Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “grid integration study”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 919 records · Page 51

Improving the geological interpretation of magnetic and gravity satellite anomalies

Quantitative analysis of the geologic component of observed satellite magnetic and gravity fields requires accurate isolation of the geologic component of the observations, theoretically sound and viable inversion techniques, and integration of collateral, constraining geologic and geophysical data. A number of significant contributions were made which make quantitative analysis more accurate. These include procedures for: screening and processing orbital data for lithospheric signals based on signal repeatability and wavelength analysis; producing accurate gridded anomaly values at constant elevations from the orbital data by three-dimensional least squares collocation; increasing the stability of equivalent point source inversion and criteria for the selection of the optimum damping parameter; enhancing inversion techniques through an iterative procedure based on the superposition theorem of potential fields; and modeling efficiently regional-scale lithospheric sources of satellite magnetic anomalies. In addition, these techniques were utilized to investigate regional anomaly sources of North and South America and India and to provide constraints to continental reconstruction. Since the inception of this research study, eleven papers were presented with associated published abstracts, three theses were completed, four papers were published or accepted for publication, and an additional manuscript was submitted for publication.

Hinze, William J.↗

Experimental Evaluation of Thermal Storage Performance of a Dual-Purpose Underground Thermal Battery

A geothermal heat pump (GHP) system is an energy-efficient building heating and cooling technology with great potential for reducing energy consumption and decarbonization. However, applications of GHP are still limited due to the high cost, of which 30% is related to the cost of installing the conventional vertical bore ground heat exchangers, which are usually installed in boreholes 60 meters deep. A dual-purpose underground thermal battery (DPUTB) has been developed to offer a low-cost ground heat exchanger with a built-in thermal storage capacity. The DPUTB innovatively integrates a shallow-bore ground heat exchanger (the outer tank), which can be installed in a borehole less than 6 m deep, with thermal energy storage (TES) (the inner tank). DPUTB has the potential to reduce the cost of a ground source heat pump system while allowing shifting the electric demand of the building served by the GHP system from peak to off-peak hours of the electric grid by charging and discharging the thermal storage. A lab-scale (1:125 in volume) DPUTB prototype was built. Phase change material (PCM) was added to increase the thermal storage capacity and maintain the supply water temperature from the TES within the desired range for direct cooling operation during the discharge period. As PCMs are critical to the TES performance of the DPUTB, this study compared the influence of different PCMs (including salt hydrate and organic PCMs) on the discharge performance of the DPUTB. The thermal State of Charge (SoC) of the DPUTB was used to compare the performance resulting from using different PCMs. Test results indicate that the organic PCM (Methyl Laurate) outperforms salt-hydrate PCMs due to a lower melting temperature and a narrower melting temperature range during the phase change process. The results of this study provide a guide for PCM selection and the optimal design of DPUTB.

Wang, Lingshi↗

Effect of Thermal Expansion Coefficient, Viscosity and Melting Range in Simulation of PCM Embedded Heat Exchangers With and Without Fins

Phase change material heat exchangers (PCMHX) have an important role in integrating renewable energy systems. PCMHX can offer high storage density at various temperatures of interest and can be used for grid load shifting purposes. Numerical models enable engineers to estimate PCMHX performance for different design parameters and operating conditions. Modeling phase change phenomena is challenging due to the complex time-dependent nature of the process. The accuracy of models is highly sensitive to PCM thermo-physical properties. Thermal expansion coefficient (β), viscosity (μ) and melting temperature range (MR) of a PCM are important properties, especially when natural convection is not negligible. In PCMHX modeling, using less than accurate values for these properties can have significant impact on the simulation outcomes. These properties and discussions thereof are not readily available in the literature. This paper presents a brief review of the literature and a numerical study investigating the model sensitivity to the above-mentioned properties for PCMHX with and without fins. CFD is used to evaluate the charging (melting) phenomena. The study quantifies the impact of uncertainty in these properties on the melting rate and temperature profile. Constant wall temperature was considered as heat source with no heat loss to ambient. Here, the results show that β and μ has significant effect on the melting rate and evolution of the melting front. For a non-finned domain when comparing results for different published values of β and μ, the deviation in melting time can be up to 12.9% and 57.6% respectively. For high wall temperatures, change in melting range did not impact melting time. But when the wall temperature is reduced, up to 9.8% deviation in melting time is observed.

