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Two different methods of analysis were developed in order to clarify the phenomenon of paper flutter. One of these is a flutter simulation using a Navier–Stokes code (N–S simulation). N–S simulation was used to determine the unsteady lift force, the amplitude of flutter, and the air-flow around a paper sheet, by means of a time-marching scheme. The other form of analysis is based on a potential-flow analysis of an oscillating thin airfoil via an eigenvalue analysis for determining stability. The flutter speeds and flutter modes obtained by each method are consistent. Aspects of the behavior of paper flutter that had not been clarified in the experimental analysis were clarified by potential flow analysis. From the results of this study, it was shown that potential flow analysis is very convenient and adequate for a parametric study of this problem.

Winding is a paper finishing process, in which the full paper web is longitudinally cut and wound in narrower paper rolls to fit later to printing machines. The quality of the paper roll is measured in terms of uniform roundness and axially symmetric internal stress and stiffness distribution. Unfortunately dynamic effects disturb winding process so that out-of-roundness shape error profiles may accumulate to the rolls. The reason for this phenomenon is mechanical oscillation, in which the set of rolls and the three winding drums are in relative motion in normal direction of their rolling contact plane. The time evolution of this process is extremely complicated since the roll size as well as contact conditions and running frequencies are changing during the complete process. To avoid unwanted resonance crossings the system eigenstates have to be as first step analyzed and compared with the roll speed harmonics at each roll diameter. This analysis is carried out using linearized spring-mass model, whose parameters are updated according to the roll growth. The spring elements represent the local stiffnesses of roll-drum contacts in both normal and tangential directions, the effect of latter ones being actually a novel element introduced in this analysis.

With brake squeal being the most prevalent noise vibration and harshness issue in modern vehicles, this paper presents an improved methodology for brake squeal propensity prediction at the design stage. The research established four clearly defined ‘Stages’ in conducting finite element squeal analyses, describing crucial input data, modelling procedures, output and validation results. Stage 1 deals with free-free modal characteristics of individual brake components and their material characteristics. Stage 2 combines individual parts, conducting brake assembly mechanical finite element analyses. Stage 3 concentrates on fully coupled thermo-mechanical finite element analyses, and the concluding stage, Stage 4, focuses on brake assembly stability analyses. Validations proved that very accurate predictions are possible, but the geometries, material characteristics and established modelling procedures must be strictly followed. Material characteristics were most prone to introduce discrepancies with measured values. ‘Generic’ values are found to be unacceptable and conducting own measurements was necessary, in particular for the friction material, whose anisotropic properties have been measured in detail, leading to high accuracy in predicting pad natural modes and frequencies. In Stage 4, the stability analyses of the full brake assembly were based on the complex eigenvalue analysis (which included thermal aspects), with the sign of the real part giving an indication of stability and the imaginary part defining the frequency of the unstable mode. Instabilities and frequencies predicted match well with the values measured in dynamometer tests, clearly demonstrating the influence of thermal effects. The final output of the procedures described in this paper is a validated three dimensional thermo-mechanical finite element noise vibration and harshness brake assembly model in which natural frequencies and modes, instabilities and contributing factors can be predicted at any time during a brake application.

This paper describes the Littauer Multivariate Statistical Package (MUSP). MUSP consists of a package of statistical subroutines for performing correlation, regression, discriminant analysis and factor analysis. Non-symmetric eigenvalue analysis, tetrachoric correlation, partial correlation, canonical correlation, and missing observation analysis may also be performed. The major statistical subroutines are listed below for purposes of reference and indeed form the principle substantive contribution of this paper. However, there are also a number of novel features in the MUSP control language. This paper will attempt to show how the MUSP subroutines are embedded in the control system.

Subsynchronous Oscillation problems caused by HVDC system are studied and analyzed intensively in this paper based on eigenvalue analysis method. By establishing the small signal linearized model of a typical HVDC system, subsynchronous oscillation characteristics of the system with or without SSDC are obtained. Further more, the influence of SSDC parameters to the system subsynchronous oscillation characteristic can be illustrated clearly. This is significant for SSDC design in order to achieve a satisfied restraining effect. Comparing with more accurate electromagnetic transient simulation results, the consistency of the two methods is verified and it can be demonstrated that eigenvalue analysis method is adequate for studying subsynchronous oscillations.

Purpose The extensive increase in power demand has challenged the ability of power systems to deal with small-signal oscillations such as inter-area oscillations, which occur under unseen operating conditions. A wide-area measurement system with a phasor measurement unit (PMU) in the power network enhances the observability of the power grid under a wide range of operating conditions. This paper aims to propose a wide-area power system stabilizer (WAPSS) based on Gaussian quantum particle swarm optimization (GQPSO) using the wide-area signals from a PMU to handle the inter-area oscillations in the system with a higher degree of controllability. Design/methodology/approach In the design of the wide-area stabilizer, a dead band is introduced to mitigate the influence of ambient signal frequency fluctuations. The location and the input signal of the wide-area stabilizer are selected using the participation factor and controllability index calculations. An improved particle swarm optimization (PSO) technique, namely, GQPSO, is used to optimize the variables of the WAPSS to move the unstable inter-area modes to a stable region in the s-plane, thereby improving the overall system stability. Findings The proposed GQPSO-based WAPSS is compared with the PSO-based WAPSS, genetic algorithm-based WAPSS and power system stabilizer. Eigenvalue analysis, time-domain simulation responses and performance index analysis are used to assess performance. The various evaluation techniques show that GQPSO WAPSS has a consistently good performance, with a higher damping ratio, faster convergence with fewer oscillations and a minimum error in the performance index analysis, indicating a more stable system with effective oscillation damping. Originality/value This paper proposes an optimally tuned design for the WAPSS with a wide-area input along with a dead-band structure for damping the inter-area oscillations. Tie line power is used as the input to the WAPSS and optimal tuning of the WAPSS is performed using an improved PSO algorithm, known as Gaussian quantum PSO.

