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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 OSTI2021

Plasma-droplet interaction study to assess transport limitations and the role of • OH, O • ,H • ,O 2 (a 1 Δ g ),O 3 , He(2 3 S) and Ar(1s 5 ) in formate decomposition

Plasmas interacting with liquid microdroplets are gaining momentum due to their ability to significantly enhance the reactivity transfer from the gas phase plasma to the liquid. This is, for example, critically important for efficiently decomposing organic pollutants in water. In this contribution, the role of •OH as well as non-•OH-driven chemistry initiated by the activation of small water microdroplets in a controlled environment by diffuse RF glow discharge in He with different gas admixtures (Ar, O 2 and humidified He) at atmospheric pressure is quantified. The effect of short-lived radicals such as O• and H• atoms, singlet delta oxygen (O 2 (a 1 Δ g )), O 3 and metastable atoms of He and Ar, besides •OH radicals, on the decomposition of formate dissolved in droplets was analyzed using detailed plasma diagnostics, droplet characterization and ex situ chemical analysis of the treated droplets. The formate decomposition increased with increasing droplet residence time in the plasma, with ~70% decomposition occurring within ~15 ms of the plasma treatment time. The formate oxidation in the droplets is shown to be limited by the gas phase •OH flux at lower H 2 O concentrations with a significant enhancement in the formate decomposition at the lowest water concentration, attributed to e – /ion-induced reactions. However, the oxidation is diffusion limited in the liquid phase at higher gaseous •OH concentrations. Here, the formate decomposition in He/O 2 plasma was similar, although with an order of magnitude higher O• radical density than the •OH density in the corresponding He/H 2 O plasma. Using a one-dimensional reaction–diffusion model, we showed that O 2 (a 1 Δ g ) and O 3 did not play a significant role and the decomposition was due to O•, and possibly •OH generated in the vapor containing droplet-plasma boundary layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Characterization of turbulence under different stability conditions using lidar scanning data

The spatiotemporal scales of turbulence in the boundary layer flow vary with the static stability of the atmosphere. For example, turbulence structures in unstable conditions are often found to be large and coherent, whereas the turbulent structures in stable conditions are relatively small and sporadic. To better understand the behavior of such turbulent structures under different atmospheric stability conditions in the lower atmosphere, herein, we use scanning lidar data collected over several months during the US Department of Energy's second Wind Forecast Improvement Project (WFIP 2) in 2016. The radial velocity data from scanning lidar were gathered along the horizontal plane (PPI mode) and were analyzed using proper orthogonal decomposition (POD) and spectral energy methods. The results from these analyses show that the turbulent structures in daytime unstable conditions are different from those present during nighttime stable conditions in terms of amount of energy and coherent structures. The POD energy is distributed more evenly in all the higher spatial modes in the daytime unstable case compared to the nighttime stable case. Besides characterizing the turbulence in the flow, the lidar data were also used to compare the simulated flow field generated from the WRF-LES framework (Weather Research and Forecasting - large-eddy simulation) with the scanning lidar data. The results from both simulated and lidar scanned data show similar structures orienting the streak-like structure along the mean wind. This indicates that the streak-like structures can exist in the real atmosphere during unstable atmospheric condition cases.

Rai, Raj K.↗
DOE OSTI2020

Longitudinal coherence and short-term wind speed prediction based on a nacelle-mounted Doppler lidar