CFD↗

Computer Science Research Needs for Parallel Discrete Event Simulation (PDES)

Historically, scientific computing efforts have demonstrated the clear need for, and effective use of, supercomputing with traditional time-stepped simulations. Nevertheless, there are several areas in the mission spaces of the U.S. Department of Energy and other agencies waiting to tap advanced computing research using a different, discrete event style of modeling, simulation, and analysis. These span a wide spectrum of applications including energy grid resilience, urban planning and policy, transportation science, building technologies, emergency response and planning, environmental impact analysis, computational epidemiology, Internet communications, cyber security, and cyber-physical systems, to name only a few. Even within traditional scientific applications, the role of discrete event modes of execution is increasing in the form of new event-based mathematical solvers such as quantized state integration methods and discrete-continuous hybrid system solvers. Co-design of advanced supercomputing hardware systems is another area that exploits discrete event simulation at its core for effective analyses. Complex systems, entity behaviors and interconnections play a significant role in all these applications, which are mapped to large-scale models with discrete event formulations. To make advancements in all the aforementioned scientific areas, many technical aspects need to be more thoroughly studied and deeply understood in parallel discrete event simulation (PDES). The unique dynamics inherent in a discrete event modeling approach, by their very nature, intersect and influence the entire stack of the computing system, including (a) the unique nature of the instruction sets exercised in PDES workloads without a predominance of high-precision floating point operations, (b) virtual time-constrained multi-threaded execution of many logical processes per processor, (c) extremely variable and difficult to predict network traffic characteristics, (d) interfaces and inter-dependencies with machine learning and artificial intelligence codes at higher software layers, and (e) highly challenging load balancing needs, especially in effectively accounting for accelerated/extremely heterogeneous computing in current and future high-performance computing systems. Efficient and accurate parallel execution of PDES workloads is also dominated by challenges in dealing with their asynchronous concurrency fundamentally present at the model level. Conservative synchronization, optimistic/speculative synchronization, and their hybrid schemes open new questions in fundamental computer science with respect to reversibility of computation and prediction (lookahead) of behaviors inherent within model codes. On the implementation front, there are relatively few scalable, general-purpose parallel discrete event simulators in the world, and even fewer have been studied on emerging hardware platforms. To enable scientific advances using PDES, the research needs in computer science must also be pursued and met in the intersection of the algorithmic and hardware-aware aspects of scalable PDES engines. This report is aimed at capturing a computer science-oriented view of this important area of research in PDES, presenting a sample of important applications with their inherent discrete event technology elements. Needs are outlined in core areas of parallel discrete event research as well as cross-cutting directions in computer science research that positively impact scientific advancements across several important application areas. A selection of priority research opportunities in advanced computing for PDES is identified to serve as reference for key research topics and their order of importance for scientific advancements.

97 MATHEMATICS AND COMPUTING↗

Optimal Control of Differentially Private EV Charging: A Scalable Learning Approach Under Uncertainty

Internet of Things (IoT)-enabled electric vehicles (IoEVs) enable intelligent charging coordination that accounts for grid congestion. However, increased data exchange raises privacy concerns, as charging patterns can reveal sensitive driver behavior to grid operators. Here, we propose a differentially private (DP) EV charging framework that enables coordinated control while protecting driver data with theoretical privacy guarantees. Nevertheless, integrating DP inevitably introduces uncertainty into the control strategy for EVs, which can lead to infeasible solutions. To tackle this challenge, we develop a feasible and scalable control algorithm based on constrained reinforcement learning (CRL) and convex hulls. While our framework is designed to handle the uncertainty introduced by DP, it is general and also applicable to other sources of uncertainty in EV charging, such as the stochastic nature of driver behavior and renewable variability. This ensures feasible and privacy-preserving coordination of EV charging at scale. Our method constructs convex hulls within the action space to guarantee feasibility under stochastic constraints and incorporates constraint reduction techniques to improve scalability. Case studies based on IEEE benchmark systems demonstrate that the proposed approach effectively balances feasibility under uncertainty, scalability, and privacy in large-scale EV charging control.

