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This paper presents a detailed model of low-frequency oscillations and their damping within the Electric Power System (EPS) of Bosnia and Herzegovina (B&H). The system is modeled using MATLAB software, analysing the steady state and dynamic responses. This research highlights the challenges and impacts of integrating renewable energy sources, such as wind farms, on grid stability and oscillation damping. The paper utilizes eigenvalue analysis to investigate the dynamic characteristics of the system, emphasizing the need for efficient damping strategies to maintain system stability. The methodology includes a comprehensive review of existing literature, the creation of a detailed EPS model of B&H, and the application of eigenvalue and oscillation amplitude analysis to determine damping ratios. The dynamic responses of hydro power plants, HPP Mostar and HPP Jablanica, to transient disturbances are analysed to validate the model and refine damping strategies. The results indicate that the B&H EPS is well-damped, with all eigenvalues possessing negative real parts, and demonstrate the system's resilience to small disturbances. The results are compared with the technical report on the integration of the wind power plant WPP Podveležje. This comparative analysis shows consistent patterns between the modeled calculations and empirical data, confirming the robustness of the EPS model. This alignment underscores the effectiveness of current damping mechanisms and provides a foundational strategy for enhancing system stability with increasing renewable energy penetration. The findings highlight the importance of developing advanced control strategies to sustain system stability as the integration of variable renewable energy sources continues to grow. [ABSTRACT FROM AUTHOR]

In this paper, a holistic nonlinear state-space model of a system with multiple converters is developed, where the converters correspond to the wind turbines in a wind farm and are equipped with grid-following control. A novel generalized methodology is developed, based on the number of the system's converters, to compute the equilibrium points around which the model is linearized. This is a more solid approach compared with selecting operating points for linearizing the model or utilizing EMT simulation tools to estimate the system's steady state. The dynamics of both the inner and outer control loops of the power converters are included, as well as the dynamics of the electrical elements of the system and the digital time delay, in order to study the dynamic issues in both high- and low-frequency ranges. The system's stability is assessed through an eigenvalue-based stability analysis. A participation factor analysis is also used to give an insight into the interactions caused by the control topology of the converters. Time domain simulations and the corresponding frequency analysis are performed in order to validate the model for all the control interactions under study. [ABSTRACT FROM AUTHOR]

In the static stability analysis of the grid-connected photovoltaic (PV) generation and energy storage (ES) system, the grid-side is often simplified using an infinite busbar equivalent, which streamlines the analysis but neglects the dynamic characteristics of the grid, leading to certain inaccuracies in the results. Furthermore, the control parameter design does not consider the coupling relationships among parameters, resulting in arbitrary values and the inability to achieve overall optimality. To address these issues, this paper presents a comprehensive parameter optimization method for the oscillation characteristics of grid-connected PV generation and ES systems in various frequency ranges. Firstly, a detailed modeling of the grid-connected PV generation and ES system is conducted, resulting in the derivation of the system's small-signal model. This study investigates the impact of parameters related to PV arrays, ES units, and the virtual synchronous generator (VSG) on the system's characteristic roots using participation factors, sensitivity analysis, and eigenvalue root trajectories. Subsequently, based on the analysis of system root trajectories and the Particle Swarm Optimization (PSO) algorithm, a holistic parameter optimization design method for the system's oscillation modes is proposed, and the parameter optimization results are obtained. Finally, the accuracy of the theoretical analysis is validated through perturbation testing using both Matlab/Simulink models and the small-signal model. [ABSTRACT FROM AUTHOR]

Summary: The modular multilevel converter (MMC) is a novel prospective multilevel converter topology for high‐voltage or high‐power applications. This paper presents the 3‐ Φ model integrated into a linear model in transient analysis and the design of current controller for MMC. This paper analyzes the control interactions of MMC on nearby turbine generator. The eigenvalue analysis is used to evaluate the impact of different controller modes of MMC. The impact of converter control with nonlinear switches is analyzed through the transient simulation. The eigenvalue analysis and controller design are carried out on a linear model, and the transient simulation analysis is performed on both the D‐Q model and a three‐phase model of MMC using MATLAB‐Simulink. The results show that the transient simulation of three‐phase model on the proposed approach is consistent with the transient simulation of D‐Q model. Also, the transient simulation results show a satisfactory response with the current controller parameters of the MMC at various operating cases. To validate the results of MATLAB‐Simulink model, the proposed system is implemented in hardware‐in‐the‐loop (HIL) simulation with an integrated subsystem built in two real‐time simulators. The subsystem of mathematical model is implemented in dSPACE, and the subsystem of 3‐ Φ MMC with controller is implemented in Typhoon. The HIL simulation results show a satisfactory response and consistent with MATLAB‐Simulink model results. [ABSTRACT FROM AUTHOR]