The spatial structure of turbulence in atmospheric boundary layer flows is highly relevant to wind energy. In particular, wind turbine control strategies based on inflow preview measurements require knowledge of the longitudinal evolution of turbulent flow as it approaches the rotor. These upstream measurements are usually obtained with nacelle-mounted wind lidars. In contrast to traditional in situ anemometry, lidars collect measurements within a probe volume which varies in size depending on the technology of the commercial system being used. Here, we address two issues related to the use of wind lidar to measure the incoming flow to a wind turbine: (i) whether existing longitudinal coherence models can be used to predict flow at the rotor, based on measurements performed at a distance away from the rotor; and (ii) what effect probe-volume averaging has on the inflow predictions. These two questions are critical to the design and implementation of robust wind turbine control strategies. To address these questions, we perform field measurements and large-eddy simulations to determine which incoming flow structures can be readily predicted with existing coherence models, and which require additional corrections to account for lidar volumetric averaging effects. Results reveal that the wind turbine induction zone has a negligible impact on the longitudinal coherence and first-order turbulence quantities, such as the standard deviation of velocity fluctuations. However, the phase of the signal, from which advection time periods of the turbulent structures are derived, is affected by the rotor blockage effect.

17 WIND ENERGY↗
DOE OSTI2024

Behavior and mechanisms of Doppler wind lidar error in complex terrain: stable flow case study at Perdigão

A numerical experiment is carried out investigating the magnitude of biases in ground-based lidar measurements in complex flow conditions. Biases assessed include those arising from flow curvature and from the interaction of turbulence with the wind field reconstruction (WFR) algorithms used by a WindCube lidars and anemometers. RANS-CFD and WRF-LES simulations were performed for the Perdig˜ao Field Experiment site for a range of atmospheric conditions. Virtual anemometer and lidar data were generated for four locations: two near exposed ridge tops and two in low-speed regions in the valley. The LES data at these four locations show that the scalar inflation terms (the relation between scalar and vector averaged wind speed) for virtual lidar and virtual cups agree very well with predictions using perturbation theory. While the lidar errors vary greatly with location and height, the contribution from the flow curvature tends to be larger than the differences arising from scalar inflation. For one lidar/mast pair near the ridge top, comparisons between simulations and measurements are carried out for a resonant mountain wave event on June 14th, 2017, and for the whole duration of the Perdigão campaign for winds perpendicular to the ridges. The lidar error during the mountain wave, a period of strong stability and low inversion height, is significantly larger than the campaign average. The sensitivity of the lidar error to atmospheric stability is confirmed by the RANS simulations, which suggests strong sensitivity of flow curvature error to stability conditions and to the shape of the wind speed profile near the top of the boundary layer.

17 WIND ENERGY↗
DOE OSTI2024

Can mesoscale models capture the effect from cluster wakes offshore?

Long wakes from offshore wind turbine clusters can extend tens of kilometers downstream, affecting the wind resource of a large area. Given the ability of mesoscale numerical weather prediction models to capture important atmospheric phenomena and mechanisms relevant to wake evolution, they are often used to simulate wakes behind large wind turbine clusters and their impact over a wider region. Yet, uncertainty persists regarding the accuracy of representing cluster wakes via mesoscale models and their wind turbine parameterizations. Here, we evaluate the accuracy of the Fitch wind farm parameterization in the Weather Research and Forecasting model in capturing cluster-wake effects using two different options to represent turbulent mixing in the planetary boundary layer. To this end, we compare operational data from an offshore wind farm in the North Sea that is fully or partially waked by an upstream array against high-resolution mesoscale simulations. In general, we find that mesoscale models accurately represent the effect of cluster wakes on front-row turbines of a downstream wind farm. However, the same models may not accurately capture cluster-wake effects on an entire downstream wind farm, due to misrepresenting internal-wake effects.

17 WIND ENERGY↗
DOE OSTI2024

Aerodynamic and production comparison of wind farms with downwind versus conventional upwind turbines

Ever-increasing turbine scales and their associated logistical challenges have reignited questions about the performance of downwind rotor configurations. A particular potential benefit of downwind rotor configurations is the farm-scale power increase that may be conferred by tilt-driven downward wake entrainment and associated wake recovery. In this work, a comprehensive aerodynamic analysis is carried out to understand the mechanisms for wake entrainment and recovery across a spectrum of velocity and inflow alignment conditions on a small, structured farm in order to understand the impact of downwind rotors on farm production. The results show that the benefits demonstrated previously in the literature for downwind-rotor farms in aligned flows are fragile, and, outside of strong farm/flow alignment conditions, power production benefits for small farms with downwind rotor configurations are significantly if not completely mitigated by misalignment effects. The work indicates that farm-scale benefits for downwind rotors must be realized either from large-scale entrainment benefits, with more exotic farm arrangements that can take advantage of the aerodynamic effects, or from beneficial fatigue impacts from entrainment of less turbulent outer boundary layer flows.

