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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Oxide Semiconductor Sensors for Monitoring Advanced Energy Conversion and Manufacturing Processes at High Temperature

To optimize the operation and functionality of high temperature systems such as slagging gasifiers, coal boilers and glass/steel smelters, it is important to monitor temperature, corrosion and erosion of the refractory used in such systems. Both thermocouple and failure sensors (and arrays of these) would be useful to monitor the health of any refractory or coatings in these systems. Many of such type of sensors are installed into the systems through open access ports within the refractory; however, there are some disadvantages of this approach where corrosive/erosive gas and molten materials can penetrate and compromise the system. The current work presents the development and performance of refractory with embedded high temperature sensors such as thermocouples, thermistors, and various spallation/crack monitoring sensors, which may be used within a variety of refractory brick in different high temperature processes and applications. The objective of our work is to develop high-temperature sensors composed of electroceramic materials that are chemically stable at high temperatures (750°-1500°C) and high pressures (up to 1000 psi) that can be used in monitoring temperature, corrosion and erosion process in refractory used in high energy systems. The high-temperature sensors investigated in this work were composed of various oxide composites directly embedded into the refractory oxides. The composites used for this work were synthesized by a mixed-oxide route. Metal oxides were inserted within a matrix material composed of refractory oxides (Al2O3, ZrO2, etc.). The physical and electrical properties were specifically manipulated by altering the level of percolation of the conductive species (metal oxides) within the refractory constituent (refractory oxide). An example of one of these embedded sensors consisted of an electroceramic-based thermocouple fabricated with two separate oxide composite compositions which were patterned to produce a couple within the interior of a refractory matrix. The thermocouple successfully displayed thermoelectric voltage trend (as a function of temperature), and the voltage was 220.0 mV near 1400 °C. In addition, corrosion tests on the refractory embedded sensors were performed. To evaluate corrosion in the refractory was exposed to high-temperature glass compositions over a 90 h period. The penetration of the glass through the refractory could be monitored by both an amperometric and voltametric based sensor. With this experiment, it was demonstrated that the embedded sensor could dynamically monitor the corrosion process, and thus, provide real-time feedback on both temperature and the refractory health.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2022

Identification of Intraday False Data Injection Attack on DER Dispatch Signals

The urgent need for the decarbonization of power grids has accelerated the integration of renewable energy. Concurrently, increasing distributed energy resources (DER) and advanced metering infrastructure (AMI) have transformed the power grids into a more sophisticated cyber-physical system with numerous communication devices. While these transitions provide economic and environmental value, they also impose increased risk of cyber attacks and operation al challenges. This paper investigates the vulnerabilit y of the power grids with high renewable penetration against an intraday false data injection (FDI) attack on DER dispatch signals and proposes a kernel support vector regression (SVR) based detection model as a countermeasure. The intraday FDI attack scenario and the detection model are demonstrated in a numerical experiment using the HCE 187-bus test system.

Kim, Jip↗
DOE OSTI2022

Association of Mesoscale Auroral Structures and Breakups With Energetic Particle Injections at Geosynchronous Orbit