Summary: As the share of wind power keeps on increasing, the interaction between synchronous and wind generators pose a challenging issue on power system stability. In order to investigate the impact of wind penetration on stability of power system, appropriate modeling of wind energy conversion systems (WECSs) is necessary. Moreover, it is needed to comprehensively study the impact of wind penetration on power system oscillations. This paper presents a didactic approach for integrating a doubly fed induction generator (DFIG)‐based wind farm from SimPower Systems library to a five‐area 68‐bus power system modeled in Simulink. Inter‐area oscillations with and without wind power penetration are investigated for their characteristics. Renewable energy sources are connected to the grid via power electronics converters at the cost of a reduction in inertia. The concept of virtual synchronous generator (VSG) produces virtual inertia by exchanging active power with the power system. The impact of superconducting magnetic energy storage (SMES) and DFIG on enhancing damping performance of inter‐area is investigated. The increase in damping ratios of inter‐area oscillatory modes verifies the enhancement in small signal stability by connecting SMES and DFIG to the power system. The usage of SMES operating in VSG mode to improve the dynamic stability with highly erratic wind profile is also investigated. The developed MATLAB/SIMULINK‐based DFIG model is simple to use and can be expanded to build efficient controllers. The fidelity of the DFIG model and VSG technology is verified in real time by Opal‐RT (OP4510). [ABSTRACT FROM AUTHOR]

The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice. [ABSTRACT FROM AUTHOR]

This work deals with doubly fed induction generator (DFIG) modeling and stability when connected to weak AC grids. A detailed state-space model that includes the phase-locked loop (PLL) is developed. This work aims to determine the influence of the network's strength on DFIG stability through the short-circuit ratio (SCR). The critical values of the proportional control parameters of the grid-side and rotor-side converters (RSC and GSC), as well as PLL, which make the system unstable, are calculated for different SCR values. Finally, PSCAD/EMTDC dynamic simulations are used to validate the critical control parameters obtained by studying the eigenvalues of the DFIG state-space model regarding system stability. [ABSTRACT FROM AUTHOR]

This paper proposes a novel strategy to design a suboptimal attitude tracking control law for a near-space hypersonic vehicle (NSHV) based on the Koopman operator and stable manifold theory. The nonlinear vector field of the NSHV attitude model is locally Lipschitz continuous and can be approximated by a high-dimensional linear system over a compact set. Linear and nonlinear parts of the attitude dynamics are determined based on this system. Subsequently, the stable manifold theory is applied to determine the unconstrained approximated optimal control law that is used to further consider the control input constraints of the NSHV attitude model. The suboptimality of the control law is analyzed, and the local exponential stability of the closed-loop system with input constraints is proven. Furthermore, the eigenvalues for the closed-loop nonlinear attitude error dynamics are analyzed. After the control input saturation, the nonlinear closed-loop error dynamics of the NSHV can be approximated by a high-dimensional linear system with a minimal dimension. The eigenvalues of this linear system indicate the stability and time response characteristics of the attitude error dynamics of the NSHV. The numerical simulation results demonstrate the effectiveness and suboptimality of the proposed attitude tracking control law and workflow of the eigenvalue analysis. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the redundancy analysis of truss bridges, the calculation of the dynamic response caused by member damage requires accuracy. This paper presents a practical method of calculating the dynamic responses of truss bridge due to member damage considering its vibration characteristic, using eigenvectors instead of using dynamic amplification factor of one-degree-of-freedom system. A steel Pratt-truss bridge of long three-span with multiple influential vibration modes was the object of this research. The investigation of the dynamic response waveform due to member damage showed that there were multiple frequency peaks close to natural frequencies of the damaged truss bridge, and that the constant term of the Fourier transform was same as the result analyzed for the member damage using static analysis. Based on these results, a method for calculating the dynamic response by adding the cross-sectional force obtained by static analysis and by eigenvector was proposed. The range of vibration modes was set using the total modal participating mass ratio as an index, and the eigenvector that most affected the dynamic response of each member was selected for each member. Indeed, the dynamic response of cross-sectional force obtained by proposed method gave redundancy evaluation close to time-history-response analysis. [ABSTRACT FROM AUTHOR]