17 WIND ENERGY↗
DOE OSTI2025

Examining future changes in coastal low-level jet properties offshore California through dynamical downscaling

The coastal low-level jet, or coastal low-level jet (CLLJ), is a synoptically-forced meteorological feature frequently present offshore the western United States (U.S.). Characterized by a wind speed maximum that resides at the top of the marine boundary layer, the CLLJ is largely controlled by the location and strength of the North Pacific High (NPH) as well as the coastal geometry. Considering the rich wind resource available in this offshore region, the Bureau of Ocean Energy Management identified wind energy lease areas offshore California and supported the deployment of two U.S. Department of Energy wind lidar buoys near Morro Bay and Humboldt. Despite our relatively good understanding of the fundamental mechanisms responsible for large-scale CLLJ properties offshore the western U.S., future changes in CLLJ characteristics are less clear. To address this research challenge, and ultimately to better inform future wind turbine deployments, we use simulations driven by three global climate models (GCMs). We apply self-organizing maps to the model outputs for a historical and two future climate periods to show the range of NPH regimes that support CLLJ conditions during the warm seasons, as well as the subtle contribution from land-falling cyclones approaching the mainland during the cold seasons. Compared to the historical period, the three GCM-driven simulations agree that CLLJ conditions will become more (less) prevalent from central California northward (southward). They agree less with respect to future changes in maximum CLLJ wind speeds and CLLJ heights. However, after considering model biases present during the historical period, wind speeds between the models are actually more similar during the 2070–2095 period than during the historical period. The potential combination of more frequent CLLJ conditions characterized by relatively consistent wind speeds occurring at lower heights across northern California suggests that the Humboldt lease area may be ideal for a long-term wind turbine deployment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Short-Term Energy and Meteorological Impacts on Thanksgiving CO2 in Salt Lake City

Abstract Long-term, high-frequency atmospheric CO2 measurements at multiple sites in the Salt Lake City (SLC), Utah, reveal that annual and monthly CO2 variability aligns with a priori estimates of emissions from anthropogenic and biological sources. In this study, we investigate whether short-term fluctuations in anthropogenic emissions, as captured in the Vulcan3 dataset for the United States, can be detected in atmospheric CO2 observations. Specifically, we focus on Thanksgiving holidays, when traffic and energy usage patterns differ from the rest of November. Onroad CO2 emissions exhibit a double peak during weekday morning and evening rush hours but remain relatively low on weekends and Thanksgiving. Interestingly, CO2 mole fractions during Thanksgiving were higher than the rest of November at all SLC monitoring sites, particularly from 2008 to 2013. This increase is partially attributed to elevated energy-related emissions — especially residential sources — and meteorological factors such as weak wind speeds, cold temperature, and a low planetary boundary layer height (PBLH).

 While CO₂ emissions and mole fraction patterns align over time, notable spatial differences exist. For instance, the near-highway site in Murray shows the highest CO₂ mole fractions despite low local emissions, suggesting pollution transport via highways and wind advection. Random Forest model-based SHapley Additive exPlanations (SHAP) analysis reveals that onroad emissions dominate CO2 contributions on weekdays and weekends, while energy-related emissions play a larger role during Thanksgiving, alongside meteorological drivers such as wind speed and PBLH. Across six urban cities, CO2 emissions display a consistent pattern: residential and commercial (onroad) emissions peak during Thanksgiving (weekday) with substantial (minimal) year-to-year variability. These findings highlight that urban CO₂ variability is driven by the combined influence of emissions and meteorology, underscoring the need for integrated mitigation strategies. Additionally, multi-site measurements are essential for accurate source attribution and the development of effective policy interventions. 

