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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 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

On the Investigation of Phase Fault Classification in Power Grid Signals: A Case Study for Support Vector Machines, Decision Tree and Random Forest

In monitoring the power grid, an ability to differentiate between fault types is essential to ensuring electrical safety. Accordingly, this study introduces a fault detection and classification method by considering different machine learning (ML) and feature extraction (FE) methods combinations. Specifically, the proposed method is established in two classification layers; the first layer determines the fault, and the second layer distinguishes the type of fault. Based on the proposed system model, this study seeks to determine the influential data attributes in a power grid signal using FE methods, including fast Fourier transform, power spectral density (PSD), auto-correlation, and wavelet transform (WT). A cross-comparison of the effectiveness of the Support Vector Machine (SVM), Decision Tree (DT), and Random Forest (RF) is also performed to accomplish the classification layers of the proposed method. The designed algorithm is analyzed under the various combinations of FE and ML methods, and outcomes are presented by considering the trade-off between computational complexity and prediction accuracy. The results reveal that the RF-based ML algorithm shows the most accurate classification performance with PSD, and the most time-saving of the models is the DT WT. Also, SVM emerges superior on a subsequent test of the simulated models on real-world signals.

Galbraith, Kelli↗
DOE OSTI2022

Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

Here, we propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reactor System Facility Modification to Detect Compromised Human Machine Interfaces

This study focuses on a multi-layered Industrial Control System (ICS)/Operational Technology (OT) security architecture to aid in the discovery and mitigation of compromised Human Machine Interface (HMI)/Instrumentation & Control (I&C) based systems for modifying a prototypical reactor condition test facility called the Flowing Autoclave System (FAS) at Idaho National Laboratory (INL). This is achieved through a three-layered combination of network security solutions, hash-based algorithms, and blockchain technologies. Hash algorithms are mathematical functions used to generate a predetermined set of fixed-length values. They are widely used in computer security to verify the integrity of system information and data, both on a local network and the wider internet. Even small amounts of unauthorized system modification will cause the hash algorithm to output a set of characters that deviate significantly from its original value. Assisting secure hash functions, blockchain technology is a secure and distributed technology used to provide an immutable set of records replicated on all devices within a decentralized network. Blockchain offers a cost-effective solution to detect system compromise by providing a traceable breadcrumb trail of all network activity and data modification happening on a system. If both are used in conjunction with network monitoring tools, the integration of this three-pronged approach can become an asset in detecting suspected system compromises before any real damage can occur.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Active Compensation of Radiation Effects on Optical Fibers for Sensing Applications

Neutron and gamma irradiation is known to compact silica, resulting in macroscopic changes in refractive index (RI) and geometric structure. The change in RI and linear compaction in a radiation environment is caused by three well-known mechanisms: (i) radiation-induced attenuation (RIA), (ii) radiation-induced compaction (RIC), and (iii) radiation-induced emission (RIE). These macroscopic changes induce errors in monitoring physical parameters such as temperature, pressure, and strain in optical fiber-based sensors, which limit their application in radiation environments. We present a cascaded Fabry–Perot interferometer (FPI) technique to measure macroscopic properties, such as radiation-induced change in RI and length compaction in real time to actively account for sensor drift. The proposed cascaded FPI consists of two cavities: the first cavity is an air cavity, and the second is a silica cavity. The length compaction from the air cavity is used to deduce the RI change within the silica cavity. We utilize fast Fourier transform (FFT) algorithm and two bandpass filters for the signal extraction of each cavity. Inclusion of such a simple cascaded FPI structure will enable accurate determination of physical parameters under the test.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

A deep learning hybrid predictive modeling (HPM) approach for estimating evapotranspiration and ecosystem respiration

