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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Implementation of a turbine farm model into the Energy Exascale Earth System Model for investigation and quantification of global climate impacts

Although there has been widespread deployment of wind farms in the United States, and plans to continue deployment into the future, the complete effects of wind farms on Earth systems are not well understood. The work performed here has incorporated wind farm models into the Energy Exascale Earth System Model (E3SM) capable of simulating the effects of extracting momentum from the atmospheric flow field using power generating wind farms. This new capability will allow scientists to quantify the impacts of wind farm induced changes on Earth systems by exploiting E3SM’s ability to couple atmospheric, oceanic, and biogeochemical (BGC) models on a global scale and monitor precipitation levels, extreme weather events, soil moisture content and jet stream location over decades-long time periods. This tool will be used to inform decision making on wind farm citing and will contribute to the Lab’s ability to assess energy technology impacts on the environment and evaluate the trade-offs between energy infrastructure investments and their impacts on natural systems.

17 WIND ENERGY↗
DOE OSTI2022

Exploring the Consistency of Water Scarcity Inferences between Large-Scale Hydrologic and Node-Based Water System Model Representations of the Upper Colorado River Basin

Water resources model development and simulation efforts have seen rapid growth in recent decades to aid evaluations and planning around water scarcity and allocation. Models are typically developed by two distinct communities: (1) large-scale hydrologic modelers emphasizing hydroclimatological processes, and (2) water systems modelers emphasizing environmental, infrastructural, and institutional features that shape water scarcity at the local basin level. This study assesses whether two representative models from these communities produce consistent insights when evaluating the water scarcity vulnerabilities in the Upper Colorado River Basin within the state of Colorado. Results showed that although the regional-scale model [model for scale adaptive river transport (MOSART)—water management (WM)] can capture the aggregate effect of all water operations in the basin, it underestimates the subbasin-scale variability in specific user’s vulnerabilities. The basin-scale water systems model [State of Colorado’s Stream Simulation Model (StateMod)] suggests a larger variance of scarcity across the basin’s water users due to its more detailed accounting of local water allocation infrastructure and institutional processes. This model intercomparison highlights potentially significant limitations of large-scale studies in seeking to evaluate water scarcity and actionable adaptation strategies, as well as ways in which basin-scale water systems model’s information can be used to better inform water allocation and shortage when used in tandem with larger-scale hydrological modeling studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Baseline Climate Variables for Earth System Modelling

The Baseline Climate Variables for Earth System Modelling (ESM-BCVs) are defined as a list of 135 variables which have high utility for the evaluation and exploitation of climate simulations. The list reflects the most frequently used elements of the Coupled Model Intercomparison Project Phase 6 (CMIP6) archive. Successive phases of CMIP have supported strong results in science and substantially influence international climate policy formulation. This paper responds to both interest in exploiting CMIP data standards in a broader range of climate modelling activities and a need to achieve greater clarity about the significance and intention of variables in the CMIP Data Request. As Earth system modelling archives grow in scale and complexity, there are emerging problems associated with weak standardisation at the variable collection level. That is, there are good standards covering how specific variables should be archived, but this paper fills a gap in the standardisation of which variables should be archived. The ESM-BCV list is intended as a resource for ESM intercomparison projects (MIPs) developing requests to enable greater consistency among MIPs and as a reference for modelling centres to enhance consistency within MIPs. Provisional planning for the CMIP7 Data Request exploits the ESM-BCVs as a core element. The baseline variable list includes 98 variables which have modest or minor data volume footprints and could be generated systematically when simulations are produced and archived for exploitation by the World Climate Research Programme (WCRP) community. A further 35 variables are classed as “high volume” and are only suitable for production when the resource implications are justified.