Ryoo, Ju-Mee (ORCID:0000000234256296)↗
DOE OSTI2022

The missing base molecules in atmospheric acid–base nucleation

Abstract Transformation of low-volatility gaseous precursors to new particles affects aerosol number concentration, cloud formation and hence the climate. The clustering of acid and base molecules is a major mechanism driving fast nucleation and initial growth of new particles in the atmosphere. However, the acid–base cluster composition, measured using state-of-the-art mass spectrometers, cannot explain the measured high formation rate of new particles. Here we present strong evidence for the existence of base molecules such as amines in the smallest atmospheric sulfuric acid clusters prior to their detection by mass spectrometers. We demonstrate that forming (H2SO4)1(amine)1 is the rate-limiting step in atmospheric H2SO4-amine nucleation and the uptake of (H2SO4)1(amine)1 is a major pathway for the initial growth of H2SO4 clusters. The proposed mechanism is very consistent with measured new particle formation in urban Beijing, in which dimethylamine is the key base for H2SO4 nucleation while other bases such as ammonia may contribute to the growth of larger clusters. Our findings further underline the fact that strong amines, even at low concentrations and when undetected in the smallest clusters, can be crucial to particle formation in the planetary boundary layer.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Contact solitons as spin pistons in one-dimensional ferromagnetic channels

Ferromagnetic channels subject to spin injection have been theoretically shown to sustain dissipative exchange flows (DEFs). In the strong injection regime, a soliton is stabilized at the injection site, which has been termed a contact soliton DEF or CS-DEF. Here, in this work, we investigate the modulation of CS-DEFs as a mechanism to inject magnons into a DEF. By varying the injection current, the parameters connecting the soliton with the DEF via a boundary layer are varied. These lead to a modification in the DEF which is interpreted as a spin piston. The injected magnons follow the expected dispersion relation of DEFs, akin to the Bogoliubov–de Gennes dispersion relation. As a result, this work demonstrates that changes in the injected current can pump magnons along a ferromagnetic channel via dissipative exchange flows.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Framework for idealized climate simulations with spatiotemporal stochastic clouds and planetary-scale circulations

In climate predictions, clouds are the leading source of uncertainty. This is partly because, to simulate the fluid dynamics of climate over the entire globe, a large grid spacing must be used, so clouds are a subgrid-scale parametrization rather than a resolved feature. Here, a framework is investigated with finer grid spacing of O(1) or O(10)km so that some clouds are not subgrid-scale; instead, clouds evolve on the numerical grid. This cloud evolution is achieved using stochastic modeling. Hence, the framework is idealized in the sense that the full fluid dynamics of cloud circulations is still not resolved, and simplified vertical structures are used. Nevertheless, the fluid dynamics model includes evolving clouds that interactively adjust in size, shape, lifetime, and regional coverage. In addition, different cloud types are included with different roles in the climate system, including deep convective clouds and also boundary-layer clouds such as shallow cumulus and stratocumulus clouds. Other basic aspects of the idealized climate system are planetary-scale circulations (e.g., Walker circulation) and radiation. With these ingredients (evolving clouds, planetary-scale circulations, and radiation), the framework has the potential for idealized investigations of climate change with interactive cloud–radiative feedback of individual clouds. Here, the formulation of the model equations is presented, and numerical simulations are shown to illustrate the model dynamics and climate change.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Non-Boussinesq subgrid-scale model with dynamic tensorial coefficients

