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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Analytical small-signal stability analysis of low-inertia power system frequency response considering secondary frequency regulation

Modern power systems are increasingly vulnerable to frequency instability as inverter-based resources (IBRs) replace synchronous machines and reduce system rotational inertia. Existing small-signal frequency stability assessment methods are either computationally intensive, relying on simulation-driven approaches, or lack analytical stability regions that explicitly account for secondary frequency response (SFR). This paper introduces new analytical frameworks that enable evaluation small-signal frequency stability while explicitly incorporating tunable IBR and SFR parameters. Using Kharitonov’s theorem with an overbounding approach, explicit small-signal stability criteria are derived. In addition, based on Białas’ criterion and Hurwitz matrix, analytical stability regions are established to reveal feasible design spaces for SFR and IBR parameters tuning. Extensive Matlab/Simulink-based simulations validate the accuracy and computational efficiency of the proposed methods, demonstrating that coordinated tuning of SFR and IBR parameters can substantially enhance system resilience. By bridging analytical rigor with practical tunability, this work provides an analytical framework for assessing small-signal frequency stability in low-inertia grids, supporting the real-time, scalable, and resilient operation of sustainable power systems.

14 SOLAR ENERGY↗
DOE OSTI2022

Utilizing lowly-reactive coal gasification fly ash (CGFA) to stabilize aggregate bases

This study explored the feasibility of utilizing lowly-reactive coal gasification fly ash (CGFA) for stabilizing road aggregate bases. Three types of aggregate stabilizers including the ordinary Portland cement (OPC)-CGFA, hydrated lime (CH)-CGFA and alkali-activated CH-CGFA were evaluated based on the performances of compacted base specimens. It was found that the OPC-CGFA stabilized bases showed better mechanical and durability properties while the CH-CGFA samples had low water stability and freeze-thaw durability due to the dissolution of unreacted CH. However, the reaction degree of CGFA associated with the performances of CH-CGFA stabilization could be considerably enhanced by the alkali-activation. The sustainability and economic feasibility analyses showed the use of CGFA could significantly reduce the CO 2 emissions and costs, highlighting the synergy between the recycling of CGFA and the construction of sustainable road bases. Here, a framework of selecting CGFA-based stabilizers for road bases was proposed considering the performance ratings of the material properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Stability boundary and optimal operating parameter identification in milling using Bayesian learning

Here, this paper describes a novel Bayesian learning approach for stability boundary and optimal parameter identification in milling without the knowledge of the underlying tool dynamics or material cutting force coefficients. The paper is divided into two parts. First, a Bayesian learning method for stability lobe identification using test results is described. Each axial depth and spindle speed combination is characterized by a probability of stability which is updated using Bayes’ rule when a test result (stable or unstable) is made available. A novel likelihood function is defined which incorporates knowledge of the stability behavior. Numerical results show convergence to the analytical stability lobe diagram. Second, an adaptive experimental strategy to identify optimal operating parameters that maximize material removal rate is described. Numerical evaluation shows convergence to the optimal operating point with error less than 15 % within ten tests on average. The approach is validated using experimental results. Results show that the proposed method is an efficient and robust learning method to identify the stability lobe diagram and optimal operating parameters with a limited number of tests/data points.

Bayesian machine learning↗
DOE OSTI2021

Buffer concentration dramatically affects the stability of S-nitrosothiols in aqueous solutions

S-nitrosothiols (RSNOs) are an important group of nitric oxide (NO)-donating compounds with low toxicity and wide biomedical applications. In this paper, we, for the first time, demonstrate that the concentration of buffer remarkably affects the stability of RSNOs including naturally occurring S-nitrosoglutathione (GSNO) and synthetic S-nitroso-N-acetylpenicillamine (SNAP). For a solution with a high concentration of GSNO (e.g., 50 mM) and an initial near-neutral pH, the optimal buffer concentration is close to the GSNO concentration under our experimental conditions. A lower buffer concentration does not have adequate buffer capacity to resist the pH drop caused by GSNO decomposition. The decreased solution pH further accelerates GSNO decomposition because GSNO is most stable at near-neutral pH according to our density functional theory (DFT) calculations. A higher-than-optimal buffer concentration also reduces the GSNO stability because buffer ingredients including phosphate, Tris base, and HEPES consume NO/N 2 O 3 . In contrast to GSNO, the highest SNAP stability is obtained when the starting solution at a neutral pH does not contain buffer species, and the stability decreases as the buffer concentration increases. Furthermore, this is because SNAP is more stable at mildly acidic pH and the SNAP decomposition-induced pH drop stabilizes the donor. When the RSNO concentration is low (e.g., 1 mM), the buffer concentration also matters because any excess buffer accelerates the donor decomposition. Since the effect of buffer concentration was previously overlooked and suboptimal buffer concentrations were often used, this paper will aid in the formulation of RSNO solutions to obtain the maximum stability for prolonged storage and sustained NO release.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Stromataxic Stabilization of a Metastable Layered ScFeO3 Polymorph

