Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “perturbation analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

A novel CMB component separation method: hierarchical generalized morphological component analysis

ABSTRACT We present a novel technique for cosmic microwave background (CMB) foreground subtraction based on the framework of blind source separation. Inspired by previous work incorporating local variation to generalized morphological component analysis (GMCA), we introduce hierarchical GMCA (HGMCA), a Bayesian hierarchical graphical model for source separation. We test our method on Nside = 256 simulated sky maps that include dust, synchrotron, free–free, and anomalous microwave emission, and show that HGMCA reduces foreground contamination by $25{{\ \rm per\ cent}}$ over GMCA in both the regions included and excluded by the Planck UT78 mask, decreases the error in the measurement of the CMB temperature power spectrum to the 0.02–0.03 per cent level at ℓ > 200 (and $\lt 0.26{{\ \rm per\ cent}}$ for all ℓ), and reduces correlation to all the foregrounds. We find equivalent or improved performance when compared to state-of-the-art internal linear combination type algorithms on these simulations, suggesting that HGMCA may be a competitive alternative to foreground separation techniques previously applied to observed CMB data. Additionally, we show that our performance does not suffer when we perturb model parameters or alter the CMB realization, which suggests that our algorithm generalizes well beyond our simplified simulations. Our results open a new avenue for constructing CMB maps through Bayesian hierarchical analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

Physiological Controls on Carbon Fluxes and Biomass Production in Miscanthus: Insights From a Process‐Based Agroecosystem Model

Biomass crops serve as essential feedstocks for renewable energy and bioproducts and play a critical role in achieving lower emissions in the transportation sector. However, dedicated perennial biomass crops such as Miscanthus × giganteus (Miscanthus) remain underrepresented in process-based agroecosystem models, limiting robust evaluation of their economic and environmental performance. In this study, we developed a data-constrained representation of the sterile triploid Miscanthus (IL clone) within the process-based model ecosys, integrating global sensitivity analysis, ensemble simulation, and parameter calibration. Planting, harvesting, and fertilization practices consistent with field management were incorporated, and phenology was constrained using PhenoCam-derived Green Chromatic Coordinate (GCC) data. Using the Morris global sensitivity analysis method, we identified 11 key physiological parameters governing plant carbon, water, and nutrient relations, particularly processes associated with CO 2 assimilation. We then conducted ensemble simulations by perturbing these parameters and calibrated the model against eddy covariance fluxes and field-measured biomass. Building on the calibrated operating state, parameter-response analyses show that different photosynthetic processes influence productivity in different ways. Protein allocation determines whether productivity increases toward a higher level, whereas electron transport capacity controls additional gains once protein allocation approaches saturation. These findings demonstrate that parameter importance depends on physiological context and on which photosynthetic processes remain limiting. Calibration and validation against observations show that ecosys can reliably reproduce carbon and water fluxes, as well as both above- and belowground biomass, with post-calibration GPP R 2 improving from 0.67 to 0.95 during the calibration period and remaining high during validation (R 2 = 0.95). These results provide a mechanistic foundation for regional simulations and sustainable bioenergy assessments.

ecosys↗

Benchmarking third-order cluster perturbation theory for electronically excited states

In this study, we investigate the reliability of cluster perturbation (CP) theory applied to the calculation of electronically excited states through a comprehensive benchmark. In CP theory, perturbative corrections are added to the properties of a parent excitation space, which converge toward the properties of a target excitation space. For the CPS(D-n) model, perturbative corrections through order n are added to the coupled cluster singles (CCS) excitation energies to target the coupled cluster singles and doubles (CCSD) excitation energies. Through a comparative analysis of excitation energy calculations across a diverse set of molecules and wavefunction methods, we present a comprehensive evaluation of the accuracy of the third-order CPS(D) model, CPS(D-3), in calculating excitation energies. Further, our findings demonstrate that CPS(D-3) is a reliable alternative to established methods, particularly CCSD, while systematically overestimating the excitation energies compared to high-level coupled cluster methods such as CC3. These results highlight the strengths and limitations of CPS(D-3), as well as the promising directions for its future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anomalous resistivity and electron heating by lower hybrid drift waves inside reconnecting current sheets