This paper presents the Cross-Border activation of the Regulating Reserve (CBRR) between participating Control Areas (CAs), which is being developed to reduce the costs of balancing energy. The main objective of the CBRR is to activate the regulating reserve in participating CAs, to release the regulating reserve and to reduce the balancing energy as part of the safe operation of the power system. However, the classic CBRR includes a frequency term and, therefore, inherently affects the frequency response of the participating CAs, which is not discussed in the literature. In this paper, the impact of the classic CBRR on frequency quality and the provision of Load-Frequency Control (LFC) is thoroughly evaluated with dynamic simulations of a three-CA test system and an eigenvalue analysis of a two-CA system. It is clearly demonstrated that the classic CBRR reduces the damping of the entire power system. Therefore, a modified implementation of the classic CBRR is presented, and a modified CBRR is proposed, which has no impact on the system's eigendynamics. Furthermore, the results of the dynamic simulations confirm that the frequency quality can be improved by the classic CBRR, although there are also cases where it can deteriorate. However, the modified CBRR improves the frequency quality in all cases. The modified CBRR also improves the indicators for the provision of LFC compared to the classic CBRR. Moreover, the modified CBRR reduces the unintended exchange of energy and the demand power, thus increasing the financial effects of the CBRR's activation.

Fluidelastic instability is a key issue in steam generator tube arrays subjected in two-phase flow. Lots of experimental analyses were conducted on fluidelastic instability of a tube array subjected to air-water cross-flow. However, there is seldom theoretical analysis to calculate the critical velocity. Therefore, considering the effect of two-phase flow, the fluidelastic instability of a rotated triangular tube array was studied in this paper. A mathematical model of a tube array with unsteady fluid force model was set up. A program based on the model was written, and an experiment was carried out to verify the correctness of the program. The results of this program were in good agreement with the experimental data. Using this program, the critical velocity of fluid-elastic instability considering the effect of two-phase flow was determined by the eigenvalue analysis. This paper investigated the critical velocities of fluid-elastic instability for void fraction ranging from 0% to 90% with five tube natural frequencies, respectively. The results show that void fraction and tube natural frequency are the key factors in fluidelastic instability, which have an obvious effect on the critical velocity of fluidelastic instability.

In this paper, an advanced non-dimensional dynamic influence function method (NDIF method) for eigenvalue analysis of arbitrarily shaped two-dimensional acoustic cavities with the mixed boundary consisting of the pressure-release and rigid-wall boundaries is proposed. The existing NDIF method has the weakness of having to calculate the singularity of the final system matrix of an analyzed acoustic cavity in the frequency band of interest to obtain the eigenvalues of the cavity because the final system matrix is dependent on the frequency. The newly proposed NDIF method in this paper provides an efficient way to extract accurate eigenvalues and eigenmodes by successfully overcoming the above weaknesses. Finally, the validity and accuracy of the proposed method are shown through verification examples.

New energy sources, storage facilities, power electronics devices, advanced and complex control concepts, economic operating doctrines, and cost-optimized construction and production of machines and equipment in power systems adversely affect small-signal stability associated with local oscillations. The objective of the article is to analyze local oscillations and the causes that affect them in order to reduce their negative impact. There are no recognized analyses of the oscillations of modern operating synchronous generators exposed to new conditions in power systems. The basic idea is to perform a numerical analysis of local oscillations of a large number of synchronous generators in the power system. The paper represents the local mode data obtained from a systematic analysis of synchronous generators in the Slovenian power system. Analyzed were 74 synchronous generators of the Slovenian power system, plus many additional synchronous generators for which data were accessible in references. The mathematical models convenient for the study of local oscillations are described first in the paper. Next, the influences of transmission lines, size of the synchronous generators, operating conditions, and control systems were investigated. The paper’s merit is the applicable rules that have been defined to help power plant operators avoid stability-problematic situations. Consequently, boundaries were estimated of the eigenvalues of local modes. Finally, experiments were performed with a laboratory-size synchronous generator to assess the regularity of the numerically obtained conclusions. The obtained results enable the prediction of local oscillations’ frequencies and dampings and will be useful in PSS planning.