Metastable polymorphs--materials with the same stoichiometry as the ground state but a different crystal structure--enable many critical technologies. This work describes the development of a stabilization approach for metastable polymorphs that are difficult to achieve through other stabilization techniques (such as epitaxy or quenching) called stromataxy. Stromataxy is a method based on controlling the precursor structure during the initial stages of material growth to dictate phase formation. To illustrate this approach, we controlled the atomic layering of the precursors of ScFeO3 and stabilized the metastable P63cm phase, under conditions that previously led to the ground-state Ia3¯ bixbyite phase. Ab initio mechanistic calculations highlight the importance of the variable oxidation state of Fe and the layer stability during layer-by-layer growth. The broad applicability of a stromataxy approach was demonstrated by stabilizing this metastable phase on substrates that have previously been shown to stabilize other polymorphs under continuous growth. Stromataxy is shown as a viable option for accessing polymorphs that are close in energy, difficult to differentiate by strain, or that lack a well epitaxially matched substrate.

calculations↗
DOE OSTI2021

Insights into the Enhanced Oxidative Thermal Stability of Nanoparticle Organic Hybrid Materials Developed for Carbon Capture and Energy Storage

Due to the growing need for Direct Air Capture (DAC) and integrated carbon capture and conversion technologies, CO 2 capture materials that can withstand a wide range of environmental conditions, including fluctuating ambient temperatures and high concentrations of oxidizing agents (i.e., oxygen and moisture), are critically needed. Liquid-like Nanoparticle Organic Hybrid Materials (NOHMs) have been proposed as candidates for DAC and electrolyte additives enabling sustainable energy storage (i.e., integrated CO 2 capture and conversion and flow batteries). Liquid-like NOHMs functionalized with an ionic bond have been shown to display greatly enhanced oxidative thermal stability compared to the untethered polymer. However, these studies were limited in terms of reaction conditions and the detailed mechanisms of the oxidative thermal degradation were not reported. In this work, a kinetic thermal degradation analysis was performed on NOHM-I-HPE and the neat polymer, Jeffamine M2070 (HPE), in both non-oxidative and oxidative conditions. NOHM-I-HPE displayed similar thermal stability to the untethered polymer in a nitrogen environment, but interestingly, the thermal stability of the ionically tethered polymer was significantly enhanced in the presence of air. This observed enhancement of oxidative thermal stability is attributed to the orders of magnitude larger viscosity of the liquid-like NOHMs compared to untethered polymer and the bond stabilization of the ionically tethered polymer in the NOHMs canopy. Further, spectroscopic analyses of the liquid residue revealed that in the presence of oxygen, the degradation of HPE and NOHM-I-HPE occurs through the formation of trace amounts of carbonyls. This study illustrated that NOHMs can serve as functional materials for sustainable energy storage applications because of their excellent oxidative thermal stability.

25 ENERGY STORAGE↗
DOE OSTI2023

Procedures for Assessing the Stability of Proposed Topological Materials

Here, we investigate the stability of MnPb 2 Bi 2 Te 6 (MPBT), which is predicted to be a magnetic topological insulator (TI), using density functional theory calculations. Our analysis includes various measures such as enthalpies of formation, Helmholtz free energies, defect formation energies, and dynamical stability. Our thermodynamic analysis shows that the phonon contribution to the energy gain from finite temperature is estimated to be less than 10 meV/atom, which may not be sufficient to stabilize MPBT at high temperatures, even with the most favorable reactions starting from binaries. While MPBT is generally robust against the formation of various defects, we find that the anti-site defect formation of MnPb is the most likely to occur, with a corresponding energy less than 60 meV. This can be attributed to the significant energy cost from compressive strain at the PbTe layer. Our findings suggest that MPBT is on the brink of stability in terms of thermodynamics and defect formation, underscoring the importance of conducting systematic analyses of the stability of proposed TIs, including MPBT, for their practical utilization. This study offers valuable insights into the design and synthesis of desirable magnetic TI materials with robust stabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Polyethylene Glycol Crowder’s Effect on Enzyme Aggregation, Thermal Stability, and Residual Catalytic Activity

