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This paper proposes a novel hybrid algorithm combining chaotic Jaya (CJaya) and sequential quadratic programming (SQP), namely CJaya-SQP, for solving the coordinated design problem of static var compensator (SVC) and power system stabilizers (PSSs). The CJaya serves as a global optimizer and the SQP as a local optimizer for fine-tuning the solution. In the proposed algorithm, chaotic maps are used to generate the initial solutions and control the search process. In order to prove the performance of the CJaya-SQP, a set of benchmark optimization problems is used where the results are compared with those of the basic Jaya and other recognized algorithms. The proposed optimization method is then applied for the optimal tuning of PSSs and SVC controllers in such a way that damping ratios and damping factors of the electromechanical modes are optimally improved. To illustrate the robustness of the CJaya-SQP-based coordinated PSSs and SVC controllers, the four-machine, two-area system is used. Eigenvalue analysis and nonlinear time-domain simulation vividly show that the CJaya-SQP-based coordinated controllers improve greatly the system’s dynamic stability with a robust damping of local and inter-area power oscillations.

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.

The flight mechanics of rigid wing Airborne Wind Energy Systems (AWESs) is fundamentally different from the one of conventional aircrafts. The presence of the tether largely impacts the system dynamics, making the flying craft to experience forces which can be an order of magnitude larger than those experienced by conventional aircrafts. Moreover, an AWES needs to deal with a sustained yet unpredictable wind, and the ensuing requirements for flight maneuvers in order to achieve prescribed control and power production goals. A way to maximize energy capture while facing disturbances without requiring an excessive contribution from active control is that of suitably designing the AWES craft to feature good flight dynamics characteristics. In this study, a baseline circular flight path is considered, and a steady state condition is defined by modeling all fluctuating dynamic terms over the flight loop as disturbances. In-flight stability is studied by linearizing the equations of motion on this baseline trajectory. In populating a linearized dynamic model, analytical derivatives of external forces are computed by applying well-known aerodynamic theories, allowing for a fast formulation of the linearized problem and for a quantitative understanding of how design parameters influence stability. A complete eigenanalysis of an example tethered system is carried out, showing that a stable-by-design AWES can be obtained and how. With the help of the example, it is shown how conventional aircraft eigenmodes are modified for an AWES and new eigenmodes, typical of AWESs, are introduced and explained. The modeling approach presented in the paper sets the basis for a holistic design of AWES that will follow this work.

Power systems may encounter disturbances during operation as a result of switching of various components, etc. Such perturbations include transformer tap-changing action, load variations, and line outages due to various types of faults of which an earth fault is the most common. Stability analysis of a transmission system is necessary for us to determine the stability state of the system so that appropriate control measures can be implemented to guarantee system stability. This article presents the use of eigenvalue obtained from the system-linearized eigenvectors to analyze the stability state of the system. The choice of the eigenvalue principle is based on the strength of accuracy of the method to determine the actual state of the system providing adequate data for easy solution to the problem. The node admittance parameters computed from the line parameters is applied to the eigenvalue–eigenvector model to determine the system stability state. The state of the eigenvalue is used as an input to a control system, which utilized static volt-ampere reactive (VAR) compensators (SVC) to automatically stabilize the non-stable buses in the transmission network. The 6 × 6 nodal admittance matrix is formed and fed to the developed eigenvalue–eigenvector model via MATLAB in order to compute the right and left eigenvectors and the diagonal or eigenvalue of the network under steady-state and contingency condition. After this, the system stability state is determined, and necessary control actions by the SVC are implemented to guarantee system security. The developed model was tested on the 6 bus Eastern Grid Nigerian Transmission Network and validated using a 41 bus network of the same country. The compensated model showed considerable efficiency in improving the transient stability state of the transmission networks in terms of ease of operation, seamless integration into existing control system, and efficient utilization of SVS to compensate for reactive power imbalances. The results from the step response graph of the compensated model shows performance accuracy as the system regained stability in less than 0.5 s, which is a significant improvement over the uncompensated model.