This paper presents a theoretical study of damping, synchronizing and inertial control laws, implemented using controllable power injection devices like HVDC, FACTS or renewable-energy/storage systems which have power-electronic grid interfaces. The approach is to use a simplified dynamical model of a power system to arrive at generalized results regarding the effect of the strategies on the electro-mechanical dynamics of the system. These results are not dependent on the size, network topology and operating condition of the power system. This paper presents a differential-algebraic formulation and generalized eigenvalue analysis to facilitate a unified study of the effects of the control laws on the electro-mechanical modes. The damping, synchronizing and inertial control laws can themselves be extended to include the possibility of mutual-damping, synchronizing and inertial effects when multiple devices are present. The control laws are not only simple and intuitive, but also are found to have a predictable and generally beneficial impact on the electro-mechanical dynamics of the grid, even when detailed models are considered.

Brake insulators often offer optimal solutions to squeal noise. In the process of engineering solutions to reduce the brake noise, a system-level finite element complex eigenvalue analysis is often used and has gained popularity in recent years. Models of insulators have also been proposed for system-level evaluation, however many challenges remain in efficiently implementing an insulator model, owing to complexities of the insulator component model. The complexities arise from the visco-elastic behavior (primarily the frequency and temperature dependence), and the thin polymer/steel multi-layer nature of the construction - typical in an insulator. As a first part of a joint investigation, this paper explores the nature of frequency and temperature dependence in insulator models and reduces the cumbersome multi-layer model into a simpler form that can be more easily implemented in a typical brake system stability analysis. Using optimization, the original multi-layer, multifrequency and multi-temperature set of models is reduced to an equivalent set of single-layer, (relatively) frequency-independent models. It is argued that this type of insulator model can be more easily extended to capture the multiple mechanisms involved, allowing the system-level stability analysis to more fully account for the effects of insulator damping. The proposed insulator model is verified through modal testing, during which it is observed that a pad-with-insulator model necessitates inclusion of the damping contributed by the brake pad assembly, particularly if an under-layer exists. A later paper will discuss the results from the full brake system stability analysis.

This paper presents the advanced control theory&rsquo, s original utilisation to realise a system that controls the fermentation process in batch bioreactors. Proper fermentation control is essential for quality fermentation products and the economical operation of bioreactors. Batch bioreactors are very popular due to their simple construction. However, this simplicity presents limitations in implementing control systems that would ensure a controlled fermentation process. Batch bioreactors do not allow the inflow/outflow of substances during operation. Therefore, we have developed a control system based on a stirrer drive instead of material flow. The newly developed control system ensures tracking of the fermentation product time course to the reference trajectory by changing the stirrer&rsquo, s speed. Firstly, the paper presents the derivation of the enhanced mathematical model suitable for developing a control system. A linearisation and eigenvalue analysis of this model were made. Due to the time-consuming determination of the fermentation model and the variation of the controlled plant during operation, the use of adaptive control is advantageous. Secondly, a comparison of different adaptive approaches was made. The model reference adaptive control was selected on this basis. The control theory is presented, and the control realisation described. Experimental results obtained with the laboratory batch bioreactor confirm the advantages of the proposed adaptive approach compared to the conventional PI-control.

This paper presents computation of swing modes of a large power system that could be significantly affected by power swing damping controllers in FACTS or HVDC devices at a given location. Modal controllability is a suitable measure to isolate these modes for analysis. Computation of the controllable swing mode spectrum is useful, especially in situations where the controller structure and feedback signals are not frozen (e.g., at the planning stage). This paper proposes two important steps that allow us to map the problem of finding highly controllable swing modes to the problem of finding the swing modes that have high transfer function residues (for which efficient algorithms are available). The steps are: (a) normalization of the eigenvectors corresponding to different modes and (b) identification of specific feedback signals for each type of FACTS/HVDC device such that the modal observability and modal controllability are tightly coupled. Once the mapping is done, a computationally efficient method like the Subspace Accelerated Dominant Pole Algorithm [16] (SADPA) can be adapted to find the highly controllable swing modes. The effectiveness of this approach is demonstrated by case studies of FACTS and HVDC devices in a 16-machine system and the Indian power grid.

Summary form only given: In this paper, it is shown that analyzing the subsynchronous oscillation (SSO) damping effectiveness of an induction machine damping unit (IMDU) only based on its torque-slip characteristic curve is not adequate. A method to directly calculate the electrical damping of an IMDU according to its parameters, which is fast and accurate, is developed. This direct calculation method makes it possible to carry out parameter optimization of the IMDU by genetic algorithms. This paper also demonstrates that the electrical damping of IMDU in the subsynchronous frequency range can be significantly increased by raising its rated frequency. In addition, the voltage-source inverter used to drive the IMDU and raise the frequency can provide a constant magnitude terminal voltage for the IMDU during disturbances. The SSO damping effectiveness of the IMDU after parameter optimization and frequency raise is verified by eigenvalue analysis, electrical damping analysis and time-domain simulation.

The present study investigates the effect of multiple dynamic absorbers on chatter generated in the end milling operations by performing stability analysis and a cutting test. The dynamic absorbers proposed in the present paper are attached to a collet chuck in order to suppress tool chatter caused by the bending vibration of the tool and spindle system. The dynamic milling model is considered to have two orthogonal degrees of freedom. The dynamic absorbers, which have identical mass, damping ratio, and natural frequency, are assumed to have a single degree of freedom that rotates with a tool and spindle system. In the present paper, stability analyses are performed by means of complex eigenvalue analysis for each angular immersion of the cutting edge in order to investigate the effect of the dynamic absorbers on the stability of the dynamic milling model. The optimal natural frequency and damping ratio of the dynamic absorbers to maximize the chatter-free axial depth of cut are shown to vary with spindle speed. Furthermore, the effect of the dynamic absorbers on chatter is validated by a cutting test, and the experimental results are confirmed to agree qualitatively with the analytical results.

