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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Agent-Based Modeling for the Circular Economy: Lessons Learned From Three Case Studies

The circular economy (CE) aims at decoupling human activities from resource use, creating wealth in the process. Recently, many scholars have questioned the link between increased circularity and sustainability, resulting in many methodological approaches being developed for that purpose. This presentation summarizes the insights gained from the application of agent-based modeling (ABM) to study the techno-economic and social conditions promoting circularity and sustainability of three technologies: photovoltaic (PV) modules, hard disk drives (HDDs), and wind blades. Four main categories of agents are defined in the ABM: asset owners, service providers (e.g., refurbishers), recyclers, and manufacturers. Two main CE strategies are represented: lifetime extension (through repair or reuse) and recycling. The developed models start by projecting installed capacities and end-of-life (EOL) quantities. Then the theory of planned behavior - a social psychology model explaining behavior adoption based on attitude, peer influence, and costs - is used to model the asset owners' EOL decision (i.e., landfill, recycle or extend the lifetime of the asset). Then, the quantities of assets flowing to the recycler and service provider agents and quantities of materials flowing to manufacturers are computed. Recyclers' economies of scale are dynamically modeled, and the value generated by the CE strategies for the recyclers, service providers, and manufacturers is computed within the model. When data are available, avoided greenhouse gas emissions resulting from the CE strategies adoption are calculated exogenously from the ABM simulations. Results show that with improved used PV modules warranties, the reuse CE strategy adoption increases from 1% to 23% between 2020 and 2050. Similarly, improved standards could enhance HDDs end-users trust in data-wiping - a prerequisite to reuse - leading to a 3-fold increase in the reuse rate and avoid about 5 million tons of CO2 eq by 2050. Regarding wind blades, 5-15 years lifetime extension could reduce EOL blade quantities by 13%. High costs and logistic issues prevent blades from being recycled in greater quantities. One insight from the case studies is the necessity to have mature secondary markets for reuse to be a viable option. Interestingly, PV reuse is limited by the willingness of PV owners to purchase used modules (on the demand side), while HDDs reuse is constrained by the lack of trust toward data-wiping (limiting the supply of used HDDs). The six limits of the CE concepts presented by Korhonen et al. (2018) are finally used to interpret the results. The HDD case study is an exemplary lock-in, where the first accepted practice (shredding) retains most of the market. The PV results illustrate the technical limitation to reuse, as the growing demand cannot be supplied entirely with used PV modules. The wind case study shows the relevance of clearly defining physical flows - what type of waste should wind blades be considered, how should they be transported and landfilled? - a crucial consideration that also applies to PV modules. Finally, the three case studies highlight the relevance of studying a technology's technical, economic, and market material efficiency potentials altogether and the potential benefit of coupling ABM to life cycle assessment.

agent-based modeling↗
DOE OSTI2021

Windowed multipole representation of R -matrix cross sections

Nuclear cross sections are basic inputs to any nuclear computation. Campaigns of experiments are fitted with the parametric R-matrix model of quantum nuclear interactions, and the resulting cross sections are documented—both pointwise and as resonance parameters (with uncertainties)—in standard evaluated nuclear data libraries (ENDF, JEFF, BROND, JENDL, CENDL, TENDL): these constitute our common knowledge of fundamental low-energy nuclear cross sections. In the past decade, a collaborative effort has been deployed to establish a new nuclear cross-section library format—the Windowed Multipole Library—with the goal of considerably reducing the computational cost of cross-section calculations in nuclear transport simulations. This work lays the theoretical foundations underpinning these efforts. From general R-matrix scattering theory, we derive the windowed multipole representation of nuclear cross sections. Though physically and mathematically equivalent to R-matrix cross sections, the windowed multipole representation is particularly well suited for subsequent temperature treatment of angle-integrated cross sections, in particular Doppler broadening, which is the averaging of cross sections over the thermal motion of the target atoms. Doppler broadening is of critical importance in neutron transport applications, as it ensures the stability of many nuclear reactors (negative thermal reactivity). Yet, Doppler broadening of nuclear cross sections has been a considerable bottleneck for nuclear transport computations, often requiring memory-costly pretabulations. We show that the windowed multipole representation can perform accurate Doppler broadening analytically (up to the first reaction threshold), from which we derive cross-section temperature derivatives to any order—all computable on the fly (without precalculations stored in memory). Furthermore, we here establish a way of converting the R-matrix resonance parameters uncertainty (covariance matrices) into windowed multipole parameters uncertainty. We show that generating stochastic nuclear cross sections by sampling from the resulting windowed multipole covariance matrix can reproduce the cross-section uncertainty in the original nuclear data file. The windowed multipole representation is therefore a novel nuclear physics formalism able to generate Doppler broadened stochastic nuclear cross sections on the fly, unlocking breakthrough computational gains for nuclear computations. Through this foundational paper, we hope to make the windowed multipole representation accessible, reproducible, and usable for the nuclear physics community, as well as provide the theoretical basis for future research on expanding its capabilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Availability of Critical Benchmark Experiments for the Pebble Tanker Transportation Model for Nuclear Criticality Safety Validation of TRISO Pebbles