This paper presents a numerical procedure using shell element to evaluate the buckling behavior of the cylindrical structure subjected to pressure load. In numerical simulation for pressure vessels using conventional shell elements, the pressure loads imposed to both top and bottom surfaces are expressed as the difference between the internal and external pressures. In this work, the special shell element, in which the surface traction is exactly expressed at the surface, is applied to the buckling analysis. In this approach, the distribution of the transverse normal stress through the thickness can be evaluated. Therefore, the influence of the difference between the internal and the external pressures to the behavior of the buckling of the cylindrical shell structures can be assessed. In the situation that a perturbative load is applied under a certain stress state, bifurcation points are searched by solving a standard eigenvalue problem. Several numerical examples are presented to examine the effectiveness of the proposed approach. The buckling behavior that cannot be considered with the conventional shell elements can be observed by this approach.

To improve transmission capacity and stability margin of the power system, the doubly fed induction generators (DFIGs) based wind farm is transmitted over lines equipped with series compensation (fixed capacitors). However, the utilisation of series compensation brings the potential risk of subsynchronous resonance (SSR) in the power system. In this study, the SSR issue in DFIGs based wind farm integrated to a series-compensated network is studied based on the eigenvalue analysis and equivalent impedance model. The linearised state-space model of DFIGs based wind farm integrated to a series-compensated network is built first. Participation factors, sensitivities of eigenvalues and root loci, obtained by linearised state-space model, are observed to investigate the mechanism and the key parameters of SSR. Then, a method that can mitigate SSR in DFIGs based wind farm integrated to a series-compensated network is proposed based on virtual series resistance of the rotor. At last, the eigenvalue analysis and simulation are conducted to verify the effectiveness of the proposed mitigation method.

The increasing wind integration in present grids to generate clean energy escalates the problem of low-frequency oscillations (LFOs) in the system. Here, a wide area-based coordinated control strategy of power system stabilisers (PSSs) and doubly fed induction generator's (DFIGs) power oscillation dampers (PODs) is presented to improve the system damping. An improved eigenvalue-based objective function is employed to optimally tune the variables of the controller using whale optimisation algorithm (WOA). The impact of DFIG location and thus the suitable wind farm locations are also found out using eigenvalue analysis and dynamic sensitivity analysis. The results are investigated on IEEE 68 bus test system highlighting the effectiveness of proposed strategy for a wide range of operating scenarios.

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.

In recent years, the low-frequency oscillation (LFO) problem has become increasingly significant with rapid increase in the size of AC/DC interconnected power system containing large-scale wind power. This article aims to conduct the LFO analysis when an offshore wind farm is integrated into the AC power system through module multilevel converter (MMC)-based high-voltage direct current (HVDC). First, the basic mathematical models including the MMC with detailed control strategy and the permanent magnet synchronous generator (PMSG) are described. The eigenvalue analysis is then applied to conduct the LFO study. An interconnected AC/DC test system with a wind farm connected though the MMC-based HVDC transmission line is designed as benchmark. To validate the analysis results, the detailed simulation models built under the PSCAD/EMTDC^TM environment together with the Prony analysis are carried out. Different simulation scenarios involving the changes of point of common coupling (PCC), wind speed, length of transmission line, and wind penetration level are elaborately studied. Some meaningful conclusions are drawn to provide basic foundation for the future design of damping controller to mitigate LFO.

The present research aims at investigating the vibration period of structural units (SUs) of a typical masonry aggregate located in the historical center of Mirandola, a municipality in the province of Modena. The clustered building consists of eighteen SUs mutually interconnected to each other, which are characterized by solid brick walls and deformable floors. First of all, non-linear static analyses are performed by adopting the 3Muri software focusing on two distinct modelling techniques concerning the analyzed SUs in isolated and clustered configurations. Congruently to the procedure adopted, in order to evaluate a reliable seismic structural response of the SUs arranged in aggregate conditions, the contribution in terms of stiffness and mass derived from adjacent buildings is considered. The analysis results are represented in terms of risk factor, stiffness, and ductility. Secondly, the eigenvalue analysis is faithfully developed to identify the main vibration modes of the investigated SUs by proposing an empirical formulation, that allows for predicting the vibration period of structural units placed in aggregate configuration starting from the corresponding isolated ones. Finally, fragility functions are derived for both the heading and intermediate SUs to point out the expected damages under earthquakes with different intensities.

