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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 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multidisciplinary benchmarks of a conservative spectral solver for the nonlinear Boltzmann equation

The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and plasma physics. While these approximations are appropriate in their respective domains, they can be violated in niche but diverse applications which require direct numerical solution of the original nonlinear Boltzmann equation. An expanded implementation of the Galerkin–Petrov conservative spectral algorithm is employed to study a wide variety of physical problems. Enabled by distributed precomputation, solutions of the spatially homogeneous Boltzmann equation can be achieved in seconds on modern personal hardware, while spatially-inhomogeneous problems are solvable in minutes. Here, several benchmarks are presented focusing on accuracy compared to both analytic theoretical predictions and other Boltzmann solvers. These benchmarks span several physical domains including weakly ionized plasma, gaseous fluids, and atomic-plasma interaction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A universal implementation of radiative effects in neutrino event generators

Due to the similarities between electron-nucleus (eA) and neutrino-nucleus scattering (νA), eA data can contribute key information to improve cross-section modeling in eA and hence in νA event generators. However, to compare data and generated events, either the data must be radiatively corrected or radiative effects need to be included in the event generators. We implemented a universal radiative corrections program that can be used with all reaction mechanisms and any eA event generator. Our program includes real photon radiation by the incident and scattered electrons, and virtual photon exchange and photon vacuum polarization diagrams. It uses the “extended peaking” approximation for electron radiation and neglects charged hadron radiation. This method, validated with GENIE, can also be extended to simulate νA radiative effects. This work facilitates data-event-generator comparisons used to improve νA event generators for the next-generation of neutrino experiments. Program Title: emMCRadCorr CPC Library link to program files:https://doi.org/10.17632/hmsxg82vnf.1 Developer's repository link:https://github.com/e4nu/emMCRadCorr Licensing provisions: AGPLv3 Programming language:C++ Nature of problem: Radiative effects can significantly modify the event kinematics and the resulting cross-sections. Such effects must be accounted for when comparing event generators to eA data. Existing radiative correction codes are tailored to specific processes and topologies, and are limited to a restricted phase space defined by the spectrometer acceptance. Therefore, a more general approach is required to apply radiative corrections to semi-inclusive and exclusive eA measurements. Solution method: Our program incorporates real photon radiation from both the incident and scattered electrons, as well as virtual photon exchange and photon vacuum polarization effects. It employs the “extended peaking” approximation for electron radiation while neglecting contributions from charged hadron radiation. The code is fully decoupled from event generator codes and can be used for all event generators in the market.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
DOE OSTI2021

Review of analytical studies on seismic fluid-structure interaction of base-supported cylindrical tanks

Analytical solutions for seismic fluid-structure interaction (FSI) of tanks are used by analysts and engineers for a number of purposes, including preliminary sizing, risk assessment, and verification of numerical models. Analytical solutions for seismic FSI of tanks were first developed in the 1930s and have been extended and/or modified in the following nine decades to accommodate different seismic inputs and boundary conditions. This report reviews published analytical solutions for rigid and flexible, base-supported, cylindrical tanks subjected to unidirectional horizontal motion of a small amplitude. The studies parsed the fluid-structure (FSI) response into an impulsive and a convective component, and addressed frequencies of lateral motions of the tank (i.e., impulsive frequencies), hydrodynamic pressures, frequencies of waves (i.e., convective frequencies), wave heights, and reactions at the base. The solutions were categorized into exact and approximate solutions based on the methodologies used. Herein, FSI responses are calculated and compared for a range of tank dimensions using the analytical solutions from the different studies. The responses presented here are normalized to be unitless, and can be used for tanks with different dimensions and mechanical properties, and subjected to different input motions. A sample steel water tank is analyzed using the normalized solutions for two earthquake ground motions with different frequency contents. Ignoring tank flexibility may significantly underestimate seismic responses of the tank and its contained fluid. The approximate solutions, which have been widely used for decades, may not be sufficiently accurate in the modern era. Calculation errors in the reviewed studies are identified and corrected, and differences are quantified for the sample tank.

