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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Optimization of Energy Storage System Economics and Controls by Incorporating Battery Degradation Costs in REopt

The use of stationary electrochemical energy storage systems utilizing lithium-ion batteries has increased rapidly as the production scale and price for lithium-ion batteries has decreased. These energy storage systems are crucial for maintaining grid resiliency, especially for grids operating with high penetration of renewable energy generation assets or for with a variety of distributed energy generation and storage systems. One challenging factor for the development of battery energy storage systems is estimating the proper sizing, in terms of both power and energy, that minimizes total costs over the lifetime of the systems; this calculation is difficult in simple cases, where a battery is costed independently, but is extremely challenging when building loads and electrical generation by photovoltaic resources are also considered. REopt is a techoeconomic optimization tool developed by NREL to address these challenges. Previously, battery degradation has been priced by simply assuming a 10-year replacement schedule for battery systems. However, this does not account for varying degradation trends observed across real-world batteries, or allow for batteries to be operated in a degradation-aware manner that optimizes battery dispatch based on operating costs. This work incorporates a battery life model into REopt. This battery life model is simple, so that it may be solvable within the constrains of a mixed-integer linear optimization problem, but is fit to accelerated aging data recorded in the lab. To achieve the best possible accuracy for lifetime estimates given these constraints, parameters for the battery life model in REopt are estimated by fitting 20-year simulations of battery life after identifying state-space battery degradation model from accelerated aging data. Comparisons of battery life predicted in REopt and from the state-space battery degradation model to ensure validity of lifetime estimates made by REopt. Battery life and cost is optimized by controlling three decision to minimize system life cost: battery sizing, daily state-of-charge, and daily energy-throughput. The cost of battery degradation as a function of these control variables is then estimated assuming two possible maintenance strategies: replacement, where the entire battery system is replaced if cell reach an end-of-life capacity threshold; and augmentation, which establishes a fund to pay for continual purchase of new batteries to maintain the initial energy capacity of the system. These two strategies offer conservative (for replacement) and optimistic (for augmentation) bounds for total system cost. The degradation cost incurred by these strategies is then used to control battery dispatch decisions, operating the battery in a degradation-aware manner that maximizes battery lifetime while also providing energy when favorable. Because the mixed-integer linear program has perfect foresight of future energy needs, batteries with degradation costs are always operated using 'just-in-time' charging, which is unrealistic, as no energy is left in the storage system to perform other energy services or to serve as emergency back-up power. To combat this, an inequality constraint on the average annual state-of-charge is imposed, and the sensitivity of system cost to average stored energy, e.g., the cost of system resiliency, can be quantified. Analysis of results has several conclusions, for instance, oversizing of battery storage systems is not a cost burden when battery storage is an optimal solution, as any additional battery capacity can simply be utilized to avoid costs of purchasing energy from a utility.

battery↗
DOE OSTI2022

Forecasting distributed energy resources adoption for power systems

Failing to incorporate accurate distributed energy resource penetration forecasts into long-term resource and transmission planning can lead to cost inefficiencies at best and system failures at worst. We have developed an open-source tool that employs an advanced Bass specification to calibrate and forecast technology adoption. The advanced specification includes geographic clustering, exogenously estimated market size, and dynamic time steps. Training on historical adoption of rooftop photovoltaics at the U.S. county-level and using detailed techno-economic estimates, our model achieves a two-year average mean-absolute-percentage-error of 19% in predicting system counts at the county-level, weighted by population. Model error was negatively correlated with market maturity - the error was 12% for counties in states with at least 28 W-per-capita of installed capacity. The advanced specification significantly reduces unweighted forecasting percent error compared to a conventional Bass specification: from 196% to 25% for capacity and from 226% to 22% for system count.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Improved heavy-ion PID using scintillation light detector with neural network analysis: a Monte Carlo simulation study