Applying droop-based hierarchical control for islanded microgrids would face several unavoidable operation issues, such as large frequency deviation, high dynamic fluctuation, and inefficient coordination between different control layers. To this end, droop-free control has been explored to achieve the power sharing goal through neighboring communication, while maintaining system frequency levels (i.e., keeping the average nodal frequency constant). Although droop-free control shows potential in mitigating the defects of droop-based control, current research on the theoretical understanding of its stability performance remains limited. Hereby, this paper discusses the stability performance of droop-free controlled islanded microgrid via eigenvalue-based analysis. Specifically, a modified eigenvalue analysis method is first proposed to prove that all effective system eigenvalues under the symmetric communication network are located in the left half-plane, indicating that the symmetric droop-free controlled microgrid is asymptotically stable. Then, the asymmetric communication network is discussed, and the analytical eigenvalues with symmetric/asymmetric communication network designs are deduced under the homogenized electrical network. With the deduced analytical eigenvalues, stability performances of the symmetric/asymmetric designs are assessed via stability margin analysis and vulnerability analysis. Numerical case studies illustrate stability performance of the proposed designs, demonstrating that the asymmetric cycle design outperforms symmetric cycle and symmetric/asymmetric chain designs in overall convergence speed and stability against communication errors between droop-free controllers. [ABSTRACT FROM AUTHOR]

This study examines the influence of a direct-power control technique for a DFIG (Doubly-Fed Induction Generator)-based wind generator on sub-synchronous resonance (SSR). A series capacitor of a transmission line will exchange power with the synchronous generator when it runs via an SSR. DFIG includes power converters built into its rotor circuit, allowing for quick control of both the active and reactive power of the device. This is made possible by the rotor converter circuit's fast IGBT switching. Examining the ability of the LQR (Linear Quadratic Regulator) on the DFIG to provide the required active power and reactive power during SSR is the primary goal of this work. Additional DFIG is added to the test system in addition to the original test system, and during SSR its performance is evaluated using an additional control signal that is obtained from the synchronous generator and supplied to DFIG through LQR. The analysis of SSR was completed based on eigenvalue analysis utilizing the D-Q model test system and transient simulation using MATLAB Simulink. Independent model control is used to control the DFIG rotor converter that dampens multimodal SSR oscillations. The test system was developed using the IEEE first benchmark model's adopted system. [ABSTRACT FROM AUTHOR]

Construction of the linearized state-space model is the key step of eigenvalue analysis for SSO study of power systems with large-scale renewable power generation (RPG) integrated. This paper proposes a novel method to construct the state matrix of the AC/DC hybrid power system with RPG within the discrete-time domain. The continuous-time state-space model of each AC/DC component as well as RPG units in the power system, is discretized together with their corresponding control. The discretized equation of each component is then represented by an equivalent circuit consisting of parallel historical current and conductance. According to the power system configuration, the discrete-time equivalent circuit of the whole AC/DC hybrid system is established, and the nodal analysis method is applied for the construction of the discrete-time state-space model of the power system. In this way, the state matrix can be acquired much more conveniently than that of continuous-time state-space method, which needs topology analysis to find independent state variables of the network from the proper tree. The proposed method has been applied in the eigenvalue analysis for the SSO study of a case system adapted from the AC/DC hybrid transmission system in northwest China. Eigenvalue results are in high accordance with time-domain simulation results in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

Suppression of noise and vibration in machine products is an important problem, and many methods have been studied. In particular, structural–acoustic coupled effects due to the weight reduction of machines cannot be ignored. In structural–acoustic coupled analysis, the finite-element method in which the acoustic space is described by sound pressure and the structure is described by displacement is often used. However, the eigenvalue analysis in that method takes a great deal of computational time because the mass and stiffness matrices are asymmetric. Instead, in this paper, we propose an efficient coupled analysis method for a three-dimensional acoustic space and a two-dimensional thin plate using a lumped-mass model. The proposed modeling method is derived systematically using Raviart–Thomas elements. In addition, we propose a coordinate transformation method that accelerates the calculations by reducing the number of degrees of freedom (DOF). In this way, a symmetric eigenvalue problem with no extra DOF is derived. The effectiveness of the proposed method is confirmed by numerical calculations. This analysis method is particularly effective for systems in which the acoustic space contributes to the majority of the DOF, since the acoustic space is sparse owing to the adoption of edge elements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As the installed capacity of the power system is scaled up and the distance of transmission increases constantly, high-voltage direct current (HVDC) transmission technology has been widely applied across the power system. The HVDC system can lead to sub-synchronous oscillations (SSO) in the turbine and new energy generation systems. When the SSO caused by HVDC are studied through small signal analysis, it is usually necessary to establish the detailed state space model and electromagnetic transient model, which shows various disadvantages such as the high complexity of the model, the high order of the state space matrix, the complex calculation of eigenvalues, and the slow pace of simulation. In the present study, a simplified model intended for the HVDC transmission system is proposed, which can be used to simplify the calculation model and accelerate the simulation by omitting the high-frequency component and simultaneously keeping the sub-synchronous frequency component unchanged. The time domain simulation method is used to compare the dynamic response of the proposed simplified simulation model with that of the original detailed model, and the accuracy of the proposed model is demonstrated. The proposed simplified simulation model is applied to explore the SSO of wind-thermal power bundling in the HVDC transmission system. Additionally, the simulation results of SSO are compared by using the simplified model and the detailed model; the results of which demonstrate the effectiveness and rapidity of the simplified simulation model. The simplified model proposed can greatly improve the efficiency of SSO risk assessment. By selecting reasonable types and parameters of new energy units, SSO of the system can be avoided under risky operation mode, and the power grid operation mode can be monitored and adjusted to ensure the safe operation of the system. Finally, it can promote the sustainable development of the power system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Interactions of identical inverters in weak grids have received wide attentions. However, in a practical wind farm, parameters of grid-side inverters and lengths of collecting lines are not completely the same. In this case, a multi-inverter system is not symmetric, and thus the interaction mechanism could be more complicated than that of identical inverters. To investigate the interaction mechanism of differently parameterized inverters, this paper proposes a clustering-based modeling method, in which inverters with identical parameters are classified as one group. The clustering-based model allows for efficient stability assessment using three low-order transfer function matrices, instead of a full-order dynamic model. The root locus analysis is applied in the clustering-based model for stability analysis. Results show that the interconnection of distinct groups of inverters deteriorates common current stability, but has no impact on interactive current stability. The simulation and rtlab-based experimental results validate the effectiveness of the proposed model and the interaction mechanism of differently parameterized inverters. [ABSTRACT FROM AUTHOR]