Climate change is reshaping vulnerable ecosystems, leading to uncertain effects on ecosystem dynamics, including evapotranspiration (ET) and ecosystem respiration (R eco ). However, accurate estimation of ET and R eco still remains challenging at sparsely monitored watersheds, where data and field instrumentation are limited. In this study, we developed a hybrid predictive modeling approach (HPM) that integrates eddy covariance measurements, physically based model simulation results, meteorological forcings, and remote-sensing datasets to estimate ET and R eco in high space–time resolution. HPM relies on a deep learning algorithm and long short-term memory (LSTM) and requires only air temperature, precipitation, radiation, normalized difference vegetation index (NDVI), and soil temperature (when available) as input variables. We tested and validated HPM estimation results in different climate regions and developed four use cases to demonstrate the applicability and variability of HPM at various FLUXNET sites and Rocky Mountain SNOTEL sites in Western North America. To test the limitations and performance of the HPM approach in mountainous watersheds, an expanded use case focused on the East River Watershed, Colorado, USA. The results indicate HPM is capable of identifying complicated interactions among meteorological forcings, ET, and R eco variables, as well as providing reliable estimation of ET and R eco across relevant spatiotemporal scales, even in challenging mountainous systems. The study documents that HPM increases our capability to estimate ET and R eco and enhances process understanding at sparsely monitored watersheds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Resilience Assessment Framework For Electric Distribution Systems Performance Under Extreme Conditions

The devastating impact of extreme weather-related events is increasingly evident on power grids, especially on distribution grids. The severity of their potential impact calls for 1) developing a suitable resilience assessment framework to capture the system performance and 2) assessing relevant mitigative strategies to lessen the impact of such events. This paper proposes a framework to identify grid vulnerabilities using the energy-at-risk concept to select, disconnect and isolate grid portions due to a resilience event. The proposed framework mainly consists of two steps; i) processing the utility's available infrastructure, i.e., a network model, possible switching combinations, and outage information for those combinations, as a graph-based database, and ii) implementing a novel optimal switching algorithm leveraging database and grid simulated metrics. These switching actions are generated to implement load curtailment in a rolling manner during anticipated grid scarcity conditions. In this study, a test case is created using two taxonomy feeders and is simulated against an extreme temperature event, e.g., a long, relatively cold, and prolonged freeze peak, thereby creating stress on the grid. It is demonstrated that the proposed framework allows utilities to predict the energy-at-risk during such resilience events and design suitable outage management strategies.

Poudel, Shiva↗
DOE OSTI2024

Error mitigation, optimization, and extrapolation on a trapped-ion testbed

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm’s sensitivity to these errors without increasing the number of required qubits. Here we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH + molecule at 0.8 Å in the presence of experimental noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time stretching the two-qubit gates, scaling the sideband detuning parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find that time stretching and sideband detuning scaling fail to scale the noise on our particular hardware in a way that can be extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve error suppression of 96.8%, resulting in an energy estimate within –0.004 ± 0.04 hartree of the ground state energy. This is an improvement, but still outside the chemical accuracy threshold of 0.0016 hartree. Furthermore, our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Improved Chemical Kinetics and Algorithms for More Accurate, Faster Simulations

Internal combustion engine design is increasingly driven by computational models used to predict change in performance due to change of design. The design process previously depended on limited intuition and expensive and time-consuming physical testing. Improved model capabilities shorten design cycles and enable the production of cleaner and more efficient engines. This project focuses on advancing the state of the art in internal combustion engine simulations. The overarching goal is to enable predictive models and reduced time to solution for simulations that impact combustion engine design.

02 PETROLEUM↗
DOE OSTI2024

Pan-tropical daily L-band microwave land surface emissivity retrieval from GNSS-R observations

The uncertainties in microwave land surface emissivity (MLSE) measurements have long limited the use of spaceborne microwave radiometer data. As an emerging observation method, Global Navigation Satellite System Reflectometry (GNSS-R) has demonstrated great potential in several land and ocean applications. In this study, a method for obtaining daily MLSE dataset in the pan-tropical region from Cyclone GNSS (CYGNSS) observations is presented and evaluated. The CYGNSS observations are first aggregated into the Equal-Area-Scalable-Earth (EASE) 2.0 36 km grid by a combined weight function of distance, time, and signal-to-noise ratio variance. Then, the method employs a pixel-by-pixel regression algorithm to conduct the daily MLSE retrieval using reference emissivity derived from the Soil Moisture Active Passive (SMAP) brightness temperature. The CYGNSS MLSE shows good agreement with SMAP MLSE, delivering an overall root-mean-square error (RMSE) of 0.022 and 0.017 for horizontal and vertical polarization, respectively, during the training set spanning the whole year of 2018. Furthermore, on the test set from January 2019 to May 2019, the RMSE values amounted to 0.030 and 0.023 for horizontal and vertical polarization, respectively. Temperature records from the International Soil Moisture Network are employed to calculate the emissivity and for in-situ validation, which yield an RMSE of 0.034 and 0.026 for the two polarizations, respectively. The proposed algorithm provides an encouraging approach to obtain accurate daily MLSE dataset for microwave remote sensing. Compared to the SMAP MLSE, the CYGNSS MLSE has a remarkable improvement of 86% in temporal resolution, greatly complementing the existing microwave emissivity datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Development of NDE/NDT Tools for High-Volume & High-Speed Inspection of CFRP Structures in Automotive Manufacturing