The photon collection efficiency of gaseous scintillator detectors varies according to the position of the impinging charged particles in the medium that generates scintillation light. Thus, when impinging particles are distributed over a large area, the intrinsic photon-number resolution of the system is affected by a large variation. This work presents and discusses a method for adjusting the total number of detected photons to account for variation in the photon collection efficiency as a function of the position of the light source within the scintillating medium. The method was developed and validated by processing data from systematic simulation studies based on GEANT4 that model the response of the Energy Loss Optical Scintillation System (ELOSS) detector. The position of the charged particle is calculated using a deep neural network algorithm. This is accomplished by analyzing the distribution of scintillation light recorded by the array of photosensors. The estimated particle position is then used to calculate the correction factor and adjust the amount of captured light to account for variations in the photon collection efficiency. The neural network algorithm provides excellent tracking capabilities, achieving sub-millimeter position resolution and an angular resolution of 12 mrad, approaching the performance of traditional tracking detectors (e.g., drift chambers). The present method can be generalized to any optical scintillation system where the photon collection efficiency depends on the position of the impinging particle.

Heavy-ion detectors↗
DOE OSTI2024

Experimental Tests of Lateral Bedload Transport Induced by a Yawed Submerged Vane Array in Open-Channel Flows

This work proposes the use of an array of yawed porous vanes to control the lateral bedload transport by locally steering bedform migration and maximize the amount of sediments redirected toward a potential sediment extraction system or bypass channel. A laboratory experiment was conducted in a quasifield-scale channel with an array of permeable vanes installed on one side, in live-bed conditions under bedload dominant regime, i.e., negligible suspended load. A baseline experiment without vanes was also performed for comparison. The evolution of migrating bedforms of different scales was tracked in space and time using a high-resolution, state-of-the-art laser scanning device. The bedload transport rate in the streamwise direction was first calculated using bedforms’ geometry and migration velocity, and then spatially distributed over the entire monitored area using a new Eulerian-averaged grid-mapping method. This allowed us to introduce a new methodology to estimate the lateral bedload transport using control volume theory and applying mass conservation. Quantitative assessments of lateral bedload transport along the channel yield consistent results, suggesting that the vanes effectively move sediments laterally as intended. Under the investigated setup, the maximum lateral sediment transport rate ranges from 9% to 18% of the whole domain-averaged streamwise transport rate. The developed methodology also allowed to identify the location where sediment capture could be maximized for the given vane spatial distribution.

42 ENGINEERING↗
DOE OSTI2026

Battery Energy Storage System (BESS) End-of-Performance and Decommissioning Considerations [Slides]

This presentation provides a comprehensive overview of end-of-performance and decommissioning considerations for large-scale Battery Energy Storage Systems (BESS). It outlines expected system lifespans, midterm assessment needs, and pathways for extending operational life through augmentation or repowering. The presentation details regulatory requirements that govern decommissioning plans, cost estimates, financial assurance mechanisms, and performance obligations across multiple jurisdictions. It further examines end-of-life equipment management, including recycling, waste handling, transportation, and environmental compliance. Designed to support Malawi's electricity-sector institutions, the presentation highlights how planning for decommissioning and environmental stewardship can be integrated early in project development to ensure safe, financially accountable, and environmentally responsible BESS system retirement.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Application of Sequential Design of Experiments (SDoE) to Large Pilot-Scale Solvent-Based CO2 Capture Process at Technology Centre Mongstad (TCM)

