Eigenvalue Sensitivity Research Articles

Stockwell‐transform and random‐forest based double‐terminal fault diagnosis method for offshore wind farm transmission line

Due to the difficulty and time-consumption in locating short-distance transmission lines for deep-sea offshore wind farm (DOWF)，this paper proposes a novel double-terminal fault location method by using Stockwell-transform (ST) and random-forest (RF). After the fault type and branch are accurately determined, the accurate transmission line fault location is located. Firstly, Stockwell-transform is employed to extract fault eigenvalues from the collected wind turbine (WT) current signals, which will reduce the sensitivity of eigenvalues to noise. And the Pearson correlation coefficient (PCC) is introduced to remove duplicate eigenvalues. Secondly, the reserved fault eigenvalues are taken as inputs to the different random-forest to classify fault types and identify the fault branch, respectively. Finally, the double-terminal fault location principle is established in fault negative sequence network (only ABCG uses positive sequence components). Newton-Raphson method (NRM) is used to eliminate the influence of asynchrony data, which implies an accurate transmission line fault location for deep-sea offshore wind farm. More than 4000 fault cases data obtained by Simulink simulation verify the feasibility and performance of the proposed method. The results show that the proposed location method has a high fault recognition rate and is immune to fault inception angle, resistance, location and noise.

A multi-objective optimization model for robust tuning of wide-area PSSs for enhancement and control of power system angular stability

A multi-objective optimization model for robust tuning of wide-area power system stabilizers (WAPSSs) aiming the improvement and control of angular stability of electric power system (EPS) is presented in this paper. In this work the WAPSSs are referred to power system stabilizers (PSSs) of fixed-structure with insertion of remote signals, from phasor measurement units (PMUs), in the control loops, that are used in a wide-area control system (WACS). The proposed model is composed of objective functions to maximize both the small-disturbance angular stability (SDAS) through the damping ratio and the large-disturbance angular stability (LDAS) using an index derived from transient energy function (TEF). Moreover, three objectives functions that contribute to the previous ones are taken into account: maximization of power system robustness for several operating conditions, minimization of eigenvalues sensitivity to small disturbances, and minimization of eigenvalues sensitivity with respect to time delay variations of remote signals. Swarm intelligence-based techniques are used to solve the multi-objective optimization model. Simulation results, with the benchmark interconnected system New England test system – New York power system (NETS-NYPS) of 16-generator and 68-bus, corroborate the applicability of the proposal.

Eigenvalue sensitivity and nuclear data uncertainty analysis for the Moroccan TRIGA Mark II research reactor using SCALE6.2 and MCNP6.2

In order to evaluate the impact of nuclear data on the reactor safety assessment, eigenvalue sensitivity and uncertainty analysis of the Moroccan TRIGA Mark II research reactor are evaluated in this paper. Using the SCALE package, a nominal criticality calculation was implemented in this work to assess the accuracy of the developed TRIGA SCALE model. The aim has been reached by comparing several neutronic parameters results with those obtained by the MCNP TRIGA model which has been performed in previous studies.To generate the sensitivity coefficients, two models of the TRIGA reactor were compared, including the averaged and detailed fuel models, based on the SCALE /TSUNAMI-3D sequence and MCNP/KSEN card. Comparison between those models was performed to evaluate and increase the efficiency of the sensitivity and uncertainty calculations. The obtained results show a good agreement between the TRIGA models studied in this work. Furthermore, the results of this analysis indicate that the uncertainty in the effective multiplication factor (keff) is mainly awarded to uncertainties on the ν‾,χ, fission reactions of 235U as well as the moderator scattering and the clad absorption.

Stability improvement of interconnected AC / DC multiarea AGC power systems using optimized virtual synchronous power strategy based on eigenvalues sensitivity and adaptive mixed GWO

Stability improvement of interconnected <scp>AC</scp> / <scp>DC</scp> multiarea <scp>AGC</scp> power systems using optimized virtual synchronous power strategy based on eigenvalues sensitivity and adaptive mixed <scp>GWO</scp>

An Efficient Eigenvalue Tracking Method for Time-Delayed Power Systems Based on Continuation of Invariant Subspaces

Time delays are inevitable in the power systems with wide-area control signals, which may compromise the control pe-rformance and thus jeopardize the stability of the power systems. To analyze the impacts of system parameters on critical oscillation modes of a time-delayed power system (TDPS), a new method for eigenvalue trajectory tracking of TDPS is proposed in this paper based on the continuation theory of invariant subspaces. When small changes are imposed on system parameters, such as parameters of wide-area damping controllers (WADCs) and time delays, the invariant subspaces are continuously predicted and corrected, followed by the eigenvalues and eigenvectors. In the process, the predictor and corrector are computed by solving linear equations sparsely and in blocks, which is highly scalable and computationally efficient for large-scale power system applications. The 16-generator 68-bus test system and two real-world power grids in China are used to test and demonstrate the proposed method. The results show that the proposed method can accurately and efficiently track eigenvalue trajectories for TDPS, especially for large-scale power grids. In addition, the sensitivities of eigenvalues and eigenvectors with respect to WADCs' parameters and time delays are obtained as by-products of the approach.