Juckes, Martin [University of Oxford (United Kingd↗
DOE OSTI2026

Modeling Large Dust Aerosols in the Community Earth System Model Version 2 (CESM2)

Dust aerosols have a wide size distribution from less than 0.1 to over 100 μm and dominate Earth's atmospheric aerosol mass. However, most Earth system models (ESMs) inadequately represent dust aerosols larger than 10 μm in diameter, limiting the accuracy of the simulated dust cycle and climate impacts. Here, we introduce a new modeling framework that captures the full observed size distribution of dust aerosols, incorporating recent advances into a mineral-resolved version of the Community ESM, while addressing known issues in previous versions. Comprehensive evaluation against diverse observations of bulk dust and component minerals demonstrates that the model reproduces the observed dust cycle across particle sizes. Incorporating the previously unrepresented large-dust fractions substantially alters dust budget estimates, highlighting potential changes in simulated climate impacts and underscoring the importance of comprehensive size-resolved dust modeling. Despite these advancements, uncertainties persist. Our results indicate that a size-dependent reduction in settling velocity is required to reproduce the observed dust size distribution downwind of source regions. Specifically, in the new model, the gravitational settling velocity of dust particles larger than 10 μm in diameter must be reduced by as much as 85% to achieve agreement with observations. This empirical reduction serves as a constraint on physics-based models of dust settling. Future developments should address misrepresented physical processes that hinder accurate modeling of the large dust aerosol transport. Expanding observational data sets covering the full-size distribution is also essential to better constrain the dust cycle and improve the representation of dust optical properties and climate effects.

Li, Longlei [Cornell Univ., Ithaca, NY (United Sta↗
DOE OSTI2023

Incorporating an Interactive Fire Plume-Rise Model in the DOE's Energy Exascale Earth System Model Version 1 (E3SMv1) and Examining Aerosol Radiative Effect

The vertical distribution of biomass burning aerosol (BBA) is important in regulating their impacts on weather and climate. The plume-rise process affects the injection height of BBA and interacts with the air parcel lifting and cloud processes. However, these processes are not represented in most global climate models. In this study, we replaced the fixed vertical profiles of monthly BBA emissions in the Department of Energy's Energy Exascale Earth System Model version 1 (E3SMv1) with an interactive fire plume-rise model. The vertical distribution of BBA emissions was calculated as a function of ambient thermodynamic conditions from the host E3SMv1, with distributions of fire sizes and sensible heat fluxes derived from the observations. The maximum fire radiative power (FRP) technique was used to determine the fire size. Scaling-FRP technique is used to calculate the wildfire heat release. Daily BBA emission, superimposed with a fire diurnal cycle retrieved from the satellite observation, was included in model simulations. The model shows improved agreement with satellite retrievals and in situ measurement during the National Oceanic and Atmospheric Administration Wildfire Experiment for Cloud chemistry, Aerosol absorption, and Nitrogen campaign. The model-observation comparison demonstrates the importance of the plume-rise model and fire diurnal cycle assumption in determining the BBA fields. We also find that E3SMv1 with new features produces a larger carbonaceous aerosol burden, leading to 0.13 W m –2 warming at the top of atmosphere compared to the default E3SMv1. This highlights the importance of accurately representing the BBA injection height and indicates a no-linear nature in the BBA-induced radiative effect.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Insights on Simulating Summer Warming of the Great Lakes: Understanding the Behavior of a Newly Developed Coupled Lake-Atmosphere Modeling System

The Laurentian Great Lakes are the world's largest freshwater system and regulate the climate of the Great Lakes region, which has been increasingly experiencing climatic, hydrological, and ecological changes. An accurate mechanistic representation of the Great Lakes thermal structure in Regional Climate Models (RCMs) is paramount to studying the climate of this region. Currently, RCMs have primarily represented the Great Lakes through coupled one-dimensional (1D) column lake models; this approach works well for small inland lakes but is unable to resolve the realistic hydrodynamics of the Great Lakes and leads to inaccurate representations of lake surface temperature (LST) that influence regional climate and weather patterns. This work overcomes this limitation by developing a fully two-way coupled modeling system using the Weather Research and Forecasting model and a three-dimensional (3D) hydrodynamic model. The coupled model system resolves the interactive physical processes between the atmosphere, lake, and surrounding watersheds; and validated against a range of observational data. The model is then used to investigate the potential impacts of lake-atmosphere coupling on the simulated summer LST of Lake Superior. By evaluating the difference between our two-way coupled modeling system and our observation-driven modeling system, we find that coupled-lake atmosphere dynamics can lead to a higher LST during June-September through higher net surface heat flux entering the lake in June and July and a lower net surface heat flux entering the lake in August and September. The unstratified water in June distributes the entering surface heat flux throughout the water column leading to a minor LST increase, while the stratified waters of July create a conducive thermal structure for the water surface to warm rapidly under the higher incoming surface heat flux. This research provides insight into the coupled modeling system behavior, which is critical for enhancing our predictive understanding of the Great Lakes climate system.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Modeling Noise: Paths toward AI-Enabled Stochastic Earth System Models and Parameterizations