The United States Department of Energy’s Carbon Capture Simulation for Industry Impact (CCSI2) program has developed a framework for sequential design of experiments (SDoE) that aims to maximize knowledge gained from budget- and schedule-limited pilot scale testing. SDoE was applied to the planning and execution of campaigns for testing CO2 capture systems at pilot-scale in order to optimally allocate resources available for the testing. In this methodology, a stochastic process model is developed by quantifying the parametric uncertainty in submodels of interest; for a solvent-based CO2 capture system, these may include physical properties and equipment performance submodels (e.g., mass transfer, interfacial area). This uncertainty is propagated through the full process model, over variable operating conditions, for estimating the resulting uncertainty in key model outputs (e.g., percentage of CO2 capture, solvent regeneration energy requirement). In developing a data collection plan, the predicted output uncertainty is incorporated into an algorithm that seeks simultaneously to select process operating conditions for which the predicted uncertainty is relatively high and to ensure that the entire space of operation is well represented. This test plan is then used to guide operation of the pilot plant at varying steady-state conditions, with resulting process data incorporated into the existing model using Bayesian inference to refine parameter distributions. The updated stochastic model, with reduced parametric uncertainty from data collected, is then used to guide additional data collection, thus the sequential nature of the experimental design. The SDoE process was implemented at the pilot test unit (12 MWe in scale) at Norway’s Technology Centre Mongstad (TCM) in a summer 2018 test campaign with aqueous monoethanolamine (MEA). During the test campaign, the varied operating conditions included the flowrates of circulated solvent, flue gas, and reboiler steam and the CO2 concentration in the flue gas. The process data were used to update probability distributions of mass transfer and interfacial area parameters of a stochastic process model developed by the CCSI2 team. Two iterations of the SDoE process were executed, resulting in the uncertainty in model predicted CO2 capture percentage decreasing by an average of 58.0 ± 4.7% over the full input space of interest. This work demonstrates the potential of the SDoE process for model refinement through reduction in process model parametric uncertainty, and ultimately risk in scale-up, in CO2 capture technology performance.

carbon capture↗
DOE OSTI2025

Resource assessment of ocean thermal energy conversion in Puerto Rico and U.S. Virgin Islands

Island communities often struggle to establish and maintain traditional electric grids and are therefore heavily reliant on costly imported fossil fuels. In the case of Puerto Rico, these challenges are enhanced by extreme weather and other natural hazards that threaten the local electricity generation and transmission infrastructure. Ocean thermal energy conversion (OTEC) could play an important role in establishing a more resilient electrical grid in the region. Here, in this study, a detailed analysis is conducted to characterize the ocean thermal resource and power potential of OTEC in Puerto Rico based on a 14-year dataset of modeled ocean temperature. The assessment considers seasonal and interannual variability in the region's thermal resource and examines the operational limitations associated with minimal thermal gradients required to run a typical OTEC heat engine. Notably, the local thermal resource is found to be sensitive to El Niño-Southern Oscillation (ENSO) climate patterns, with La Niña conditions linked to greater OTEC power availability. Seven areas of opportunity are identified based on their resource potential and proximity to existing electrical distribution lines, including two that could benefit the nearby U.S. Virgin Islands. The greatest OTEC power potential is observed to the south of the main island of Puerto Rico in the Caribbean Sea with an estimated capacity of 138 MW for a plant pumping cold water from a depth of 1,000 m, or the equivalent amount of electricity required to power 219,000 households.

OTEC↗
DOE OSTI2025

Benchmarking greenhouse gas emissions from US wastewater treatment for targeted reduction

Here, in this study, to assess the national climate impact of wastewater treatment and inform decarbonization, we assembled a comprehensive greenhouse gas inventory of 15,863 facilities in the contiguous USA. Considering location and treatment configurations, we modelled on-site CH 4 , N 2 O and CO 2 production and emissions associated with energy, chemical inputs and solids disposal. Using Monte Carlo simulations, we estimated median national emissions at 47 million tonnes of CO 2 equivalent per year, with on-site process CH 4 and N 2 O emissions exceeding current government estimates by 41%. Treatment configurations with anaerobic digesters are responsible for 16 million tonnes of CO 2 equivalent per year of fugitive methane, outweighing benefits achieved through on-site electricity generation. Systems designed for nutrient removal have the highest greenhouse gas emissions intensity, attributable to energy requirements and N 2 O production, demonstrating current trade-offs between meeting water quality and climate objectives. We analysed key sensitivities and included a geospatial analysis to highlight the scale and distribution of opportunities for reducing life cycle greenhouse gas emissions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Uncertainty Quantification for Capacity Expansion Planning