Geomagnetic substorms are associated with characteristic energetic particle injection signatures at geosynchronous orbit that are often dispersionless in both electrons and ions near the magnetic local time sector of auroral onset locations and are dispersed farther away from this region. Although the precise mechanism responsible for the coherent injection signatures at geosynchronous orbit have been the topic on considerable ongoing debate for decades, recent work on bursty bulk flows (BBFs) in the tail have led to the hypothesis that they may be the result of multiple, overlapping flow bursts penetrating into the inner magnetosphere from more distant downtail reconnection sites. Since auroral streamers are thought to be ionospheric signatures of BBFs in the tail, they can be used as proxies for testing this hypothesis. Using high resolution auroral imagery from the POLAR/VIS instrument combined with multi-spacecraft observations of energetic particle injections at geosynchronous orbit, we examine the association of mesoscale auroral structures with particle injection signatures over many hours during the 9 November 1998 storm. We find that the explosive types of auroral activations, such as pseudo-breakups and substorm onset breakups, are associated with the more intense and well-defined dispersed injection signatures, while intervals of isolated streamer activity appear to be associated with smaller dispersed “injectionlet” signatures. Furthermore, intervals of sustained, intense, and late expansion phase/recovery phase streamer activity appear to be associated with sustained elevated dispersed particle fluxes. These results are consistent with the hypothesis that it is the overlapping effects of sustained, intense multiple flow bursts penetrating toward the Earth that result in classical substorm particle injection signatures at geosynchronous orbit. However, it is also suggested that torches/omega-band tongues are the prime fate of braking isolated flow bursts (streamers) rather than the development of breakups, bulges, and substorm current wedge formation. A statistical analysis is presented showing that 93% of the observed torches evolved from streamers, 93% of streamers arriving in the equatorward regions of the bulge led to torches, 10.5% of such streamers led to breakups (either pseudo-breakups or substorm onsets), and only 3.5% of such streamers led to substorm onsets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Improving a Multilevel Turbulence Closure Model for a Shallow Lake in Comparison With Other 1-D Models

Lakes differ from lands in water availability, heat capacity, albedo, and roughness, which affect local surface-atmospheric interactions. This study modified a multilevel upper ocean model (UOM) for lake applications and evaluated its performance in Lake Taihu (China) with comprehensive measurements against three popular one-dimensional (1-D) lake models. These models were based on different concepts, including the self-similarity (FLake), the wind-driven eddy diffusion (LISSS), the k-ε turbulence closure (SIMSTRAT), and a simplified turbulence closure (UOM). The surface flux scheme in these models was unified to exclude the discrepancies in representing air-lake exchanges. All models in their default formulations presented obvious cold water temperature biases and largely underestimated the lake surface temperature (LST) diurnal range. For each model, these deficiencies were significantly reduced by incorporating new physics schemes or calibrated tunable parameters based on systematic sensitivity tests. The primary modifications for UOM included (1) a new scheme of decreased surface roughness lengths to better characterize the shallow lake, (2) a solar radiation penetration scheme with increased light extinction coefficient and surface absorption fraction to account for the high water turbidity, and (3) turbulent Prandtl number increased by a factor of 20 to reduce the turbulent vertical mixing. All other models were improved in these three aspects (roughness, extinction, and mixing) within their original formulations. Given these improvements, UOM showed superior performance to other models in capturing LST diurnal cycle and daily to seasonal variations, as well as summer-autumn vertical stratification changes. The new UOM is well suited for application in shallow lakes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Changes in Physical Properties of Everglades Peat Soils Induced by Increased Salinity at the Laboratory Scale: Implications for Changes in Biogenic Gas Dynamics

Abstract Saltwater intrusion due to sea level rise is a major concern for the Florida Everglades because it may induce shifts in ecosystem productivity and physical soil properties. However, the effects of saline water intrusion into the current carbon gas dynamics of the Everglades (particularly in terms of biogenic gas production and emissions, i.e., CH 4 and CO 2 ) are still uncertain. In this work, we present a laboratory‐based study to simulate how sea level rise may alter the physical properties (i.e., hydraulic conductivity) of peat soils from the Everglades and consequently affect the accumulation and release of biogenic gases within the peat matrix. Peat monoliths collected from the Everglades were subjected to progressive increases in salinity from a NaCl solution, and changes to the biogenic gas dynamics regime were simultaneously monitored using a combination of time‐lapse ground‐penetrating radar measurements, manometers, time‐lapse photography, and gas traps. Physical changes to the peat matrix at each salinity interval were assessed using constant head permeameter tests. Consistent with previous research, results show that a progressive increase in salinity (from fresh to saltwater) results in (1) a progressive increase in hydraulic conductivity and (2) a progressive decrease in gas content within the peat matrix (i.e., production) and gas releases. This work has implications for better understanding the potential effects of saltwater intrusion into freshwater peatland systems in the Everglades, particularly in terms of carbon gas dynamics.

