grids were starting to rely more and more heavily on renewables, and the difference was showing up on aggregate load curves. This was perhaps noticed first in California, where aggressive renewable policies led to significant renewable power generation large enough to affect the overall shape of the diurnal load curve for the Independent Systems Operator.

14 SOLAR ENERGY↗
NASA NTRS1999

Design Optimization and Analysis of a Composite Honeycomb Intertank

Intertanks, the structure between tanks of launch vehicles, are prime candidates for weight reduction of rockets. This paper discusses the optimization and detailed follow up analysis and testing of a 96 in. diameter, 77 in. tall intertank. The structure has composite face sheets with an aluminum honeycomb core. The ends taper to a thick built up laminate for a double lap bolted splice joint interface. It is made in 8 full length panels joined with bonded double lap joints. The nominal load is 4000 lb/in. Optimization is by Genetic Algorithm and minimizes weight by varying core thickness, number and orientation of acreage and buildup plies, and the size, number and spacing of bolts. A variety of design cases were run with populations up to 2000 and chromosomes as long as 150 bits. Constraints were buckling; face stresses (normal, shear, wrinkling and dimpling); bolt stress; and bolt hole stresses (bearing, net tension, wedge splitting, shear out and tension/shear out). Analysis is by a combination of elasticity solutions and empirical data. After optimization, a series of coupon tests were performed in conjunction with a rigorous analysis involving a variety of finite element models. This analysis and testing resulted in several small changes to the optimized design. The equation used for hole bearing strength was found to be inadequate, resulting in thicker ends. The core thickness increased 0.05", and potting compound was added in the taper to strengthen the facesheet bond. The intertank has undergone a 250,000 lb limit load test and been mated with a composite liquid hydrogen tank. The tank/intertank unit is being installed in a test stand where it will see 200 thermal/load cycles. Afterwards the intertank will be demated and loaded in compression to failure.

Finckenor, Jeff↗
DOE OSTI2021

Deep learning approaches to semantic segmentation of fatigue cracking within cyclically loaded nickel superalloy

Improvements to synchrotron-based micro-computed tomography scanning capabilities have gifted researchers the ability to characterize 4D material thermomechanical responses more thoroughly than ever before. These advancements, however, have brought about new challenges in analyzing the resulting deluge of data. We report on a nickel-based superalloy specimen imaged 26 times in-situ during cyclic loading at Argonne National Laboratory Advanced Photon Source beamline 1ID, in order to monitor crack growth within the microstructure. Therefore, several deep learning approaches which utilize convolutional neural networks are implemented to segment crack features from reconstructed tomography scans. U-Net architecture implementations are found to be especially effective, achieving IoU = 0.995 +/- 0.004 and Matthews correlation coefficient scores of Φ = 0.826 +/- 0.085. These advancements broaden possibilities for scientists seeking to automate segmentation analyses of similar large datasets.

36 MATERIALS SCIENCE↗
NASA NTRS1980

Solar energy system performance evaluation: Seasonal report for Contemporary Newman, Newman, Georgia

A hot solar heating and hot water system's operational performance from June 1979 through April 1980 is evaluated. Solar energy satisfied 42 percent of the total measure load (hot water plus space heating), which was somewhat higher than the solar fraction of 32 percent. When system losses into the heating space from duct leaks and storage are included, the heating solar fraction increases from 42 to 64 percent. Net electrical energy savings were 5.47 million BTUs.

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