This report quantifies the uncertainty in output decisions from a Capacity Expansion Planning (CEP) model. The need to understand how uncertainties within CEP models and modeling assumptions affect Quantities of Interest (QoIs) such as expansion and operating costs, as well as expansion decisions remains an ongoing challenge in scientific research and industrial operations. This area of research is particularly important for models which seek to capture how large networks will evolve and operate under increased sources of variable generation, i.e., higher penetration of renewable technologies such as solar and wind generators. Uncertainty quantification (UQ) of CEP models which estimate expansion costs and decisions, and production cost models which estimate operating costs and dispatch decisions, is a key focus of research at NREL. The Regional Energy Deployment System (ReEDS) represents a state-of-the-art CEP model and considers a range of possible grid evolutions in an attempt to identify key drivers, ramifications, and decisions which contribute to better informed investment and policy decisions. However, research to quantify how uncertainties and model assumptions, such as unit commitment (UC), within ReEDS may be affecting its outputs remains challenging due to to size and complexity of the model

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Model predictive control for matrix converter operating in current control mode with load current estimation

A matrix converter system operating in current control mode is provided. The matrix converter includes a switching matrix coupled between a low voltage side and a high voltage side, wherein the matrix converter is coupled at its low voltage side to a generator for receiving an input power including an input current and transforming the input power into an output power at its high voltage side, wherein a load is coupled to the high voltage side. The control system includes a load observer and a model predictive controller (MPC). The load observer is configured to estimate a load current that flows to the load from the high voltage side of the matrix converter as a function of a switching state of the switching matrix, an output voltage output at the high voltage side of the matrix converter, and the input current. The MPC is configured to select the switching state of the switching matrix to meet one or more control objectives defined by minimization of a multi-objective function that tracks the output voltage and the input current using the estimated load current.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Introducing the SLICE Method for estimating pebble-bed reactor inventories at equilibrium operation with SCALE

This paper introduces the SCALE Leap-In method for Cores at Equilibrium (SLICE) for estimating pebble-bed reactor equilibrium core isotopic inventories using capabilities in the SCALE code system, requiring only a small computational cluster and a few days of computation. This method uses an iterative approach that relies on (1) a surrogate spectrum model that captures spatial and time-dependent spectral conditions, (2) a multi-pass model that captures the pebble’s evolving nuclide inventory as a function of location and time in the core, and (3) a full-core model that captures the core’s spatial neutron flux distribution. The SLICE approach is applied to a generic fluoride salt–cooled high-temperature reactor, demonstrating fuel inventory convergence through nuclide concentration inspection across iterations and comparisons for core realizations with varying discretizations. Results agree within ~5% with another state-of-the-art code, with differences attributed to input parameter or modeling assumption variations in the equilibrium generation methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

A Review of Value of Solar Studies In Theory and In Practice

This brief summarizes a collection of state- and utility-commissioned value-of-solar (VoS) studies and related literature, with a focus on who commissioned the study, which value and cost categories were discussed and/or quantified, and the methods used. Our objective is to compile information on prior VoS studies to inform state regulators and other stakeholders that may pursue related studies or integrate findings into rate design. The brief is organized into three parts: 1) an introduction to distributed solar photovoltaic (DPV) compensation; 2) a review of theoretical research on VoS; and 3) a review of VoS studies. The vast majority of VoS studies have served an informational role of quantifying the net benefits of PV. Three studies were commissioned in states or utility service territories that subsequently implemented VoS tariffs in California, New York, and Austin, Texas. When applied as a tariff, VoS aims to compensate PV output as efficiently as possible by doing so at rates that reflect the marginal benefits and costs of PV through value and cost categories that may vary temporally and/or geographically. This could lead to higher compensation in locations and times where more PV output is more valuable and consequently drive adoption in those locations to provide more societal benefits. Value and cost factors can be broadly grouped into five categories: generation, transmission, distribution, other utility, and other social categories. Those conducting VoS studies must weigh various tradeoffs when deciding which categories to include and quantify. Tradeoffs include prioritizing values based on their magnitude of value or cost impact, as well as taking into account the feasibility of data collection and accurate quantification. Values of higher magnitude and estimation feasibility are quantified in the majority of studies, including the earliest of studies conducted in the 2000s and 2010s. Additionally, some values of higher magnitude but low feasibility in the earliest of studies have become quantifiable in recent years. There are some values with low average system-wide levels but very high magnitude in specific locations or hours. The value magnitude in some cases can be tied to DPV penetration with low value in areas with little congestion and/or low penetration and vice versa. In these cases, values that are easier to quantify are often incorporated, while those that are more difficult are often addressed via a placeholder value. The placeholder value is paired with a discussion around data needs and methods to improve future estimates, as well as a conversation about when these value categories may increase in magnitude and necessitate more rigorous quantification. This brief summarizes findings from two meta-analyses of VoS studies that took place between 2005 and 2018, as well as findings from four additional studies published from 2018 to 2023. Table ES-1 summarizes the various value and cost categories included in each respective study and whether they were quantified, discussed, or omitted. Values such as avoided energy, capacity, transmission capacity, line losses, and avoided environmental costs are quantified in every study. Some categories were deemed harder to quantify and less impactful at the time of the study, so they were discussed but not quantified (e.g., ancillary services). Other categories, including many at the distribution level, were very locationally and/or temporally specific and dependent on high DPV penetration. These were sometimes quantified and at other times discussed. Notably, when it came to utility costs, integration costs were discussed in all cases, though they were deemed to have a small impact. Other utility costs were omitted for the most part; however, the utility-commissioned study (by NorthWestern Energy in Montana) included both lost utility revenue and programmatic/administrative cost categories. While there are some similarities across studies, each had fairly unique methods that are detailed in the body of this brief.