Some of the key challenges in Earth system prediction arise from an uncertain representation of unpredictable natural variability, across time and space scales. This variability, hereafter referred to as noise, represents the quantity against which the strength of a signal of interest is measured to assess predictability. Underestimating or overestimating this noise in Earth system models can lead to issues ranging between overconfidence in an erroneous prediction and a lack thereof in an otherwise accurate one. Noise is part of the physical processes in the Earth system and can amplify or damp a signal of interest in a complex manner that is not systematically characterized. Specifically, while there has been significant progress in our understanding of multiscale interactions among known modes of variability (potentially predictable signals), how these are impacted by the noise is not clear. Recent effort toward stochastic parametrization schemes that provide a representation of noise due to uncertain sub-grid processes in climate models (Berner et al., 2017 and references therein) has shown promise not only in reducing biases and improving probabilistic prediction but also in improving the representation of natural variability in the model toward what is observed. However, today’s standard schemes for stochastic parametrization are still simplistic as they do not take the state of the atmosphere into account (other than by the use of multiplicative noise for model tendencies). Furthermore they require hand-tuning and trial-and-error testing for the magnitude of the added noise, which is difficult in a chaotic system that is as complex as the Earth system.

58 GEOSCIENCES↗
DOE OSTI2023

Evaluation of native Earth system model output with ESMValTool v2.6.0

Earth system models (ESMs) are state-of-the-art climate models that allow numerical simulations of the past, present-day, and future climate. To extend our understanding of the Earth system and improve climate change projections, the complexity of ESMs heavily increased over the last decades. As a consequence, the amount and volume of data provided by ESMs has increased considerably. Innovative tools for a comprehensive model evaluation and analysis are required to assess the performance of these increasingly complex ESMs against observations or reanalyses. One of these tools is the Earth System Model Evaluation Tool (ESMValTool), a community diagnostic and performance metrics tool for the evaluation of ESMs. Input data for ESMValTool needs to be formatted according to the CMOR (Climate Model Output Rewriter) standard, a process that is usually referred to as “CMORization”. While this is a quasi-standard for large model intercomparison projects like the Coupled Model Intercomparison Project (CMIP), this complicates the application of ESMValTool to non-CMOR-compliant climate model output. In this paper, we describe an extension of ESMValTool introduced in v2.6.0 that allows seamless reading and processing of “native” climate model output, i.e., operational output produced by running the climate model through the standard workflow of the corresponding modeling institute. This is achieved by an extension of ESMValTool's preprocessing pipeline that performs a CMOR-like reformatting of the native model output during runtime. Thus, the rich collection of diagnostics provided by ESMValTool is now fully available for these models. For models that use unstructured grids, a further preprocessing step required to apply many common diagnostics is regridding to a regular latitude–longitude grid. Extensions to ESMValTool's regridding functions described here allow for more flexible interpolation schemes that can be used on unstructured grids. Currently, ESMValTool supports nearest-neighbor, bilinear, and first-order conservative regridding from unstructured grids to regular grids. Example applications of this new native model support are the evaluation of new model setups against predecessor versions, assessing of the performance of different simulations against observations, CMORization of native model data for contributions to model intercomparison projects, and monitoring of running climate model simulations. For the latter, new general-purpose diagnostics have been added to ESMValTool that are able to plot a wide range of variable types. Currently, five climate models are supported: CESM2 (experimental; at the moment, only surface variables are available), EC-Earth3, EMAC, ICON, and IPSL-CM6. As the framework for the CMOR-like reformatting of native model output described here is implemented in a general way, support for other climate models can be easily added.