A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data have shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [J. Bardina, J. Ferziger, and W. Reynolds, Improved subgrid-scale models for large-eddy simulation, in Proceedings of the 13th Fluid and Plasmadynamics Conference, AIAA (1980); C. Meneveau and K. Katz, Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid Mech. 32, 1 (2000)]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g., Bardina et al., Proceedings of the 13th Fluid and Plasmadynamics Conference (1980); R. A. Clark, J. Ferziger, and W.C. Reynolds. Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech. 91, 1 (1979); S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11, 1699 (1999)]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for large-eddy simulation (LES), vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence, and wall-modeled turbulent channel flow at high Reynolds numbers. The results show favorable agreement with DNS data. It has been shown that DTCSM offers similar predictive capabilities as the dynamic Smagorinsky model for canonical flows. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump (Boeing speed bump) exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to existing static coefficient (Vreman) and dynamic Smagorinsky model. The computational cost of performing LES with this model is up to 15% higher than the dynamic Smagorinsky model.

42 ENGINEERING↗
DOE OSTI2021

Quincke Oscillations of Colloids at Planar Electrodes

Dielectric particles in weakly conducting fluids rotate spontaneously when subject to strong electric fields. Such Quincke rotation near a plane electrode leads to particle translation that enables physical models of active matter. In this Letter, we show that Quincke rollers can also exhibit oscillatory dynamics, whereby particles move back and forth about a fixed location. We explain how oscillations arise for micron-scale particles commensurate with the thickness of a field-induced boundary layer in the nonpolar electrolyte. This work enables the design of colloidal oscillators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

We establish a holographic duality between d -dimensional mixed-state symmetry-protected topological (mSPT) phases and ( d + 1 ) -dimensional subsystem symmetry-protected topological (SSPT) states. Specifically, we show that the reduced density matrix of the boundary layer of a ( d + 1 ) -dimensional SSPT state with subsystem symmetry S and global symmetry G corresponds to a d -dimensional mSPT phase with strong S and weak G symmetries. Conversely, we demonstrate that the wave function of an SSPT state can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT phase. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wave functions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPT phases that are unique to open quantum systems, without pure-state analogues. We show that strange correlators and twisted Rényi- N correlators can diagnose these nontrivial phases and we explore their connection to strange correlators in pure-state SSPT phases. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT phases through the duality. Published by the American Physical Society 2025

Sun, Shijun (ORCID:0000000168880030)↗
DOE OSTI2025

Modeling Offshore Wind Farm Performance in Coastal Low-Level Jets Using Coupled Mesoscale-Microscale Large Eddy Simulations

Accurately predicting wind farm reliability under complex offshore atmospheric conditions remains a key challenge, particularly during noncanonical meteorological events such as coastal low-level jets (LLJs). LLJs, characterized by strong nonmonotonic vertical shear and directional veer, depart significantly from the simplified inflow assumptions embedded in conventional design standards, low-fidelity engineering models, and microscale large eddy simulations of the atmospheric boundary layer. In this work, we use the virtual wind farm framework—an exascale, graphics processing unit–accelerated large eddy simulation platform coupled with high-fidelity aeroservoelastic turbine models and advanced mesoscale-microscale coupling via the ExaWind software stack—to investigate turbine responses under realistic LLJ forcing. Simulations are performed over the U.S. North Atlantic offshore domain with the use of meteorological inputs from New York State Energy Research and Development Authority buoy data, focusing on a representative LLJ case impacting the International Energy Agency 15 MW reference turbine. Our results show that LLJs can cause up to 50% power deficits in downstream turbine rows and significantly amplify low-speed shaft and tower loads through nonlinear coupling between complex inflow characteristics and turbine structural dynamics. Two primary mechanisms drive these load amplifications: (1) unique LLJ inflow features—including veer and vertical/lateral shear—and (2) the downstream evolution of the flow under stable thermal stratification, which suppresses turbulence mixing and alters wake recovery. These mechanisms produce streamwise variations in turbine loading not captured by standard hub height–based metrics or existing design load case (DLC) definitions. This study highlights the critical role of rotor-scale flow gradients in driving fatigue and system-level aeroelastic responses, challenging current DLC and control strategies. We advocate the integration of full-flow field, environment-aware wind inputs into load modeling and control algorithms. By leveraging exascale computing to resolve mesoscale-microscale coupling, this work lays the groundwork for next-generation offshore wind turbine design and operation in meteorologically complex marine environments.