Engineering - Power transmission and distribution↗

Quantitative Metrics for Grid Resilience Evaluation and Optimization

Power system resilience has become a critical topic in recent years because of the increasing trend of extreme events and the growing integration of intermittent renewable energy sources. To enhance grid resilience against high-impact, low-frequency events, two questions should be answered: how to quantify the resilience of a given grid and how to incorporate the quantification into power system planning, operation, and restoration. Here this paper develops a new set of quantitative metrics with clear physical interpretation to comprehensively evaluate power system resilience. Using microgrids as an example, an event-based corrective scheduling (ECS) model and an online model predictive control (OMPC) model are developed to integrate the proposed quantitative resilience metrics into power system optimization models for resilience enhancement. The ECS model employs extreme event data to investigate the optimal restoration solution and to help microgrid operators prepare to respond to similar events. The OMPC model provides online decision-making support for operators to handle ongoing outages in the most resilient fashion. The effectiveness and superiority of the proposed quantitative resilience metrics and the resilience enhancement models are demonstrated through simulations and comparative studies on an IEEE test feeder and a real distribution feeder in Southern California.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Applying and validating the RANS-3D flow-solver for evaluating a subsonic serpentine diffuser geometry

Subsonic inlet ducts for advanced, high-performance aircraft are evolving towards complex three-dimensional shapes for reasons of overall integration and weight. These factors lead to diffuser geometries that may sacrifice inlet performance, unless careful attention to design details and boundary layer management techniques are employed. The ability of viscous computational fluid dynamic (CFD) analysis of such geometries to aid the aircraft configurator in this complex design problem is herein examined. The RANS-3D Reynolds-Averaged Navier-Stokes solver is applied to model the complex flowfield occurring in a representative diffuser geometry and the solutions are compared to experimental results from a static test of the inlet duct. The computational results are shown to compare very favorably with experimental results over a range of mass flow rates, including those involving large amounts of separation in the diffuser. In addition, a novel grid topology is presented, and two turbulence models are evaluated in this study as part of the RANS-3D code.

Fletcher, Michael J.↗

Using Reanalysis in Crop Monitoring and Forecasting Systems

Weather observations are essential for crop monitoring and forecasting but they are not always available and in some cases they have limited spatial representativeness. Thus, reanalyses represent an alternative source of information to be explored. In this study, we assess the feasibility of reanalysis-based crop monitoring and forecasting by using the system developed and maintained by the European Commission- Joint Research Centre, its gridded daily meteorological observations, the biased-corrected reanalysis AgMERRA and the ERA-Interim reanalysis. We focus on Europe and on two crops, wheat and maize, in the period 1980-2010 under potential and water-imited conditions. In terms of inter-annual yield correlation at the country scale, the reanalysis-driven systems show a very good performance for both wheat and maize (with correlation values higher than 0.6 in almost all EU28 countries) when compared to the observations-driven system. However, significant yield biases affect both crops. All simulations show similar correlations with respect to the FAO reported yield time series. These findings support the integration of reanalyses in current crop monitoring and forecasting systems and point to the emerging opportunities linked to the coming availability of higher-resolution reanalysis updated at near real time.

Reanalysis↗

Studying performance portability of LAMMPS across diverse GPU-based platforms

The molecular dynamics simulation software, LAMMPS, utilizes the Kokkos acceleration library to port computation to a diverse set of architectures including those based on GPU accelerators. In addition to Kokkos, LAMMPS contains a vast code base that leverages the CUDA application programming interface using library functions such as cuFFT, CUDA's fast-fourier transform (FFT) library, and, more recently, also support for AMD's Heterogeneous Interface for Portability (HIP) that is rapidly growing. While preparing LAMMPS tests for the AMD GPU-based test system precursors to Frontier, we investigated several strategies for accelerating LAMMPS on AMD GPUs, using the AMD Instinct MI100 and MI250X. In this work, we integrated the HIP FFT library, hipFFT, into the particle-particle particle-mesh (PPPM) long-range solver, which allowed the porting of PPPM calculations to the GPUs. Kokkos behavior on the MI100 and MI250X was also investigated through the package kokkos command of LAMMPS, targeting communication, memory usage, and particle grid decomposition. The Tersoff, Reax, Lennard-Jones (LJ), EAM, Granular, and PPPM potentials were investigated in this effort, and results from these experiments are provided. In conclusion, the selected potentials were run on Spock (AMD Instinct MI100), Crusher (AMD Instinct MI250X), AFW HPC11 (NVIDIA A100) and Summit (NVIDIA V100), for comparison. Operational roofline models were constructed and analyzed for the Tersoff, Reax, and Lennard–Jones potentials on Crusher and Summit.