In this paper a novel supplementary subsynchronous damping controller (SSDC) is proposed for the STATic synchronous COMpensator (STATCOM) which is capable of damping out subsynchronous oscillations in power system with series compensated transmission lines. An auxiliary subsynchronous damping controller (SSDC) for a STATCOM using the generator rotor speed deviation signal as the stabilizing signal has been designed to damp subsynchronous oscillations. Eigenvalue analysis and transient simulations of detailed nonlinear system are considered to investigate the performance of the controller. Robustness of the controller has been analyzed by facing the system with disturbances leading to significant changes in generator operating point. This paper deals with a cascaded multilevel converter model, which is a 48-pulse (three levels) source converter. The IEEE Second Benchmark (SBM) model is considered for the analysis and the complete digital simulation of the STATCOM within the power system is performed in the MATLAB/Simulink environment.

This paper presents stability a study on multi-machine power system is equipped with PSS based on global signal as a control signal. Filters in PSS structure is designed based on frequency response, whereas the lead-lag parameters optimized by PSO. The performance of design proposed tested on 3-Machine 4-Bus power system that disturb with load increasing. The eigenvalue and participation factor analysis results show that system with PSS based on coordination between local and global signal have a performance such us damping ratio, settling time and overshoot are better than system with PSS based on local signal only. Keywords : Multi-machine, PSS, global signal, PSO, eigenvalue analysis, participation factor, stability. Abstrak —Paper ini menyajikan studi stabilitas pada sistem tenaga multimesin yang dilengkapi dengan PSS berbasis sinyal global sebagai sinyal kendali. Filter dalam struktur PSS dirancang berdasarkan tanggapan frekuensinya, sedangkan parameter lead-lag dioptimisasi dengan PSO. Unjuk kerja dari rancangan ini diuji pada test system 3-Mesin 4-Bus yang diganggu dengan kenaikan beban. Hasil analisis eigenvalue , participation factor dan simulasi domain waktu menunjukkan bahwa sistem dengan PSS berbasis koordinasi antara sinyal lokal dan sinyal global memiliki unjuk kerja berupa rasio redaman, settling time dan overshoot yang lebih baik dari PSS berbasis sinyal lokal saja. Kata Kunci : Multimesin, PSS, sinyal global, PSO, analisis eigenvalue, participation factor, stabilitas.

This paper proposes a method for PSS parameter tuning. The proposed method is based on the system identification using a Kalman filter. To eliminate the influence of inaccuracies of the mathematical model due to incomplete data of the system parameters, this paper proposes a procedure for identifying system parameters based on a Kalman filter. The identified system is the basis for determining the eigenvalue sensitivity function. PSS tuning is carried out based on the eigenvalue sensitivity analysis of changes of PSS parameters. In order to obtain the eigenvalue sensitivity function on the PSS parameter in a wider range of parameter values, it has been proposed to determine eigenvalues on the basis of the Bairstow method for solving polynomial equations. The entire procedure can be applied on-line, so the PSS structure and settings can be adaptive. Experimental tests carried out on a synchronous generator connected to an AC system demonstrate the effectiveness of the proposed method. Performance of the PSS tuned by using the proposed method was compared with the performance of the PSS tuned by using eigenvalue sensitivity.

Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr's circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjugacy property of the moment of inertia vectors. A new general expression is derived which specifies the principal directions of inertia, as well as the directions of the maximum and minimum product of inertia. A comparative study of the five presented approaches is given, which is of interest from both conceptual and methodological points of view. The con- nection between the deviatoric part of the moment of inertia tensor and Land's circle of inertia is also given. The presented analysis applies to any two-by-two symmetric second order tensor. The determination of the principal moments of inertia of a plane area and their principal directions is of great importance in the mechanics of rigid and deformable bodies, as evidenced by its detailed coverage in every undergraduate textbook on these subjects. The three commonly used methods to accomplish this are based on: (i) the condition of stationary axial moment of inertia about an arbitrary axis, (ii) the eigenvalue analysis of the moment of inertia tensor, and (iii) Mohr's circle. The objective of this paper is to present two additional deriva- tions, which have not been reported in the literature before. The first is based on the matrix diagonalization of the moment of inertia tensor and its invariant tensor properties, and the second on the conjugacy property of the moment of inertia vectors. These methods also apply to an analogous determination of the principal stresses and their directions in two dimensional continuum mechanics problems (or any other two-by-two symmetric second order tensor), with the main difference that the moment of inertia tensor is a positive definite tensor, while the stress tensor is not necessarily so. In Sect. 2 we diagonalize the moment of inertia tensor and use its invariant tensor properties to derive the expressions for the principal moments of inertia, and the expressions for the tangens of the angle that specifies each principal direction separately. The well-known derivation based on the eigenvalue analysis is included for comparison. In Sect. 3 we introduce the conjugacy property of the moment of inertia vectors, previously not explored in the literature in the context of moments of inertia, but well-known in the context of stress