Sirianni, Matthew J.↗
DOE OSTI2022

Modeling the Effects of Drift Orbit Bifurcation on Radiation Belt Electrons

Abstract Drift orbit bifurcation (DOB) has been suggested to play a major role in the loss and transport of radiation belt electrons since it violates the second adiabatic invariants of particles and makes the third invariant undefined. Results from our guiding‐center test particle simulations using the Tsyganenko‐1989c magnetic field model show that the DOB could affect a broad region of the outer radiation belt, which can penetrate inside the geosynchronous orbit at Kp ≥ 3, and its effects are more significant further away from the Earth, at a higher Kp and for higher electron energies. Specifically, the short‐term simulation results after one electron drift show both traditional and nontraditional DOB transport of electrons, with the nontraditional DOB, caused by a third minimum of the magnetic field strength near the equator, reported here for the first time. Moreover, our results show large ballistic jumps in the second invariant and radial distance for electrons at high equatorial pitch angles after one drift. In addition, long‐term DOB transport coefficients of electrons over many drifts are calculated based on our simulation results. We find that the pitch angle and radial diffusion coefficients of electrons due to DOB could be comparable to or even larger than those caused by electron interactions with chorus and Ultra‐Low‐Frequency waves, respectively. In sum, our results demonstrate that DOB could cause effective loss and transport of radiation belt electrons even in the absence of waves.

Astronomy & Astrophysics↗
DOE OSTI2023

Utilizing grid–supportive load response to shape resilient frequency control of the power grid

The increasing penetration of renewable energy sources and the retirement of conventional generation units have decreased system inertia, making power systems more vulnerable to resilience and stability issues. To address this problem, this paper proposes a novel approach using grid-supportive loads (GSLs) to provide a fast and concise primary frequency response and a deep deterministic policy gradient agent-based secondary controller to restore the system frequency to the nominal value. The proposed method is evaluated on the single-area and multi-area test systems. The simulation results demonstrate that using GSLs enhances the power system's stability and resilience. Compared to conventional controllers, the frequency nadir is improved with GSLs. Additionally, the proposed method effectively enhances resilience even with high penetration. These findings indicate that the proposed approach can improve the resilience and stability of power systems and provide a promising solution for future power systems. The results of this study underscore the importance of utilizing innovative approaches to enhance the stability and resilience of power systems in the context of high penetration of renewable energy sources and the retirement of conventional generation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

National energy savings potential of cellular shades: A measurement and simulation study

Windows are major contributors to energy demand in residential homes because of their inferior thermal resistance compared with the opaque envelope, and sometimes from unwanted solar heat gain. Window attachments can help mitigate the energy demand by controlling the solar heat gains and enhancing window thermal resistance. Cellular shades have the potential of superior thermal performance compared with generic shades because of its honeycomb structure. Here, in this study, the team analyzed the energy savings potential of cellular shades in residential homes via experimental testing for two heating seasons and energy simulations. Five shading devices—three single-cell and two double cellular/cell-in-cell shades—were used to compare the performance with generic horizontal venetian blinds using two nearly identical side-by-side rooms in a residential home. The experimental testing showed daily heating energy savings in the range of 17%–36% compared with the case without shades. The experimental testing data also exhibited improvements in thermal comfort when using cellular shades. Additionally, energy simulations were performed to evaluate the energy savings potential of the cellular shades using a residential prototype home, which demonstrated energy savings up to 9 kWh/m2/year in cold climates. The total site energy savings for heating and cooling from cellular shades was up to ~9% for the home with a heat pump and up to ~15% for a home with a gas furnace compared with cases without any shading devices. The energy savings at a national scale were up to 14.6 TWh assuming a 20% penetration rate in residential homes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Fused x-ray and fast neutron CT reconstruction for imaging large and dense objects