In this article an overall procedure is proposed, for the numerical investigation of the structural response of ancient monuments made of megalithic stones. The procedure is implemented on the middle temple of the Mnajdra Megalithic structure, listed as UNESCO World Heritage and regarded as one of the oldest structures from early civilization dating back to about the 4th millennium BC. First, the geometry of the structure is obtained from a point cloud using terrestrial laser scanning. To investigate and estimate the material properties of the structural system, parametric eigenvalue analysis is conducted using the finite element method and results are compared with experimental data from ambient vibration sensors applied to the same structure. The structural response of the system is then evaluated, using nonlinear finite element analysis. Variation of unilateral, frictional contact conditions between megaliths in a preceding analysis step may influence the eigenvalue analysis which follows, indicating the importance of the proper consideration of contact conditions, on the response of the structure. An old collapse in a part of the structure is also reproduced by the numerical model. The proposed scheme, which combines numerical analysis and experimental vibration output to derive structural properties of the monument, can be used in similar structural systems, consisting of multi-body megalithic stones. [ABSTRACT FROM AUTHOR]

This paper is concerned with polynomial approximations of the spectral abscissa function (defined by the supremum of the real parts of the eigenvalues) of a parameterized eigenvalue problem, which are closely related to polynomial chaos approximations if the parameters correspond to realizations of random variables. Unlike previous work, we highlight the major role of this function smoothness properties. Even if the eigenvalue problem matrices are analytic functions of the parameters, the spectral abscissa function may not be differentiable, and even non-Lipschitz continuous, due to multiple rightmost eigenvalues counted with multiplicity. This analysis demonstrates smoothness properties not only heavily affect the approximation errors of the Galerkin and collocation based polynomial approximations, but also the numerical errors in the evaluation of coefficients in the Galerkin approach with integration methods. A documentation of the experiments, conducted on the benchmark problems through the software Chebfun, is publicly available. [ABSTRACT FROM AUTHOR]

Converters are the key for increasing the development of renewable energy generation but their dynamic interaction with the grid has an important impact on stability. Oscillatory instabilities in different grid‐connected converter systems at several frequency ranges are reported. In particular, sub and supersynchronous oscillatory instabilities in AC power systems with type‐3 and type‐4 wind turbine generators (WTGs) were recently registered at several wind farm areas. A number of works based on eigenvalue analysis and frequency domain approaches are carried out to analyse this new stability issue and more research is going on to analyse in detail the electric and control parameters that may affect this phenomenon. This study contributes analysing in detail the influence of system parameters on the subsynchronous oscillations (SSOs) in AC power systems with type‐4 WTGs. This study is based on a new approach for subsynchronous stability assessment which could also be used for analysing other types of SSOs (e.g. subsynchronous control interactions between doubly‐fed induction generators and series‐compensated networks) as well as supersynchronous oscillations. A representative example of weak AC grids with type‐4 WTGs is used to illustrate the contributions of the study. Results are validated with PSCAD/EMTDC time‐domain simulations. [ABSTRACT FROM AUTHOR]

This paper presents two modified Hager–Zhang (HZ) Conjugate Gradient methods for solving large-scale system of monotone nonlinear equations. The methods were developed by combining modified forms of the one-parameter method by Hager and Zhang (2006) and the hyperplane projection technique. Global convergence and numerical results of the methods are established. Preliminary numerical results show that the proposed methods are promising and more efficient compared to the methods presented by Mushtak and Keyvan (2018) and Sun et al. (2017). [ABSTRACT FROM AUTHOR]