42 ENGINEERING↗
DOE OSTI2025

Assessing electrification readiness in U.S. single-family homes based on a nationwide survey of electrical panel capacities

Electrification of residential buildings is a key strategy for increasing the use of renewable energy sources. Central to this transition is understanding the capacity of existing electrical infrastructure—specifically electrical panels—to safely and effectively manage increased electricity demands from electrification technologies. However, comprehensive nationwide data on electrical panel capacities in U.S. single-family homes is currently lacking. To address this gap, we conducted a nationwide survey of single-family homes, collecting detailed data on electrical panel capacities, breaker slot availability, major electric and gas appliances, electrical panel models, and home characteristics such as construction year and floor area. Photographic documentation was used to verify electrical panel data and appliance information. Results show that approximately 60% of surveyed homes have electrical panels rated at ≥200 amperes (A), indicating that a significant portion of the existing housing stock can accommodate additional electric loads. However, 31% of homes possess panels rated at ≤100 A, potentially restricting their ability to adopt new electric appliances without significant upgrades. Panel capacities positively correlate with both home size and construction year, with newer and larger homes generally better suited for electrification. Homes with higher-capacity panels tend to have fewer gas appliances, reflecting a gradual shift toward electric technologies. Conversely, homes with lower-capacity panels frequently rely on multiple gas appliances, highlighting substantial electrification challenges. Additionally, approximately 3% of surveyed homes had potentially hazardous electrical panel models, emphasizing important safety considerations in the residential electrification process. Our findings underscore the need for targeted policies, financial incentives, and infrastructure investments designed specifically to address infrastructural and safety barriers, particularly in older and smaller homes, to support equitable and efficient electrification across the U.S. residential sector.

Gul, Sadia↗
DOE OSTI2021

Benzo[a]pyrene (BaP) metabolites predominant in human plasma following escalating oral micro-dosing with [ 14 C]-BaP

Benzo[a]pyrene (BaP) is formed by incomplete combustion of organic materials (petroleum, coal, tobacco, etc.). BaP is designated by the International Agency for Research on Cancer as a group 1 known human carcinogen; a classification supported by numerous studies in preclinical models and epidemiology studies of exposed populations. Risk assessment relies on toxicokinetic and cancer studies in rodents at doses 5–6 orders of magnitude greater than average human uptake. Using a dose–response design at environmentally relevant concentrations, this study follows uptake, metabolism, and elimination of [ 14 C]-BaP in human plasma by employing UPLC - accelerator mass spectrometry (UPLC-AMS). Volunteers were administered 25, 50, 100, and 250 ng (2.7–27 nCi) of [ 14 C]-BaP (with interceding minimum 3-week washout periods) with quantification of parent [ 14 C]-BaP and metabolites in plasma measured over 48 h. [ 14 C]-BaP median T max was 30 min with C max and area under the curve (AUC) approximating dose-dependency. Marked inter-individual variability in plasma pharmacokinetics following a 250 ng dose was seen with 7 volunteers as measured by the C max (8.99 ± 7.08 ng × mL -1 ) and AUC0-48hr (68.6 ± 64.0 fg × hr -1 × mL -1 ). Approximately 3–6% of the [ 14 C] recovered (AUC 0-48 hr ) was parent compound, demonstrating extensive metabolism following oral dosing. Metabolite profiles showed that, even at the earliest time-point (30 min), a substantial percentage of [ 14 C] in plasma was polar BaP metabolites. The best fit modeling approach identified non-compartmental apparent volume of distribution of BaP as significantly increasing as a function of dose (p = 0.004). Bay region tetrols and dihydrodiols predominated, suggesting not only was there extensive first pass metabolism but also potentially bioactivation. AMS enables the study of environmental carcinogens in humans with de minimus risk, allowing for important testing and validation of physiologically based pharmacokinetic models derived from animal data, risk assessment, and the interpretation of data from high-risk occupationally exposed populations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

The short-term comprehensive impact of the phase-out of global coal combustion on air pollution and climate change