Inside an electron diffusion region of laboratory reconnection experiments, the quasi-electrostatic lower hybrid drift wave (ES-LHDW) is observed when a significant guide field component is present. Through direct measurement of the anomalous drag term and quasilinear analysis, it is shown that ES-LHDW can account for approximately 20% of the mean reconnection electric field in a case with moderate guide field. This value exceeds the contribution from classical resistivity, which is around 10%. The effects of the Lorentz force term, often neglected for electrostatic waves, are crucial for the observed correlation between electric field and density fluctuations. Anomalous electron heating by the perturbed current and resistivity (2.6 MW/m 3 ) also surpasses the classical Ohmic heating, which is about 2.0 MW/m 3 . For the case with a high guide field, significantly higher local electron temperatures were observed during periods of strong ES-LHDW activity. A statistical analysis further supports electron heating by LHDW, showing a larger increase in electron temperature with a high guide field. Finally, data from the Magnetospheric Multiscale mission provide evidence of Landau damping of ES-LHDW, suggesting that ES-LHDW may contribute to the generation of nonthermal electrons along the direction parallel to the magnetic field.

Magnetic reconnection↗

Improving constraints on inflation with CMB delensing

Abstract The delensing of cosmic microwave background (CMB) maps will be increasingly valuable for extracting as much information as possible from future CMB surveys. Delensing provides many general benefits, including sharpening of the acoustic peaks, more accurate recovery of the damping tail, and reduction of lensing-inducedB-mode power. In this paper we present several applications of delensing focused on testing theories of early-universe inflation with observations of the CMB. We find that delensing the CMB results in improved parameter constraints for reconstructing the spectrum of primordial curvature fluctuations, probing oscillatory features in the primordial curvature spectrum, measuring the spatial curvature of the universe, and constraining several different models of isocurvature perturbations. In some cases we find that delensing can recover almost all of the constraining power contained in unlensed spectra, and it will be a particularly valuable analysis technique to achieve further improvements in constraints for model parameters whose measurements are not expected to improve significantly when utilizing only lensed CMB maps from next-generation CMB surveys. We also quantify the prospects of testing the single-field inflation tensor consistency condition using delensed CMB data; we find it to be out of reach of current and proposed experimental technology and advocate for alternative detection methods.

Astronomy & Astrophysics↗

Data for Physiological Controls on Carbon Fluxes and Biomass Production in Miscanthus: Insights From a Process- Based Agroecosystem Model

Biomass crops serve as essential feedstocks for renewable energy and bioproducts and play a critical role in achieving lower emissions in the transportation sector. However, dedicated perennial biomass crops such as Miscanthus × giganteus (Miscanthus) remain underrepresented in process- based agroecosystem models, limiting robust evaluation of their economic and environmental performance. In this study, we developed a data- constrained representation of the sterile triploid Miscanthus (IL clone) within the process- based model ecosys, integrating global sensitivity analysis, ensemble simulation, and parameter calibration. Planting, harvesting, and fertilization practices consistent with field management were incorporated, and phenology was constrained using PhenoCam- derived Green Chromatic Coordinate (GCC) data. Using the Morris global sensitivity analysis method, we identified 11 key physiological parameters governing plant carbon, water, and nutrient relations, particularly processes associated with CO2 assimilation. We then conducted ensemble simulations by perturbing these parameters and calibrated the model against eddy covariance fluxes and field- measured biomass. Building on the calibrated operating state, parameter- response analyses show that different photosynthetic processes influence productivity in different ways. Protein allocation determines whether productivity increases toward a higher level, whereas electron transport capacity controls additional gains once protein allocation approaches saturation. These findings demonstrate that parameter importance depends on physiological context and on which photosynthetic processes remain limiting. Calibration and validation against observations show that ecosys can reliably reproduce carbon and water fluxes, as well as both above- and belowground biomass, with post- calibration GPP R2 improving from 0.67 to 0.95 during the calibration period and remaining high during validation (R2 = 0.95). These results provide a mechanistic foundation for regional simulations and sustainable bioenergy assessments.