Main advantages of the air-coupled ultrasound testing (ACUT) and electromagnetic testing (EMT) techniques for NDE of CFRP composites were non-contact sensing, scalability for high-speed inspection, cost-effectiveness, and non-hazardous operation. Despite these advantages, no systems that would satisfy the project requirements were commercially available. Hence, one of the major efforts of the Michigan State University (MSU) team at the initial stage of the project was to close this technological gap by developing, optimizing, and validating array sensors that would provide sufficient sensitivity, spatial coverage, and resolution for robust defect detection. Optimization of the ACUT and EMT sensor designs was performed using experimentally validated finite element models. Initial experiments using array probes were conducted on relatively flat CFRP samples. In parallel, the MSU team designed and assembled a portable platform with two robotic arms. The robots were equipped with newly designed sensors that enabled high-speed NDE of curved CFRP parts. Presently, the developed robotic platform can be used as a demo/template NDE system, which is easily adaptable to manufacturing environments and in-line NDE. The ACUT NDE system developed by the MSU team used a high-power 4-channel pulser receiver for parallel data acquisition. The array probes were designed by stacking commercially available ACUT transducers, which operated in the frequency range between 100 kHz and 500 kHz. MSU optimized the excitation procedure and developed wave focusing cones so as to reduce the crosstalk between the transducers and to provide higher pulse repletion frequency (PRF). The through-transmission (TT) and single-side access (SSA) inspection modes were successfully implemented. In the TT-ACUT, structural defects in CFRP were detected by passing ultrasonic waves through the test part. Hence, the ACUT transmitters and receivers needed to be placed on the opposite sides of the test part. In the SSA-ACUT, guided waves (GW) were excited in the test part using the transmitters and were sensed by the receivers from the same side. Multi-channel TT-ACUT and SSA-ACUT provided high-speed NDE, and were successfully validated on CFRP test samples with interlaminar delaminations and other embedded defects The EM techniques developed by the MSU team included: 1) eddy current testing (ECT), 2) capacitive imaging (CI) and hybrid dual-mode imaging. In ECT, structural damage was detected in CFRP using coils sensor arrays. In ECT, the excitation magnetic field is generated by passing an alternating current through a coil, which is placed above the test sample. The excitation field penetrates the conductive sample and induces the eddy currents in its transect. In turn, the eddy currents generate the reaction field, which affects the total field sensed by a coil. Hence, the presence of structural flaws will alter the eddy current flow and the picked-up signal. ECT is mostly sensitive to local changes of the electric conductivity of the test sample, and CFRPs are mostly conductive in the direction of carbon fibers. Hence, ECT was well suited for the detection of fiber damage/fiber irregularities. The MSU team developed printed circuit boards (PCB) with coil sensor arrays optimized for NDE of CFRP. Unlike most commercial probes designed for ECT of metallic structures, the MSU array probes were designed for operation in [1-10] MHz frequency range, which was optimal for low-conductive CFRP. Multiple sensing topologies (coil groups excitation/sensing arrangements) were implemented and successfully validated. Capacitive Imaging (CI) technique developed by MSU was complementary to ECT. In contrast to ECT, which was sensitive to local changes of the electrical conductivity, the CI was sensitive to local changes of the dielectric constant. Therefore, CI could provide information about matrix damage/matrix irregularities in CFRP. The MSU CI sensor arrays were made of multiple circular or rectangular open-plate capacitors printed on PCB. Sensors of this type are not commercially available. In addition to ECT and CI, the MSU team developed a hybrid (dual-mode) inductive/capacitive measurement technique that synergistically combined the benefits of inductive and capacitive sensing for rapid NDE of fiber reinforced polymer (FRP) composite structures. Fiber damage and fiber irregularities in FRPs were detected by configuring hybrid sensors as coil sensors. Similarly, matrix damage, matrix irregularities and interlaminar delaminations were detected by configuring hybrid sensors as capacitive sensors. ECT and CI were performed sequentially by means of electronic switching. Hence, eliminating the need for mounting two separate sensor arrays on the probe. Portable robotic platform was developed by MSU for multi-technique high-speed NDE of CFRP test parts. The platform had two 6-axis robots, which enabled inspection of curved parts in approximately a 6×6×6 ft 3 active scan area. On the software side, the MSU team integrated scripts for NDE hardware control with scripts for robot motion control. MSU also implemented automated path planning for the robots, reconstruction of part’s surfaces via stereovision, 3D rendering of inspection data, and image processing algorithms for enhanced defect detection. Automotive composite parts manufactured by Plasan Composites from Phase I were used to validate the ACUT and EMT techniques on representative testbeds. Among those parts were three X-braces for a Dodge Viper, one composite calibration plaque with known defects at known locations, and four other test sections, including sections from a front splitter, a corner section from a composite hood, and a high-pressure RTM panel made using non crimp fabric. Other test samples included CFRP and GFRP calibration plates with fiber/matrix defects fabricated at MSU/CVRC.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Proposed Analytical Methods for Determining Filter Media Properties