With the continuous intensification of global warming, the reduction and ultimate phase-out of coal combustion is an inevitable trend in the future global energy transformation. This study comprehensively analyzed the impact of phasing out coal combustion on global emissions and concentrations of air pollutants, radiative fluxes, meteorology and climate using Community Earth System Model 2 (CESM2). The results indicate that after the global phase-out of coal combustion, there is a marked decrease in the concentrations of sulfur dioxide (SO 2 ), nitrogen oxides (NO x ) and fine particulate matter (PM 2.5 ), with some regions experiencing a reduction of exceeding 50%. There is no significant change in global ozone (O 3 ) concentration. There are decreasing AOD and positive radiative fluxes globally in the short term, though the cloud contributes minor negative radiative fluxes. The global air temperature may increase by approximately (0.02 ± 0.15) °C on average with regional and seasonal variations, and the precipitation may potentially increase by approximately (2.7 ± 40.6) mm yr −1 globally and over 20% in equatorial regions in the short term. But combined with the decreasing trend of cloud water content in the Northern Hemisphere, it indicates a potential increase in the extremity of precipitation events. In conclusion, this study provides references for global control of air pollution, mitigation strategies of climate change, and transformation of energy structures under the objective of “carbon neutrality”, such as focusing on the negative climate impacts of exacerbating regional warming and increasing extreme precipitation resulting from the rapid reduction of aerosols in the short term.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2020

Stochastic DC optimal power flow with reserve saturation

We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator’s target level hits its limit, it abandons the affine policy and produces at that limit. This is a particularly interesting feature in models where wind power plants, which have uncertain upper generation limits, are scheduled to provide reserves to balance load fluctuations. Here, the resulting model is a nonsmooth nonconvex two-stage stochastic program, and we use a stochastic approximation method to find stationary solutions to a smooth approximation. Computational results on 6-bus and 118-bus test instances demonstrate that by considering the effects of saturation, our model can yield solutions with lower expected generation costs (at the same target line violation probability level) than those obtained from a model that enforces the affine policy to stay within generator limits with high probability.

17 WIND ENERGY↗
DOE OSTI2022

On the operational characteristics and economic value of pumped thermal energy storage

Pumped thermal energy storage (PTES) systems use an electrically-driven heat pump to store electricity in the form of thermal energy, and subsequently dispatch the stored thermal energy to generate electricity using a thermodynamic heat engine. Optimal day-ahead operational scheduling and annual value of a PTES system based on Joule-Brayton thermodynamic cycles and two-tank molten salt hot thermal storage is evaluated in this work. Production cost models, which simultaneously optimize commitment and dispatch schedules for an entire set of generators to minimize the cost of satisfying electricity demand, are employed to determine system-optimal operation and day-ahead energy value of the PTES system within each of six hypothetical near-future grid scenarios intended to approximately represent the U.S. Western Interconnection or the Texas Interconnection. Sensitivity to grid scenario (including the contribution of variable renewable energy sources), thermal storage capacity, relative heat pump and heat engine capacities, and startup/shutdown cycling costs are evaluated. PTES energy value and heat engine annual capacity factor increase strongly as the contribution of variable renewable resources increases, heat pump capacity increases relative to heat engine capacity, or PTES cycling costs decrease. Grid scenarios in which the contribution of variable renewable energy is dominated by solar photovoltaics (PV) vs. wind produce inherently different PTES operational patterns. Annual PTES energy value within PV-dominated scenarios increased with storage capacity only up to approximately seven hours of full-load discharge capacity, whereas that within wind-dominated scenarios exhibited a continual increase with storage duration up to at least 16 hours.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Improved cycle stability and high-rate capability of LiNbO 3 -coated Li 3 VO 4 as anode material for lithium-ion battery