Carbon↗

Uncertainty Quantification and Sensitivity Analysis of Non-Nuclear Advanced Controls Testbed Reactor Mockup

The research presented in this report describes our progress in applying stochastic methods and uncertainty quantification, parametric study, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated with Griffin, with the goal of developing a reduced order (surrogate) model which can be rapidly sampled while perturbing multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums, which are controlled by a hybrid proportional, integral and derivative (PID) controller, actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time and $\beta$ from a transient Griffin simulation executed with the improved quasi-static method to provide the kinetic parameters) as inputs to functions which control the CD rotation angle. Using a number of stochastic method approaches, we developed a dual purpose training-surrogate model of the NTP system using polynomial regression. The trained model can be rapidly sampled while simultaneously perturbing various input parameters of the model, such as coefficients on the PID control, or temperature (directly affect the neutron cross section). The surrogate model delivers accurate results orders-of-magnitude faster (minutes, not days) than the base model. Once the base model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs and their effect on the output. For example, coefficients used in the PID control system may vary due to some physical interference, or there may be uncertainty in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters and operational boundaries can be determined. The goal of this work is to support development of an advanced control system to operate CDs in a functioning NTP system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Geometry and dynamics of lipid membranes: The Scriven-Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. Here, a new dimensionless number, named the Scriven-Love number, and the well-known Föppl–von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl–von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl–von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces—with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

2D Gravity↗

Numerical study of implosion instability mitigation in magnetically driven solid liner dynamic screw pinches

Magnetized liner inertial fusion experiments on the Z accelerator suffer from magneto-Rayleigh–Taylor instabilities (MRTI) that compromise integrity of the imploding cylindrical liner, limiting achievable fusion fuel conditions and ultimately reducing magneto-inertial fusion target performance. Dynamic screw pinches (DSP) provide a method to reduce MRTI in-flight via application of magnetic field line tension to the imploding liner outer surface. In contrast with z-pinches that drive implosions with an azimuthal magnetic field, dynamic screw pinches enforce an additional axial drive magnetic field component, making the overall drive magnetic field helical. As the liner implodes, cumulative MRTI development is reduced by dynamically shifting the orientation of the fastest growing instability modes. Three-dimensional magnetohydrodynamic simulations show that the DSP mechanism effectively stabilizes initially solid cylindrical liner implosions driven by Z-scale current pulses, indicating that MRTI mitigation increases with the ratio of axial to azimuthal drive magnetic field components (i.e., the drive field ratio). We also performed a spectral analysis of the simulated imploding density distributions, extracting wavelength and pitch angle of the simulated MRTI structures to study their dynamics during the implosion. Simulations of liners initially perturbed with drive-field-aligned sinusoidal structures indicate that MRTI mitigation in DSP implosions decreases with perturbation wavelength, once again suggestive of magnetic field line tension effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

FOS: Physical sciences↗

Supersymmetric Virasoro minimal strings

A random matrix model definition of a family of N = 1 supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Assessment of the Impact of Realistic Sensor Physics and the Integration of Ex-Core Sensors on Reactor Power Synthesis