97 MATHEMATICS AND COMPUTING↗

Comparison of structurally diverse simulation models for prediction of epidemic outcomes caused by a long-distance dispersed pathogen

Long-distance dispersal (LDD) pathogens pose substantial challenges for epidemic control due to their ability to generate new infection foci at great distances. While various modeling approaches have been developed to understand and manage such outbreaks, little work has compared how models of different structures behave under shared conditions. Here, in this study, we compare four structurally distinct epidemiological models — EPIMUL, GEMF, PoPS, and Warwick — each adapted to simulate the spread of wheat stripe rust (WSR), a wind-dispersed LDD pathogen, under identical epidemiological parameters and dispersal kernel. Using data from a controlled field experiment, we evaluate the ability of each model to replicate disease prevalence under nine intervention scenarios that vary in timing and culling area. While the models differ substantially in design — ranging from spatial grid-based to network-based and raster-based frameworks — the shared dispersal kernel allowed for close alignment in their predictions. All models accurately captured general epidemic trends, particularly the strong effect of early intervention on disease suppression. We qualitatively compared their behavioral responses across scenarios and also evaluated an ensemble prediction by averaging across model outputs. Our findings highlight how integrating shared epidemiological components into distinct modeling frameworks can improve consistency and accuracy, while reinforcing the importance of early culling in managing LDD pathogen outbreaks.

Dispersal kernel↗

Studying Performance Portability of LAMMPS across Diverse GPU-based Platforms

The molecular dynamics simulation software, LAMMPS, utilizes the Kokkos acceleration library to port computation to a diverse set of architectures including those based on GPU accelerators. In addition to Kokkos, LAMMPS contains a vast code base that leverages the CUDA application programming interface using library functions such as cuFFT, CUDA’s fast-fourier transform (FFT) library, and, more recently, also support for AMD’s Heterogeneous Interface for Portability (HIP) that is rapidly growing. While preparing LAMMPS tests for the AMD GPU-based test system precursors to Frontier, we investigated several strategies for accelerating LAMMPS on AMD GPUs, using the AMD Instinct MI100 and MI250X. In this work, we integrated the HIP FFT library, hipFFT, into the particle-particle particle-mesh (PPPM) long-range solver, which allowed the porting of PPPM calculations to the GPUs. Kokkos behavior on the MI100 and MI250X was also investigated through the package kokkos command of LAMMPS, targeting com- munication, memory usage, and particle grid decomposition. The Tersoff, Reax, Lennard-Jones (LJ), EAM, Granular, and PPPM potentials were investigated in this effort, and results from these experiments are provided. The selected potentials were run on Spock (AMD Instinct MI100), Crusher (AMD Instinct MI250X), AFW HPC11 (NVIDIA A100) and Summit (NVIDIA V100), for comparison. Operational roofline models were constructed and analyzed for the Tersoff, Reax, and Lennard-Jones potentials on Crusher and Summit.

Hagerty, Nick↗

WECC Wide-Area Oscillation Assessment and Trending Study Report

This project, Wide-area Oscillation Analysis and Trending Study, is sponsored by the Office of Electricity (OE) of the Department of Energy (DOE) who tasked Northwest National Laboratory (PNNL) to conduct this research. Staff of Federal Energy Regulatory Commission (FERC) have been involved in the project as observers and have provided advisory comments and suggestions. The primary objective of this study is to assess whether there are significant trends in the wide-area oscillatory behavior with respect to the significant generation-mix changes brought by the increased penetration of RES in the WECC system. The work performed in this project is considered to be complimentary to previous work by NERC/industry and covers the aspects that have not been studied or trended before. The trending analysis presented in this report can serve as reference for future grid planning and operation of the WECC system. In this report, how the changes in the generation mix can impact the frequency and damping ratio (DR) of WECC wide-area oscillation modes has been studied. Thorough data-based and model-based analyses have been carried out to analyze the current trends and then extended to evaluate the oscillation behaviors of the future WECC system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