Protein stability and performance in various natural and artificial systems incorporating many other macromolecules for therapeutic, diagnostic, sensor, and biotechnological applications attract increasing interest with the expansion of these technologies. Here we address the catalytic activity of lysozyme protein (LYZ) in the presence of a polyethylene glycol (PEG) crowder in a broad range of concentrations and temperatures in aqueous solutions of two different molecular mass PEG samples (Mw = 3350 and 10000 g/mol). The phase behavior of PEG–protein solutions is examined by using dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS), while the enzyme denaturing is monitored by using an activity assay (AS) and circular dichroism (CD) spectroscopy. Molecular dynamic (MD) simulations are used to illustrate the effect of PEG concentration on protein stability at high temperatures. The results demonstrate that LYZ residual activity after 1 h incubation at 80 °C is improved from 15% up to 55% with the addition of PEG. The improvement is attributed to two underlying mechanisms. (i) Primarily, the stabilizing effect is due to the suppression of the enzyme aggregation because of the stronger PEG–protein interactions caused by the increased hydrophobicity of PEG and lysozyme at elevated temperatures. (ii) The MD simulations showed that the addition of PEG to some degree stabilizes the secondary structures of the enzyme by delaying unfolding at elevated temperatures. The more pronounced effect is observed with an increase in PEG concentration. This trend is consistent with CD and AS experimental results, where the thermal stability is strengthened with increasing of PEG concentration and molecular mass. Overall, the results show that the highest stabilizing effect is approached at the critical overlap concentration of PEG.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

A Polymer-in-Salt Electrolyte with Enhanced Oxidative Stability for Lithium Metal Polymer Batteries

Lithium (Li) metal polymer batteries (LMPBs) are a promising candidate of solid-state batteries with high safety. However, rare progress has been demonstrated so far in high voltage stability of polyethylene oxide (PEO) based polymer electrolytes for LMPBs. Herein, we revived the polymer-in-salt electrolyte (PISE) strategy based on the PEO-LiFSI system with EO/Li = 8 through a dry process to avoid the contamination of the residual solvent. The obtained PISEs exhibit quite different morphologies and coordination structures which greatly enhance the oxidative stability of polymer electrolytes. P(EO)1LiFSI has a low melting temperature, a high ionic conductivity at 60 ?C and an oxidative stability of ~4.5 V vs. Li/Li+ (overcoming the inherent low oxidative stability of PEO). With an effective interphase rich in inorganic species, in combination with good stability of the hybrid polymer electrolyte towards Li metal, the cycling stability of Li||LiNi1/3Co1/3Mn1/3O2 is greatly improved. The LMPB can retain 74.4% of capacity after 186 cycles at 60 ?C under the charge cutoff voltage of 4.3 V. The findings point out a promising strategy to develop high-voltage stable polymer electrolytes for high energy-density and safe LMPBs.

Polymer-in-salt electrolyte, lithium metal battery↗
DOE OSTI2026

Composition, Activity, and Stability of IrO x Oxygen Evolution Reaction Electrocatalysts

The oxygen evolution reaction (OER) is integral to several electrochemical energy conversion and storage technologies, including carbon dioxide reduction to value added fuels, nitrogen reduction to ammonia, reversible fuel cells, rechargeable metal−air batteries, and water electrolysis to produce hydrogen. Iridium oxide (IrO x ) is widely recognized as the benchmark OER catalyst for acidic environments. Despite widespread use of IrO x catalysts, most notably in proton-exchange membrane water electrolyzers (PEMWEs), a comprehensive understanding of the physicochemical properties of commercial catalysts and the impact of these properties on both the activity and stability of these catalysts is lacking. Here, we study commercial IrO x catalysts with different physicochemical properties, three nominally considered amorphous and three rutile, to elucidate how structural and compositional variations affect OER activity and stability. Utilizing standardized aqueous electrochemical protocols, time-resolved dissolution quantification using inductively-coupled plasma mass spectrometry, and physicochemical characterization, including multiple synchrotron X-ray techniques, we systematically correlate catalyst properties with OER performance and degradation behavior aided by principal component analysis (PCA). Our results demonstrate the general trend of amorphous IrO x having higher intrinsic activity but limited stability and crystalline rutile IrO 2 having lower activity but enhanced stability against dissolution. The trends within the amorphous and rutile catalyst groups correlate with inherent material properties, including phase composition and structure, crystallinity, particle size, surface area, and surface structure/chemistry. Notably, we identify a rutile catalyst with the largest crystallite/ domain sizes, moderate surface area, a small fraction of hydrous phase, and a favorable pore structure (trimodal distributions of pore sizes ranging from 2−5 nm) that exhibits the best balance between activity and stability among the six catalysts studied here. These findings illustrate a fundamental structure-governed trade-off between activity and stability and highlight the critical role of surface chemistry modification and structure engineering in IrO x catalyst optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Insights Into Nature-Based Climate Solutions: Managing Forests for Climate Resilience and Carbon Stability