In the work documented in this report, a weighting function–based core power synthesis method was applied to multiple Monte Carlo N-Particle (MCNP) reactor models, which are informed based on simulated self-powered neutron detector (SPND) responses. The weighting function method used has been coined the point-based iterative (PBI) method. The goal of this application is to assess the impact of considering realistic sensor physics in the generation of the simulated SPND outputs as well as to consider how the synthesis is impacted based on the inclusion of ex-core detectors in the model. The NuScale small modular reactor (SMR) and Westinghouse AP1000 pressurized water reactor (PWR) are the models that served as the testbeds for the assessment of realistic sensor physics; this was achieved by using Geant4 SPND models in comparison with analytical models, such that the effect of electron transport in realistic SPND geometries in the Geant4 model can be understood in terms of synthesis error and convergence time. The comparison was considered for fuel burnup–induced perturbations, for a range of sensor string densities and synthesized power distribution axial fidelities. The Texas A&M Testing, Research, Isotopes, General Atomics Reactor (TAMU TRIGA) reactor MCNP model was used to assess the impact of ex-core sensors; this was done by performing synthesis with and without the ex-core detectors and by quantifying the synthesis error and number of iterations associated with Gaussian-type perturbations in many locations in the core. The TAMU TRIGA model was particularly pertinent for this study because of the interest in future experimental tests with SPNDs in this reactor, as well as the ease of modifying the MCNP model to include ex-core detectors with heterogeneously described response functions. Results from the comparison between the Geant4 and analytical SPND models indicate that similar average and maximum synthesis errors were obtained for burnup-induced perturbations in both the NuScale SMR and the AP1000. This was true for a range of sensor string densities and axial fidelities. However, there were marked differences between both the Geant4 and analytically informed models in terms of the iterations required to converge on the synthesized power distribution. Namely, the Geant4-informed models tended to lead to fewer iterations, except for a few sensor–core configurations that had particularly numerous iterations. Results from the ex-core sensor assessment with the TAMU TRIGA model indicate that the inclusion of ex-core sensors drastically reduces the synthesis error of Gaussian-type perturbations close to the edge of the core, and it slightly reduces synthesis errors for perturbations closer to the center of the core. This was achieved with a minimal increase in computational cost—that is, the number of iterations required for convergence. The errors were identified to be in the same location as the perturbation in the core, indicating that the methodology remains robust for unperturbed regions of the core. A secondary result from this study with the TAMU TRIGA was yielded by analysis of the neutron flux levels in the in-core and ex-core sensor locations of the core; these flux levels indicate that SPNDs could be used as both in-core and ex-core sensors, so long as the emitter material is sensitive to thermal neutrons. The results from these studies provide a quantitative understanding of the importance of considering realistic sensor physics and including ex-core sensors to perform accurate and timely power distribution synthesis of a reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING↗

Isochronic Evolution and the Radioactive Decay of r-process Nuclei

Abstract We report on the creation and application of a novel decay network that uses the latest data from experiment and evaluation. We use the network to simulate the late-time phase of the rapid neutron capture ( r ) process. In this epoch, the bulk of nuclear reactions, such as radiative capture, have ceased, and nuclear decays are the dominant transmutation channels. We find that the decay from short-lived to long-lived species naturally leads to an isochronic evolution in which nuclei with similar half-lives are populated at the same time. We consider random perturbations along each isobaric chain to initial solar-like r -process compositions to demonstrate the isochronic nature of the late-time phase of the r -process. Our analysis shows that detailed knowledge of the final isotopic composition allows for the prediction of late-time evolution with a high degree of confidence despite uncertainties that exist in astrophysical conditions and the nuclear physics properties of the most neutron-rich nuclei. We provide the time-dependent nuclear composition in the Appendix as supplemental material.

79 ASTRONOMY AND ASTROPHYSICS↗

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Physics of parameter correlations around the solar-scale enhancement in neutrino theory with unitarity violation

We discuss the physics of the three neutrino flavor transformation with non-unitary mixing matrix, with particular attention to the correlation between the $\nu$SM- and the $\alpha$ parameters which represent the effect of unitarity-violating (UV) new physics. Towards this goal, a new perturbative framework is created to illuminate the effect of non-unitarity in the region of the solar-scale enhanced oscillations. We refute the skepticism about the physical reality of the $\nu$Standard Model CP phase $\delta$–$\alpha$ parameter phase correlation by analysis with the SOL convention of $U_{{\tiny MNS}}$, in which $e^{\pm i \delta}$ is attached to $s_{12}$. Then, a comparative study between the solar- and atmospheric-scale oscillation regions allowed by the framework reveals a dynamical $\delta$–(blobs of the $\alpha$ parameters) correlation in the solar oscillation region, in sharp contrast to the “chiral”-type phase correlation $[e^{- i \delta} \bar{\alpha}_{\mu e},\ e^{- i \delta} \bar{\alpha}_{\tau e},\ \bar{\alpha}_{\tau \mu}]$ in the Particle Data Group convention seen in the atmospheric oscillation region. An explicit perturbative calculation to the first order in the $\nu_{\mu} \rightarrow \nu_{e}$ channel allows us to decompose the UV related part of the probability into the unitary evolution part and the genuine non-unitary part. We observe that the effect of non-unitarity tends to cancel between these two parts, as well as between the different $\alpha_{\beta \gamma}$ parameters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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

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

42 ENGINEERING↗