This research systematically analyzes the behaviors of correlations among stock prices and the eigenvalues for correlation matrices by utilizing random matrix theory (RMT) for Chinese and US stock markets. Results suggest that most eigenvalues of both markets fall within the predicted distribution intervals by RMT, whereas some larger eigenvalues fall beyond the noises and carry market information. The largest eigenvalue represents the market and is a good indicator for averaged correlations. Further, the average largest eigenvalue shows similar movement with the index for both markets. The analysis demonstrates the fraction of eigenvalues falling beyond the predicted interval, pinpointing major market switching points. It has identified that the average of eigenvector components corresponds to the largest eigenvalue switch with the market itself. The investigation on the second largest eigenvalue and its eigenvector suggests that the Chinese market is dominated by four industries whereas the US market contains three leading industries. The study later investigates how it changes before and after a market crash, revealing that the two markets behave differently, and a major market structure change is observed in the Chinese market but not in the US market. The results shed new light on mining hidden information from stock market data. [ABSTRACT FROM AUTHOR]

Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, twogrid theory plays an important role in motivating and analyzing multigrid algorithms. For symmetric positive definite problems, the convergence theory of two-grid methods with exact solution of the Galerkin coarse-grid system is mature, and the convergence factor of exact two-grid methods can be characterized by an identity. Compared with the exact case, the convergence theory of inexact twogrid methods (i.e., the coarse-grid system is solved approximately) is of more practical significance, while it is still less developed in the literature (one reason is that the error propagation matrix of inexact coarse-grid correction is not a projection). In this paper, we develop a theoretical framework for the convergence analysis of inexact two-grid methods. More specifically, we present two-sided bounds for the energy norm of the error propagation matrix of inexact two-grid methods, from which one can readily obtain the identity for exact two-grid convergence. As an application, we establish a unified convergence theory for multigrid methods, which allows the coarsest-grid system to be solved approximately. [ABSTRACT FROM AUTHOR]

This paper develops an accurate small signal model for line commutated converter based HVDC (LCC-HVDC). The overall process of the model establishment is demonstrated from five parts: AC system, DC system, control system, phase-locked loop (PLL) and the converter. Considering the limitations of the traditional converter equations, the proposed small signal model takes the commutation process into account so that the overlap angle and AC current are calculated with the actual value rather than the estimated value. The accuracy of the proposed model is verified both in the time-domain simulation in PSCAD/EMTDC and by eigenvalue analysis. The results show better performance than the traditional modeling methods, which provides valuable guidance for future LCC-HVDC project design. [ABSTRACT FROM AUTHOR]

One of the major ways of delivering renewable energy generation from large-scale energy bases in northeast, northwest, and northern China, is to bundle the power from wind-photovoltaic-thermal units and then transmit it by alternating current/direct current (AC/DC) systems. The interactions among wind power units, photovoltaic (PV) power units, and high voltage direct current (HVDC) systems make the stability of the interconnected power system more complicated. In this paper, a framework model of wind-PV-thermal-bundled power transmitted by AC/DC systems is constructed based on the mathematical models of thermal power units, wind power units, PV power units, and HVDC transmission systems. Considering the fluctuations of wind power outputs and PV power outputs, a small-signal stability model of an interconnected power system with wind-PV-thermal-bundled power transmitted by AC/DC systems is established based on an existing stability theorem. The interactions among various forms of energy and their impacts on wind-PV-thermal-bundled power transmitted by AC/DC systems are studied through theoretical analysis and dynamic simulation. A sample interconnected power system is used to demonstrate the proposed method. It is shown by simulation results that the wind-PV-thermal-bundled power transmission distance; the electrical distance among wind power units, PV power units, and thermal power units; the grid-connected capacities of wind, PV, and thermal power units; and the power loading ratios of AC lines over DC lines all have various degrees of impacts on the stability of the interconnected power system. [ABSTRACT FROM AUTHOR]

