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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 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Ancient Rapid Radiation Explains Most Conflicts Among Gene Trees and Well-Supported Phylogenomic Trees of Nostocalean Cyanobacteria

Prokaryotic genomes are often considered to be mosaics of genes that do not necessarily share the same evolutionary history due to widespread horizontal gene transfers (HGTs). Consequently, representing evolutionary relationships of prokaryotes as bifurcating trees has long been controversial. However, studies reporting conflicts among gene trees derived from phylogenomic data sets have shown that these conflicts can be the result of artifacts or evolutionary processes other than HGT, such as incomplete lineage sorting, low phylogenetic signal, and systematic errors due to substitution model misspecification. Here, we present the results of an extensive exploration of phylogenetic conflicts in the cyanobacterial order Nostocales, for which previous studies have inferred strongly supported conflicting relationships when using different concatenated phylogenomic data sets. We found that most of these conflicts are concentrated in deep clusters of short internodes of the Nostocales phylogeny, where the great majority of individual genes have low resolving power. We then inferred phylogenetic networks to detect HGT events while also accounting for incomplete lineage sorting. Our results indicate that most conflicts among gene trees are likely due to incomplete lineage sorting linked to an ancient rapid radiation, rather than to HGTs. Moreover, the short internodes of this radiation fit the expectations of the anomaly zone, i.e., a region of the tree parameter space where a species tree is discordant with its most likely gene tree. In this work, we demonstrated that concatenation of different sets of loci can recover up to 17 distinct and well-supported relationships within the putative anomaly zone of Nostocales, corresponding to the observed conflicts among well-supported trees based on concatenated data sets from previous studies. Our findings highlight the important role of rapid radiations as a potential cause of strongly conflicting phylogenetic relationships when using phylogenomic data sets of bacteria. We propose that polytomies may be the most appropriate phylogenetic representation of these rapid radiations that are part of anomaly zones, especially when all possible genomic markers have been considered to infer these phylogenies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Blinded challenge for precision cosmology with large-scale structure: Results from effective field theory for the redshift-space galaxy power spectrum

An accurate theoretical template for the galaxy power spectrum is key for the success of ongoing and future spectroscopic surveys. We examine to what extent the effective field theory (EFT) of large-scale structure is able to provide such a template and correctly estimate cosmological parameters. To that end, we initiate a blinded challenge to infer cosmological parameters from the redshift-space power spectrum of high-resolution mock catalogs mimicking the BOSS galaxy sample but covering a 100 times larger cumulative volume. This gigantic simulation volume allows us to separate systematic bias due to theoretical modeling from the statistical error due to sample variance. The challenge is to measure three unknown input parameters used in the simulation: the Hubble constant, the matter density fraction, and the clustering amplitude. We present analyses done by two independent teams, who have fitted the mock simulation data generated by yet another independent group. This allows us to avoid any confirmation bias by analyzers and to pin down possible tuning of the specific EFT implementations. Both independent teams have recovered the true values of the input parameters within subpercent statistical errors corresponding to the total simulation volume.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Dynamical simulation via quantum machine learning with provable generalization

Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. Our algorithm is thus resource efficient in terms of qubit and data requirements. Furthermore, our preliminary numerics for the XY model exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Experimental testing of a control barrier function on an automated vehicle in live multi-lane traffic

This paper experimentally tests an implementation of a control barrier function (CBF) designed to guarantee a minimum time-gap in car following on an automated vehicle (AV) in live traffic, with a majority occurring on freeways. The CBF supervises a nominal unsafe PID controller on the AV’s velocity. The experimental testing spans two months of driving, of which 1.9 hours of data is collected in which the CBF and nominal controller are active. We find that violations of the guaranteed minimum time-gap are observed, as measured by the vehicle’s on-board radar unit. There are two distinct causes of the violations. First, in multi-lane traffic, Cut-ins from other vehicles represent external disturbances that can immediately violate the minimum guaranteed time gap provided by the CBF. When cut-ins occur, the CBF does eventually return the vehicle to a safe time gap. Second, even when cut-ins do not occur, system model inaccuracies (e.g., sensor error and delay, actuator error and delay) can lead to violations of the minimum time-gap. These violations are small relative to the violations that would have occurred using only the unsafe nominal control law.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Raytracing the long trace profiler