This work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity—due to the fourth order derivative terms, the non-linearity and the parameter dependence—provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a framework in which one can identify and predict the numerical instability of the steady state solution due to the solution reconstruction for cell-centered finite volume methods on unstructured meshes and to stabilize the problem by optimizing the reconstruction stencil. In this work, we first develop and extend a mathematical method, introduced by Haider and his colleagues, to measure the stability impact of the reconstruction phase for both linear and nonlinear problems regardless of the solution. Second order and third order accurate advection and Burgers problems as well as second order Euler problems are used to present detailed practical results and discussion around the use of the local reconstruction map for stability analysis. This method shows that for a range of different physical problems, increasing the stencil size will usually lead to more stable problems. Additionally, an empirical study is performed which sheds light on connections between the mesh properties and the stability of the reconstruction, which in turn helps choose the reconstruction stencil more wisely. Secondly, we propose a systematic approach to optimize both the shape and the size of the reconstruction stencil for better numerical stability through eigenvalue analysis. In this approach, one can directly optimize the solution reconstruction stencil for every control volume to obtain better numerical stability and convergence properties for steady state problems. A second order accurate Euler problem as well as a third order accurate laminar Navier-Stokes problem are used to showcase the applicability of the algorithm. • Identifying and predicting the numerical stability due to the solution reconstruction. • Better numerical stability through eigenvalue analysis and optimization of the solution reconstruction. • Extending solution reconstruction map theory to measure the impact of reconstruction for nonlinear and higher order problems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved sub-synchronous resonance (SSR) damping controller (SSRDC) and a related control strategy to mitigate the SSR in a capacitive series-compensated double-fed induction generator based wind farms, based on the damping torque analysis. The proposed strategy is utilized for enhancing the system stability. Compared with the traditional damping controller, the proposed SSRDC is simultaneously embedded into the $d$ -axis and $q$ -axis control channels in the inner current loop of the rotor-side converter. On this basis, combined with the eigenvalue analysis and improved particle swarm optimization algorithm, the optimum gain coefficients of the SSRDC can be determined for maximizing the mitigation effect under different operation conditions of the series compensation levels and wind speeds. Moreover, the effect of the weight coefficients in the objective function on the SSR suppression is also investigated. Finally, the time-domain simulations are carried out to demonstrate the effectiveness of the proposed control strategy for mitigating the SSR and suppressing the connected power system oscillations. [ABSTRACT FROM AUTHOR]

A multi-scale structure optimization method was proposed based on eigenvlue analysis, to find the macrostructure and microstructure of maximum macro stiffness under the worst load. The constraint that the Euclidian norm of the uncertain load is 1 was introduced, the structural compliance was calculated according to the Rayleigh-Ritz theorem, and the compliance was transformed to a symmetric matrix with the same dimensions as the local load vector. In this way, the compliance minimization problem under the worst load was transformed to the minimum problem of the maximum eigenvalue of the symmetric matrix. Moreover, the worst load case was determined with the eigenvector corresponding to the maximum eigenvalue of the matrix. Several numerical experiments demonstrated the validity of the proposed method, and illustrated the reasonability of the macro topological structure and the micro material distribution. The proposed multi-scale optimization method has virtues of iterative stability and rapid convergence. The update of the density function in the topological optimization was performed based on sensitivity analysis and the method of moving asymptotes (MMA). [ABSTRACT FROM AUTHOR]

This paper addresses modeling, stability analysis and control of the doubly fed induction generator (DFIG) for wind turbines (WTs). In the present work, imperialist competitive and artificial bee colony algorithms are used for optimizing parameters of controllers of a WT with DFIG. Algorithms for optimizing the controllers' parameters are described. Based on this, an eigenvalue-based objective function is utilized to optimize the parameters. To evaluate the optimized gains, simulations are performed on a single machine-infinite bus system, and the dynamic responses of system with parameters obtained from two optimization techniques are compared. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability analysis of systems modeled as neutral delay differential equations (NDDEs). These systems include delays in both the state variables and their time derivatives. The proposed approach consists of a descriptor model transformation that constructs an equivalent set of delay differential algebraic equations (DDAEs) of the original NDDEs. We first rigorously prove the equivalency between the original set of NDDEs and the transformed set of DDAEs. Then, the effect on stability analysis is evaluated numerically through a delay-independent stability criterion and the Chebyshev discretization of the characteristic equations. [ABSTRACT FROM AUTHOR]

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In recent years, the low-frequency oscillation (LFO) problem has become increasingly significant with rapid increase in the size of AC/DC interconnected power system containing large-scale wind power. This article aims to conduct the LFO analysis when an offshore wind farm is integrated into the AC power system through module multilevel converter (MMC)-based high-voltage direct current (HVDC). First, the basic mathematical models including the MMC with detailed control strategy and the permanent magnet synchronous generator (PMSG) are described. The eigenvalue analysis is then applied to conduct the LFO study. An interconnected AC/DC test system with a wind farm connected though the MMC-based HVDC transmission line is designed as benchmark. To validate the analysis results, the detailed simulation models built under the PSCAD/EMTDCTM environment together with the Prony analysis are carried out. Different simulation scenarios involving the changes of point of common coupling (PCC), wind speed, length of transmission line, and wind penetration level are elaborately studied. Some meaningful conclusions are drawn to provide basic foundation for the future design of damping controller to mitigate LFO. [ABSTRACT FROM AUTHOR]