LIQUID AIR COMBINED CYCLE

Hybrid integration of thermal energy storage with gas turbines can provide compact, cost-effective, long-duration energy storage while reducing the fuel consumption of dispatchable resources needed for the reliability of renewable dominant electric grids. The Liquid Air Combined Cycle™ (LACC) is a hybrid energy storage system using cryogenic liquid air as an energy storage medium and gas turbine exhaust heat to extract stored energy. The storage tank is charged using liquefaction processes employing electric motor-driven compressors to pressurize the air, heat exchangers to reject heat of compression, and expanders to reduce the temperature and liquefy the air. Proven cryogenic refrigeration processes can be selected based on capital cost (per kg/s of liquid air produced), efficiency (kJ per kg of air produced), and operating factors including startup speed and load following capability. This paper presents results of studies undertaken for the U.S. Department of Energy to evaluate cost and performance tradeoffs for charge and discharge cycle components, optimize charge and discharge cycles, and assess the techno-economic potential of LACC technology.

Conlon, William↗

Climate Reanalysis: Progress and Future Prospects

Reanalysis is the process whereby an unchanging data assimilation system is used to provide a consistent reprocessing of observations, typically spanning an extended segment of the historical data record. The process relies on an underlying model to combine often-disparate observations in a physically consistent manner, enabling production of gridded data sets for a broad range of applications including the study of historical weather events, preparation of climatologies, business sector development and, more recently, climate monitoring. Over the last few decades, several generations of reanalyses of the global atmosphere have been produced by various operational and research centers, focusing more or less on the period of regular conventional and satellite observations beginning in the mid to late twentieth century. There have also been successful efforts to extend atmospheric reanalyses back to the late nineteenth and early twentieth centuries, using mostly surface observations. Much progress has resulted from (and contributed to) advancements in numerical weather prediction, especially improved models and data assimilation techniques, increased computing capacity, the availability of new observation types and efforts to recover and improve the quality of historical ones. The recent extension of forecast systems that allow integrated modeling of meteorological, oceanic, land surface, and chemical variables provide the basic elements for coupled data assimilation. This has opened the door to the development of a new generation of coupled reanalyses of the Earth system, or integrated Earth system analyses (IESA). Evidence so far suggests that this approach can improve the analysis of currently uncoupled components of the Earth system, especially at their interface, and lead to increased predictability. However, extensive analysis coupling as envisioned for IESA, while progressing, still presents significant challenges. These include model biases that can be exacerbated when coupled, component systems with different physical characteristics and different spatial and temporal scales, and component observations in different media with different spatial and temporal frequencies and different latencies. Quantification of uncertainty in reanalyses is also a critical challenge and is important for expanding their utility as a tool for climate change assessment. This talk provides a brief overview of the progress of reanalysis development during recent decades, and describes remaining challenges in the progression toward coupled Earth system reanalyses.

IES↗

Outage Forecast-Based Preventative Scheduling Model for Distribution System Resilience Enhancement: Preprint

Distribution system resilience enhancement is an important topic to ensure customers have access to the power supply during extreme events. In fact, certain weather-related extreme events can be predicted ahead of time. Therefore, it is important to investigate how to predict grid outages using extreme weather forecasts, and how outage predictions can be incorporated into distribution system resilience enhancement. In this paper, a preventative scheduling model for distribution systems is proposed. The model targets at allocating resources, especially mobile responsive resources such as mobile backup generators and mobile energy storage systems, to prepare for an extreme event in the day-ahead context. To achieve efficient resource allocation and scheduling, a machine learning-based outage prediction module is developed to predict vulnerable or risky segments of the distribution system based on historical operating records and extreme weather event forecasts. By integrating the outage prediction results into the scheduling model, optimal resource allocation can be derived to help distribution systems prepare for an upcoming event and improve resilience performance. A real distribution feeder in North Carolina, U.S. is used in the case study to validate the proposed approach.

distributed energy resources↗

Outage Forecast-Based Preventative Scheduling Model for Distribution System Resilience Enhancement