A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System

With the rapid development of power-electronics- enabled power systems, the new converter-based generators are deteriorating the small-signal stability of the power system. Although the numerical differentiation method has been widely used for approximately calculating the eigenvalue sensitivities, its accuracy has not been carefully investigated. Besides, the element-based formulation for computing closed-form eigenvalue sensitivities has not been used in any commercial software due to the average efficiency, complicated formulation, and error-prone characteristics. Based on the matrix calculus, this paper proposes an easily manipulated formulation of the closed-form eigenvalue sensitivities with respect to the power generation. The distinguishing feature of the formulation is that all the formulas consist of vector and matrix operations, which can be performed by developed numerical algorithms to take full advantages of architectural features of the modern computer. The tests on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system, and IEEE 54-machine 118-bus system show that the accuracy of the proposed formulation is superior to the numerical differentiation method and the efficiency is also greatly improved compared to the element-based closed-form formulation. The proposed formulation will be helpful to perform a more accurate and faster stability analysis of a power grid with converter-based devices.

Comparative study on structural sensitivity of eigenvalue–based molecular descriptors

Structural sensitivity is one of the most important and the least investigated property of the topological molecular descriptors. This paper reports results on the structural sensitivity of graph energy, Estrada index, and resolvent energy on several series of catacondensed and pericondensed isomeric benzenoid hydrocarbons. Recently, a novel method for assessing the structural sensitivity of topological molecular descriptors was put forward, which is applied here. This algorithm consists of several different steps and it is based on Tanimoto index and Morgan circular fingerprints. It was found that graph energy, Estrada index, and resolvent energy exert similar structural sensitivity on catacondensed isomers. The graph energy showed the best performance on pericondensed molecules. Additionally, the sensitivities of these descriptors were tested on the catacondensed isomers with the increasing number of bays, coves, and fjords. It was revealed that these descriptors gradually change with the increasing number of these structural features. The Estrada index and resolvent energy perform similarly and in some cases with the same structural sensitivity. This may be attributed to the high correlation between them. The graph energy showed superiority over the Estrada index and resolvent energy on pericondensed isomers.

Optimization to POD parameters of DFIGs based on the 2nd order eigenvalue sensitivity of power systems

Optimization to POD parameters of DFIGs based on the 2nd order eigenvalue sensitivity of power systems

Analytical Model for Enhanced Eigen-Mode Sensitivities in a Coupled Micro-Resonator Array for Ultra-Sensitive Mass Measurement

Abstract Resonant sensors using coupled micro-cantilever array have applications in a wide range of areas including ultrasensitive mass detection of bio-molecules and chemical analytes. A target mass deposited on one of the cantilevers can be detected by measuring shift in eigen-spectrum. Experimental observations indicate that eigenmodes are more sensitive to mass perturbation than resonant frequencies or eigenvalues. However, analytical works, available in literatures, are limited to only two and three cantilever array for eigenvalue sensitivity and only two cantilever array for eigenmode sensitivity. In the present work, an analytical foundation for estimation of eigenmode sensitivities for a general n-array micro-resonator sensor is developed using matrix perturbation theory. The formulation characterizes the modal spectrum and eigenmode sensitivities as a function of elastic interconnection stiffness parameter and unperturbed eigenmodes. Measurement of added mass is demonstrated for different analyte locations using numerically constructed frequency response function (FRF) curves. Error in measurement is also investigated as a function of interconnection stiffness ratio, position of analyte mass, and selection of particular eigenmode to be measured.

On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems

Abstract

A modified optimization method for robust partial quadratic eigenvalue assignment using receptances and system matrices

In this paper, we focus on the robust partial quadratic eigenvalue assignment problem for vibrating structures by active feedback control. This problem is reformulated as an minimization problem, where the cost function can measure both the sensitivity of the closed-loop eigenvalues and the feedback norms. This can be seen as a modified version of the minimization problem proposed by Bai et al. (2016) [5], where there exist additional equality constraints involving determinants of linear functions of the parameter matrix. By using the receptance measurements, the system matrices and a few undesired open-loop eigenvalues and associated eigenvectors, we propose a modified gradient-based optimization method for solving the minimization problem, where the explicit gradient formula of the cost function is derived. To implement our method in real operation, the real form of our method is also presented. Finally, some numerical examples are given to illustrate the validity of the proposed method.