58 GEOSCIENCES↗
DOE OSTI2025

Evaluation of Flow Routing on the Unstructured Voronoi Meshes in Earth System Modeling

Flow routing is a fundamental process of Earth System Models' (ESMs) river component. Traditional flow routing models rely on Cartesian rectangular meshes, which exhibit limitations, particularly when coupled with unstructured mesh-based ocean components. They also lack the support for regionally refined models. While previous studies have highlighted the potential benefits of unstructured meshes for flow routing, their widespread application and comprehensive evaluation within ESMs remain limited. This study extends the river component of the Energy Exascale Earth System Model to unstructured Voronoi meshes. We evaluated the model's performance in simulating river discharge and water depth across three watersheds spanning the Arctic, temperate, and tropical regions. The results show that while providing several benefits, unstructured mesh-based flow routing can achieve comparable performance to structured mesh-based routing, and their difference is often less than 10%. Although the unstructured mesh-based method could address several existing limitations, this research also shows that additional improvements in the numerical method are needed to fully exploit the advantages of unstructured mesh for hydrologic and ESMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

How Earth System Models Can Inform Key Dimensions of Marine Food Security in the Alaskan Arctic

The Arctic is home to several groups of Indigenous Peoples, each with distinct ways of interacting with their environment and ways of life. Arctic, Indigenous Peoples’ food sovereignty is tightly linked with food security. Subsistence harvesting activities provide nutritious and culturally vital foods for Alaska Native households and communities. Climate change is causing rapid and more unpredictable shifts in environmental conditions that impact three of the key aspects of food security, availability, stability, and accessibility. While communities monitor the abundance and health of food webs and environments as part of subsistence harvest practices, anticipating major transformations and changes in these systems is challenging. We explored the potential of Earth System Model output in helping anticipate or project physical or ecosystem changes relevant to Alaska Indigenous peoples’ food security needs. Through examples of model products, that provide measures of accessibility and availability of marine resources, we show that modern models, such as the Energy Exascale Earth System Model presented here, can provide estimates of a broad suite of variables relevant to food security. We investigate how Earth System Model output could contribute to exploring questions related to aspects of Arctic food security such as accessibility and availability and highlight present model shortcomings that, if addressed, would move Earth System Models closer to being a useful tool for understanding environmentally driven changes to the availability and accessibility of harvestable food resources. Our example model-derived food security indicators illustrate how Earth System Model output could be combined with relevant, non-model, information sources; These model products are meant only as a starting point and a tool for engaging community members and to present, in an accessible way, the model’s potential utility, or current lack thereof, to rights holders and stakeholders concerned about food security. We are hopeful that with example products in hand, additional model development efforts will have a higher likelihood of success in achieving an iterative discussion with stakeholders regarding feasible and desired products.

Gibson, Georgina A.↗
DOE OSTI2025

A Fortran–Python interface for integrating machine learning parameterization into earth system models

Abstract. Parameterizations in earth system models (ESMs) are subject to biases and uncertainties arising from subjective empirical assumptions and incomplete understanding of the underlying physical processes. Recently, the growing representational capability of machine learning (ML) in solving complex problems has spawned immense interests in climate science applications. Specifically, ML-based parameterizations have been developed to represent convection, radiation, and microphysics processes in ESMs by learning from observations or high-resolution simulations, which have the potential to improve the accuracies and alleviate the uncertainties. Previous works have developed some surrogate models for these processes using ML. These surrogate models need to be coupled with the dynamical core of ESMs to investigate the effectiveness and their performance in a coupled system. In this study, we present a novel Fortran–Python interface designed to seamlessly integrate ML parameterizations into ESMs. This interface showcases high versatility by supporting popular ML frameworks like PyTorch, TensorFlow, and scikit-learn. We demonstrate the interface's modularity and reusability through two cases: an ML trigger function for convection parameterization and an ML wildfire model. We conduct a comprehensive evaluation of memory usage and computational overhead resulting from the integration of Python codes into the Fortran ESMs. By leveraging this flexible interface, ML parameterizations can be effectively developed, tested, and integrated into ESMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

The Impact of Model Resolution on the Southern Hemisphere in Community Climate System Model Version 4 Idealized Climate Simulations