This study addresses the need for comprehensive investigations into TRi-structural ISOtropic (TRISO) fuel pebble transportation validation. In this work, an exploratory model, the pebble tanker(PT), was developed with the aim of facilitating the validation of nuclear criticality safety calculations in the context of industrial-scale transportation of TRISO fuel. The PT model was designed to investigate the availability and applicability of critical benchmark experiments crucial for assessing the transportation of these pebbles. This work incorporated sensitivity/uncertainty (S/U) similarity studies to quantify the applicability of critical benchmark experiments and to address nuclear data uncertainties in the context of TRISO transportation. Two container models were investigated: one for the Hermes-type pebble and one for the Pebble Bed Modular Reactor (PBMR)–type pebble. The models were simplified, considering fuel, containment, and either water or air, to enable a focus on the underlying physics of applications involving TRISO fuel pebbles using the PT model. A crucial aspect under consideration was the capacity of the transport package to hold pebbles while ensuring subcriticality in the flooded state. An approach in the criticality validation process involves assessing the similarity between systems through an integral index parameter evaluation. This involves calculating a correlation coefficient (referred to as c k ) based on shared nuclear data–induced uncertainty between a benchmark experiment and the application of the PT model. To facilitate this analysis, the SCALE tools, particularly the CSAS6-Shift, TSUNAMI-3D-Shift, and TSUNAMI-IP sequences, were employed for comprehensive studies in neutronics and S/U analysis. Our findings showed that there are sufficient critical experimental benchmarks to perform this validation of the PT model in the most reactive state, i.e. when the tanker is flooded. This paper provides valuable insights into validating a transport package for Generation IV TRISO fuel pebbles.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Technoeconomic Analysis of Infrastructure Buildout Scenarios

The success of CCUS deployment in the southeast will depend on the optimized pipeline network from CO 2 point sources to geologic sinks for CO 2 storage. An optimal pipeline framework will reduce both environmental impacts and pipeline building cost. However, finding an optimal pipeline/transport infrastructure design is a non-trivial task and requires simultaneous usage of large volumes of data, computational resources, and a state-of-the-art simulator. Such a transport infrastructure model must consider point sources for CO 2 capture and associated volumes, sinks for CO 2 storage, and transportation from source to sink via pipeline networks. These considerations must be addressed simultaneously and systemically in an optimization process, in which a defined objective function (i.e., capital, variable CO 2 capture, transport, and storage cost function) is required to be minimized with the consideration of practical constraints (e.g., CO 2 flow through pipelines is less than the maximum capacity). Although optimization has been widely used in subsurface resources production and CO 2 storage, its application in large scale CCUS infrastructure design is rarely reported in the literature. SimCCS, developed by Los Alamos National Laboratory, is an open-source CCUS pipeline infrastructure design toolset that facilitates the optimization of pipeline infrastructure networks.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Engineering Li/Na selectivity in 12-Crown-4–functionalized polymer membranes