The application of high-power DC equipment further increases the power supply scale of DC systems. But, it is difficult for a single converter to support high transmission power, so multiple converters must operate in parallel for efficient power transmission. In a parallel system comprising many IPOS phase-shifting full-bridge converters, current sharing can be realized via droop control. However, the stability of the parallel system using current-sharing control will appear poor in light load conditions, so it is necessary to analyze the stability of parallel systems in light load conditions. Firstly, a single IPOS phase-shifted full-bridge control system is modeled; on this basis, the state space model of the n-module paralleled IPOS phase-shifted full-bridge converters system is derived. Then, the influence of load power and the number of parallel IPOS phase-shifted full-bridge converters on the system stability is analyzed via eigenvalue analysis, and an optimal control strategy based on a particle swarm optimization algorithm is proposed. The control parameters are optimized for the parallel system of eight IPOS phase-shifted full-bridge converters. Finally, the above results are simulated to verify the accuracy of the stability analysis and the feasibility of the optimized control strategy. [ABSTRACT FROM AUTHOR]

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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents the modal analysis of different HVDC cable bundles. Using modal theory, specific transformation matrices are presented, and the modal equivalent circuits are illustrated. The behavior of the resulting modes is studied in a wide frequency range, the impact of different cable parameters and burial configurations on the modal characteristics are analyzed. A concept for online fault localization in HVDC cable transmission based on the difference between the modal velocities and consequently the arrival times of the modal traveling wave initial peaks is presented. In this method, modal voltages and currents are used instead of direct measurements and the proposed concept uses one-sided measurement without needing to detect the second TW reflections. Multiple faults are applied to CIGRE HVDC models in PSCAD/EMTDC and the modal analysis is obtained in MATLAB. The impact of different sampling frequencies, fault resistance, fault location and different grounding schemes on the proposed modal fault location principle is analyzed. The theoretical results show the accuracy of the proposed modal fault localization concept for different HVDC cable bundles. [ABSTRACT FROM AUTHOR]

The static series synchronous compensator (SSSC) has demonstrated its capability in providing voltage support and improving power system stability. The objective of this paper is to analyze the dynamic interaction stability mechanism of a hybrid renewable energy system connected with doubly-fed induction generators (DFIGs) and solid oxide fuel cell (SOFC) energy with the SSSC. For this purpose, a linearized mathematical model of this modified hybrid single-machine infinite-bus (SMIB) power system is developed to analyze the physical mechanism of the SSSC in suppressing oscillations and the influence on the dynamic stability characteristics of synchronization. Typical impacting factors such as the series compensation level, the SOFC penetration and tie-line power are considered in the SMIB and two-area systems. The impact of dynamic interactions on enhancing damping characteristics and improving transient performance of the studied systems is demonstrated using eigenvalue analysis and dynamic time-domain simulations, which validates the validity of the proposed physical mechanism simultaneously. [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]

The potential instability issues caused by the dynamic interactions between parallel grid-forming inverters are examined. The approach adopted for analysis is s-domain admittance-based eigenvalue and mode shape analysis. This admittance is based on a five-node circuit diagram after the conversion of each electric circuit element and inverter control unit into impedance models. Eigenvalue analysis results show that unstable resonance modes may exist due to the interactions of two parallel inverters. Impacts of transmission line length, the converter control's virtual impedance unit, and the voltage feed-forward unit are examined via the eigenvalue and mode shape analysis. The results show that the virtual impedance control has a negligible influence on the resonance while the voltage feed-forward unit stabilizes the resonance. Finally, the stability analysis is validated using electromagnetic transient (EMT) simulations. [ABSTRACT FROM AUTHOR]