Model resolution plays a large role in accurately simulating the Southern Hemisphere circulation in both the ocean and atmosphere. Resolving the mesoscale field is important as it has been shown to have a significant impact on the large-scale climate in eddy-rich regions, which are regions of large CO2 absorption. The presence of ocean and atmospheric mesoscale features can affect sea surface temperatures, the strength and location of storm tracks, and many other air-sea processes. Additionally, with an improvement in resolution, the eddy kinetic energy in the ocean can be expected to change considerably. The significance model resolution has on the Southern Hemisphere is examined using the Community Climate System Model, Version 4, eddy-parameterizing and eddy-resolving simulations. The CO2 concentrations and ozone levels are specified independently to better understand how the mesoscale field responds to extreme changes in external forcing and the resulting climate impacts. Overall, in the eddy-parameterizing simulations, the ozone forcing is found to be more important than the changes in CO2 concentrations. However, in the case of the eddy-resolving simulations, the CO2 concentrations are found to be more dominant, especially in eddy-rich regions. These results demonstrate the need for an increase in model resolution for climate prediction.

Daher, Houraa (ORCID:0000000200177346)↗
DOE OSTI2023

Network-Wide Traffic Signal Control Using Bilinear System Modeling and Adaptive Optimization

This study proposes a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks. With signal green time splits as the control input and traffic delay changes as the output for each intersections in the network, a bilinear system model was developed, which, on the basis of linear system modeling, takes interactions among traffic delays and signal timing splits into consideration. Based on the bilinear system modeling framework, we conducted two steps in each time interval to derive traffic control strategies: (1) we used the normalized least-squared algorithm to estimate system parameters; and (2) we solved an online optimization problem to obtain the updated traffic control inputs for the signal timing that minimizes future traffic delays. We evaluated the proposed method in a microscopic traffic simulation environment (VISSIM) with a 35-intersection network of Bellevue city in Washington. Two different traffic demand patterns: (1) normal traffic demands; and (2) time-varying traffic demands were simulated to compare the performance of different control strategies. Experimental results show that (1) the proposed bilinear system model can better describe traffic system dynamics than linear-model based methods, such as our previously developed linear-quadratic regulator control; and (2) the proposed method outperforms the state-of-the-art signal control strategies, namely the max-pressure and the self-organizing traffic light control methods. We have also shown that the proposed method is applicable to all other possible network layouts and signal controller phasing structures.

42 ENGINEERING↗
DOE OSTI2022

Atmospheric river representation in the Energy Exascale Earth System Model (E3SM) version 1.0

Abstract. The Energy Exascale Earth System Model (E3SM) project is an ongoing, state-of-the-science Earth system modeling, simulation, and prediction project developed by the US Department of Energy (DOE). With an emphasis on supporting the DOE's energy mission, understanding and quantifying how well the model simulates water cycle processes is of particular importance. Here, we evaluate E3SM version 1.0 (v1.0) for its ability to represent atmospheric rivers (ARs), which play significant roles in water vapor transport and precipitation. The characteristics and precipitation associated with global ARs in E3SM at standard resolution (1∘ × 1∘) are compared to the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA2). Global patterns of AR frequencies in E3SM show high degrees of correlation (≥0.97) with MERRA2 and low mean absolute errors (MAEs; <1 %) annually, seasonally, and across different ensemble members. However, some large-scale condition biases exist, leading to AR biases – most significant of which are the double intertropical convergence zone (ITCZ), a stronger and/or equatorward-shifted subtropical jet during boreal and austral winters, and enhanced Northern Hemisphere westerlies during summer. By comparing atmosphere-only and fully coupled simulations, we attribute the sources of the biases to the atmospheric component or to a coupling response. Using relationships revealed in Dong et al. (2021), we provide evidence showing the stronger North Pacific jet in winter and the enhanced Northern Hemisphere westerlies during summer, associated with E3SM's double ITCZ and related weaker Atlantic meridional overturning circulation (AMOC), respectively, which are significant sources of the AR biases found in the coupled simulations.