Lithium vanadate (Li 3 VO 4 ) has garnered considerable attention as an alternative negative electrode material for non-aqueous lithium-ion batteries due to its high capacity, energy efficiency, and stable discharge voltage. Nonetheless, the Li 3 VO 4 material displays a low rate capability, attributed mainly to its poor intrinsic electronic conductivity. Here, in this study, we report the synthesis of lithium niobate LiNbO 3 -coated Li 3 VO 4 (LVO@LNO) using a one-pot sol-gel method. The resulting LVO@LNO demonstrates a high reversible capacity of approximately 530 mAh/g, which is more than double that of free Li 3 VO 4 . To explore the effect of the LNO coating process on the morphological and structural properties, Raman, XRD, operando XRD, XPS, SEM and HTEM analyses were conducted. To explain the enhancement of electronic conductivity in our modified material after a LiNbO 3 coating, we conducted an Ex-Situ electrochemical impedance (EIS) and Density Functional Theory (DFT) computational study. Additionally, we designed a full cell utilizing a 1 wt% LNO-coated LVO anode and NMC-811 cathode. The cell yielded an output voltage of approximately 2.8 V with a high initial specific capacity of 350 mAh/g versus to the anode, at 1C with a capacity retention of 85 % after 100 cycles.

25 ENERGY STORAGE↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for inverse problems: Determining material properties for heterogeneous systems

Here, we determine spatially varying discontinuous material properties using a domain-decomposition based physics-informed neural networks (PINNs) framework named the Adaptive Interface-PINNs or AdaI-PINNs (Roy et al., 2024). We propose the use of distinct neural networks for the field variables and material properties within each material, utilizing adaptive activation functions. While the neural networks across different materials share the same weights and biases, their activation functions are uniquely tailored using a hyperparameter that influences the slope of the activation function. The proposed framework is tested on several one-dimensional and two-dimensional benchmark examples, and its performance is compared with conventional PINNs and existing domain-decomposition PINNs frameworks, namely, the Multi-domain physics-informed neural network (M-PINN), and the eXtended physics-informed neural networks (XPINNs). The results demonstrate that the proposed approach can determine randomly distributed discontinuous material properties with an L 2 error of $\mathscr{O}$ (10 -3 ) for the material property and the root-mean-square error of $\mathscr{O}$ (10 -3 ) for the primary variable while the other approaches yield errors that are approximately two orders of magnitude larger (that is, $\mathscr{O}$ (10 -1 )). Moreover, the spatial distribution of material properties obtained using the proposed framework is in close agreement with the true distribution, whereas the other approaches fare much worse. Additionally, the proposed approach is approximately 40% faster than its competitors, indicating its potential as a robust alternative for solving inverse problems in heterogeneous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Microstructural diversity and digestion yields of select bituminous and subbituminous coals as raw material candidates for carbon fiber precursor production

Here, this work investigates the use of coals as raw materials for carbon fiber precursor production as a new alternative to coal utilization. Coal being a highly complex and heterogeneous material with different macerals and minerals complicates this task. Extensive microstructural characterization as well as preliminary digestion studies are performed on three bituminous coals (Herrin and Springfield from the Illinois Basin and the Blue Gem from the Central Appalachians) and one subbituminous coal from the Powder River Basin (Monarch), as raw material candidates. The subbituminous coal was richer in oxygen, lower in sulfur, and had a higher volatile matter yield. Microstructural investigations were performed using X-ray diffraction, X-ray/neutron computed tomography, scanning electron microscopy with energy dispersive spectroscopy, and petrology. Mild solvent extraction studies were conducted using creosote and decant oil as solvents in microreactors. The extraction yield was sensitive to temperature and time (350 to 450 °C between 30 and 120 mins.) for both creosote and decant oil digestions. While the Blue Gem coal had more desirable microstructural properties with less mineral content and cleaner macerals, it had the lowest coal conversion to quinoline soluble ‘liquid’ (of the bituminous coals). The lower coal conversion yield was hypothesized to be connected to the lack of FeS2 which could act as a catalyst when Fe is liberated from the structure under solvent extraction conditions. The Herrin and Springfield coals revealed similar microstructures and coal conversion efficiencies (higher than Blue Gem). These coals were the most promising candidates for further examination from this first approximations study. The subbituminous Monarch coal, however, was deemed less suitable due to poor coal conversion and less desirable microstructures. Additionally, the presented results with combined microstructural data from multiple length scales established a framework necessary for a first approximations study in this new coal utilization approach.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