Successful implementation of forest management as a nature-based climate solution is dependent on the durability of management-induced changes in forest carbon storage and sequestration. As forests face unprecedented stability risks in the face of ongoing climate change, much remains unknown regarding how management will impact forest stability, or how interactions with climate might shift the response of forests to management across spatiotemporal scales. Here, we used a process-based model to simulate multidecadal projections of forest dynamics in response to changes in management and climate. Simulations were conducted across gradients in forest type, edaphic factors, and management intensity under two alternate radiative forcing scenarios (RCP4.5 and RCP8.5). This allowed for the quantification of forest stability shifts in response to climate change, and the role of management in modulating that response, where ecosystem stability is characterized as the resilience and temporal stability of net primary production, aboveground biomass, and soil carbon. Our results indicate that forest structure is primarily shaped by management, but the same management strategy often produced divergent structures over time, due to interactions with regional climate change. We found that management can be used to increase stability and minimize the release of stored carbon by reducing mortality, but also highlight the regional dependency of management-induced changes in resilience to climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Isotope effects and Alfvén eigenmode stability in JET H, D, T, DT, and He plasmas

While much about Alfvén eigenmode (AE) stability has been explored in previous and current tokamaks, open questions remain for future burning plasma experiments, especially regarding exact stability threshold conditions and related isotope effects; the latter, of course, requiring good knowledge of the plasma ion composition. In the JET tokamak, eight in-vessel antennas actively excite stable AEs, from which their frequencies, toroidal mode numbers, and net damping rates are assessed. The effective ion mass can also be inferred using measurements of the plasma density and magnetic geometry. Thousands of AE stability measurements have been collected by the Alfvén Eigenmode Active Diagnostic in hundreds of JET plasmas during the recent Hydrogen, Deuterium, Tritium, DT, and Helium-4 campaigns. In this novel AE stability database, spanning all four main ion species, damping is observed to decrease with increasing Hydrogenic mass, but increase for Helium, a trend consistent with radiative damping as the dominant damping mechanism. These data are important for confident predictions of AE stability in both non-nuclear (H/He) and nuclear (D/T) operations in future devices. In particular, if radiative damping plays a significant role in overall stability, some AEs could be more easily destabilized in D/T plasmas than their H/He reference pulses, even before considering fast ion and alpha particle drive. Active MHD spectroscopy is also employed on select HD, HT, and DT plasmas to infer the effective ion mass, thereby closing the loop on isotope analysis and demonstrating a complementary method to typical diagnosis of the isotope ratio.

Alfvén eigenmodes↗
DOE OSTI2024

Validation study of RWM stability in DIII-D high- β N plasmas

The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high-β N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems

Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.

DC–AC power systems↗
DOE OSTI2023

A Stability Analysis Tool for Bulk Power Systems Using Black-Box Models of Inverter-Based Resources

This paper presents a small-signal stability analysis tool for large-scale power systems with high penetration of inverter-based resources (IBRs). Firstly, a network transfer function matrix (NTFM), which represents the information of the system topology, transmission lines, loads, IBRs locations, etc., is derived to model the entire power system network. Secondly, small-signal perturbation method is applied to obtain the sequence impedance/admittance models of the block-box IBRs considering the frequency cross-coupling effects. With the obtained NTFM as well as IBR models, a multi-input, multi-output (MIMO) feedback system is constructed, and the generalized Nyquist criterion (GNC)-based stability method is employed to analyze the stability of the entire power system. Furthermore, based on the developed stability analysis method, sensitivity analysis is conducted on an unstable case to identify which parameter has a high impact on the system stability. As a result, different test cases based on a modified IEEE 14- bus system as well as a reduced 240-bus WECC system are studied to verify the proposed stability analysis tool.