Significance Lithium is a key ingredient in batteries, which are integral components of next-generation automobiles, airplanes, grid energy storage, and electronic devices. Unfortunately, lithium extraction from natural sources is laborious, slow, and costly, motivating the search for more efficient isolation techniques. While polymeric membranes could reduce the cost of lithium recovery, current membrane materials lack sufficient lithium-ion selectivity. To address this challenge, we introduce a class of polymeric membranes that incorporate ion binding sites, which significantly increases the transport selectivity of LiCl over NaCl. These studies provide guidelines and practical considerations for incorporating specific interactants into polymers that mediate selective ion transport.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accurately measuring the ionic conductivity of membranes via the direct contact method

Accurately measuring the ionic conductivity of membranes is important both for assessing the performance of new membranes as well as for advancing the fundamental understanding of electric field-driven ion transport in membranes. Yet, despite a considerable number of reports on the topic, there is no standardized method for ionic conductivity measurements. One of the main challenges with ionic conductivity measurements is isolating the membrane resistance from the other resistances in the electrochemical cell. In this study, we present a detailed discussion of factors that affect ionic conductivity measurements with the commonly used direct contact method, in which the membrane contacts the electrodes. Such factors include external resistances due to imperfect contact between the membrane and electrodes, residual impedances due to the sample holder and wiring, and fringe effects. Further, we also present and validate simple methods for isolating the true membrane ionic conductivity in both the through-plane and in-plane orientations. These methods can be implemented with virtually any membrane to obtain accurate and reproducible ionic conductivity values. Finally, we outline recommendations for performing ionic conductivity measurements with the direct contact method and a set of parameters to verify when reporting these results.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Universal Relationship between Limiting Current and Electrochemical Transport Properties in Malonate-Based Polymer Electrolytes

There is considerable interest in developing high-performance electrolytes for rechargeable lithium batteries. For practical applications, the electrolyte must support large dc currents. However, the parameters most often reported in the literature, conductivity, κ, and current fraction, ρ + , reflect ion transport in the limit of infinitesimal currents. In this limit, the efficacy of an electrolyte is given by the product κρ + . The limiting current density, i lim , is the maximum current density that can be applied across an electrolyte; the cell voltage diverges if the applied current density exceeds ilim. This parameter reflects ion transport in the limit of large dc currents and is therefore of practical interest. It would therefore be convenient if i lim could be predicted from measurements of κρ + . In order to explore this possibility, we studied six malonate-based polymers and PEO at a fixed salt concentration (r = 0.08) and temperature (90°C) using symmetric cells with planar electrodes. Unfortunately, there is no correlation between ilim and κρ + . When the applied current density, i, is less than ilim, the cell voltage approaches a stable plateau, ϕ plateau . Here, we found a linear dependence between i and thickness-normalized plateau potential, ϕ plateau L –1 , irrespective of the magnitude of the applied current. In all seven polymer electrolytes, we found a linear correlation between ilim and the slopes of these lines, σ. In other words, measurements of σ can be used to predict the limiting current.

Jana, Rounak [Lawrence Berkeley National Laborator↗
DOE OSTI2024

Coherent structures in stably stratified wall-bounded turbulent flows

To date, a growing body of literature has documented the existence and impacts of coherent structures known as large- and very-large-scale motions within wall-bounded turbulent flows under neutral and unstable thermal stratification. These coherent structures can account for a considerable fraction of the overall turbulent transport and have been found to modulate small-scale turbulent fluctuations near the wall. In the context of stably stratified flows, however, the examination of such coherent structures has garnered relatively little attention. Stable stratification limits vertical transport and turbulent mixing within flows, which makes it unclear the extent to which previous findings on coherent structures under unstable and neutral stratification are applicable to stably stratified flows. In this study, we investigate the existence and characteristics of coherent structures under stable stratification with a wide range of statistical and spectral analyses. Outer peaks in premultiplied spectrograms under weak stability indicate the presence of large-scale motions, but these peaks become weaker and eventually vanish with increasing stability. Quadrant analysis of turbulent transport efficiencies (the ratio of net fluxes to their respective downgradient components) demonstrates dependencies on both stability and height above ground, which is evidence of morphological differences in the coherent structures under increasing stability. Amplitude modulation by large-scale streamwise velocity was found to decrease with increasing gradient Richardson number, whereas modulation by large-scale vertical velocity was approximately zero across all stability ranges. For sufficiently stable stratification, large eddies are suppressed enough to limit any inner–outer scale interactions.