Leakage flelds are one of the main issues in design of electromagnetic systems. Some of these flelds close their paths through the core and air, giving rise to non-ideal behavior of the magnetic systems. This paper explains a novel concept of active shielding which consists of two compensation coils in series and generates a counter fleld opposite to the leakage flelds leaking from an iron-core system. As the method is based on physical reasoning of electromagnetic coupled circuit theory, the design criterions for the compensating coils parameters, their number of turns and their adaptation to the systems, were considered. The state of the art is presented by a model which is verifled by roots of system characteristic equations, using state equations. In a case study, this method was investigated in a 25kA (125kVA) current injection transformer (CIT) system delivering a secondary current as closely proportioned to the primary current as possible, using flnite element method (FEM) simulation. This paper will also push the state of the art by reducing the age efiect of the CIT through mechanical force reduction.

Vibration modes of an extremely thin rotating circular membrane subjected to transverse distributed load are investigated. In the previous paper, the author proposed an analytical method to obtain equilibrium states with large transverse deformations employing the von Karman theory and taking account of buckling under the assumptions of rotationally symmetric deformations. In this paper, transverse vibration equation around the equilibrium state under transverse load is derived and modal equation is formulated. The equation is numerically solved and modal frequencies and modal shapes are obtained. Typical vibration modes are illustrated. In order to confirm the validity of the analysis, eigenvalue analysis of a spring-mass system model for the membrane are performed to obtain vibration modes. A fairly good agreement is found between the theoretical and numerical results. Experiments of thin rotating circular membranes under gravity in vacuum are also conducted and transverse vibration frequencies are measured for a variety of rotation speed and air pressure. Analytical results are compared with the experimental results to verify the validity of the present analysis.

The search for tools and techniques aimed at model analysis has gained momentum in the system dynamics community during the last decade. A variety of approaches have been developed, modified and applied to replace or enhance the traditional intuitive-based schemes for understanding the behavior of dynamic models according to their feedback structure. In spite of the diversity of the methods developed for model analysis, recent studies suggest that there is considerable convergence in the results they produce. This paper explores the metrics used by the pathway participation approach and eigenvalue elasticity analysis in order to explain how, despite the significant differences in the process of model analysis, they can produce similar and comparable results. The paper discusses the application of pathway participation metrics in four well-known models that have been previously analyzed using the eigenvalue elasticity method. The case studies highlight some of the similarities and differences between the two approaches in detecting the dominant structure. Copyright © 2009 John Wiley & Sons, Ltd.

In the past, wear at the pad interface of disc brakes has rarely been accounted for in studies of brake squeal using the finite element method, and its effect on disc brake squeal has been investigated largely through experimental methods. In the present paper, wear taking place at this interface over time is simulated using a modified wear rate formula. The surface topographies of two new and unworn pairs of brake pads are measured. The same brake pads are tested under braking applications of three time durations. For each braking application, the static contact pressure distribution is measured using pressure-indicating film. The results are used to compare with the simulated results predicted by the three-dimensional finite element model of a real disc brake. The paper also investigates squeal generation due to the above braking applications using complex eigenvalue analysis that is available in a commercial software package. It is found that the predicted unstable frequency is very close to the observed squeal frequency and that they take place in the same braking duration.

In Vibro-Acoustic System, [I] complex eigenvalue analysis and [II] CMS (unconstrained mode, without residual) are widely used for eigenvalue analysis. The method [I] needs huge computer resources, but it can obtain the exact eigen value and vector. In the opposite, the method [II] needs fewer resources, but accuracy of eigen-vector is not acceptable in some cases. To improve the accuracy, [III] CMS (unconstrained mode, with residual) can be used. But the method [III] deteriorates the advantage of the method [II], because physical degrees need to be remained in the equation of motion. In this paper, [IV] novel CMS method, based on unconstrained mode and residual mode, is proposed. The required computer resource is less than the methods [III], because the equation of motion is described on the modal coordinates. And the accuracy is better than the method [II]. In this paper, applying the methods [I] [II] and the proposed method [IV] to finite element models, it is shown that the proposed method is one of the effective methods for the eigenvalue analysis of Vibro-Acoustic System.

In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is reduced to eigenvalue analysis of $\eta$-Hermitian adjacency matrices. First, we investigate coefficients of the characteristic polynomials of $\eta$-Hermitian adjacency matrices. We show that the characteristic polynomials of mixed trees and their underlying graphs are same. We also define $n+1$ types of mixed cycles and show that every mixed cycle is switching equivalent to one of them. We use these results to discuss periodicity. We show that the mixed paths are periodic for any $\eta$. In addition, we provide a necessary and sufficient condition for a mixed cycle to be periodic and determine their periods., Comment: 22 pages, 12 figures

This paper represents validation of yaw plane and yaw-roll models of a tractor/semitrailer combination with TruckSim software package. A linear 3 degree-of-freedom (DOF) yaw-plane model and a linear 5 DOF yaw-roll model of tractor/semitrailer have been generated, compared and evaluated. This paper investigates the applicability of vehicle models with linear tire model. The models of the articulated heavy vehicle (AHV) yield excellent simulation results which are validated by comparing the simulation results obtained from TruckSim. This paper also includes eigenvalue analysis of the models to estimate their unstable motion modes. Benchmark comparison of the models has been performed to investigate the fidelity, complexity and applicability.