Megavolt x-ray computed tomography (CT) is a powerful tool for three-dimensional characterization. However, its utility is limited for large objects composed of high-atomic number (Z) materials, where x rays fail to penetrate. Information from fast neutron CT (FNCT) can complement x-ray CT reconstructions since fast neutrons can more readily penetrate high-Z objects. In this work, we demonstrate a method for combining FNCT and x-ray CT data to create a single reconstruction, more accurate than could be achieved with either x rays or fast neutrons alone. The algorithm was tested on an exemplar comprising multiple concentric, nested cylinders of different materials. Simulated and empirical x-ray CT data were acquired for the exemplar using a 9 MV bremsstrahlung spectrum. Additional simulated and empirical FNCT data were acquired using an accelerator based fast neutron source. The FNCT data were used to synthesize x-ray CT data and augment the x-ray CT data missing due to lack of penetration. This approach mitigates artifacts that would otherwise negatively affect the accuracy and resolution of a single-modality reconstructed volume.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Demonstration of Ego Vehicle and System Level Benefits of Eco-Driving on Chassis Dynamometer

Eco-Driving with connected and automated vehicles has shown potential to reduce energy consumption of an individual (i.e., ego) vehicle by up to 15%. In a project funded by ARPA-E, a team led by Southwest Research Institute demonstrated an 8-12% reduction in energy consumption on a 2017 Prius Prime. This was demonstrated in simulation as well as chassis dynamometer testing. The authors presented a simulation study that demonstrated corridor-level energy consumption improvements by about 15%. This study was performed by modeling a six-kilometer-long urban corridor in Columbus, Ohio for traffic simulations. Five powertrain models consisting of two battery electric vehicles (BEVs), a hybrid electric vehicle (HEV), and two internal combustion engine (ICE) powered vehicles were developed. The design of experiment consisted of sweeps for various levels of traffic, penetration of smart vehicles, penetration of technology, and powertrain electrification. The large-scale simulation study consisted of doing approximately 96,000 powertrain simulations. A sophisticated clustering scheme was built and utilized to down select representative traces for each scenario from the simulation study for vehicle testing on a chassis dynamometer. Furthermore, this paper provides a summary of individual ego vehicle testing as well as a comprehensive overview of the method utilized for down selecting representative traces from large scale simulation studies that can be used to quantify corridor level benefits. Vehicle test results along with corresponding analyses are presented.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

The Design of a Multiphase CO2 Turbine Test Facility

As the energy market continues to evolve with increased renewables, such as solar and wind energy, the need to balance energy demand with its availability has become increasingly more challenging. The country’s aggressive decarbonization goals in the upcoming decades will increase renewable energy market penetration, thus exacerbating the disparity between energy demand and renewable resource availability. Long-duration energy storage technologies, such as pumped thermal energy storage (PTES), are potential solutions to this challenge with high potential round-trip efficiency (RTE), no geological or geographical constraints, and low safety risks. The charge mode of a PTES system operates a heat pump cycle, converting input power to thermal energy in hot and cold reservoirs. Fundamentally, heat pumps are commonly used in daily life, but the operating conditions required by high RTE PTES systems are outside the design experience of these systems. The low-pressure side of the cycle for a supercritical CO2 (sCO2) PTES operates just above the vapor-dome and potentially drives the turbine to expand into the dome, resulting in multiphase operation in the rear stages of the turbine. This paper presents the design of the test facility for an advanced multiphase-tolerant sCO2 turbine for the heat pump of a PTES system. Heat rejection and pressure loss estimations for the multiphase sections of the test loop presented unforeseen challenges.