Greene, Brian R. (ORCID:0000000343766818)↗
DOE OSTI2025

Synthesis, Stability, and Magnetic Properties of Antiperovskite Co 3 PdN

Experimental synthesis and characterization of theoretically predicted compounds are important steps in the materials discovery pipeline. Here, we report on the synthesis of Co 3 PdN, which was recently predicted to be a stable magnetic antiperovskite. The Co 3 PdN thin films were grown by reactive sputtering and were confirmed to form in an antiperovskite crystal structure. The thermal stability of the compound is demonstrated up to 600 K by in situ X-ray diffraction, though the phase persists at slightly higher temperatures (700 K) in an air-free magnetometer. Both ab initio calculations and magnetization measurements find Co 3 PdN to be ferromagnetic with an experimentally determined Curie temperature of T C = 560 ± 5 K. The saturation magnetization of 1.2 μ B /Co found in the experiment is slightly lower than the 1.7 μ B /Co value expected by theory. A narrow magnetic hysteresis loop with a coercive field of 100 Oe at low temperature suggests that Co 3 PdN might be useful in electronic applications requiring fast switching of the magnetization vector. While prior prediction of Co 3 PdN showed a gapped electronic band structure for each spin channel, we show that this was due to incomplete sampling of Brillouin zone paths and that band crossings exist along R-X|M and X|M-R paths. The metallic nature of Co 3 PdN is further confirmed by temperature-dependent transport measurements, which also show a considerable anomalous Hall effect. Altogether, this work represents an appreciable step toward understanding the synthesis, structure, stability, and properties of a new magnetic material.

14 SOLAR ENERGY↗
DOE OSTI2022

Argyrodite-type advanced lithium conductors and transport mechanisms beyond paddle-wheel effect

Abstract Development of next-generation solid-state Li-ion batteries requires not only electrolytes with high room-temperature (RT) ionic conductivities but also a fundamental understanding of the ionic transport in solids. In spite of considerable work, only a few lithium conductors are known with the highest RT ionic conductivities ~ 0.01 S/cm and the lowest activation energies ~0.2 eV. New design strategy and novel ionic conduction mechanism are needed to expand the pool of high-performance lithium conductors as well as achieve even higher RT ionic conductivities. Here, we theoretically show that lithium conductors with RT ionic conductivity over 0.1 S/cm and low activation energies ~ 0.1 eV can be achieved by incorporating cluster-dynamics into an argyrodite structure. The extraordinary superionic metrics are supported by conduction mechanism characterized as a relay between local and long-range ionic diffusions, as well as correlational dynamics beyond the paddle-wheel effect.

25 ENERGY STORAGE↗
DOE OSTI2019

Molecular conducting magnetic heterostructures

Building molecular conducting magnets has been of considerable interest due to their metallic transport and magnetic properties. Conjugated aniline anions and transition-metal cations are recognized to synthesize such π–d interaction frameworks. Here, an interfacial assembly of quasi-two-dimensional aniline heterojunction frameworks is developed, which consists of a proton-aniline conducting layer (conductivity of 9.2 × 10 2 S cm -1 ) and a transition metal–aniline magnetic layer. The two-dimensional aniline coordination framework with pronounced π–d interactions is indispensable for obtaining ordered spin states and metallic transport conductivity. We apply optical and Raman spectroscopy to study the interactions between the metal cations and nitrogen atoms in the aniline chains. The bilayer heterostructure maintains a high conductivity of 3.5 × 10 2 S cm -1 and increased magnetization, while the coupling of metallic conducting and magnetic layers leads to an enhanced magnetoconductance of 0.4% under a magnetic field of 70 kOe.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Band structure of Bi surfaces formed on Bi 2 Se 3 upon exposure to air