The optical design of the Long Trace Profiler optical system is explored with a commercial raytrace program, Zemax OpticStudio™ (ZOS)1, with the intent of finding and correcting sources of systematic error. ZOS provides both geometric raytracing tools and physical optics Gaussian beam propagation and diffraction image calculation tools, and two design modes, sequential component (SC) and non-sequential component (NSC) that are optimized for different aspects of the design process. The original LTP-II system employs a singlet lens with a 1250 mm focal length. It is optimized to provide minimum distortion over a surface slope angle range of ±5 mrad. Using the ZOS tools, we are able to simulate ghost rays that produce distortion in the beam spot image and can minimize the distortion by deliberate misalignment of the beamsplitter (BS) components. Unfortunately, the reference beam is compromised because of the component tilts. The most recent LTP500 system design simplifies the optical system and makes the reference beam usable again, even with misalignment of the polarizing beamsplitter (PBS). Two lenses are designed for the LTP500 - a cemented doublet that has been fabricated, and a singlet with one aspheric surface. Both have focal distances of 500 mm with an expanded angular measurement range of ±10 mrad. The aspheric singlet provides superior performance. ZOS allows the import of wavefront measurement data produced by commercial interferometer software. We apply the wavefront error measurement from the cemented doublet to the model to show that the 19nm RMS wavefront error needs to be improved by at least a factor of ten in order to reduce the systematic error to a level that will allow the LTP to approach its design limit of a few tens of nanoradians.

Takacs, Peter Z.↗
DOE OSTI2026

OpenStudio®-MCP [SWR-26-035]

OpenStudio®-MCP is a Model Context Protocol (MCP) server that lets AI assistants perform building energy modeling through natural language. Rather than requiring users to learn the OpenStudio® SDK, EnergyPlus® scripting, or Ruby/Python automation, the server translates conversational requests into sequences of tool calls that create models, design HVAC systems, run simulations, and extract results — all within a single chat session. The server's 124 tools are organized into a skills architecture where each skill encapsulates a domain of building energy modeling (envelope, HVAC, loads, weather, simulation, results) behind typed, LLM-friendly interfaces. High-leverage operations like applying ASHRAE 90.1 baseline systems or generating standards-compliant typical buildings are exposed as single tool calls that internally wire dozens of OpenStudio® objects. Bundled measures from ComStock™ and Openstudio® -common-measures-gem are wrapped with dedicated tools and typed arguments rather than exposed through a generic measure interface, so AI models get consistent, error-resistant recipes without needing to discover measure arguments at runtime. A key design decision is structured results extraction: six SQL-based tools return surgical ~300–1,000 token responses (end-use breakdowns, envelope summaries, HVAC sizing, timeseries data) instead of requiring the AI to parse ~100K-token raw HTML reports, making iterative design exploration practical within context window limits. The codebase is designed as a reference implementation — explicit, well-commented, and modular — so that other simulation engines (EnergyPlus® standalone, TRNSYS, DOE-2) can use it as a template for building their own MCP servers.

Ball, Brian [National Laboratory of the Rockies (N↗
DOE OSTI2021

A Short-Term Solar Forecasting Platform Using a Physics-Based Smart Persistence Model and Data Imputation Method