Abstract Curve squeal noise is a severe railway noise problem that can occur when a railway vehicle negotiates a sharp curve. It is usually characterised by a very loud tonal noise and can be very annoying for people in the vicinity. It is generally attributed to friction-induced instability, either due to a falling friction characteristic with increasing sliding velocity or to a mode coupling mechanism which can lead to instability even for a constant friction coefficient. The squeal frequency is usually associated with one or more wheel modes. However, the wheel is coupled dynamically to the track and insufficient attention has been paid in previous research to the role played by the rail dynamic behaviour. In this paper, the effect of the rail dynamics on curve squeal under constant friction conditions is investigated by means of different modelling approaches. The rail is firstly modelled using a waveguide finite element (WFE) model and it is found that the inclusion of the rail dynamics in the model can lead to squeal in some situations where it would otherwise not occur. Various effects are then considered that may introduce additional resonant behaviour into the rail dynamics. These include the effect of the rail cross mobility, rail cross-section deformation, the influence of the periodic support of the rail and reflections between multiple wheels on the rail. The effect of the rail pad stiffness is also explored. However, the results show that all these factors have little influence on the predicted curve squeal instabilities. By means of a reduced model, the main characteristics of the rail dynamics that can result in squeal are then assessed. It is shown that the mass and damping-like behaviour of the infinite rail are at the origin of the instabilities rather than any modal behaviour of the track. Curve squeal may occur for a single wheel mode even if the rail is represented by a damper, which is a close approximation to the vertical mobility of the track at high frequencies. This forms a third possible mechanism for curve squeal in addition to falling friction and wheel mode coupling. [ABSTRACT FROM AUTHOR]

Abstract The ITER large power supplies of the superconducting magnets and heating and current drive systems, fed by the Pulsed Power Electrical Network, can absorb from the grid active and reactive power up to 500 MW and 950 Mvar respectively. In this paper, a new analytical approach based on the state space formulation is proposed to investigate the dynamic stability of such complex system, including the main power components and their control, with the aim of identifying possible instability phenomena due to interactions among the ac/dc converters, reactive power compensation systems and related controllers. This model describes the dynamics of the main components of the ITER pulsed power supply systems and it is based on small signal approach to tackle the non linearity of the ac/dc conversion and reactive power compensation systems; the discrete phenomena have been approximated by continuous transfer functions, so the linear control theory can be applied for the stability analysis, making this method very effective and fast. Moreover a modular approach is adopted; thus this analytical model can be also easily adapted to other similar electrical power systems. [ABSTRACT FROM AUTHOR]

Solar power being stochastic and asynchronous in nature, its integration with conventional power generation has so many challenges in damping of low‐frequency oscillations. This[AQ ID=Q2] study presents an investigation of low‐frequency oscillation and damping of stochastic solar power integrated power system by a unified power flow controller (UPFC)‐based dual optimal controller, which gains are optimised by a novel hybrid particle swarm optimisation and improved grey wolf optimiser. The[AQ ID=Q3] dual controller simultaneously controls the modulation index of series and phase angle of shunt converters of UPFC, which co‐operate with each other, optimising its efficacy and thereby implementing the advantages of both static synchronous series compensator and static synchronous compensator. A detailed Eigen value analysis has been performed with time domain simulations to study the damped oscillatory response of variable and random solar penetration with a power system along with the interaction of solar power with variable synchronous power generations. For a multi‐machine system, a multi‐input single output dual controller is proposed. A maximum sensor and time delay have been considered to design the controller providing a realistic approach. It[AQ ID=Q4] is observed that random and heavy solar penetration has a more detrimental effect on system oscillations, which can be damped heavily with the proposed controller, in contrast to particle swarm optimisation, differential evolution, grey wolf optimiser, differential evolution particle swarm optimisation optimised lead‐lag and dual controllers. [ABSTRACT FROM AUTHOR]