Bi 2 Se 3 has been the focus of intense interest over the past decade due to its topological properties. Bi surfaces are known to form on Bi 2 Se 3 upon exposure to atmosphere, but their electronic structure has not been investigated. Here, we report band structure measurements of such Bi surfaces using angle-resolved photoemission spectroscopy. Measured spectra can be well explained by the band structure of a single bilayer of Bi on Bi 2 Se 3 , and show that Bi surfaces consistently dominate the photoemission signal for air exposure times of at least 1 hour. These results demonstrate that atmospheric effects should be taken into consideration when identifying two-dimensional transport channels, and when designing surface-sensitive measurements of Bi 2 Se 3 , ideally limiting air exposure to no more than a few minutes.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Energy 101 Transportation [Slides]

The Energy 101: Transportation presentation, developed for the Energy Technology Innovation Partnership Project (ETIPP), provides an overview of transportation. It covers fundamental concepts, technologies, considerations, case studies, and additional resources.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Regulatory Development Challenges and Opportunities for the Safe and Secure Transport of Radioactive Materials

Drafting regulations for transport safety and transport security achieve two separate objectives, which can lead to divergent outcomes. With transport safety, the principle goal is to protect the public and the environment from the effects of ionizing radiation, while in contrast, the principle goal of transport security is to protect the material from malicious actors. While many Member States may have transport safety regulations for radioactive materials, transport security regulatory development is still in its nascent stages globally. Trying to develop harmonized transport safety and transport security regulations could lead to challenges ranging from differences in terminology used in transport safety versus terminology uses in transport security, roles and responsibilities for the variety of stakeholders involved in transport, and finally, the possible role of multiple competent authorities in governing the transport of dangerous goods, which includes radioactive material. While the International Atomic Energy Agency (IAEA) is currently developing a process of a methodology for drafting transport security regulations, any process must address both safety considerations and security requirements. (As the most vulnerable part of the life cycle of radioactive materials, the need for harmonized transport safety/transport security regulations is essential.) This paper investigates the regulatory elements of the safety-security interface for nuclear and other radioactive material in transport. Examining challenges including use of terms, the role of multiple competent authorities, and practical challenges involved in the safe and secure transport of radioactive material, the paper analyzes the need for integrated regulatory development for the safe and secure transport of these materials.

Anderson, Kimberly↗
DOE OSTI2022

Defect-driven anomalous transport in fast-ion conducting solid electrolytes

We report solid-state ionic conduction is a key enabler of electrochemical energy storage and conversion. The mechanistic connections between material processing, defect chemistry, transport dynamics, and practical performance are of considerable importance, but remain incomplete. Here, inspired by studies of fluids and biophysical systems, we re-examine anomalous diffusion in the iconic two-dimensional fast-ion conductors, the β- and β"-aluminas. Using large-scale simulations, we reproduce the frequency dependence of alternating-current ionic conductivity data. We show how the distribution of charge-compensating defects, modulated by processing, drives static and dynamic disorder, which lead to persistent sub-diffusive ion transport at macroscopic timescales. We deconvolute the effects of repulsions between mobile ions, the attraction between the mobile ions and charge-compensating defects, and geometric crowding on ionic conductivity. Our quantitative framework based on these model solid electrolytes connects their atomistic defect chemistry to macroscopic performance with minimal assumptions and enables mechanism-driven 'atoms-to-device' optimization of fast-ion conductors.

25 ENERGY STORAGE↗
DOE OSTI2020

Role of sheared E × B flow in self-organized, improved confinement states in magnetized plasmas