Electrical energy plays vital role in our socio-economic activity and therefore ensuring the reliability of the electric grid, from the generation, transmission and distribution level is critical. In order to maintain the power system parameter viz., frequency, voltage, etc., optimally, balancing of generation and consumption is very much essential. However, solar energy is infirm power by nature this is due to cloud cover / other local phenomena. Hence, Photovoltaic (PV) power generation brings a significant challenge to the grid operator due to the variability of the solar energy. The complexity of this challenge in terms of planning and dispatch ability of PV resources, aggravates with the high penetration of solar energy into the electric grid. In this setting, reliable solar radiation forecasting models based on accurate and quality input data become essential. In order to develop a suitable model for predicting solar radiation, quality historical / real time measurement is also needed. Under this study NIWE and NREL jointly developed / tested short-term solar forecasting frameworks using a smart persistence and physics-based smart persistence models for intra-hour forecasting of solar radiation (PSPI) and benchmarked 9 different data imputation techniques in 15 Solar Radiation Resource Assessment (SRRA) stations, located at different parts of India. During any measurement campaign, due to various technical reasons, we may miss few observations. However, the missing observation often reduce the performance of any forecasting model. Therefore, suitable data imputation method would assist us to obtain continuous observation of solar radiation. A station-by-station and method-by-method analysis was carried out to understand the performance of each model. Based on our analysis, among all the data imputation methods, the Kalman data imputation method is better for Indian Weather condition. In addition, Kalman StructTS, Linear, Stine and Arima methods yield slightly inferior accuracy compared to Kalman, but outperform the other methods. The extended solar radiation data are used by solar forecasting models to provide the prediction of solar radiation at 15 SRRA stations. As far as short term forecasting model is concerned, the PSPI model outperforms the Smart Persistence model. However, the forecast error is increases with the forecasting horizon.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

The right conditions for high-precision dynamic temperature and heat capacity measurement via pyrometry and conductivity

The pursuit of accurate bulk temperature T under extreme conditions has been a long-standing goal of the high pressure science community, complicated by a lack of data to inform models. To reach these extremely high-pressure, high-temperature (high P − T) conditions, a combination of dynamic and heated static experiments (e.g., diamond or gem anvil cel experiments) are used. For example, in a diamond anvil cell (DAC) experiment, a sample placed in the DAC is first pressurized. Following pressurization, the sample T is increased either by heating the entire DAC (usually using resistive heating, and limited to ∼1000K) or by applying intense laser power to the sample surfaces. In a dynamic experiment, the process of pressurizing the sample also heats it. In the case of shock physics experiments, such heating is substantial, easily reaching thousands of Kelvin; in our work we have seen T ∼17000K. Most methods of measuring temperature at ambient are not compatible with experiments under these high-pressure, high-temperature conditions: thermocouples break, melt, or have conductivity properties that differ from ambient where they are calibrated; thermometers would melt; both are too slow. As a result most methods are based on non-contact techniques such as x-ray diffraction broadening, neutron scattering, or optical methods. Of these, optical methods using the visible and near-infrared region of the spectrum are the most commonly used as the sources and detectors are readily available. In the case of optical methods the optical depth, and therefore the measurement location, is limited to the surface. When a window or anvil material is used, heat flows from the sample into the window/anvil. Likewise, if the sample undergoes a change in thermodynamic state, such as expansion upon release, different T may be expected. As a result, the surface or apparent temperature T app measurement will differ from the bulk or interior temperature that is desired. This surface measurement must be related to the bulk measurement using thermal transport models and material models. While it is tempting to conclude that one should just use x-ray methods that directly probe the interior, even these methods have been shown to depend on thermal transport and material models. Regardless of the method used to create the high P − T condition, therefore, we must understand the role of thermal transport and material models upon our interpretation of the T measurement, as well as the errors and uncertainties associated with the choice of models used in the analysis. This is a substantial area of research and this paper is by no means a complete survey of the relevant sources of uncertainty. For example, we have yet to begin to address alternate transport models in a detailed manner (e.g., Tan-Ahrens), or the many models that use additional layers to approximate melting, turbulence, or epitaxial phenomena). Likewise, we have not explored the impact upon uncertainty of thermal models that use temperature-dependent thermal transport coefficients, or the wide range of material models that can be applied. Instead, this paper focuses on using one simple model, the Urtiew-Grover model, to understand the sources of error in T measurement so that we may identify how best to focus future research efforts to return the best improvements and avoid working on over-optimizing a single type of measurement. To this end, we work through some of the best and worst case scenarios for T measurement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Thermal field reconstruction and compressive sensing using proper orthogonal decomposition

Model order reduction allows critical information about sensor placement and experiment design to be distilled from raw fluid mechanics simulation data. In many cases, sensed information in conjunction with reduced order models can also be used to regenerate full field variables. In this paper, a proper orthogonal decomposition (POD) inferencing method is extended to the modeling and compressive sensing of temperature, a scalar field variable. The method is applied to a simulated, critically stable, incompressible flow over a heated cylinder (Re = 1000) with Prandtl number varying between 0.001 and 50. The model is trained on pressure and temperature data from simulations. Field reconstructions are then generated using data from selected sensors and the POD model. Finally, the reconstruction error is evaluated across all Prandtl numbers for different numbers of retained modes and sensors. The predicted trend of increasing reconstruction accuracy with decreasing Prandtl number is confirmed and a Prandtl number/sensor count error matrix is presented.