In this research, we offer eigenvalue analysis and path following continuation to describe the impact, stick, and non-stick between the particle and boundaries to understand the nonlinear dynamics of an extended Fermi oscillator. The principles of discontinuous dynamical systems will be utilized to explain the moving process in such an extended Fermi oscillator. The motion complexity and stick mechanism of such an oscillator are demonstrated using periodic and chaotic motions. The major parameters are the frequency, amplitude in periodic excitation force, and the gap between the top and bottom boundary. We employ path-following analysis to illustrate the bifurcations that lead to solution destabilization. We present the evolution of the period solutions of the extended Fermi oscillator as the parameter varies. From the viewpoint of eigenvalue analysis, the essence of period-doubling, saddle-node, and Torus bifurcation is revealed. Numerical continuation methods are used to do a complete one- and two-parameter bifurcation analysis of the extended Fermi oscillator. The presence of codimension-one bifurcations of limit cycles, such as saddle-node, period-doubling, and Torus bifurcations, is shown in this work. Bifurcations cause all solutions to lose stability, according to our findings. The acquired results provide a better understanding of the extended Fermi oscillator mechanism and demonstrate that we may control the system dynamics by modifying the parameters. [ABSTRACT FROM AUTHOR]

The impact of subsynchronous oscillation (SSO) on grid security is becoming increasingly prominent with the rapid development of a large new energy base. However, the SSO modes and characteristics in complex power systems where series-complementary AC systems, DC systems, wind farms, and thermal power plants co-exist simultaneously are still not well understood, and relevant research has yet to be conducted. To address these issues, this study aims to investigate the SSO oscillation modes and the participation of specific influencing factors using eigenvalue and participation factor analysis. Additionally, the influence of system operation mode and control parameters on the SSO characteristics is studied through eigenvalue analysis. The findings of this study suggest that multiple oscillation sources and the co-existence of various oscillation patterns in hybrid AC–DC transmission systems cause SSO problems. The SSOs arise due to inappropriate system operation or parameter selection. As the series compensation increases, the system tends to become unstable. The system stability improves when the wind power output increases or the thermal power output decreases while keeping the output power of other sources constant. On the other hand, the system stability decreases as the DC transmission power gradually decreases. In terms of the control parameters, a higher value of the inner-loop proportionality coefficient of the converter current on the rotor side of the wind turbine results in a more unstable system. However, the rotor-side converter outer loop parameters and the stator-side control loop PI parameters have a negligible effect on the oscillation frequency and damping of the system. Matlab time domain simulations are conducted to verify the accuracy of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Subsynchronous control interaction (SSCI) is the interaction between the power-electronics control and the series-compensated transmission system that occurs at frequencies below the system nominal frequency. SSCI may occur between the doubly-fed induction generator (DFIG) control system and the series-compensated transmission line, to which the wind park (WP) is connected. Not only do the DFIG control system parameters, but also the WP operating conditions have a significant impact on SSCI. In this paper, the impact of WP operating conditions and DFIG control system parameters on SSCI is analyzed in detail. Guidelines are presented for modifying the DFIG control system parameters to ensure safe operation and acceptable transient responses due to faults. This paper also examines the accuracies of various analytical tools used for SSCI problem identification and proposes a new frequency scan analysis approach for accurate prediction of potential SSCI problems. [ABSTRACT FROM PUBLISHER]

Wind power integration through the voltage source converter-based high-voltage direct current (VSC-HVDC) system will be a potential solution for delivering large-scale wind power to the "Three-North Regions" of China. However, the interaction between the doubly-fed induction generator (DFIG) and VSC-HVDC system may cause the risk of subsynchronous oscillation (SSO). This paper establishes a small-signal model of the VSC based multi-terminal direct current (VSC-MTDC) system with new energy access for the problem, and the influencing factors causing SSO are analyzed based on the eigenvalue analysis method. The theoretical analysis results show that the SSO in the system is related to the wind farm operating conditions, the rotor-side controller (RSC) of the DFIG and the interaction of the controller in the VSC-MTDC system. Then, the phase lag characteristic is obtained based on the signal test method, and a multi-channel variable-parameter subsynchronous damping controller (SSDC) is designed via selecting reasonable parameters. Finally, the correctness of the theoretical analysis and the effectiveness of the multi-channel variable-parameter SSDC are verified based on time-domain simulation. [ABSTRACT FROM AUTHOR]

In this paper, we present a family of Perry conjugate gradient methods for solving large-scale systems of monotone nonlinear equations. The methods are developed by combining modified versions of Perry (Oper. Res. Tech. Notes 26(6), 1073–1078, 1978) conjugate gradient method with the hyperplane projection technique of Solodov and Svaiter (1998). Global convergence and numerical results of the methods are established and preliminary numerical results shows that the proposed methods are promising and more effective compared to some existing methods in the literature. [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]