25 ENERGY STORAGE↗
DOE OSTI2025

Establishing a silica gel zone in well annulus and evaluating its performance in blocking vertical water flow

Wells are often constructed for monitoring purposes with relatively long screen lengths (e.g., >10 m). Vertical water flows can occur within the artificial or natural filterpack annulus that surrounds the screened interval, bypassing packer assemblies installed inside the wellbore. Attempts to isolate discrete vertical zones during groundwater sampling are unsuccessful when annular flow occurs and lead to remedy decisions based on biased or incorrect interpretations. Blocking vertical annular water flow and contaminant transport will help obtain more accurate concentrations of contaminants from sampling in targeted depth intervals. The application of silica gels formed from the injected colloidal silica CS suspensions is a novel approach to minimize or prevent movement of vertical movement of groundwater in the surrounding filterpack annulus. In this work, we tested the feasibility of injecting CS suspensions to target locations and developed a modified CS formulation that is injectable and prevents gravity sinking. We studied the distribution and penetration of silica gel at laboratory scale in mock well annulus with surrounding formations. We evaluated the performance of the silica gel in blocking vertical water flow in the annulus and in minimizing chemical transport through the gel zone. CS suspension formulations have been defined that are ready for injection, stay in target locations, and form gel within desired time frames. Injection of CS suspensions achieved uniform distribution in a well annulus filter pack, fully occupied the annulus pore space, and penetrated the formation surrounding the filter packer with a sufficient distance to create a hydraulic annular seal when the injection was applied at a sufficient rate. The depth of penetration into the formation was dependent on the permeability contrast between the filter pack and the surrounding formation. Silica gel that formed in the annulus blocked vertical water flow and stopped the chemical transport through the gel zone. In conclusion, this research reveals that using CS suspension injection and sequential gelation (CS-GEL) is a promising technology for blocking vertical water flow and chemical transport through the filter pack in targeted zones within the annulus of long-screened well systems.

Colloidal silica suspension↗
DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗
DOE OSTI2024

Puck Loop Seal (Final Project Technical Report)

Sandia National Laboratories (SNL) is advancing technical capabilities used in passive loop seals. The “Puck” seal used a set of International Atomic Energy Agency (IAEA) requirements for new passive loop seals published in 2020 as a design guide. The seal is based on an oxygen-sensitive inner mixture encased in an oxygen-impermeable shell, is monolithic rather than two-part, incorporates self-capturing wire features, contains colored water beads and bubbles formed during processing as unique identifiers (UIDs), and visually indicates tamper (whether from seal body penetration or from seal wire removal) by irreversibly changing the seal body from multi-colored to black. This paper will provide details on the design, development, and testing of Puck seal prototypes.

42 ENGINEERING↗
DOE OSTI2023

LOCOMOTIVES - Comprehensive Impact and Cost Assessment Framework of Carbon Lowering Approaches for the US Rail Freight System