High Efficiency Particulate Air (HEPA) filters, commonly used in nuclear filtration applications, are an integral part of the waste management processes in nuclear plants. HEPA filters are 99.97% efficient filtration devices characterized by their high resistance to air flow, or pressure drop. From theoretical models, the initial pressure drop across a clean filter is proven to be a function of the filter media fiber diameters and porosity of the media. These filter properties are relatively difficult to obtain with traditional manual methods; therefore, there is a need to develop analytical methods to find the fiber diameter and porosity to determine the pressure drop. Typically, these values can be found by substituting a calculated representative value based upon measured values, such as equivalent fiber diameter based upon a clean pressure drop. However, these values may also be directly recorded and measured by incorporating Scanning Electron Microscope (SEM) image analysis and other measurement methods to analyze the filter media and determine its physical properties without the need for media testing. DiameterJ, an open source Java plug-in, used with ImageJ, can process images of filter media taken by an SEM to find statistical data such as mean fiber diameter and porosity. To produce the raw data, SEM images of two filter media type samples are taken and segmented in DiameterJ using the traditional and statistical region merging segmentation algorithms. Manual segmentation is necessary after the initial segmentation by the algorithms as the images tend to be too complex for the algorithms to output with the necessary accuracy. However, complications exist in the manual segmentation process as these methods can be time intensive and prone to the individual bias of the user. This in turn can skew the final mean fiber diameter result, and lead to either an over or under prediction of the pressure drop. It was also discovered that the porosity data produced by DiameterJ is inaccurate, as the SEM analyzes the three-dimensional filter media by projecting its geometry onto a plane and analyzing it as a two-dimensional binary image. Thus, the porosity is artificially inflated through the segmentation process, rendering this result incorrect. Alternatively, density determination, gravimetric analysis, and thickness testing of the filter media is collectively used to determine the filter fiber porosity. Together, the SEM image analysis and analytical lab methods produce results through direct measurements which allow for the prediction of the initial pressure drop from clean filter media without the need for prior media testing to collect pressure data. By improving upon this proposed analytical method in the future, there is potential to streamline the process of finding these filter properties into a more direct methodology for determining the pressure drop across HEPA filters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

An objective inter-comparison of trash mark constellations generated by manual and automated detection methods

Trash marks are unintentional markings observed on printed, scanned, or photocopied documents that result from permanent defects or transient material in office machines and can be used for source attribution of questioned documents. Trash mark examinations have been in use in forensic laboratories for decades, yet the method remains relatively untested and relies on training, experience, and anecdotal information to support its validity. Herein this study generated and harnessed objective data to empirically test one of the foundational theories for assessing the origin of photocopied documents: provided trash marks are present in sufficient quantity and/or quality, no two machines will exhibit a constellation of trash marks that is indistinguishable from another. In this project, objective trash mark location and size data was generated for 50 known photocopiers using both a traditional and a novel, automated method. Inter-machine comparisons were conducted using a novel variant of the Hausdorff distance algorithm to generate a quantitative assessment of how similar or different the 2450 pairs of trash mark constellations were from one another. This study found that each of the machines bearing one or more trash marks exhibited objective differences in their trash mark constellations, ultimately providing support for the tested hypothesis

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Experimental Examination of Additively Manufactured Patterns on Structural Nuclear Materials for Digital Image Correlation Strain Measurements