Thermoacoustic stabilization of a longitudinal combustor using adjoint methods

We construct a low-order thermoacoustic network model that contains the most influential physical mechanisms of a thermoacoustic system. We apply it to a laboratory-scale longitudinal combustor that has been found to be thermoacoustically unstable in experiments. We model the flame, which is behind a bluff body, by a geometric level-set method. We obtain the thermoacoustic eigenvalues of this configuration and examine a configuration in which six eigenmodes are unstable. We then derive the adjoint equations of this model and use the corresponding adjoint eigenmodes to obtain the sensitivities of the unstable eigenvalues to modifications of the model geometry. These sensitivities contain contributions from changes to the steady base flow and changes to the fluctuating flow. We find that these two contributions have similar magnitudes, showing that both contributions need to be considered. We then wrap these sensitivities within a gradient-based optimization algorithm and stabilize all six eigenvalues by changing the geometry. The required geometry changes are well approximated by the first step in the optimization process, showing that this sensitivity information is useful even before it is embedded within an optimization algorithm. We examine the acoustic energy balance during the optimization process and identify the physical mechanisms through which the algorithm is stabilizing the combustor. The algorithm works by, for each mode, reducing the work done by the flame while simultaneously increasing the work done by the system on the outlet boundary. We find that only small geometry changes are required in order to stabilize every mode. The network model used in this study deliberately has the same structure as one used in the gas turbine industry in order to ease its implementation in practice.

Impedance Modeling and Controllers Shaping Effect Analysis of PMSG Wind Turbines

Oscillation issues of permanent magnet synchronous generator (PMSG) wind turbines (WTs) have an increasingly significant impact on grid stability, especially with their increased generation capacity. However, the machine-side model (MSM), involving machine-side converter (MSC) and generator, is generally simplified as an ideal voltage source to comprising the impedance model of a PMSG-WT used for stability analysis, thus causing deficiency in describing the machine dynamics. Besides, the impedance-based method considering the PMSG-WT as a black box only describes the system from the external output characteristics; as such, the shaping effect of the internal controllers on the impedance model has not been fully studied yet. This article proposes the impedance model of PMSG-WTs consisting of generator, MSC, dc-bus and grid-side converter (GSC) for more accurate stability analysis. Furthermore, based on the general Nyquist criteria (GNC) and eigenvalue sensitivity analysis method, the shaping effect of the controllers inside GSC and MSC on the PMSG external impedance is quantitatively studied. The influence of the MSM on the system stability is investigated by comparing with the simplified model through extensive simulation studies.

Parametric control to quasi-linear systems based on dynamic compensator and multi-objective optimization

This paper considers a parametric approach for quasi-linear systems by using dynamic compensator and multi-objective optimization. Based on the solutions of generalized Sylvester equations, we establish the more general parametric forms of dynamic compensator and the left and right closed-loop eigenvector matrices, and give two groups of arbitrary parameters. By using the parametric approach, the closed-loop system is converted into a linear constant one with a desired eigenstructure. Meanwhile, it also proposes a novel method to realize multi-objective design and optimization. Multiple performance objectives, containing overall eigenvalue sensitivity, $H_2$ norm, $H_\infty$ norm and low compensation gain, are formulated by arbitrary parameters, then robustness and low compensation gain criteria are expressed by a comprehensive objective function which contains each performance index weighted. By utilizing degrees of freedom (DOFs) in arbitrary parameters, we can optimize the comprehensive objective function such that an optimized dynamic compensator is found to satisfy the robustness and low compensation gain criteria. Finally, an example of attitude control of combined spacecrafts is presented which proves the effectiveness and feasibility of the parametric approach.

Robust Nonminimal State Feedback Control for a Furuta Pendulum With Parametric Modeling Errors

Nonminimal state feedback control, also known as proportional-integral-plus control, together with antiwindup integrator, is applied, for the first time, to stabilize a Furuta pendulum (FP). The key elements in the nonminimal state space (NMSS) state transition matrix is obtained directly from the original minimal state space model. The NMSS model is proved to be controllable if the controllability conditions are met. In order to demonstrate the potential robustness of NMSF control, the controller is designed based on the model with two deliberate plant parameter mismatches. The feedback gains are optimized in an eigenvalue assignment way by minimizing a robust cost function, which is related to the closed-loop state matrix's eigenvalues' sensitivities to the two mismatched plant parameters. The sum of the normalized eigenvalue sensitivities (NES) is defined as cost function. In this article, multiple simulations with different plant parameters are implemented to evaluate the robustness. The optimized FP control system shows smaller envelope of multiple time responses compared to the one before optimization. Experimental results also confirm the optimized controller's improved robustness under parametric mismatches.