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

• Proposing a hierarchical battery sizing approach to improve dynamic performance of MG. • Optimal sizing of BESS based on stochastic models to minimize frequency fluctuations. • Secondary BESS optimal sizing and placement to improve static and dynamic stability. • Proposing a dynamic objective function based on system eigenvalues. Integration of energy storage systems (ESSs) to microgrids (MGs) due to the growing penetration of intermittent energy resources is a great motivation to develop studies in the context of optimal sizing and placement of these systems. In this paper, a multi-objective bi-level optimization problem is addressed based on the stochastic nature and dynamic model of power system elements. As a preliminary step, the optimal size and capacity of the battery energy storage system (BESS) are determined to minimize frequency fluctuations. This level has been performed based on three approaches considering the daily intra-hour stochastic data. In the secondary level, the dynamic behaviour of all MG elements has been considered and correspondingly a dynamic objective function based on system eigenvalues and voltage sensitivity index (VSI) has been developed. According to the proposed objective function, the secondary step for sizing and placement of the battery units has been performed by adaptive particularly tuneable fuzzy particle swarm optimization (APT-FPSO) algorithm to reduce power losses, improve the voltage profile/ stability, and mitigate low-frequency fluctuations. Finally, the effectiveness of the proposed approach is evaluated using time-domain simulations, voltage sensitivity studies, and eigenvalue analysis. [ABSTRACT FROM AUTHOR]

High-frequency oscillation is one of the critical issues threatening the stability of modular multilevel converter (MMC) based high-voltage direct current (HVDC) system. A new 2 kHz high-frequency oscillation has occurred in the wind farm-side MMC station of Rudong wind farm integrated MMC-HVDC project of China during no-load charging process. The mechanism of this high-frequency oscillation is different to previous ones. Apart from the time delay of MMC, the stray capacitance of converter transformer makes a significant contribution to the high-frequency oscillation. This paper investigates the high-frequency oscillation mechanism of wind farm-side MMC station during no-load charging process. First, the harmonic state space (HSS) model of a wind farm-side MMC station is established. In addition to the leakage inductance, the stray capacitance is considered in the converter transformer model. To reveal the significance of the converter transformer stray capacitance in this new high-frequency oscillation, the root loci of the system are calculated with varying stray capacitance. Then, the state variables with high degree of participation in the high-frequency oscillation modes are determined by the participation factor analysis. A reduced-order model suitable for the high-frequency oscillation analysis is further established based on the participation factor analysis results. Next, the high-frequency oscillation mechanism is revealed by impedance analysis. Finally, the effects of system parameters are analyzed by the combination of eigenvalue analysis and impedance analysis. The analysis results are validated by electromagnetic transient simulations. • High-frequency oscillation mechanism of MMC charging with transformer is revealed. • The transformer stray capacitance must be considered in the oscillation analysis. • Participation factor analysis is carried out to determine main influencing factors. • A reduced-order model suitable for high-frequency oscillation analysis is proposed. • AC voltage control of MMC has significant effects on the high-frequency oscillation. [ABSTRACT FROM AUTHOR]

One mechanism to generate optical rogue waves is the soliton fusion phenomenon. The impact of initial parameters such as pulse spacing, frequency separation, and phase difference between adjacent soliton shape pulses for soliton fusion phenomenon has been analyzed based upon soliton's eigenvalue. Numerical simulation results reveal that the parameter space can be divided to three regions, i.e., co-propagation, soliton fusion, and repulsion, which are sensitively dependent on the initial parameter.

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.

This paper presents the advanced control theory’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’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.

Active power outputs of a wind farm connected to a weak power grid greatly affect the stability of grid-connected voltage source converter (VSC) systems. This paper studies the impact of active power outputs and control parameters on the subsynchronous oscillation characteristics of full-converter wind farms connected weak power grids. Eigenvalue and participation factor analysis was performed to identify the dominant oscillation modes of the system under consideration. The impact of active power output and control parameters on the damping characteristics of subsynchronous oscillation is analysed with the eigenvalue method. The analysis shows that when the phase-locked loop (PLL) proportional gain is high, the subsynchronous oscillation damping characteristics are worsened as the active power output increases. On the contrary, when the PLL proportional gain is small, the subsynchronous oscillation damping characteristics are improved as the active power output increases. By adjusting the control parameters in the PLL and DC link voltage controllers, system stability can be improved. Time-domain results verify the analysis and the findings.

