Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis?
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Stability Analysis of Substituted Cobaltocenium [Bis(cyclopentadienyl)cobalt(III)] Employing Chemistry-Informed Neural Networks
Cobaltocenium derivatives are promising components of the anion exchange membranes due to their excellent thermal and alkaline stability under the operating conditions of a fuel cell. Here we present an efficient modeling approach of assessing the chemical stability of substituted cobaltocenium CoCp 2 + based on the computed electronic structure enhanced by machine learning techniques. Within the aqueous environment, the positive charge of the metal cation is balanced by the hydroxide anion through formation of the CoCp 2 + OH¯ complexes, whose dissociation is studied within the implicit solvent employing density functional theory. The data set of about 118 species based on 42 substituent groups characterized by a range of electron- donating (ED) and electron-withdrawing (EW) properties is constructed and analyzed. Given 12 carefully chosen chemistry-informed descriptors of the complexes and relevant fragments, the stability of the complexes is found to strongly correlate with the energies of the highest occupied and lowest unoccupied molecular orbitals, modulated by a switching function of the Hirshfeld charge. The latter is used as a measure of the electron withdrawing-donating character of the substituents. Based on this observation from the conventional regression analysis, two fully connected, feed-forward neural network (FNN) models with different unit structures, called the chemistry-informed (CINN) and the quadratic (QNN) neural networks, are developed. Both models predict the bond dissociation energies of the cobaltocenium complexes with mean relative errors less than 5.40% and average absolute errors less than 0.94 kcal/mol. The results show the potential of QNN to efficiently capture more complex relationships. Here, the concept of incorporating the domain (chemical) knowledge/insight into the neural network structure paves the way to applications of machine learning techniques with small data sets, ultimately leading to better predictive models compared to the conventional regression analysis.
36 MATERIALS SCIENCE↗
Efficient and robust stability analysis in the internal energy, volume, and moles (UVN) space
Hydrodynamic simulation of fluids in vessels is often based on the internal energy (U), volume (V), and the number of moles of all components ( re N = N 1 , N 2 , ..., N n ) as the working variables to determine the thermodynamic state by finding the global maximum of entropy. The procedure of finding the equilibrium state may be divided into two steps: stability analysis and phase-split computations. Stability analysis is performed first, and the phase-split computation proceeds if the system is unstable. Most of the past work on UVN space has been based on phase-split computations, while the stability analysis is barely investigated. Furthermore, previous studies for the stability analysis use only Newton's method to solve the non-linear algebraic equations. We present an efficient and robust approach for stability analysis where UVN is specified. The successive substitution iteration (SSI) is used to provide good initial guesses for Newton's method. The proposed approach results in a reduced number of unknowns and does not require a large number of iterations to achieve convergence in Newton's method. Overall, our proposed formulation is compatible with different equations of state and is applicable to both pure component and multi-components. The robustness and efficiency of the algorithm for stability analysis are demonstrated in various examples.
02 PETROLEUM↗
MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry
We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number (n) and frequency (ω) in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field (E||), ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfv\'en wave (KAW), ion sound wave (ISW), low-n kink, high-n ion temperature gradient mode (ITG) and kinetic ballooning mode (KBM). Moreover, MAS is successfully applied to model the Alfv\'en eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of reversed shear Alfv\'en eigenmode (RSAE), the tunneling damping of toroidal Alfv\'en eigenmode (TAE), as well as the polarization characteristics of kinetic beta-induced Alfv\'en eigenmode (KBAE) and beta-induced Alfv\'en-acoustic eigenmode (BAAE) being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
A New Impedance-Based Modeling and Stability Analysis Approach for Power Oscillations Between Grid-Forming Inverters
This paper presents a new modeling and analysis approach to address the small-signal stability issues among interconnected grid-forming (GFM) inverters. A novel phasor domain “power impedance” model is developed to capture the terminal characteristics of GFM inverters. Based on the developed models, a sum-type impedance stability criterion is proposed to analyze the power oscillations between GFM Inverters. The developed models are validated with EMT simulations and the stability analysis results using the proposed stability criterion can match both EMT simulations and eigenvalue analysis. In addition, the application of the developed model can be extended to the stability analysis of large-scale power system with high penetration of GFM inverters.