Matulis, John↗
DOE OSTI2023

A Data-Driven Framework for Direct Local Tensile Property Prediction of Laser Powder Bed Fusion Parts

This article proposes a generalizable, data-driven framework for qualifying laser powder bed fusion additively manufactured parts using part-specific in situ data, including powder bed imaging, machine health sensors, and laser scan paths. To achieve part qualification without relying solely on statistical processes or feedstock control, a sequence of machine learning models was trained on 6299 tensile specimens to locally predict the tensile properties of stainless-steel parts based on fused multi-modal in situ sensor data and a priori information. A cyberphysical infrastructure enabled the robust spatial tracking of individual specimens, and computer vision techniques registered the ground truth tensile measurements to the in situ data. The co-registered 230 GB dataset used in this work has been publicly released and is available as a set of HDF5 files. The extensive training data requirements and wide range of size scales were addressed by combining deep learning, machine learning, and feature engineering algorithms in a relay. The trained models demonstrated a 61% error reduction in ultimate tensile strength predictions relative to estimates made without any in situ information. Lessons learned and potential improvements to the sensors and mechanical testing procedure are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The Initial–Final Mass Relation for Hydrogen-deficient White Dwarfs

The initial–final mass relation represents the total mass lost by a star during the entirety of its evolution from the zero age main sequence to the white-dwarf cooling track. The semiempirical initial–final mass relation (IFMR) is largely based on observations of DA white dwarfs, the most common spectral type of white dwarf and the simplest atmosphere to model. We present a first derivation of the semiempirical IFMR for hydrogen-deficient (non-DA) white dwarfs in open star clusters. We identify a possible discrepancy between the DA and non-DA IFMRs, with non-DA white dwarfs ≈0.07 M {sub ⊙} less massive at a given initial mass. Such a discrepancy is unexpected based on theoretical models of non-DA formation and observations of field white dwarf mass distributions. If real, the discrepancy is likely due to enhanced mass loss during the final thermal pulse and renewed post-AGB evolution of the star. However, we are dubious that the mass discrepancy is physical and instead is due to the small sample size, to systematic issues in model atmospheres of non-DAs, and to the uncertain evolutionary history of Procyon B (spectral type DQZ). A significantly larger sample size is needed to test these assertions. In addition, we also present Monte Carlo models of the correlated errors for DA and non-DA white dwarfs in the initial–final mass plane. We find the uncertainties in initial–final mass determinations for individual white dwarfs can be significantly asymmetric, but the recovered functional form of the IFMR is grossly unaffected by the correlated errors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The Simons Observatory: Beam Characterization for the Small Aperture Telescopes

Abstract We use time-domain simulations of Jupiter observations to test and develop a beam reconstruction pipeline for the Simons Observatory Small Aperture Telescopes. The method relies on a mapmaker that estimates and subtracts correlated atmospheric noise and a beam fitting code designed to compensate for the bias caused by the mapmaker. We test our reconstruction performance for four different frequency bands against various algorithmic parameters, atmospheric conditions, and input beams. We additionally show the reconstruction quality as a function of the number of available observations and investigate how different calibration strategies affect the beam uncertainty. For all of the cases considered, we find good agreement between the fitted results and the input beam model within an ∼1.5% error for a multipole range ℓ = 30–700 and an ∼0.5% error for a multipole range ℓ = 50–200. We conclude by using a harmonic-domain component separation algorithm to verify that the beam reconstruction errors and biases observed in our analysis do not significantly bias the Simons Observatory r -measurement