The goal of this project is to develop a tool to aid railroads and other stakeholders assess and approach the decarbonization of freight rail operations by identifying new, viable low-carbon energy storage and conversion systems for future locomotive systems and how they should be deployed on the existing US freight rail network. In the first quarter, the project focused on collecting data, establishing a simulation workflow, and engaging industry through the creation of the Industry Advisory Board (IAB). In the second quarter, the project focused on selecting fuel pathways and powertrain technologies, setting performance targets, conducting a techno-economic analyses, and developing the simulation framework that would serve as the backbone of the future toolhead. The third quarter involved developing an industry-oriented interactive dashboard powered by a five-step sequential framework, as well as holding industry advisory board meetings as per the initial technology-to-market plan. In the remaining project quarters, the NUFRIEND dashboard were fine-tuned with the help of IAB member feedback and in-depth scenario analyses were conducted to support the techno-economic analysis of energy sources. Additionally, dashboard documentation, project insights, and open-source code on GitHub were prepared and released. Throughout the project, the team completed testing and analysis of all model components, integrated all initial test scenarios, and conducted stakeholder engagement. Lower-carbon drop-in fuels can be deployed as admixtures and are considered uniform across the network at a desired penetration rate, while hydrogen and battery-electric technology deployment poses a more complex problem as they require significant investments to be made in the siting of refueling/charging facilities and the replacement of locomotive fleets. Thus, strategies for locating and sizing refueling/charging facilities on a railroad’s network to meet their energy demands were developed to inform deployment decisions. To address this challenge, the Northwestern University Freight Rail Infrastructure & Energy Network Decarbonization (NUFRIEND) framework presents a five-step sequential framework to select O-D paths, locate facilities, reroute flows, size facilities, and evaluate the deployment for alternative energy sources that require locomotive powertrains to be converted and new refueling infrastructure to be deployed. The NUFRIEND Framework is an industry-oriented tool for simulating the deployment of new energy technologies across the US freight rail network. The framework provides a comprehensive network-level optimization and scenario simulation tool for decarbonizing the freight rail sector, addressing the uncertainties surrounding technological developments by supporting sensitivity analyses for different operational and technological parameters through a transparent and flexible input module. It offers practical alternatives to diesel locomotives and can be applied for any railroad considering the specific network structure and freight demand, outputting evaluation metrics for the associated emissions and costs relative to diesel operations. A number of relevant simulation scenarios were run and analyzed for key insights on the value of different alternative technologies for freight rail decarbonization. The project developments and findings have been presented at numerous conferences and events.

08 HYDROGEN↗
DOE OSTI2021

A Data-Driven Multi-Period Importance Sampling Strategy for Stochastic Economic Dispatch

Power systems with high penetrations of renewable energy (e.g., wind power) require sophisticated approaches to optimize system performance due to uncertainty in short-term system generation capacity. In this paper, we combine a data-driven analog scenario selection method with importance sampling to create a novel scenario construction approach for two-stage stochastic economic dispatch problems with a large number of wind farms on a network. The proposed method produces scenarios with realistic physics by finding high-fidelity analogs that can describe future states of the system. We show how to extend this method to multi-period operations and demonstrate the effectiveness of this technique by simulating economic dispatch operations on a synthetic test system over the course of a week.

data-driven forecasting↗
DOE OSTI2023

Increased range and contrast in fog with circularly polarized imaging

Fogs, low lying clouds, and other highly scattering environments pose a challenge for many commercial and national security sensing systems. Current autonomous systems rely on optical sensors for navigation whose performance is degraded by highly scattering environments. In our previous simulation work, we have shown that polarized light can penetrate through a scattering environment such as fog. We have demonstrated that circularly polarized light maintains its initial polarization state better than linearly polarized light, even through large numbers of scattering events and thus ranges. This has recently been experimentally verified by other researchers. In this work, we present the design, construction, and testing of active polarization imagers at short-wave infrared and visible wavelengths. We explore multiple polarimetric configurations for the imagers, focusing on linear and circular polarization states. The polarized imagers were tested at the Sandia National Laboratories Fog Chamber under realistic fog conditions. Here, we show that active circular polarization imagers can increase range and contrast in fog better than linear polarization imagers. We show that when imaging typical road sign and safety retro-reflective films, circularly polarized imaging has enhanced contrast throughout most fog densities/ranges compared to linearly polarized imaging and can penetrate over 15 to 25 m into the fog beyond the range limit of linearly polarized imaging, with a strong dependence on the interaction of the polarization state with the target materials.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Computational Experiment Design for Operations Model Simulation

Computer simulations that demonstrate the value of novel approaches are crucial to developing more flexible and robust power systems operations with high penetrations of renewable energy at multiple geographic and temporal scales. However, optimization-based simulations that depend on forecast data often face challenges in evaluating performance, reproducing results, and testing under realistic simulation scenarios. In this paper, we develop scientific computing best-practices for the validation and reproduction of power systems operational models. We then employ two case studies to demonstrate the proposed validation and reproduction framework.

MATHEMATICS AND COMPUTING,POWER TRANSMISSION AND D↗