42 ENGINEERING↗
DOE OSTI2020

Low-Frequency Stability Analysis of Inverter-Based Islanded Multiple-Bus AC Microgrids Based on Terminal Characteristics

For system planning of three-phase inverter-based islanded ac microgrids, the low frequency instability issue caused by interactions of inverter droop controllers is a major concern. When internal control information of procured commercial inverters is unknown, impedance-based small-signal stability criteria facilitate prediction of resonances in medium and high frequency ranges, but they usually assume the grid fundamental frequency as constant and thus they are incapable of analyzing the low-frequency oscillation of the fundamental frequency in islanded microgrids. Aiming at solving this issue, this paper proposes two stability analysis methods based on terminal characteristics of inverters and passive connection network including the dynamics of the fundamental frequency for analysis of low-frequency stability in islanded multiple-bus microgrids. Based on the Component Connection Method (CCM) to systematically separate inverters from the passive connection network, a general approach is developed to model the microgrid as a multiple-input-multiple-output (MIMO) negative feedback system in the common system d-q reference frame. By applying the generalized Nyquist stability criterion (GNC) to the return-ratio and return-difference matrices of the MIMO system model, the low-frequency stability related to the fundamental frequency can be analyzed using the measured terminal characteristics of inverters. Finally, analysis and simulation of a 37-bus microgrid verify the effectiveness of the proposed stability analysis methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Moisture Stability of Sulfide Solid-State Electrolytes

In this report we detail a comprehensive study on the moisture stability of sulfide solid-state electrolytes in dry room environments. Although sulfide SSEs have many favorable attributes, this class of materials suffers from poor stability with water. Sulfide SSEs react with water to form gaseous H 2 S and a variety of solid byproducts like Li 3 PO 4 and LiOH, which go on to increase the interfacial impedance of solid-state batteries. Lab-scale research typically utilizes gloveboxes with <1 ppm water, however, the large-scale manufacturing of Li-ion batteries occurs in –40°C dewpoint dry rooms with around 126 ppm water. Consequently, the moisture stability of sulfide SSEs must be addressed if the manufacture of solid-state batteries based on sulfide SSEs is to be scaled up. Here, we are the first to characterize the moisture stability of sulfide SSEs according to both H 2 S and the degradation of ionic conductivity at different moisture setpoints ranging from –76°C to –40°C dewpoint. A variety of different SSE compositions are studied; namely, (Li 2 S) 75 (P 2 S 5 ) 25 , (Li 2 S) 70 (P 2 S 5 ) 30 , (Li 2 O) 7 (Li 2 S) 68 (P 2 S 5 ) 25 , (Li 2 O) 7 (Li 2 S) 63 (P 2 S 5 ) 30 , and (Li 2 S) 75 (P 2 S 5 ) 25 + 20 mol% LiI. We find that moisture stability improves with 75 mol% Li2S modifier content and the introduction of a Li 2 O co-modifier. After a 30 min exposure in a –40°C dewpoint dry room environment we found that (Li 2 S) 75 (P 2 S 5 ) 25 + 20 mol% LiI powder generated 0.1 cc/g H 2 S and its ionic conductivity decreased by over 50%. However, when SSE powder was exposed as a slurry in a dodecane carrier the same SSE composition generated 0 cc/g H 2 S and its ionic conductivity only dropped by 14%. Our results show that sulfide SSEs have acceptable moisture stability when appropriately processed in a dry room environment.

25 ENERGY STORAGE↗
DOE OSTI2020

Analyzing Impact of Distributed PV Generation on Integrated Transmission & Distribution System Voltage Stability—A Graph Trace Analysis Based Approach

The use of a Graph Trace Analysis (GTA)-based power flow for analyzing the voltage stability of integrated Transmission and Distribution (T&D) networks is discussed in the context of distributed Photovoltaic (PV) generation. The voltage stability of lines and the load carrying capability of buses is analyzed at various PV penetration levels. It is shown that as the PV generation levels increase, an increase in the steady state voltage stability of the system is observed. Moreover, within certain regions of stability margin changes, changes in voltage stability margins of transmission lines are shown to be linearly related to changes in the loading of the lines. Two case studies are presented, where one case study involves a model with eight voltage levels and 784,000 nodes. In one case study, a voltage-stability heat map is used to demonstrate the identification of weak lines and buses.

14 SOLAR ENERGY↗