Liu, Hanchao↗
A Laplace-Domain Circuit Model for Fault and Stability Analysis Considering Unbalanced Topology
For systems subject to unbalanced faults, analytical model building for stability assessment is a challenging task. This letter presents a straightforward modeling approach. A generalized dynamic circuit representation is achieved by use of the Laplacian transform variable s . Here, we translate the voltage and current relationship at the fault location into the relationship of three subsystems. The final circuit model is an interconnected sequence network with impedances in the Laplace domain. This circuit can be directly converted from a steady-state sequence network. This modeling procedure is illustrated by an example case of an induction motor served by a grid through a series compensated line. Electromagnetic transient simulation results demonstrate that sub-synchronous oscillations can be mitigated when a single-line to ground fault is applied at the motor terminal. Stability analysis results based on the dynamic circuit corroborate the simulation results. What's more, the derived circuit effortlessly reveals why unbalance can enhance stability.
42 ENGINEERING↗
Impedance Scan of Inverter-Based Resources and Diesel Generator for Stability Analysis
Impedance-based methods are widely used for power system stability analysis with inverter-based resources (IBRs), e.g., assessing dynamic interactions between the power grid and an IBR, control interactions between multiple IBRs, and the sub-synchronous oscillation and damping phenomenon. Since it is difficult to get a numerical model 100% matching with the hardware IBR, using the hardware inverter directly to obtain its output impedance has become a prominent approach nowadays. Therefore, this article presents the impedance scan using hardware IBRs, and also a hardware diesel generator as it still stays with the grid before the grid completely goes to renewable. The devices under test (DuTs) for the impedance scan includes two 3-..phi.., 480 V, 60 Hz commercial grid-forming IBRs (one of 250 kVA and another of 125 kVA rating) in series with ..delta..-Y transformers, one 3-..phi.., 480 V, 60 Hz commercial grid-following IBR (of 125 kVA rating), and a 3-..phi.., 480 V, 60 Hz commercial diesel generator (of 187.5 kVA rating). Using voltage signals perturbed with sub-, inter-, and higher harmonic components, and measuring the current response, the positive-sequence impedances are computed via an offline-based post-analysis. Moreover, best-fit transfer functions are estimated that closely resemble the measured data points of the positive-sequence impedances. Based on the observations from various outcomes of the hardware experiments, this article also provides some fundamental insights on the equivalent positive-sequence impedance of a combination of multiple hardware components by comparing the estimated and the empirically computed impedances. A comparative insight on the damping capability of the DuTs using the positive-sequence impedances of the hardware is also discussed.
current measurement↗
Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition
Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet-Neumann conditions.
97 MATHEMATICS AND COMPUTING↗
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 responses of IBRs considering the frequency cross-coupling effects. With the obtained NTFM as well as IBRs' 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. Different testing cases based on a modified IEEE-14 bus system are leveraged to verify the proposed stability analysis tool.
Sun, Dongsen↗
Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems
Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.
DC–AC power systems↗
Measuring Commercial Wind Turbine Impedances for Stability Analysis
This presentation provides an overview of measuring commercial wind turbine impedances for stability analysis.