Distribution system resilience enhancement is an important topic to ensure customers have access to power supply during extreme events. In fact, certain weather-related extreme events can be predicted ahead of time. Therefore, it is important to investigate how to predict grid outages using extreme weather forecasts, and how outage predictions can be incorporated into distribution system resilience enhancement. In this paper, a preventative scheduling model for distribution systems is proposed. The model targets at allocating resources, especially mobile responsive resources such as mobile backup generators and mobile energy storage systems, to prepare for an extreme event in the day-ahead context. To achieve efficient resource allocation and scheduling, a machine learning-based outage prediction module is developed to predict vulnerable or risky segments of the distribution system based on historical operating records and extreme weather event forecast. By integrating the outage prediction results into the scheduling model, optimal resource allocation can be derived to help distribution systems prepare for an upcoming event and improve resilience performance. A real distribution feeder in North Carolina, U.S. is used in the case study to validate the proposed approach.

distributed energy resources↗

The Essential Role of Integrated Nuclear-Renewable Energy Systems in Achieving Economy-wide Net Zero Solutions

Background/Objectives. The Biden administration has committed to full decarbonization of the U.S. electricity grid by 2035 and economy-wide net zero emissions by 2050. These aggressive goals demand immediate action if we are to be successful, and they require us to think more holistically about our clean energy options. Focused laboratory initiatives, such as the INL Integrated Energy Systems (IES) Initiative, and multiple programs within the Department of Energy are working together to address these holistic solutions. Approach/Activities. Traditionally, electricity generation and management and meeting energy demands for industry and transportation are considered independently. As we seek to achieve net zero, we need to reassess our energy demands. When we consider overall energy use, only one-third is in the form of electricity. Additional energy demands are in the form of heat or steam for industrial processes, as well as transportation. Emissions across these sectors are much harder to abate, and electrification may not be the best option. Reducing environmental emissions at an affordable cost, while maintaining grid reliability and resilience, will require us to use all of the clean energy resources that we have available. That means coordinating the use of nuclear, renewables, and fossil fuels with carbon capture to meet growing demands for electricity, industrial applications, and mobility. The primary focus of IES research is to assess the technical and economic potential of various IES solutions to enhance the flexibility and utilization of nuclear energy generators working alongside renewable generators to meet an array of energy demands—thereby maximizing the utilization of clean energy resources across all energy sectors. Various energy applications and product streams beyond electricity are being evaluated, ranging from generation of potable water to production of hydrogen, fertilizers, synthetic fuels, and various chemicals. Results/Lessons Learned. This presentation will highlight the wide array of RD&D being conducted to develop and deploy nuclear-based IES that will be key to achieving our net zero goals. By working with key collaborators in the nuclear industry, analytical studies are now becoming a reality in multiple demonstration projects.

08 HYDROGEN↗

Long-term impact of electrification and retrofits of the U.S residential building in diverse locations

The U.S. buildings sector contributes 30% of operational carbon emissions, with residential buildings accounting for 56%. Reducing residential carbon emissions is crucial for achieving net-zero carbon goal. While many studies examine energy efficiency retrofit (EER) and electrification, few explore their long-term impacts across diverse climates and dynamic grid clean energy penetrations, as well as their economic effects on households. Here, this study proposes a method to assess how EER and electrification affect long-term decarbonization and economics across different climates, focusing on carbon emissions, energy burden (the percentage of household income spent on energy), and payback period in four locations: Tampa, San Diego, Denver, and Great Falls. The study also introduces the concept of implicit energy burden by considering investment costs. Results show that while electrification can reduce long-term emissions with increased clean energy penetration, it may not always achieve decarbonization due to mismatches between clean energy availability and demand. In cooling-dominant locations, electrification lowers energy burden and peak demand, but in heating-dominant locations, it increases energy burden to 8.24%, raises peak demand by 632.78%, and shifts it from summer to winter. After integrating investment costs, the implicit energy burden can reach 8.35% in cold climates. For already highly electrified buildings in Denver and Great Falls, the payback period of EER measures can be shortened by up to 48.98%. The study highlights a tradeoff between decarbonization and energy burden alleviation, showing that while EER measures can reduce the energy burden, they only achieve one-quarter of the carbon emission reduction of electrification.

24 POWER TRANSMISSION AND DISTRIBUTION↗