Coordinated Design of Supplementary Controllers in VSC-HVDC Multi-Terminal Systems to Damp Electromechanical Oscillations

High Voltage Direct Current Transmission (HVDC) systems are called to play an important role in modern electric power systems. Among the many aspects of HVDC currently under active research, this paper presents a proposal to design supplementary controllers in multi-terminal HVDC systems based on Voltage Source Converters (VSC-MTDC, for short) to damp electromechanical oscillations (Power Oscillation Damping or POD). In the proposed POD controllers (PODC), each VSC station compares the average of the frequencies measured at the AC connection points of the VSC stations of the MTDC system (frequency set point) with its own AC output frequency. This difference is then used to manipulate the active- (P) and reactive-power (Q) injections of each one of the VSC stations. The proposed PODCs are designed systematically by using a coordinated-design method using the concept of eigenvalue sensitivity, in order to achieve the required damping ratio of a set of electromechanical modes of interest in the power system where the VSC-MTDC is connected. The proposed designed methodology has been tested in the Cigré Nordic32A system with an embedded VSC-MTDC system. Results show that the proposed PODCs are effective damping successfully the electromechanical modes of interest and they are robust against communication latencies.

Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

A discrete framework to calculate eigenvalue sensitivity gradients to geometrical changes is introduced and applied to the compressible Navier-Stokes equations. The novel formulation is used to control global instabilities in compressible turbulent flow scenarios, modeled through Reynolds-averaged Navier-Stokes approaches. The sensitivity gradients are exploited to include local surface deformations that delay or enhance the onset of instabilities and can modify their associated frequency.

Observer-based multi-objective parametric design for spacecraft with super flexible netted antennas

A multi-objective parametric design method that based on therobust observer is proposed for the attitude control of satellites withsuper flexible netted antennas. First, a parametric observer-based controller is obtained based on the eigen-structure assignment theory. The closed-loop poles are assigned to desiredpositions or regions, and full degrees of freedom of the design, which are characterized by a set of parameters, are preserved under the proposed control law. Second, the obtainedparameters are comprehensively optimized to make the closed-loop system havelower eigenvalue sensitivity, a smaller control gain, and stronger toleranceto high-order unmodeled dynamics and external disturbances. Finally,comparative simulations are carried out based on practical engineeringparameters of a satellite in order to verify the effect of the proposed method, andalso to show their superiority over the traditional proportional-integral-derivative (PID) controller with filters and thetraditional dynamic compensators.

Small-Signal Modeling and Analysis of DC-Link Dynamics in Type-IV Wind Turbine System

It has been found in existing research works that the dc-link dynamics are significant internal dynamics in the type-IV wind turbine system, which can shape system characteristics and influence system stability. If dc-link dynamics are weakly damped, this dynamic behavior may reduce system damping and worsen system stability. Considering that dc-link dynamics are determined by the interaction effects of controllers and different control structures can be adopted to regulate dc-link voltage in the type-IV wind turbine system, analytical models are needed to accurately evaluate and analyze dc-link dynamics under different control structures, which are lacked in existing publications. In this article, the mechanism of dc-link dynamics in the system is described at first. A single-in-single-out indicator function is proposed to model the dc-link dynamics, based on which a linearized state-space model of dc-link dynamics is obtained. Then, the eigenvalue sensitivity matrix is applied to determine the influencing factors of dc-link dynamics and possible causes of weakly damped dc-link dynamics. DC-link dynamics under different control structures are compared. The influenced system characteristics can also be modeled by the proposed model of dc-link dynamics and the system stability with weakly damped dc-link dynamics is also investigated with experiments based on control-hardware-in-loop platform.

Robust Adaptive Identification of Linear Time-Varying Systems Under Relaxed Excitation Conditions

An on-line modified least-squares identification algorithm is proposed for linear time-varying systems with bounded disturbances under relaxed excitation conditions. An extra term which enhances the tracking ability for time-varying parameters is added to the covariance’s update law. An indicator of the regressor’s excitation level based on the maximum eigenvalue of the covariance matrix is developed. By combining the maximum eigenvalue with its variation trend shown by the sensitivity of the maximum eigenvalue to change in the covariance matrix, a novel identification law, which is switched between a modified least-squares algorithm and a gradient algorithm based on fixed $\sigma $ -modification, is proposed. The boundedness of the estimation error and the covariance matrix are guaranteed via Lyapunov stability theory. The superiority of the proposed method is verified by simulations.