58 GEOSCIENCES↗
DOE OSTI2022

Nitrification, denitrification, and competition for soil N : Evaluation of two Earth System Models against observations

Abstract Earth System Models (ESMs) have implemented nitrogen (N) cycles to account for N limitation on terrestrial carbon uptake. However, representing inputs, losses, and recycling of N in ESMs is challenging. Here, we use global rates and ratios of key soil N fluxes, including nitrification, denitrification, mineralization, leaching, immobilization, and plant uptake (both NH 4 + and NO 3 − ), from the literature to evaluate the N cycles in the land model components of two ESMs. The two land models evaluated here, E3SM Land Model version 1 (ELMv1)‐ECA and CLM5.0, originated from a common model but have diverged in their representation of plant–microbe competition for soil N. The models predict similar global rates of gross primary productivity (GPP) but have approximately two‐fold to three‐fold differences in their underlying global mineralization, immobilization, plant N uptake, nitrification, and denitrification fluxes. Both models dramatically underestimate the immobilization of NO 3 − by soil bacteria compared with literature values and predict dominance of plant uptake by a single form of mineral nitrogen (NO 3 − for ELM, with regional exceptions, and NH 4 + for CLM5.0). CLM5.0 strongly underestimates the global ratio of gross nitrification:gross mineralization and both models are likely to substantially underestimate the ratio of nitrification:denitrification. Few experimental data exist to evaluate this last ratio, in part because nitrification and denitrification are quantified using different techniques and because denitrification fluxes are difficult to measure at all. More observational constraints on soil nitrogen fluxes such as nitrification and denitrification, as well as greater scrutiny of the functional impact of introducing separate NH 4 + and NO 3 − pools into ESMs, could help to improve confidence in present and future simulations of N limitation on the carbon cycle.

Nevison, Cynthia↗
DOE OSTI2024

Quantifying spectral albedo effects on bifacial photovoltaic module measurements and system model predictions

We provide a comprehensive analysis of the effect of spectral albedo on photovoltaic (PV) module measurements and system model predictions. We demonstrate how to account for albedo in indoor bifacial device measurements by adjusting the applied irradiance using the scaled rear irradiance method, exemplified on fabricated silicon heterojunction (SHJ) modules. System model performance is studied using a detailed 3D finite-element model, DUET, for fixed-tilt and horizontal single-axis tracked (SAT) arrays between 15 and 75°N. Spectral effects cause variations in measured SHJ module short-circuit current up to 2% and efficiency variation up to 0.3% abs. We further demonstrate that rear-side spectral mismatch factors (SMMs) resulting from including or omitting spectral albedo in PV system modeling vary between ±13%, while total (front+rear) SMMs vary up to 3%, depending on the deployment configuration and latitude. SAT array SMMs are weakly correlated with latitude, while fixed-tilt array SMMs increase with latitude, driven by an increasing proportion of ground-reflected light on the front-side of modules. Ground-reflections can constitute between 2% and 32% of total incident module irradiance, with notably high (>10%) contributions for fixed-tilt arrays at high latitude. Effects of spectral albedo are most significant for: (1) fixed-tilt deployments at high latitudes, (2) wide bandgap technologies such as perovskite and cadmium telluride cells, (3) albedos which vary steeply over the technology's absorption range, and (4) high albedo ground covers. Overall, we demonstrate that omitting spectral albedo effects can result in PV measurement and system-level modeling uncertainties on the order of several percent in these cases.

14 SOLAR ENERGY↗
DOE OSTI2021

Assessing the Accuracy of Balanced Power System Models in the Presence of Voltage Unbalance

Traditional models of electric power systems represent distribution systems with unbalanced three-phase network models and transmission systems with balanced single-phase-equivalent network models. This distinction poses a challenge for coupled models of transmission and distribution systems, which are becoming more prevalent due to the growth of distributed energy resources connected to distribution systems. In order to maintain a balanced network representation, transmission system models typically assume that the voltage phasors at the interface to the distribution system are balanced. Inaccuracies resulting from this assumption during unbalanced operation can lead to erroneous values for line currents in the transmission system model. This paper empirically quantifies the accuracy of this balanced operating assumption during unbalanced operating conditions for both a simple two-bus system along with a more complex transmission and distribution co-simulation. This paper also characterizes the performance of different methods for translating the unbalanced voltage phasors into a balanced representation in order to give recommendations for modeling coupled transmission and distribution systems.

power distribution↗