Abstract Background There are a limited number of commercially available sensors for monitoring the deformation of materials in-situ during harsh environment applications, such as those found in the nuclear and aerospace industries. Such sensing devices, including weldable strain gauges, extensometers, and linear variable differential transformers, can be destructive to material surfaces being investigated and typically require relatively large surface areas to attach (> 10 mm in length). Digital image correlation (DIC) is a viable, non-contact alternative to in-situ strain deformation. However, it often requires implementing artificial patterns using splattering techniques, which are difficult to reproduce. Objective Additive manufacturing capabilities offer consistent patterns using programmable fabrication methods. Methods In this work, a variety of small-scale periodic patterns with different geometries were printed directly on structural nuclear materials (i.e., stainless steel and aluminum tensile specimens) using an aerosol jet printer (AJP). Unlike other additive manufacturing techniques, AJP offers the advantage of materials selection. DIC was used to track and correlate strain to alternative measurement methods during cyclic loading, and tensile tests (up to 1100 µɛ) at room temperature. Results The results confirmed AJP has better control of pattern parameters for small fields of view and facilitate the ability of DIC algorithms to adequately process patterns with periodicity. More specifically, the printed 100 μm spaced dot and 150 μm spaced line patterns provided accurate measurements with a maximum error of less than 2% and 4% on aluminum samples when compared to an extensometer and commercially available strain gauges. Conclusion Our results highlight a new pattern fabrication technique that is form factor friendly for digital image correlation in nuclear applications.

Novich, K. A. (ORCID:0000000204466022)↗
DOE OSTI2020

Moment preserving constrained resampling with applications to particle-in-cell methods

The Moment Preserving Constrained Resampling (MPCR) algorithm for particle resampling is introduced and applied to particle-in-cell (PIC) methods to increase simulation accuracy, reduce compute cost, and/or avoid numerical instabilities. The general algorithm partitions the system space into smaller subsets and resamples the distribution within each subset. Further, the algorithm is designed to conserve any number of particle and grid moments with a high degree of accuracy (i.e. machine accuracy). The effectiveness of MPCR is demonstrated with several numerical tests, including a use-case study in gyrokinetic fusion plasma simulations. Finally, the computational cost of MPCR is negligible compared to the cost of particle evolution in PIC methods, and the tests demonstrate that periodic particle resampling yields a significant improvement in the accuracy and stability of the results.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗
DOE OSTI2024

Sensitive and error-tolerant annotation of protein-coding DNA with BATH

We present BATH, a tool for highly sensitive annotation of protein-coding DNA based on direct alignment of that DNA to a database of protein sequences or profile hidden Markov models (pHMMs). BATH is built on top of the HMMER3 code base, and simplifies the annotation workflow for pHMM-based translated sequence annotation by providing a straightforward input interface and easy-to-interpret output. BATH also introduces novel frameshift-aware algorithms to detect frameshift-inducing nucleotide insertions and deletions (indels). BATH matches the accuracy of HMMER3 for annotation of sequences containing no errors, and produces superior accuracy to all tested tools for annotation of sequences containing nucleotide indels. These results suggest that BATH should be used when high annotation sensitivity is required, particularly when frameshift errors are expected to interrupt protein-coding regions, as is true with long-read sequencing data and in the context of pseudogenes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Towards the Flexibility of HVDC-Interconnected Systems: A Novel Emergency Freqeuncy Response Model

In this paper, we propose a novel multi-time scale emergency frequency response model by unlocking the flexibility of High Voltage Direct Current (HVDC) systems. Unlike assigning power ramping rates for FACTS to regulate frequency in traditional methods, this paper designs a step-change electromagnetic power frequency response (EPFR) scheme, by leveraging the temporal over/under DC voltage capability of HVDC. Wherein the Kullback-Leibler Divergence is adopted to convexify the modified swing equation after integrating the step-change power. Further, to avoid the complicated differential equations, we equivalently reformulate the duration limits of DC voltage deviation into the HVDC decreasing power ramping rates, which participate in the system primary frequency response. Finally, the new steady-state operation level of HVDC is involved with the secondary frequency response. As a result, an improved three-level algorithm is developed to solve the model, wherein the instant step-change, primary, and secondary frequency response are coordinated together. After applying the proposed frequency response scheme on the test system, the EPFR is validated to effectively provide the most instantaneous supports when faced with bulk power loss due to extreme contingencies, and the resilience is ensured within acceptable expenditures.

Jiang, Sufan↗