14 SOLAR ENERGY↗
DOE OSTI2025

Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material properties, equation of state (EOS), opacities, and initial conditions. Typically, however, these parameters are not directly observable. What is observed instead is a time sequence of radiographic projections using X-rays. In this work, we define a set of sparse hydrodynamic features derived from the outgoing shock profile and outer material edge, which can be obtained from radiographic measurements, to directly infer such parameters. Our machine learning (ML)-based methodology involves a pipeline of two architectures, a radiograph-to-features network (R2FNet) and a features-to-parameters network (F2PNet), that are trained independently and later combined to approximate a posterior distribution for the parameters from radiographs. We show that the machine learning architectures are able to accurately infer initial conditions and EOS parameters, and that the estimated parameters can be used in a hydrodynamics code to obtain density fields, shocks, and material interfaces that satisfy thermodynamic and hydrodynamic consistency. Finally, we demonstrate that features resulting from an unknown EOS model can be successfully mapped onto parameters of a chosen analytical EOS model, implying that network predictions are learning physics, with a degree of invariance to the underlying choice of EOS model. To the best of our knowledge, our framework is the first demonstration of recovering both thermodynamic and hydrodynamic consistent density fields from noisy radiographs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Updating PV and Battery Bill Savings Calculations for Net Billing: New Best Practices for Input Data and Uncertainty

Jurisdictions are increasingly adopting compensation structures for distributed PV and PV-battery systems that price exported energy lower than energy consumed onsite (net billing rates). Standard methods for calculating the bill savings from PV and PV-battery systems were developed for net metering structures, and applying these same methods to net billing structures (such as using Typical Meteorological Year weather with actual year load) introduces bias errors that underestimate PV-battery system bill savings by between 1.5\% and 9\%, depending on the utility rate. We assess the magnitude of these errors and compare them to other sources of uncertainty when estimating the bill savings from PV and PV-battery systems under more complex utility rates.

14 SOLAR ENERGY↗
DOE OSTI2025

Learning robust parameter inference and density reconstruction in flyer plate impact experiments