A new way to reduce the eigenvalue computation effort in structural dynamics is presented in this paper. The degrees of freedom of a structure may be classified into groups that are termed as sub-degrees of freedom. The eigenvalue analysis is performed with each of sub-degrees of freedom so that the computing time is much shortened. Since the dynamic coupling between sub-degrees of freedom is selected to be small and it may be considered as a perturbation, the perturbation algorithm is used to obtain an accuratae result. The accuracy of perturbation depends on the coupling between sub-degrees of freedom. The weaker the coupling is, the more accurate the result is. The procedure can be used to simplify a problem of three dimensions to that of two dimensions or from two dimensions to one dimension. The application to a truss and a space frame is shown in the paper.

The structural-acoustic coupling vibration problem is very important for the quality control of vehicles and there have already been many studies on this subject. However, as far as we know, no-one has yet considered the physical meaning of the coupling strength. In this paper, we adopt the operator theoretical matrix formulation of the problem and to clarify the meaning of the coupling strength, we introduce a coupling strength parameter e as a multiplier in front of the non-diagonal coupling terms. We show its adequacy through numerical examples. We use a perturbation series with respect to e which enables us to express the eigen-pairs for the coupled case by those for the decoupled case. The results of this paper suggest that it would not be necessary to perform time consuming coupling eigenvalue analysis, and hence have a great engineering importance.

With the integration of large-scale wind farm of direct-driven permanent magnet synchronous generator (PMSG) type into power systems, the impacts on the existing power system have to be evaluated elaborately and systematically. This paper will discuss the impact of grid-connected wind farm of PMSG type on power system small signal stability. First, a simplified practical model of wind farm of PMSG type is derived for analyzing small signal stability in this paper. The rotor-flux-oriented control strategy is applied in the modelling of PMSG. Second, the simulation scenario involving replacing synchronous generator with wind farm of PMSG type based on the IEEE 3-generator-9-bus test system as benchmark is carried out to conduct the eigenvalue analysis and to assess the effect of wind farm of PMSG type on power system small signal stability. Finally, some preliminary conclusions and comments are drawn according to the simulation results.

Low-frequency inter-area oscillations are threat to secure operation of power systems. Power system stabilizer and Power oscillation damping controllers are used to provide damping to oscillatory modes. Such oscillatory modes, inter-area modes in particular, are significantly affected by change in operating conditions and load characteristics. In this paper, influence of load characteristics on performance of two distinct power oscillation damping controllers is being examined. The interaction between load characteristic and performance of power oscillation damping controller is explored in terms of damping contribution by individual controller on inter-area mode. Eigenvalue analysis approach is used to evaluate the performance of power oscillation controllers, which are designed based on residue compensation technique and H ∞ loop-shaping technique respectively. This paper also addresses the dynamic behaviour of the two controllers under different operating conditions and load characteristics.

In order to treat the diseases caused by hepatitis C virus (HCV) more efficiently, the concentration of HCV in blood, cells, tissues and the body has attracted widespread attention from related scholars. This paper studies a dynamic dependent HCV model (more specifically, including age structure and treatment methods model) that concludes states of infection-free and infected equilibrium. Through eigenvalue analysis and Volterra integral formula, it proves that $ E_0 $ is globally asymptotically stable when $ \mathcal{R} < 1 $. After explaining the existence, uniqueness and positive properties of the solution of the system, we have proved the global asymptotic stability of $ E^* $ when $ \mathcal{R} > 1 $ by constructing a suitable Lyapunov function. Through the above proofs, it can be concluded that effective treatment measures can significantly reduce the number of HCVs, so many related researchers are aware of the importance of highly efficient nursing methods and are committed to applying relevant methods to practice.

This paper presents the results of a small-signal stability study conducted on a large power system. The tools and techniques applied have been reported in previous work. The novelty of this paper and study is that these tools and techniques are being applied here to a system that is at least an order of magnitude larger than the systems previously studied. As a result this study presents an interesting learning opportunity.

This paper provides an H∞ robust control strategy for a permanent magnet synchronous generator (PMSG)-based wind farm to realize subsynchronous resonance suppression (SSR) subject to uncertain system distortions and parameter perturbation. Firstly, an eighth-order state space mathematical model of a PMSG-based wind farm is established, including the grid-side converter (GSC), GSC controller, and phase-locked loop (PLL) model. Secondly, the SSR characteristics of a PMSG-based wind farm are analyzed through eigenvalue analysis. Thirdly, a robust subsynchronous damping controller is designed based on eigenvalue analysis of SSR. Finally, the designed robust subsynchronous damping controller is validated with case studies of wind farms. The results show that the controller can increase the stability of PMSG-based wind farm systems and restrain SSR.