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Iterative Workflow for Quantification and Minimization of Reduced Chemistry-Induced Uncertainties in Reacting Flow Simulation

Reduced chemistry models mitigate computational cost but introduce two sources of uncertainties in reacting flow simulation, including chemical information loss due to model reduction, and approximation errors due to non-optimal projection. We present an iterative workflow for quantification and minimization of reduced chemistry-induced uncertainties in reacting flow simulations.

chemistry↗
DOE OSTI2025

Understanding Model Inadequacy in TRISO Nuclear Fuel Fission Products Release Models: Empirical and Mechanistic Approaches

The increasing use of tristructural isotropic (TRISO) particle fuel in both advanced and existing reactors necessitates a thorough evaluation of uncertainties and shortcomings in TRISO fission product release models. These inadequacies arise from the simplifications made in computational models compared to experimental data. Utilizing the BISON fuel performance code and experimental data from the Advanced Gas Reactor (AGR) program provides a unique chance to rigorously assess these inadequacies within a Bayesian uncertainty quantification (UQ) framework. This study contrasts the standard Bayesian framework with the Kennedy-O'Hagan (KOH) framework, which explicitly accounts for modeling inadequacies, in the context of UQ for TRISO silver release models. It examines both the traditional Arrhenius equation and a more advanced lower-length-scale (LLS)-informed model that incorporates microstructure information. The inverse UQ process applied to AGR-2 and AGR-3/4 datasets identified modeling inadequacy as the primary source of uncertainty, with experimental noise also being significant, while model parameter uncertainty was minimal. Both the Arrhenius and LLS-informed models showed similar levels of modeling inadequacy. For forward predictive UQ using the AGR-1 dataset, the KOH framework enhanced the accuracy and quality of quantified uncertainties by approximately 30% and 40%, respectively, compared to the standard Bayesian framework. This improvement was observed for both the Arrhenius and LLS-informed models. At the engineering scale, both models performed similarly, but the LLS-informed model outperformed the Arrhenius equation at the mesoscale. These findings underscore the importance of explicitly considering modeling inadequacy in the UQ process and highlight the need for ongoing refinement of physics-based models to address these shortcomings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Robust Statistical Approach for Determination of Graphite Nitridation Using Bayesian Model Comparison

A better estimation of surface reaction efficiency of semiconductor-grade graphite with atomic nitrogen, as well as the calibration error are calculated using Bayesian updating based on experimental data. Compared with a conventional deterministic model, the stochastic model approach is a powerful tool in the sense that the model is capable of taking into account underlying error correlations among the data quantities. In this paper, we investigate four different stochastic models (called “stochastic system model classes” herein) corresponding to different descriptions of modeling and measurement error structures, given one deterministic physical model. These stochastic system model classes differ in the covariance matrix structure that is used in the uncertainty model to represent uncertainties associated with the physical model and experimental measurements. For each model class, Bayesian inference is used to estimate the posterior probabilities of the physical model parameters as well as of the stochastic model parameters. Model comparison and selection are then applied based on two measures including Bayesian evidence and Bayesian information criterion, as well as the deviance information criterion. Both measures suggest the stochastic model class, which considers that a correlation between errors in two data quantities among different data points is the most plausible. With the stochastic model class, the range of uncertainty in surface reaction efficiency is estimated to be about two orders of magnitude at [Formula: see text].

Engineering↗
DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗
DOE OSTI2024

Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation

The multivariate adaptive regression spline (MARS) approach of Friedman and its Bayesian counterpart are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. Here, we propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Improving the PMU Standard

The Phasor Measurement Unit (PMU) is perhaps the first representational measurement widely dispersed in the electric power system. Its usefulness has been demonstrated on many occasions. It is shown in this paper that the excellent performance of the PMU is a tribute to PMU makers, and not attributable to the standards that are supposed to specify the performance. The IEEE and IEC standards illustrate, by means of a “reference model,” how a PMU can be made. Both standards base the model on two fundamental conceptual errors. Without these errors several improvements in performance could be made. The standards should be revised to remove the restrictive “guidance” that the reference model presently offers, and to correct the text so that the appropriate concepts are presented.

Phasor Measurement, reference model↗