Approach to startup inventory for viable commercial fusion power plant

With the increasing efforts to commercialize fusion power, private and government organizations are investing heavily in the development of technology to support a viable fusion power plant. Deuterium-Tritium (DT) fueled reactors are more prevalent than other proposed designs, requiring tritium processing and handling technology for safe operations and self-sufficiency. Further, each fusion power plant will need a specific-to-design startup inventory of tritium to begin operations. This startup inventory is required prior to breeding and is the minimum tritium inventory required to fill each processing component in the fuel cycle, to offset radioactive decay losses, and to avoid a zero-fuel situation for continuous operation. We present an approach to calculate the startup tritium inventory for a 500 MW th reactor, with considerations for reserve inventory for maintenance and commissioning. A baseline startup inventory was calculated to be approximately 327 gs. This value was obtained using modest assumptions about the technology and operating parameters of a fusion power plant. The required operating reserve inventory or the inventory necessary to keep a fusion power plant operational using only direct internal recycling for 24 h for the same plant design is approximately 642 gs. The approach and findings of this paper will enable fusion energy stakeholders to better utilize the existing scarce global tritium supply.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Coupled feldspar dissolution and secondary mineral precipitation in batch systems: 6. Labradorite dissolution, calcite growth, and clay precipitation at 60 °C and pH 8.2–8.4

Here, we conducted experiments on concurrent labradorite dissolution, calcite precipitation, and clay precipitation in batch reactor systems and tracked reaction processes using multiple isotope tracers. Labradorite was chosen for its role as a major and reactive component in basalt; the experiments thus directly impact our understanding of CO 2 storage in basalt aquifers and enhanced rock weathering. We doped initial solutions with 29 Si, 43 Ca, and Ca 13 CO 3 (s). Experiments were conducted at 60 °C and pH ~ 8.3 for up to 840 h, with isotope ratios in the experimental aqueous solutions measured using MC-ICP-MS. Unidirectional rates of labradorite dissolution near equilibrium were approximately two orders of magnitude slower than far-from-equilibrium rates reported in the literature. Calcite growth occurred near equilibrium and the rates were limited by the labradorite dissolution rates. In the steady state phase, the interplay of these three heterogeneous reactions—labradorite dissolution, calcite growth, and clay precipitation—results in a coupled system that approaches a near-equilibrium state. The system does not reach true equilibrium because labradorite continues to dissolve, albeit at a much slower rate near equilibrium. The overall reaction can be approximated as, Na 0.4 Ca 0.6 Al 1.6 Si 2.4 O 8 + 0.6HCO 3 - + 1·.7H 2 O + 0.4H + → 0.4Na + + 0.6CaCO 3(s) + 0.5Al 2 Si 2 O 5 (OH) 4(s) + 0.6Al(OH) 4 - + 1.4SiO 2 o (aq). The experimental results show that using short-term far-from-equilibrium rate constants would lead to an overestimation of feldspar weathering rates at the Earth’s surface (e.g., basalt weathering and enhanced rock weathering) and CO 2 mineralization in basalt aquifers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Identification and Online Updating of Dynamic Models for Demand Response of an Industrial Air Separation Unit

Demand-response operation of air separation units requires frequent changes in production rate(s), and scheduling calculations must explicitly consider process dynamics to ensure feasibility of the solutions. To this end, scale-bridging models (SBMs) approximate the scheduling-relevant dynamics of a process and its controller in a low-order representation. In contrast to previous works that have employed nonlinear SBMs, this paper proposes linear SBMs, developed using time-series analysis, to facilitate online scheduling computations. Using a year-long industrial dataset, we nd that compact linear SBMs are suitable approximations over typical scheduling horizons, but that their accuracies are unpredictable over time. We introduce a strategy for online updating of the SBMs, based on Kalman ltering schemes for online parameter estimation. The approach greatly improves the accuracy of SBM predictions and will enable the use of linear SBM-based demand-response scheduling in the future.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