Oscillatory instability in modern power system has increased due to increasing complexity and integration of dynamic loads. Stability analysis of such interconnected power system is very prominent in the presence of uncertain load/generation. In this paper, a power system stabilizer (PSS) design approach, which aims at enhancing the oscillatory stability of the multi-machine power system over the specified uncertainty range in forecasted load/generation, is presented. With non-statistical uncertainty, problem of selecting design parameters of the PSS is formulated as an optimization problem with minimization of eigenvalues and damping ratios based multi-objective function. In order to account the non-statistical uncertainties, a boundary active power loss (BAPL) based objective function is proposed. This non-linear BAPL objective function is minimized for determining the optimal setting of the generators voltage and taps of the online tap changing transformers (OLTC) under various power system constraints. In this paper, both the objective functions are solved by a new metaheuristic technique known as gray wolf optimization (GWO). Boundary value-based approach is used to minimize the repeated load flows under uncertain load/generation scenarios. Improved small-signal stability (SSS) is achieved with optimal active power loss of uncertain power system. Eigenvalue and time domain analysis for New England system are carried out under wide range of disturbances to demonstrate the potential of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, some issues related to the impedance-based stability criterion, such as RHP poles in the minor-loop gain, how to specify source and load impedances, and node-dependent stability margins are discussed and the vector fitting method is used to improve the method. This results in an eigenvalue analysis of the system instead of using the Nyquist diagram, and leads to obtain more information about the system. Furthermore, a participation factor analysis can be used to identify the problematic subsystem. The proposed method is examined in the assessment of a stable and an unstable system, and simulation results are used for verification. [ABSTRACT FROM AUTHOR]

This paper focuses on the impact of control system on small‐signal stability of the Hybrid Multi‐Infeed HVDC(H‐MIDC) system, in which the Line‐Commutated‐Converter based HVDC (LCC‐HVDC) and Voltage‐Sourced‐Converter based HVDC (VSC‐HVDC) links feed into an AC system in close mutual proximity. A comprehensive linearized small‐signal model is developed for an H‐MIDC system. Based on the eigenvalue analysis and participation factor analysis, the inherent oscillatory modes of the H‐MIDC system are revealed. Then, the impact of the most sensitive control system parameters on the least‐damped modes are investigated. The studies show that (i) the proportional gains of PLL functions of LCC and VSC stations, and AC voltage outer loop controller of VSC station are highly coupled, and presents the most sensitivity to the least damped modes; (ii) parameters of PLL in LCC station, and outer loop of AC voltage control and PLL in VSC station can highly impact the damping of the oscillatory modes and even cause instability, and (iii) smaller PLL gains in LCC and VSC stations, and smaller proportional gain of AC voltage control of VSC station are preferable and can enhance damping of dominant modes. [ABSTRACT FROM AUTHOR]

Summary: The traditional droop control method in a DC microgrid (DCMG) fails to achieve accurate current sharing among parallel‐connected dispatchable units when the connecting feeders have unequal resistances, or when the units supply local loads apart from loads at the common dc bus. In this paper, a novel modification of the droop control strategy (additional feedback term in the outer control loop) is suggested to overcome the above limitations. The proposed method is robust, noise‐resilient, amenable to the "plug and play model", and employs local measurements, thereby, dispensing with the need for communication between remote nodes. A small‐signal model of the system with the proposed control strategy is derived for carrying out eigenvalue and participation factor analysis. A sensitivity analysis is also carried out to inspect the impact of variation of system parameters on small‐signal stability. The effect of time delay and noise on system small‐signal stability is also studied. A robust stability analysis is also carried out. The proposed control strategy is easily implementable on digital hardware. Time domain simulations using PSCAD (Power System Computer Aided Design)/EMTDC(Electromagnetic Transients including DC) is carried out to validate and compare the performance of the proposed technique vis‐a‐vis other existing methods. Performance of the proposed method is good even with time delay and noise. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model with delay which describes the dynamics of three fish populations. The equilibrium points and their stability properties of the non-delay model are studied using Eigenvalue analysis. For the system with single delay model and multiple delays model, the existence of the interior equilibrium point and its stability are studied using the characteristic equation for the linearized system. [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]

This paper presents a new methodology to predict behavioural changes in manufacturing supply chains due to endogenous and/or exogenous influences in the short and long term horizons. Additionally, the methodology permits the identification of the causes that may induce a negative behaviour when predicted. Initially, a dynamic model of the supply chain is developed using system dynamics simulation. Using this model, a neural network is trained to make online predictions of behavioural changes at a very early decision making stage so that an enterprise would have enough time to respond and counteract any unwanted situations. Eigenvalue analysis is used to investigate any undesired foreseen behaviour, and principles of stability and controllability are used to study several decision configurations that eliminate or mitigate such behaviour. A case study of an actual electronics manufacturing company demonstrates how to apply this methodology and its real benefits for enterprises. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a frequency domain approach for eigenvalue-based detection of a primary user, based on equal gain combining (EGC) and spectrum estimation with Bartlett’s method. This paper considers two techniques for eigenvalue detection which are Maximum Eigenvalue Detection (MED) and the Maximum-Minimum Eigenvalue (MME) detector. We exploit the eigenvalues that are associated with the Hermitian form representation of Bartlett’s estimate to assess the performance of the aforementioned eigenvalue techniques in the frequency domain. For each case, we quantify the performance based on the probabilities of false alarm and missed detection over Rayleigh and Rician fading. A bivariate Mellin transform approach is employed to obtain the probability distribution function for the ratio of the extreme eigenvalues under each hypothesis. All obtained formulas are validated via Monte-Carlo simulations, and the results give a clear insight into the performance of the investigated methods. In frequency domain, MED outperforms both the MME detector and Periodogram-based energy detection even in a worst case scenario of noise uncertainty, while the MME detector exhibits heavy-tailed statistical characteristics and thus its receiver operating characteristics tend to stay on the line of no-discrimination. The performance of MED is further enhanced by careful choice of combinations of the total length of the sensing frame and number of sub-slots. [ABSTRACT FROM PUBLISHER]