A great scientific success story of magnetic fusion research in the past several decades is the theoretical development and experimental testing of the process of turbulence decorrelation and stabilization by sheared E×B flow which shows that E×B shear effects are ubiquitous in magnetized plasmas. This concept of turbulence decorrelation and stabilization has the universality needed to explain the H-mode edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines; the broader edge transport barrier seen in VHmode plasmas; and the core transport barriers formed in tokamaks. Similar effects are seen in linear devices. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to reduce transport when an additional source of free energy is applied to it. The transport decrease associated with E×B velocity shear is also of great practical benefit to fusion research, since it contributed to substantially increased fusion yield in all DT magnetic fusion experiments conducted to date. The fundamental physics involved in transport reduction is the effect of E×B shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same basic transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field Er. An important secondary theme in this area is the synergistic effect of E×B velocity shear and magnetic shear. Although the E×B velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of E×B velocity shear and facilitate turbulence stabilization. Our present understanding in this area is the result of a multi-decade, intertwined effort in theory, modeling and diagnostic development combined with continuing experimental investigations. These experiments have clearly demonstrated that increased E×B shear causes reductions in turbulence and transport. Finally, the experimental findings are generally consistent with the basic theoretical models although considerable work remains to be done before we have a fully predictive theory of transport in magnetized plasmas including E×B shear effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Third international challenge to model the medium- to long-range transport of radioxenon to four Comprehensive Nuclear-Test-Ban Treaty monitoring stations

In 2015 and 2016, atmospheric transport modeling challenges were conducted in the context of the Comprehensive Nuclear-Test-Ban Treaty (CTBT) verification, however, with a more limited scope with respect to emission inventories, simulation period and number of relevant samples (i.e., those above the Minimum Detectable Concentration (MDC)) involved. Therefore, a more comprehensive atmospheric transport modeling challenge was organized in 2019. Stack release data of Xe-133 were provided by the Institut National des Radioéléments/IRE (Belgium) and the Canadian Nuclear Laboratories/CNL (Canada) and accounted for in the simulations over a three (mandatory) or six (optional) months period. Best estimate emissions of additional facilities (radiopharmaceutical production and nuclear research facilities, commercial reactors or relevant research reactors) of the Northern Hemisphere were included as well. Model results were compared with observed atmospheric activity concentrations at four International Monitoring System (IMS) stations located in Europe and North America with overall considerable influence of IRE and/or CNL emissions for evaluation of the participants’ runs. Participants were prompted to work with controlled and harmonized model set-ups to make runs more comparable, but also to increase diversity. It was found that using the stack emissions of IRE and CNL with daily resolution does not lead to better results than disaggregating annual emissions of these two facilities taken from the literature if an overall score for all stations covering all valid observed samples is considered. A moderate benefit of roughly 10% is visible in statistical scores for samples influenced by IRE and/or CNL to at least 50% and there can be considerable benefit for individual samples. Effects of transport errors, not properly characterized remaining emitters and long IMS sampling times (12–24 h) undoubtedly are in contrast to and reduce the benefit of high-quality IRE and CNL stack data. Complementary best estimates for remaining emitters push the scores up by 18% compared to just considering IRE and CNL emissions alone. Despite the efforts undertaken the full multi-model ensemble built is highly redundant. An ensemble based on a few arbitrary runs is sufficient to model the Xe-133 background at the stations investigated. The effective ensemble size is below five. An optimized ensemble at each station has on average slightly higher skill compared to the full ensemble. However, the improvement (maximum of 20% and minimum of 3% in RMSE) in skill is likely being too small for being exploited for an independent period.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Equity-driven Planning of Distributed Solar PV using Optimal Transport

Typically, distribution system planning processes do not explicitly incorporate energy equity considerations, such as identifying consumers most affected by energy costs and determining how investments in the distribution system can address existing energy burden imbalances. This paper proposes a novel optimal transport (OT)-based method to improve the energy burden distribution of consumers. The approach involves the strategic siting and sizing of solar PV in order to assist customers with high energy burden and improve the overall energy burden distribution of the community. The desired energy burden distribution is defined using the equal distribution equivalent (EDE) concept. The OT-based method is then used to estimate the distributed solar PV capacity to be installed at various locations and the tariffs to be adjusted, all while improving the energy burden distribution and providing valuable insights into distributed generation (DG) planning. The results on IEEE 37 bus test system demonstrate how DG planning, considering EDE and OT, can help reduce the energy burden of low-income consumers. Additionally, the approach also reveals optimal tariff adjustments needed to ensure revenue neutrality for distribution utilities.

Optimal transport, equal distribution equivalent, ↗