In this paper, a near-optimal and robust SEDC (supplemental excitation damping control) has been developed for damping SSR (subsynchronous resonance) in Shangdu power plant in China . This paper first gives a brief analysis of the multi-mode SSR in Shangdu system, and then provides the configuration of SEDC to provide damping for all SSR modes. The primary contribution of this paper lies in the presented method GASA, in which GA (genetic algorithm) and SA (simulated annealing) are combined to solve the SEDC optimal parameter-searching problem. The details of this approach are presented, and the performance of the SEDC obtained by GASA is verified with the Shangdu system through eigenvalue analysis and electromagnetic simulations.

This paper studies influence of control system dynamics on the small-signal stability of modular multilevel converter (MMC) based multi-terminal DC (MTDC) transmission system. The small signal model is derived based on the state–space model of an MMC-based MTDC. Eigenvalue analysis and participation factor analysis are applied to study the inherent oscillatory modes of MMC-based MTDC transmission systems. The impacts of control system parameters on small-signal stability of the system are investigated through sensitivity analysis. The study shows that the control systems strongly affected the small signal stability of the MMC-based MTDC and the d-axis proportional gains in d–q decoupling main controllers have great impact on system stability, which needs to be properly selected for stability enhancement.

Homogeneous eigenvalue analysis is a useful tool for analysis of homogeneous systems. We obtained necessary conditions for asymptotic stability in our previous paper. However, any sufficient conditions are not obtained. In this paper, we introduce Euler sphere, and analyze the properties of solutions of homogeneous systems using dilations of Euler sphere. Moreover, we show the equivalence between a trajectory of a projection of a solution and a trajectory of a solution of a projection system. Then, we prove sufficient conditions for asymptotic stability of homogeneous systems. Finally, we demonstrate the effectiveness of the proposed method for a system which has an uncontrollable linear approximation.

Eigenvalues of a power system can explain the system stability in its operating point. In this paper the linear analysis capabilities of two software packages are evaluated and compared. The paper also illustrates the impact of the models of the power system components (like generators) on the location of the eigenvalues. Eigenvalue analysis are not only dependent on the properties of the investigated system, but also on the software package which is used, as well as on how the components of the power system are modeled. Therefore, conclusions can differ when studying the same power system with different software packages.

Fluidelastic instability of a tube array is extremely important to the security of a nuclear power plant. Lots of experimental analyses were conducted on the fluidelastic instability of a tube array subjected to two-phase flow in the transverse direction. Streamwise fluid-elastic instability of a tube array has been ignored for a long time until recently observations of streamwise tube failure in a steam generator in the USA. However, there are a few theoretical analysis to calculate the critical velocity. Therefore, the streamwise fluidelastic instability of a rotated triangular tube array was studied in this paper. A mathematical model of a tube array with seven tubes was established. A program based on the model was written, and an experiment was conducted to verify the program. The numerical results were in good agreement with the experimental data. The critical velocity of streamwise fluidelastic instability considering the two-phase flow was determined by the eigenvalue analysis. The numerical results illustrate that void fraction has an obvious effect on the critical velocity and the instability mode of the streamwise fluidelastic instability of a tube array. The influences of tube natural frequency were also investigated within void fraction range from 0 to 80%. The results indicate that void fraction and tube natural frequency are the key factors in streamwise fluidelastic instability.

The major purpose of this paper is to study the effects of load models on the power system stabilizers and static VAr compensators for the Taiwan power system low-frequency oscillation studies. Frequency domain is used to estimate the impact of load models on the system dynamic performance with and without power system stabilizers and static VAr compensators during a low-frequency oscillation incident in the Taiwan power system. Time domain simulation results are utilized to confirm the validity of the various eigenvalue analysis results. The study results are presented in this paper.

This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

This paper proposes a novel robust thyristor-controlled series compensator (TCSC) controller based on proportional integral derivative with filter (PIDF) and uses a new hybrid optimisation evolutionary programming sine cosine algorithm (EPSCA) to improve the power system’s angle stability. The problem of the PIDF-TCSC design is transformed into an optimisation problem based on performance indices, such as damping factor, damping ratio, and eigenvalues, where the multi-objective function is employed to obtain the optimal stabiliser parameters. To examine the robustness of PIDF-TCSC, it was tested on a single-machine infinite-bus power system under different operating conditions. The performance of the system with the PIDF-TCSC controller was compared with the simulation results, and the results obtained with the proposed EPSCA were compared with those obtained with SCA, moth flame optimisation, and EP-based PIDF-TCSC methods. Simulation results showed the effectiveness of EPSCA for the PIDF-TCSC design and the superior robust performance for the enhancement of power system stability compared with other techniques in different cases.

It is well know that the two-fluid single pressure model is currently widely used to analyze reactor transient accidents such as LOCA. Current mainstream reactor safety analysis codes such as RALAP5 and CATHARE are based on this single pressure model. However this model has been proved to be ill posed in the sense that the equation system is non-hyperbolic which will lead to numerical unphysical oscillation. Currently reactor safety analysis codes use the interfacial pressure and virtual mass force to solve the ill-posed non-hyperbolicity issue. The development of China’s self-owned reactor high fidelity system analysis code has attracted much attention in recent years, and studying on the ill-posedness of the two-fluid model and the improvement of the ill-posedness is an important basis to analyze these reactor accidents. In this paper, the ill-posedness regions of the two-fluid single pressure model is first investigated using the eigenvalue analysis method based on the Cauchy problem with initial conditions. Then the effect of the virtual mass force and the interfacial pressure is studied by this eigenvalue analysis method, and three types of virtual mass term in the momentum equation are discussed. The results show that the appropriate virtual mass force and interfacial pressure can well improve the ill-posedness of the single pressure model, and the appropriate combination of them can significantly improve the ill-posedness.