49 EE - Wind and Water Power Program - Wind (EE-4W↗
An ideal MHD δW stability analysis that bypasses the Newcomb equation
In the following work, we demonstrate the efficacy of a Riccati δW ideal MHD stability analysis that bypasses the numerically intractable integration of the Newcomb equation. By transforming the linear Newcomb equation into a quadratic Riccati equation, an accurate and equivalent δW analysis is performed that is shown to enjoy some numerical advantages. Additionally, we demonstrate that the Riccati approach is better conditioned than its Newcomb counterpart at the magnetic axis, and we apply dynamical systems insights to examine its behavior at singular points. We further discuss the constraints involved in solving for the extremal admissible perturbations of a δW analysis.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Low-Frequency Stability Analysis of Inverter-Based Islanded Multiple-Bus AC Microgrids Based on Terminal Characteristics
For system planning of three-phase inverter-based islanded ac microgrids, the low frequency instability issue caused by interactions of inverter droop controllers is a major concern. When internal control information of procured commercial inverters is unknown, impedance-based small-signal stability criteria facilitate prediction of resonances in medium and high frequency ranges, but they usually assume the grid fundamental frequency as constant and thus they are incapable of analyzing the low-frequency oscillation of the fundamental frequency in islanded microgrids. Aiming at solving this issue, this paper proposes two stability analysis methods based on terminal characteristics of inverters and passive connection network including the dynamics of the fundamental frequency for analysis of low-frequency stability in islanded multiple-bus microgrids. Based on the Component Connection Method (CCM) to systematically separate inverters from the passive connection network, a general approach is developed to model the microgrid as a multiple-input-multiple-output (MIMO) negative feedback system in the common system d-q reference frame. By applying the generalized Nyquist stability criterion (GNC) to the return-ratio and return-difference matrices of the MIMO system model, the low-frequency stability related to the fundamental frequency can be analyzed using the measured terminal characteristics of inverters. Finally, analysis and simulation of a 37-bus microgrid verify the effectiveness of the proposed stability analysis methods.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Stability Analysis of Parallel Connected Bidirectional WPT System
This paper presents a stability analysis of parallel-connected bi-directional series-series resonant network wireless power transfer (WPT), optimized for Electric Vehicle (EV) charging and vehicle-to-grid (V2G) applications. The study addresses critical stability challenges in systems integrated with diverse distributed energy resources (DERs), including photovoltaics, fuel cells, wind turbines, energy storage systems, and the AC grid. The stability of such integrated DC grid systems is paramount for ensuring reliable operation, particularly under varying power flow conditions and dynamic interactions between parallel WPT systems. The analysis included system impedance characterization, state-space modeling, and open and closed-loop stability evaluations. The results demonstrated that the integration of a robust control architecture effectively mitigates instability risks and supports scalable, efficient operation. This work underscores the converter's adaptability and its potential for large-scale deployment in wireless EV charging infrastructures and integrated DC grid systems.
Asa, Erdem [ORNL] (ORCID:0000000190884812)↗
Linear stability analysis via simulated annealing and accelerated relaxation
Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. In conclusion, since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Neutrino fast flavor oscillations with moments: Linear stability analysis and application to neutron star mergers
Providing an accurate modeling of neutrino physics in dense astrophysical environments such as binary neutron star mergers presents a challenge for hydrodynamic simulations. Nevertheless, understanding how flavor transformation can occur and affect the dynamics, the mass ejection, and the nucleosynthesis will need to be achieved in the future. Computationally expensive, large-scale simulations frequently evolve the first classical angular moments of the neutrino distributions. By promoting these quantities to matrices in flavor space, we develop a linear stability analysis of fast flavor oscillations using only the first two “quantum” moments, which notably requires generalizing the classical closure relations that appropriately truncate the hierarchy of moment equations in order to treat quantum flavor coherence. After showing the efficiency of this method on a well-understood test situation, we perform a systematic search of the occurrence of fast flavor instabilities in a neutron star merger simulation. Here, we discuss the successes and shortcomings of moment linear stability analysis, as this framework provides a time-efficient way to design and study better closure prescriptions in the future.
79 ASTRONOMY AND ASTROPHYSICS↗
Linear Stability Analysis of HTR-like Micro-reactors
This paper develops a linear stability analysis of high temperature gas micro-reactors to investigate the dynamic stability of the reactors.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