17 WIND ENERGY↗
DOE OSTI2023

Design and Stability Analysis of Control System in Multiport Autonomous Reconfigurable Solar Power Plants (MARS)

The Multiport Autonomous Reconfigurable Solar Power Plant (MARS) is an integrated photovoltaic (PV) power generation and energy storage system (ESS), that is designed to connect to both alternating current (AC) transmission grids and high-voltage direct current (HVDC) links. It is a three-phase plant consisting of numerous components with a complex hardware and hierarchical control architecture. This paper presents an approach to decouple the multivariable system of MARS using a recursive reduced-order and boundary layer system methodology. This approach enables efficient computation of the control parameters for the Ll, L2, and L3 controllers. To validate the effectiveness of the proposed control strategy, cyclic tests in accordance with pre-defined performance criteria using controller Hardware-in-the-Loop (cHIL) experiments are conducted. The results demonstrate that the MARS system operates consistently under steady-state conditions. Furthermore, the dynamic response of the MARS system to various grid events is analyzed, underlining the resilience of MARS in presence of faults or loss of generation within the connected WECC system.

Xia, Qian↗
DOE OSTI2022

Vortex Induced Vibration Test of the WITT Device in a Tidal Channel

Fluid flow around a bluff body causes vibrations as the boundary layer separates and vortices are shed. This phenomenon, called vortex induced vibration (VIV), is minimized in most engineering applications, but can be utilized for power generation. Vortex induced vibration has potential for energy harvesting in low velocity water flows and therefore could open many locations to marine renewable energy. Here we present the results of a field test of a device that utilizes VIV to harvest energy from flow in a tidal channel. The pendulum-type device has been designed to generate electricity from motion around and along three axes. It is named the Whatever Input to Torsion Transfer (WITT) energy device and in this test is mounted on top of a pipe. During the field test, the WITT generated electricity at flow velocities from 0.27 to 2.82 m/s. The field test has proven that the WITT can utilize VIV to produce electricity and charge a battery in tidal flows with velocities as low as 0.27 m/s. In the future, the electricity could be used to charge a battery for ocean observation instruments such as temperature and nitrate sensors. In-situ power generation by the WITT would extend deployment times and increase the frequency of measurements.

Branch, Ruth A.↗
DOE OSTI2024

Singular Perturbation-Based Large-Signal Order Reduction of Microgrids for Stability and Accuracy Synthesis With Control

The increasing penetration of distributed energy resources (DERs) highlights the growing importance of microgrids (MGs) in enhancing power system reliability. Employing electromagnetic transient (EMT) analysis in MGs becomes crucial for controlling the rapid transients. However, this requires an accurate but high-order model of power electronics and their underlying control loops, complexifying the stability analysis from the viewpoint of a higher control level. To overcome these challenges, this paper proposes a large-signal order reduction (LSOR) method for MGs with considerations of external control inputs and the detailed dynamics of underlying control levels based on singular perturbation theory (SPT). Specially, we innovatively proposed and strictly proved a general stability and accuracy assessment theorem that allows us to analyze the dynamic stability of a full-order nonlinear system by only leveraging our derived reduced-order model (ROM) and boundary layer model (BLM). Furthermore, this theorem furnishes a set of conditions that determine the accuracy of the developed ROM. Lastly, by embedding such a theorem into the SPT, we propose a novel LSOR approach with guaranteed accuracy and stability analysis equivalence. Case studies are conducted on MG systems to show the effectiveness of the proposed approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