A surface-wave-based endfire antenna with an enhanced impedance bandwidth is presented in this paper. The antenna consists of a surface-wave guide (SWG) and five strips printed on the SWG. The endfire radiation benefits from the surface-wave diffraction of the SWG which is investigated with the Snell's law, effective surface impedance and eigenvalue analysis. A prototype is fabricated and measured, and the measured results indicate that the antenna has two resonances and its bandwidth is enhanced up to 16.1% (4.0-4.73 GHz). The proposed endfire antenna also exhibits high gain, good gain flatness, low cross-polarization level and low profile. [ABSTRACT FROM AUTHOR]

A small signal model of a multi-infeed high-voltage direct current (HVdc) transmission system containing a line commutated converter (LCC) and a voltage source converter (VSC) is developed. This model represents the LCC and VSC converters as operational impedances as seen from the converter ac busbar. This permits the converters to be included in the effective short-circuit ratio (ESCR) calculations. The resulting ESCR is referred to in this paper as the “Impedance based Effective Short Circuit Ratio” (IESCR). It is shown that the maximum power transfer limit (referred to as the maximum available power or MAP) of the converters is better predicted by this index compared to the conventional ESCR which ignores the operational impedances of the converters. The question also arises as to how close to this theoretical maximum power transfer limit can the HVdc system operate. Using the small-signal model, it is shown that with commonly used control strategies, the predicted MAP can only be achieved by reducing the controller gains. The results are validated using detailed electromagnetic transients simulation of the multi-infeed VSC-LCC system. [ABSTRACT FROM PUBLISHER]

This paper presents a method for small-signal dynamic studies of power systems including utility-scale PV energy systems considering the effects of dc-side components. Existing methods commonly model a PV energy system as a dc source connected to a grid-tied inverter. This paper shows that the dc components of a PV energy system can also contribute in the dynamics of the power system in the range of small-signal studies. The paper first develops the model of a PV energy system by merging the submodels of dc- and ac-side components. Then, a method to obtain the augmented model of the power system including a PV energy system will be explained using a study system. The study system consists of a PV energy system in parallel with a synchronous generator connected to a grid. Then, based on eigenvalue analysis, verified by time-domain simulations, it is shown that the dc-link capacitor, front-end converter, and its controller can introduce oscillatory modes in subsynchronous range of frequencies. Furthermore, it is shown that the damping of the sensitive modes can significantly vary with respect to the parameters of the dc-side components. [ABSTRACT FROM PUBLISHER]

In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of the constraints on the cBSSN formulation and on some adjusted formulations with constraints added to the evolution equations. The adjusted formulations have a higher numerical stability than the cBSSN formulation from the viewpoint of the CAF. [ABSTRACT FROM AUTHOR]

A coupled-inductor-based fourth-order buck converter is introduced in this article. The salient features of this topology are lower source current ripples like in conventional buck converter with input filter, no need of connecting an additional damping network across the input filter capacitor, additional flexibility provided by the coupling in the performance tuning, and the existing input C1–L1m structure itself acts as a ripple steering network. The detailed steady-state analysis is evolved and conditions for source current ripple reductions are formulated. Subsequently, small-signal analysis is established and a proportional plus integral plus derivative type controller is designed to ensure load voltage regulation. To enhance the dynamic performance, a two-loop voltage-mode controller is designed. The stability analysis of the closed-loop coupled-inductor-based buck converter is carried out through the eigenvalue sensitivity and participation factors approach. The impact of converter parameters on the converter system stability is discussed. In comparison with the single-loop voltage-mode controller, the two-loop voltage-mode controller is able to ensure that the closed-loop poles stay away from the jω-axis and, thus, the two-loop voltage-mode controller exhibits better dynamic performance. Analytical findings are validated on a 75 W, 60 to 36 V prototype converter. Steady-state and dynamic performance characterizing measurement results are given for validation of the concept. [ABSTRACT FROM AUTHOR]