There are several techniques employed for analyzing the subsynchronous resonance (SSR) phenomena. Among the most common are frequency scanning analysis, eigenvalue analysis and time-domain simulations. This paper presents the implementation of a frequency scanning program based on the PSS/E power system software package. The tool is developed on Python and makes use of the PSS/E API.

This paper presents a generalized yet simple mapping rule for image point identification in 3D bounding surface plasticity (BSP) models. It is based on the determination of the correct loc...

This paper investigates the nonlinear dynamics of power systems affected by the dynamics of static VAr compensators (SVC). The study reveals that the variety of dynamics of a power system have a tight relationship with a particular bifurcation which could be greatly affected by the parameters of SVC. Furthermore, the result of eigenvalue analysis indicates that those parameters can also decide the occurrence of the bifurcations and change the loci of the bifurcation points. The paper especially emphasizes the potential threat of the boost limits of SVC to voltage stability. The study provides an insight into voltage instability mechanisms based on the dynamics of SVC. The conclusions of the paper are verified by time domain simulation.

In this paper, an extensive numerical study is performed with the aim to investigate the elastic buckling behavior of simply supported cylindrically curved steel panels subjected to a pure shear load. The main objective is to understand the influence of geometrical parameters, such as curvature and aspect ratio, but also of the edge in-plane constraints. Finally, a new formula is proposed, which allows simple and accurate estimation of the critical shear stress of unstiffened curved panels with three different types of edge constraints, for various curvatures (1

In recent years, a new type SSO issue, which has occurred in direct-drive permanent magnetic synchronous generators (PMSGs) based wind farm, brings a new challenge to the stability of the power system. In this paper, the SSO issue in grid-connected PMSGs system is studied by the eigenvalue analysis. The linearised state-space model of this system is built firstly. The impacts on the SSO characteristics from short-circuit ratio (SCR), impedance-frequency characteristic, resonant frequency of AC network and control parameters of PMSGs are observed by the root loci analysis. After that, electromagnetic transient simulation is carried out to verify the eigenvalue analysis. Meanwhile, the participation factors of SSO mode are calculated to analyse the subsynchronous control interaction (SSCI) between AC network and PMSG. The result shows that there is a SSO mode which is greatly influenced by AC network and DC capacitor, grid side converter (GSC) control of PMSG. The characteristics of AC network will affect the SSCI between AC network and PMSG.

the present paper investigates the effect of penetration of photovoltaic generation (PVGs)systems on the transient and small signal stability. Recently interest in photovoltaic (PV)power generation systems is increasing rapidly and the installation of large PV systems orlarge groups of PV systems that are interconnected with the power system grid is acceleratingdespite their high cost and low efficiency due to environmental issues and depletions of fossilfuels. Photovoltaic generators (PVGs) have significant impacts on the existing power systems,these impacts may be either positively or negatively depending on many factors such as PVGslocation, size and inverter characteristics. The eigenvalue analysis and the transient analysisof the system are done without any PVGs penetration and with PVGs penetration and then theresults are compared. The investigation is applied on IEEE-39 bus test system. The stabilityanalysis is carried out using simulation program of power system analysis tool box (PSAT). في ھذا البحث تم دراسة تأثير اضافة أنظمة توليد الطاقة الکھروضوئيةبسرعة ، وتسارع ترکيب أنظمة کھروضوئية (PV) والصغير. تزايد الاھتمام مؤخرا بنظم توليد الطاقة الکھروضوئيةکبيرة أو مجموعات کبيرة من الأنظمة الکھرو ضوئية المترابطة مع شبکة نظام الطاقة على الرغم من کلفتھا العاليةوانخفاض کفاءتھا بسبب المشکلات البيئية واستنزاف الطاقة و الوقود الحفري. المولدات الکھروضوئية لھا تأثيرات کبيرةعلى أنظمة الطاقة الحالية ، وقد تکون ھذه التأثيرات إما إيجابية أو سلبية اعتمادا ع لى العديد من العوامل مثل موقعوحجمھا وخصائصھا العاکسة. يتم تحليل القيمة الذاتية والتحليل العابر للنظام دون اضافة اي خلايا کھروضوئية PVGsوتم تنفيذ تحليل .IEEE- وکذلک مع اضافة خلايا کھروضوئية ثم تتم مقارنة النتائج. تم تطبيق الاختبارات علي شبکة 39.(PSAT) الاستقرار باستخدام برنامج محاکاة

The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reaction-diffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the production rate of the activator as the bifurcation parameter, we show the decisive effect of each part in the source term on the patterns and the evolutionary process among stripes, spots and mazes. Finally, it is illustrated that weakly linear coupling in the activator-inhibitor model can cause synchronous and anti-phase patterns.