Estimating physical parameters or material properties from experimental observations is a common objective in many areas of physics and material science. In many experiments, especially in shock physics, radiography is the primary means of observing the system of interest. However, radiography does not provide direct access to key state variables, such as density, which prevents the application of traditional parameter estimation approaches. Here we focus on flyer plate impact experiments on porous materials, and resolving the underlying parameterized equation of state (EoS) and crush porosity model parameters given radiographic observation(s). We use machine learning as a tool to demonstrate with high confidence that using only high impact velocity data does not provide sufficient information to accurately infer both EoS and crush model parameters, even with fully resolved density fields or a dynamic sequence of images. We thus propose an observable data set consisting of low and high impact velocity experiments/simulations that capture different regimes of compaction and shock propagation, and proceed to introduce a generative machine learning approach which produces a posterior distribution of physical parameters directly from radiographs. We demonstrate the effectiveness of the approach in estimating parameters from simulated flyer plate impact experiments, and show that the obtained estimates of EoS and crush model parameters can then be used in hydrodynamic simulations to obtain accurate and physically admissible density reconstructions. Finally, we examine the robustness of the approach to model mismatches, and find that the learned approach can provide useful parameter estimates in the presence of out-of-distribution radiographic noise and previously unseen physics, thereby promoting a potential breakthrough in estimating material properties from experimental radiographic images.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Inverse rendering of fusion plasmas: Inferring plasma composition from imaging systems

In this work, we develop a differentiable rendering pipeline for visualising plasma emission within tokamaks, and estimating the gradients of the emission and estimating other physical quantities. Unlike prior work, we are able to leverage arbitrary representations of plasma quantities and easily incorporate them into a non-linear optimisation framework. The efficiency of our method enables not only estimation of a physically plausible image of plasma, but also recovery of the neutral Deuterium distribution from imaging and midplane measurements alone. We demonstrate our method with three different levels of complexity showing first that a poloidal neutrals density distribution can be recovered from imaging alone, second that the distributions of neutral Deuterium, electron density and electron temperature can be recovered jointly, and finally, that this can be done in the presence of realistic imaging systems that incorporate sensor cropping and quantisation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Hierarchical semi-Markov models with duration-aware dynamics for activity sequences

Residential electricity demand at granular scales is driven by what people do and for how long. Accurately forecasting this demand for applications like microgrid management and demand response therefore requires generative models for activities that can produce realistic daily activity sequences, capturing both the timing and duration of human behavior. This paper develops a generative model of human activity sequences using nationally representative time-use diaries at a 10-min resolution. We use this model to quantify which demographic factors are most critical for improving predictive performance. We propose a hierarchical semi-Markov framework that addresses two key modeling challenges. First, a time-inhomogeneous Markov router learns the patterns of “which activity comes next.” Second, a semi-Markov hazard component explicitly models activity durations, capturing “how long” activities realistically last. To ensure statistical stability when data are sparse, the model pools information across related demographic groups and time blocks. The entire framework is trained and evaluated using survey design weights to ensure our findings are representative of the U.S. population. On a held-out test set, we demonstrate that explicitly modeling durations with the hazard component provides a substantial and statistically significant improvement over purely Markovian models. Furthermore, our analysis reveals a clear hierarchy of demographic factors: Sex, Day-Type, and Household Size provide the largest predictive gains, while Region and Season, though important for energy calculations, contribute little to predicting the activity sequence itself. The result is an interpretable and robust generator of synthetic activity traces, providing a high-fidelity foundation for downstream energy systems modeling.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Granger Causality for prediction in Dynamic Mode Decomposition: Application to power systems

Here, the dynamic mode decomposition (DMD) technique extracts the dominant modes characterizing the innate dynamical behavior of the system within the measurement data. For appropriate identification of dominant modes from the measurement data, the DMD algorithm necessitates ensuring the quality of the input measurement data sequences. On that account, for validating the usability of the dataset for the DMD algorithm, the paper proposed two conditions: Persistence of excitation (PE) and the Granger Causality Test (GCT). The virtual data sequences are designed with the hankel matrix representation such that the dimensions of the subspace spanning the essential system modes are increased with the addition of new state variables. The PE condition provides the lower bound for the trajectory length, and the GCT provides the order of the model. Satisfying the PE condition enables estimating an approximate linear model, but the predictability with the identified model is only assured with the temporal causation among data searched with GCT. The proposed methodology is validated with the application for coherency identification (CI) in a multi-machine power system (MMPS), an essential phenomenon in transient stability analysis. The significance of PE condition and GCT is demonstrated through various case studies implemented on 22 bus six generator system.

24 POWER TRANSMISSION AND DISTRIBUTION↗