This paper discusses the numerical solution of the generalized non-Hermitian eigenvalue problem. It provides a comprehensive comparison of existing algorithms, as well as of available free and open-source software tools, which are suitable for the solution of the eigenvalue problems that arise in the stability analysis of electric power systems. The paper focuses, in particular, on methods and software libraries that are able to handle the large-scale, non-symmetric matrices that arise in power system eigenvalue problems. These kinds of eigenvalue problems are particularly difficult for most numerical methods to handle. Thus, a review and fair comparison of existing algorithms and software tools is a valuable contribution for researchers and practitioners that are interested in power system dynamic analysis. The scalability and performance of the algorithms and libraries are duly discussed through case studies based on real-world electrical power networks. These are a model of the All-Island Irish Transmission System with 8640 variables; and, a model of the European Network of Transmission System Operators for Electricity, with 146,164 variables.

The DC-link voltage control (DVC) timescale (i.e., the frequency dynamics covering converter outer controls) instabilities in wind generation have gained increased attention recently. This paper presents DVC timescale modeling and stability analysis for multi doubly-fed induction generators (DFIGs) connected to weak AC grids. A reduced-order, small-signal model of a grid-tied multi-DFIG system, designed for DVC dynamics analysis, is firstly proposed. The model allows for the dynamic interactions among the DC-link voltage control, active power control (APC), terminal voltage control (TVC) and phase-locked loop (PLL). Eigenvalue and participation factor analyses are conducted to explore the potential instabilities and correlated critical factors for such a multi-machine system. The sensitivity studies find that instability can occur at high levels of power generations or low short-circuit ratio (SCR) conditions. In addition, the dominant mode is identified to be highly related to the PLL, and its modal damping is decreased when the bandwidths of PLLs in different generators are close. Detailed model-based time domain simulations verified the analysis above.

In recent years, ultralow-frequency oscillation has repeatedly occurred in asynchronously connected regional power systems and brought serious threats to the operation of power grids. This phenomenon is mainly caused by hydropower units because of the water hammer effect of turbines and the inappropriate Proportional-Integral-Derivative (PID) parameters of governors. In practice, hydropower and solar power are often combined to form an integrated photovoltaic (PV)-hydro system to realize complementary renewable power generation. This paper studies ultralow-frequency oscillations in integrated PV-hydro systems and analyzes the impacts of PV generation on ultralow-frequency oscillation modes. Firstly, the negative damping problem of hydro turbines and governors in the ultralow-frequency band was analyzed through the damping torque analysis. Subsequently, in order to analyze the impact of PV generation, a small-signal dynamic model of the integrated PV-hydro system was established, considering a detailed dynamic model of PV generation. Based on the small-signal dynamic model, a two-zone and four-machine system and an actual integrated PV-hydro system were selected to analyze the influence of PV generation on ultralow-frequency oscillation modes under different scenarios of PV output powers and locations. The analysis results showed that PV dynamics do not participate in ultralow-frequency oscillation modes and the changes of PV generation to power flows do not cause obvious changes in ultralow-frequency oscillation mode. Ultra-low frequency oscillations are mainly affected by sources participating in the frequency adjustment of systems.

Some organisms using undulatory locomotion show the transition of the swimming frequency and the wavelength of the undulation. This transition of swimming behavior is achieved by sensory feedback, and may have the role to cope with the environmental change. Especially, one of the nematode: Caenorhabditis elegans can modulate its frequency from approximately 0.3 to 2 Hz, and vary the wavelength of undulating body from less than a single body length to almost twice the body length. With this modulation, C. elegans achieves the movement under the conditions from in water to on the surface of an agar. Inspired by this finding, we propose the adaptive control for the multilink swimming robot because the environmental change demands a mobile robot the change of the pattern of the locomotion. Proposed adaptive control employs the sensory feedback from joint angles to inputs of actuators at joints to generate the self-excited oscillation. At first, we construct the multilink model in fluid with sensory feedback. After that, we construct the linearized model to obtain the relationship among the external resistive force, parameters of the multilink model and the swimming frequency by using the eigenvalue analysis. We confirm whether the proposed adaptive control simulates the modulation of undulation like C. elegans. Moreover, we specify parameters of the multilink model which are related to the frequency and wavelength of undulation significantly.